An adaptive response surface method for crashworthiness optimization

NASA Astrophysics Data System (ADS)

Shi, Lei; Yang, Ren-Jye; Zhu, Ping

2013-11-01

Response surface-based design optimization has been commonly used for optimizing large-scale design problems in the automotive industry. However, most response surface models are built by a limited number of design points without considering data uncertainty. In addition, the selection of a response surface in the literature is often arbitrary. This article uses a Bayesian metric to systematically select the best available response surface among several candidates in a library while considering data uncertainty. An adaptive, efficient response surface strategy, which minimizes the number of computationally intensive simulations, was developed for design optimization of large-scale complex problems. This methodology was demonstrated by a crashworthiness optimization example.

Experimental design for estimating unknown groundwater pumping using genetic algorithm and reduced order model

NASA Astrophysics Data System (ADS)

Ushijima, Timothy T.; Yeh, William W.-G.

2013-10-01

An optimal experimental design algorithm is developed to select locations for a network of observation wells that provide maximum information about unknown groundwater pumping in a confined, anisotropic aquifer. The design uses a maximal information criterion that chooses, among competing designs, the design that maximizes the sum of squared sensitivities while conforming to specified design constraints. The formulated optimization problem is non-convex and contains integer variables necessitating a combinatorial search. Given a realistic large-scale model, the size of the combinatorial search required can make the problem difficult, if not impossible, to solve using traditional mathematical programming techniques. Genetic algorithms (GAs) can be used to perform the global search; however, because a GA requires a large number of calls to a groundwater model, the formulated optimization problem still may be infeasible to solve. As a result, proper orthogonal decomposition (POD) is applied to the groundwater model to reduce its dimensionality. Then, the information matrix in the full model space can be searched without solving the full model. Results from a small-scale test case show identical optimal solutions among the GA, integer programming, and exhaustive search methods. This demonstrates the GA's ability to determine the optimal solution. In addition, the results show that a GA with POD model reduction is several orders of magnitude faster in finding the optimal solution than a GA using the full model. The proposed experimental design algorithm is applied to a realistic, two-dimensional, large-scale groundwater problem. The GA converged to a solution for this large-scale problem.

A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems.

PubMed

Gong, Pinghua; Zhang, Changshui; Lu, Zhaosong; Huang, Jianhua Z; Ye, Jieping

2013-01-01

Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterparts in several sparse learning settings. However, solving the non-convex optimization problems associated with non-convex penalties remains a big challenge. A commonly used approach is the Multi-Stage (MS) convex relaxation (or DC programming), which relaxes the original non-convex problem to a sequence of convex problems. This approach is usually not very practical for large-scale problems because its computational cost is a multiple of solving a single convex problem. In this paper, we propose a General Iterative Shrinkage and Thresholding (GIST) algorithm to solve the nonconvex optimization problem for a large class of non-convex penalties. The GIST algorithm iteratively solves a proximal operator problem, which in turn has a closed-form solution for many commonly used penalties. At each outer iteration of the algorithm, we use a line search initialized by the Barzilai-Borwein (BB) rule that allows finding an appropriate step size quickly. The paper also presents a detailed convergence analysis of the GIST algorithm. The efficiency of the proposed algorithm is demonstrated by extensive experiments on large-scale data sets.

Active subspace: toward scalable low-rank learning.

PubMed

Liu, Guangcan; Yan, Shuicheng

2012-12-01

We address the scalability issues in low-rank matrix learning problems. Usually these problems resort to solving nuclear norm regularized optimization problems (NNROPs), which often suffer from high computational complexities if based on existing solvers, especially in large-scale settings. Based on the fact that the optimal solution matrix to an NNROP is often low rank, we revisit the classic mechanism of low-rank matrix factorization, based on which we present an active subspace algorithm for efficiently solving NNROPs by transforming large-scale NNROPs into small-scale problems. The transformation is achieved by factorizing the large solution matrix into the product of a small orthonormal matrix (active subspace) and another small matrix. Although such a transformation generally leads to nonconvex problems, we show that a suboptimal solution can be found by the augmented Lagrange alternating direction method. For the robust PCA (RPCA) (Candès, Li, Ma, & Wright, 2009 ) problem, a typical example of NNROPs, theoretical results verify the suboptimality of the solution produced by our algorithm. For the general NNROPs, we empirically show that our algorithm significantly reduces the computational complexity without loss of optimality.

Optimal rail container shipment planning problem in multimodal transportation

NASA Astrophysics Data System (ADS)

Cao, Chengxuan; Gao, Ziyou; Li, Keping

2012-09-01

The optimal rail container shipment planning problem in multimodal transportation is studied in this article. The characteristics of the multi-period planning problem is presented and the problem is formulated as a large-scale 0-1 integer programming model, which maximizes the total profit generated by all freight bookings accepted in a multi-period planning horizon subject to the limited capacities. Two heuristic algorithms are proposed to obtain an approximate optimal solution of the problem. Finally, numerical experiments are conducted to demonstrate the proposed formulation and heuristic algorithms.

Simulator for multilevel optimization research

NASA Technical Reports Server (NTRS)

Padula, S. L.; Young, K. C.

1986-01-01

A computer program designed to simulate and improve multilevel optimization techniques is described. By using simple analytic functions to represent complex engineering analyses, the simulator can generate and test a large variety of multilevel decomposition strategies in a relatively short time. This type of research is an essential step toward routine optimization of large aerospace systems. The paper discusses the types of optimization problems handled by the simulator and gives input and output listings and plots for a sample problem. It also describes multilevel implementation techniques which have value beyond the present computer program. Thus, this document serves as a user's manual for the simulator and as a guide for building future multilevel optimization applications.

Near-Optimal Guidance Method for Maximizing the Reachable Domain of Gliding Aircraft

NASA Astrophysics Data System (ADS)

Tsuchiya, Takeshi

This paper proposes a guidance method for gliding aircraft by using onboard computers to calculate a near-optimal trajectory in real-time, and thereby expanding the reachable domain. The results are applicable to advanced aircraft and future space transportation systems that require high safety. The calculation load of the optimal control problem that is used to maximize the reachable domain is too large for current computers to calculate in real-time. Thus the optimal control problem is divided into two problems: a gliding distance maximization problem in which the aircraft motion is limited to a vertical plane, and an optimal turning flight problem in a horizontal direction. First, the former problem is solved using a shooting method. It can be solved easily because its scale is smaller than that of the original problem, and because some of the features of the optimal solution are obtained in the first part of this paper. Next, in the latter problem, the optimal bank angle is computed from the solution of the former; this is an analytical computation, rather than an iterative computation. Finally, the reachable domain obtained from the proposed near-optimal guidance method is compared with that obtained from the original optimal control problem.

The pseudo-Boolean optimization approach to form the N-version software structure

NASA Astrophysics Data System (ADS)

Kovalev, I. V.; Kovalev, D. I.; Zelenkov, P. V.; Voroshilova, A. A.

2015-10-01

The problem of developing an optimal structure of N-version software system presents a kind of very complex optimization problem. This causes the use of deterministic optimization methods inappropriate for solving the stated problem. In this view, exploiting heuristic strategies looks more rational. In the field of pseudo-Boolean optimization theory, the so called method of varied probabilities (MVP) has been developed to solve problems with a large dimensionality. Some additional modifications of MVP have been made to solve the problem of N-version systems design. Those algorithms take into account the discovered specific features of the objective function. The practical experiments have shown the advantage of using these algorithm modifications because of reducing a search space.

Very Large Scale Optimization

NASA Technical Reports Server (NTRS)

Vanderplaats, Garrett; Townsend, James C. (Technical Monitor)

2002-01-01

The purpose of this research under the NASA Small Business Innovative Research program was to develop algorithms and associated software to solve very large nonlinear, constrained optimization tasks. Key issues included efficiency, reliability, memory, and gradient calculation requirements. This report describes the general optimization problem, ten candidate methods, and detailed evaluations of four candidates. The algorithm chosen for final development is a modern recreation of a 1960s external penalty function method that uses very limited computer memory and computational time. Although of lower efficiency, the new method can solve problems orders of magnitude larger than current methods. The resulting BIGDOT software has been demonstrated on problems with 50,000 variables and about 50,000 active constraints. For unconstrained optimization, it has solved a problem in excess of 135,000 variables. The method includes a technique for solving discrete variable problems that finds a "good" design, although a theoretical optimum cannot be guaranteed. It is very scalable in that the number of function and gradient evaluations does not change significantly with increased problem size. Test cases are provided to demonstrate the efficiency and reliability of the methods and software.

Quantum algorithm for energy matching in hard optimization problems

NASA Astrophysics Data System (ADS)

Baldwin, C. L.; Laumann, C. R.

2018-06-01

We consider the ability of local quantum dynamics to solve the "energy-matching" problem: given an instance of a classical optimization problem and a low-energy state, find another macroscopically distinct low-energy state. Energy matching is difficult in rugged optimization landscapes, as the given state provides little information about the distant topography. Here, we show that the introduction of quantum dynamics can provide a speedup over classical algorithms in a large class of hard optimization problems. Tunneling allows the system to explore the optimization landscape while approximately conserving the classical energy, even in the presence of large barriers. Specifically, we study energy matching in the random p -spin model of spin-glass theory. Using perturbation theory and exact diagonalization, we show that introducing a transverse field leads to three sharp dynamical phases, only one of which solves the matching problem: (1) a small-field "trapped" phase, in which tunneling is too weak for the system to escape the vicinity of the initial state; (2) a large-field "excited" phase, in which the field excites the system into high-energy states, effectively forgetting the initial energy; and (3) the intermediate "tunneling" phase, in which the system succeeds at energy matching. The rate at which distant states are found in the tunneling phase, although exponentially slow in system size, is exponentially faster than classical search algorithms.

Optimal Full Information Synthesis for Flexible Structures Implemented on Cray Supercomputers

NASA Technical Reports Server (NTRS)

Lind, Rick; Balas, Gary J.

1995-01-01

This paper considers an algorithm for synthesis of optimal controllers for full information feedback. The synthesis procedure reduces to a single linear matrix inequality which may be solved via established convex optimization algorithms. The computational cost of the optimization is investigated. It is demonstrated the problem dimension and corresponding matrices can become large for practical engineering problems. This algorithm represents a process that is impractical for standard workstations for large order systems. A flexible structure is presented as a design example. Control synthesis requires several days on a workstation but may be solved in a reasonable amount of time using a Cray supercomputer.

Large-scale linear programs in planning and prediction.

DOT National Transportation Integrated Search

2017-06-01

Large-scale linear programs are at the core of many traffic-related optimization problems in both planning and prediction. Moreover, many of these involve significant uncertainty, and hence are modeled using either chance constraints, or robust optim...

A novel heuristic algorithm for capacitated vehicle routing problem

NASA Astrophysics Data System (ADS)

Kır, Sena; Yazgan, Harun Reşit; Tüncel, Emre

2017-09-01

The vehicle routing problem with the capacity constraints was considered in this paper. It is quite difficult to achieve an optimal solution with traditional optimization methods by reason of the high computational complexity for large-scale problems. Consequently, new heuristic or metaheuristic approaches have been developed to solve this problem. In this paper, we constructed a new heuristic algorithm based on the tabu search and adaptive large neighborhood search (ALNS) with several specifically designed operators and features to solve the capacitated vehicle routing problem (CVRP). The effectiveness of the proposed algorithm was illustrated on the benchmark problems. The algorithm provides a better performance on large-scaled instances and gained advantage in terms of CPU time. In addition, we solved a real-life CVRP using the proposed algorithm and found the encouraging results by comparison with the current situation that the company is in.

Aerospace Applications of Integer and Combinatorial Optimization

NASA Technical Reports Server (NTRS)

Padula, S. L.; Kincaid, R. K.

1995-01-01

Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in formulating and solving integer and combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem, for example, seeks the optimal locations for vibration-damping devices on an orbiting platform and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.

Aerospace applications on integer and combinatorial optimization

NASA Technical Reports Server (NTRS)

Padula, S. L.; Kincaid, R. K.

1995-01-01

Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in formulating and solving integer and combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem. for example, seeks the optimal locations for vibration-damping devices on an orbiting platform and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.

A sequential linear optimization approach for controller design

NASA Technical Reports Server (NTRS)

Horta, L. G.; Juang, J.-N.; Junkins, J. L.

1985-01-01

A linear optimization approach with a simple real arithmetic algorithm is presented for reliable controller design and vibration suppression of flexible structures. Using first order sensitivity of the system eigenvalues with respect to the design parameters in conjunction with a continuation procedure, the method converts a nonlinear optimization problem into a maximization problem with linear inequality constraints. The method of linear programming is then applied to solve the converted linear optimization problem. The general efficiency of the linear programming approach allows the method to handle structural optimization problems with a large number of inequality constraints on the design vector. The method is demonstrated using a truss beam finite element model for the optimal sizing and placement of active/passive-structural members for damping augmentation. Results using both the sequential linear optimization approach and nonlinear optimization are presented and compared. The insensitivity to initial conditions of the linear optimization approach is also demonstrated.

Decomposing Large Inverse Problems with an Augmented Lagrangian Approach: Application to Joint Inversion of Body-Wave Travel Times and Surface-Wave Dispersion Measurements

NASA Astrophysics Data System (ADS)

Reiter, D. T.; Rodi, W. L.

2015-12-01

Constructing 3D Earth models through the joint inversion of large geophysical data sets presents numerous theoretical and practical challenges, especially when diverse types of data and model parameters are involved. Among the challenges are the computational complexity associated with large data and model vectors and the need to unify differing model parameterizations, forward modeling methods and regularization schemes within a common inversion framework. The challenges can be addressed in part by decomposing the inverse problem into smaller, simpler inverse problems that can be solved separately, providing one knows how to merge the separate inversion results into an optimal solution of the full problem. We have formulated an approach to the decomposition of large inverse problems based on the augmented Lagrangian technique from optimization theory. As commonly done, we define a solution to the full inverse problem as the Earth model minimizing an objective function motivated, for example, by a Bayesian inference formulation. Our decomposition approach recasts the minimization problem equivalently as the minimization of component objective functions, corresponding to specified data subsets, subject to the constraints that the minimizing models be equal. A standard optimization algorithm solves the resulting constrained minimization problems by alternating between the separate solution of the component problems and the updating of Lagrange multipliers that serve to steer the individual solution models toward a common model solving the full problem. We are applying our inversion method to the reconstruction of the·crust and upper-mantle seismic velocity structure across Eurasia.· Data for the inversion comprise a large set of P and S body-wave travel times·and fundamental and first-higher mode Rayleigh-wave group velocities.

A general optimality criteria algorithm for a class of engineering optimization problems

NASA Astrophysics Data System (ADS)

Belegundu, Ashok D.

2015-05-01

An optimality criteria (OC)-based algorithm for optimization of a general class of nonlinear programming (NLP) problems is presented. The algorithm is only applicable to problems where the objective and constraint functions satisfy certain monotonicity properties. For multiply constrained problems which satisfy these assumptions, the algorithm is attractive compared with existing NLP methods as well as prevalent OC methods, as the latter involve computationally expensive active set and step-size control strategies. The fixed point algorithm presented here is applicable not only to structural optimization problems but also to certain problems as occur in resource allocation and inventory models. Convergence aspects are discussed. The fixed point update or resizing formula is given physical significance, which brings out a strength and trim feature. The number of function evaluations remains independent of the number of variables, allowing the efficient solution of problems with large number of variables.

A framework for modeling and optimizing dynamic systems under uncertainty

DOE PAGES

Nicholson, Bethany; Siirola, John

2017-11-11

Algebraic modeling languages (AMLs) have drastically simplified the implementation of algebraic optimization problems. However, there are still many classes of optimization problems that are not easily represented in most AMLs. These classes of problems are typically reformulated before implementation, which requires significant effort and time from the modeler and obscures the original problem structure or context. In this work we demonstrate how the Pyomo AML can be used to represent complex optimization problems using high-level modeling constructs. We focus on the operation of dynamic systems under uncertainty and demonstrate the combination of Pyomo extensions for dynamic optimization and stochastic programming.more » We use a dynamic semibatch reactor model and a large-scale bubbling fluidized bed adsorber model as test cases.« less

A framework for modeling and optimizing dynamic systems under uncertainty

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nicholson, Bethany; Siirola, John

Algebraic modeling languages (AMLs) have drastically simplified the implementation of algebraic optimization problems. However, there are still many classes of optimization problems that are not easily represented in most AMLs. These classes of problems are typically reformulated before implementation, which requires significant effort and time from the modeler and obscures the original problem structure or context. In this work we demonstrate how the Pyomo AML can be used to represent complex optimization problems using high-level modeling constructs. We focus on the operation of dynamic systems under uncertainty and demonstrate the combination of Pyomo extensions for dynamic optimization and stochastic programming.more » We use a dynamic semibatch reactor model and a large-scale bubbling fluidized bed adsorber model as test cases.« less

A Scalable and Robust Multi-Agent Approach to Distributed Optimization

NASA Technical Reports Server (NTRS)

Tumer, Kagan

2005-01-01

Modularizing a large optimization problem so that the solutions to the subproblems provide a good overall solution is a challenging problem. In this paper we present a multi-agent approach to this problem based on aligning the agent objectives with the system objectives, obviating the need to impose external mechanisms to achieve collaboration among the agents. This approach naturally addresses scaling and robustness issues by ensuring that the agents do not rely on the reliable operation of other agents We test this approach in the difficult distributed optimization problem of imperfect device subset selection [Challet and Johnson, 2002]. In this problem, there are n devices, each of which has a "distortion", and the task is to find the subset of those n devices that minimizes the average distortion. Our results show that in large systems (1000 agents) the proposed approach provides improvements of over an order of magnitude over both traditional optimization methods and traditional multi-agent methods. Furthermore, the results show that even in extreme cases of agent failures (i.e., half the agents fail midway through the simulation) the system remains coordinated and still outperforms a failure-free and centralized optimization algorithm.

Optimization by nonhierarchical asynchronous decomposition

NASA Technical Reports Server (NTRS)

Shankar, Jayashree; Ribbens, Calvin J.; Haftka, Raphael T.; Watson, Layne T.

1992-01-01

Large scale optimization problems are tractable only if they are somehow decomposed. Hierarchical decompositions are inappropriate for some types of problems and do not parallelize well. Sobieszczanski-Sobieski has proposed a nonhierarchical decomposition strategy for nonlinear constrained optimization that is naturally parallel. Despite some successes on engineering problems, the algorithm as originally proposed fails on simple two dimensional quadratic programs. The algorithm is carefully analyzed for quadratic programs, and a number of modifications are suggested to improve its robustness.

Sub-problem Optimization With Regression and Neural Network Approximators

NASA Technical Reports Server (NTRS)

Guptill, James D.; Hopkins, Dale A.; Patnaik, Surya N.

2003-01-01

Design optimization of large systems can be attempted through a sub-problem strategy. In this strategy, the original problem is divided into a number of smaller problems that are clustered together to obtain a sequence of sub-problems. Solution to the large problem is attempted iteratively through repeated solutions to the modest sub-problems. This strategy is applicable to structures and to multidisciplinary systems. For structures, clustering the substructures generates the sequence of sub-problems. For a multidisciplinary system, individual disciplines, accounting for coupling, can be considered as sub-problems. A sub-problem, if required, can be further broken down to accommodate sub-disciplines. The sub-problem strategy is being implemented into the NASA design optimization test bed, referred to as "CometBoards." Neural network and regression approximators are employed for reanalysis and sensitivity analysis calculations at the sub-problem level. The strategy has been implemented in sequential as well as parallel computational environments. This strategy, which attempts to alleviate algorithmic and reanalysis deficiencies, has the potential to become a powerful design tool. However, several issues have to be addressed before its full potential can be harnessed. This paper illustrates the strategy and addresses some issues.

An Optimization Code for Nonlinear Transient Problems of a Large Scale Multidisciplinary Mathematical Model

NASA Astrophysics Data System (ADS)

Takasaki, Koichi

This paper presents a program for the multidisciplinary optimization and identification problem of the nonlinear model of large aerospace vehicle structures. The program constructs the global matrix of the dynamic system in the time direction by the p-version finite element method (pFEM), and the basic matrix for each pFEM node in the time direction is described by a sparse matrix similarly to the static finite element problem. The algorithm used by the program does not require the Hessian matrix of the objective function and so has low memory requirements. It also has a relatively low computational cost, and is suited to parallel computation. The program was integrated as a solver module of the multidisciplinary analysis system CUMuLOUS (Computational Utility for Multidisciplinary Large scale Optimization of Undense System) which is under development by the Aerospace Research and Development Directorate (ARD) of the Japan Aerospace Exploration Agency (JAXA).

Optimal processor assignment for pipeline computations

NASA Technical Reports Server (NTRS)

Nicol, David M.; Simha, Rahul; Choudhury, Alok N.; Narahari, Bhagirath

1991-01-01

The availability of large scale multitasked parallel architectures introduces the following processor assignment problem for pipelined computations. Given a set of tasks and their precedence constraints, along with their experimentally determined individual responses times for different processor sizes, find an assignment of processor to tasks. Two objectives are of interest: minimal response given a throughput requirement, and maximal throughput given a response time requirement. These assignment problems differ considerably from the classical mapping problem in which several tasks share a processor; instead, it is assumed that a large number of processors are to be assigned to a relatively small number of tasks. Efficient assignment algorithms were developed for different classes of task structures. For a p processor system and a series parallel precedence graph with n constituent tasks, an O(np2) algorithm is provided that finds the optimal assignment for the response time optimization problem; it was found that the assignment optimizing the constrained throughput in O(np2log p) time. Special cases of linear, independent, and tree graphs are also considered.

On the decentralized control of large-scale systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Chong, C.

1973-01-01

The decentralized control of stochastic large scale systems was considered. Particular emphasis was given to control strategies which utilize decentralized information and can be computed in a decentralized manner. The deterministic constrained optimization problem is generalized to the stochastic case when each decision variable depends on different information and the constraint is only required to be satisfied on the average. For problems with a particular structure, a hierarchical decomposition is obtained. For the stochastic control of dynamic systems with different information sets, a new kind of optimality is proposed which exploits the coupled nature of the dynamic system. The subsystems are assumed to be uncoupled and then certain constraints are required to be satisfied, either in a off-line or on-line fashion. For off-line coordination, a hierarchical approach of solving the problem is obtained. The lower level problems are all uncoupled. For on-line coordination, distinction is made between open loop feedback optimal coordination and closed loop optimal coordination.

A linear decomposition method for large optimization problems. Blueprint for development

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, J.

1982-01-01

A method is proposed for decomposing large optimization problems encountered in the design of engineering systems such as an aircraft into a number of smaller subproblems. The decomposition is achieved by organizing the problem and the subordinated subproblems in a tree hierarchy and optimizing each subsystem separately. Coupling of the subproblems is accounted for by subsequent optimization of the entire system based on sensitivities of the suboptimization problem solutions at each level of the tree to variables of the next higher level. A formalization of the procedure suitable for computer implementation is developed and the state of readiness of the implementation building blocks is reviewed showing that the ingredients for the development are on the shelf. The decomposition method is also shown to be compatible with the natural human organization of the design process of engineering systems. The method is also examined with respect to the trends in computer hardware and software progress to point out that its efficiency can be amplified by network computing using parallel processors.

Implementation and Performance Issues in Collaborative Optimization

NASA Technical Reports Server (NTRS)

Braun, Robert; Gage, Peter; Kroo, Ilan; Sobieski, Ian

1996-01-01

Collaborative optimization is a multidisciplinary design architecture that is well-suited to large-scale multidisciplinary optimization problems. This paper compares this approach with other architectures, examines the details of the formulation, and some aspects of its performance. A particular version of the architecture is proposed to better accommodate the occurrence of multiple feasible regions. The use of system level inequality constraints is shown to increase the convergence rate. A series of simple test problems, demonstrated to challenge related optimization architectures, is successfully solved with collaborative optimization.

Divergent estimation error in portfolio optimization and in linear regression

NASA Astrophysics Data System (ADS)

Kondor, I.; Varga-Haszonits, I.

2008-08-01

The problem of estimation error in portfolio optimization is discussed, in the limit where the portfolio size N and the sample size T go to infinity such that their ratio is fixed. The estimation error strongly depends on the ratio N/T and diverges for a critical value of this parameter. This divergence is the manifestation of an algorithmic phase transition, it is accompanied by a number of critical phenomena, and displays universality. As the structure of a large number of multidimensional regression and modelling problems is very similar to portfolio optimization, the scope of the above observations extends far beyond finance, and covers a large number of problems in operations research, machine learning, bioinformatics, medical science, economics, and technology.

Solving optimization problems on computational grids.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wright, S. J.; Mathematics and Computer Science

2001-05-01

Multiprocessor computing platforms, which have become more and more widely available since the mid-1980s, are now heavily used by organizations that need to solve very demanding computational problems. Parallel computing is now central to the culture of many research communities. Novel parallel approaches were developed for global optimization, network optimization, and direct-search methods for nonlinear optimization. Activity was particularly widespread in parallel branch-and-bound approaches for various problems in combinatorial and network optimization. As the cost of personal computers and low-end workstations has continued to fall, while the speed and capacity of processors and networks have increased dramatically, 'cluster' platforms havemore » become popular in many settings. A somewhat different type of parallel computing platform know as a computational grid (alternatively, metacomputer) has arisen in comparatively recent times. Broadly speaking, this term refers not to a multiprocessor with identical processing nodes but rather to a heterogeneous collection of devices that are widely distributed, possibly around the globe. The advantage of such platforms is obvious: they have the potential to deliver enormous computing power. Just as obviously, however, the complexity of grids makes them very difficult to use. The Condor team, headed by Miron Livny at the University of Wisconsin, were among the pioneers in providing infrastructure for grid computations. More recently, the Globus project has developed technologies to support computations on geographically distributed platforms consisting of high-end computers, storage and visualization devices, and other scientific instruments. In 1997, we started the metaneos project as a collaborative effort between optimization specialists and the Condor and Globus groups. Our aim was to address complex, difficult optimization problems in several areas, designing and implementing the algorithms and the software infrastructure need to solve these problems on computational grids. This article describes some of the results we have obtained during the first three years of the metaneos project. Our efforts have led to development of the runtime support library MW for implementing algorithms with master-worker control structure on Condor platforms. This work is discussed here, along with work on algorithms and codes for integer linear programming, the quadratic assignment problem, and stochastic linear programmming. Our experiences in the metaneos project have shown that cheap, powerful computational grids can be used to tackle large optimization problems of various types. In an industrial or commercial setting, the results demonstrate that one may not have to buy powerful computational servers to solve many of the large problems arising in areas such as scheduling, portfolio optimization, or logistics; the idle time on employee workstations (or, at worst, an investment in a modest cluster of PCs) may do the job. For the optimization research community, our results motivate further work on parallel, grid-enabled algorithms for solving very large problems of other types. The fact that very large problems can be solved cheaply allows researchers to better understand issues of 'practical' complexity and of the role of heuristics.« less

Structural optimization by multilevel decomposition

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, J.; James, B.; Dovi, A.

1983-01-01

A method is described for decomposing an optimization problem into a set of subproblems and a coordination problem which preserves coupling between the subproblems. The method is introduced as a special case of multilevel, multidisciplinary system optimization and its algorithm is fully described for two level optimization for structures assembled of finite elements of arbitrary type. Numerical results are given for an example of a framework to show that the decomposition method converges and yields results comparable to those obtained without decomposition. It is pointed out that optimization by decomposition should reduce the design time by allowing groups of engineers, using different computers to work concurrently on the same large problem.

Influence maximization in complex networks through optimal percolation

NASA Astrophysics Data System (ADS)

Morone, Flaviano; Makse, Hernán A.

2015-08-01

The whole frame of interconnections in complex networks hinges on a specific set of structural nodes, much smaller than the total size, which, if activated, would cause the spread of information to the whole network, or, if immunized, would prevent the diffusion of a large scale epidemic. Localizing this optimal, that is, minimal, set of structural nodes, called influencers, is one of the most important problems in network science. Despite the vast use of heuristic strategies to identify influential spreaders, the problem remains unsolved. Here we map the problem onto optimal percolation in random networks to identify the minimal set of influencers, which arises by minimizing the energy of a many-body system, where the form of the interactions is fixed by the non-backtracking matrix of the network. Big data analyses reveal that the set of optimal influencers is much smaller than the one predicted by previous heuristic centralities. Remarkably, a large number of previously neglected weakly connected nodes emerges among the optimal influencers. These are topologically tagged as low-degree nodes surrounded by hierarchical coronas of hubs, and are uncovered only through the optimal collective interplay of all the influencers in the network. The present theoretical framework may hold a larger degree of universality, being applicable to other hard optimization problems exhibiting a continuous transition from a known phase.

Influence maximization in complex networks through optimal percolation.

PubMed

Morone, Flaviano; Makse, Hernán A

2015-08-06

The whole frame of interconnections in complex networks hinges on a specific set of structural nodes, much smaller than the total size, which, if activated, would cause the spread of information to the whole network, or, if immunized, would prevent the diffusion of a large scale epidemic. Localizing this optimal, that is, minimal, set of structural nodes, called influencers, is one of the most important problems in network science. Despite the vast use of heuristic strategies to identify influential spreaders, the problem remains unsolved. Here we map the problem onto optimal percolation in random networks to identify the minimal set of influencers, which arises by minimizing the energy of a many-body system, where the form of the interactions is fixed by the non-backtracking matrix of the network. Big data analyses reveal that the set of optimal influencers is much smaller than the one predicted by previous heuristic centralities. Remarkably, a large number of previously neglected weakly connected nodes emerges among the optimal influencers. These are topologically tagged as low-degree nodes surrounded by hierarchical coronas of hubs, and are uncovered only through the optimal collective interplay of all the influencers in the network. The present theoretical framework may hold a larger degree of universality, being applicable to other hard optimization problems exhibiting a continuous transition from a known phase.

Structural design using equilibrium programming formulations

NASA Technical Reports Server (NTRS)

Scotti, Stephen J.

1995-01-01

Solutions to increasingly larger structural optimization problems are desired. However, computational resources are strained to meet this need. New methods will be required to solve increasingly larger problems. The present approaches to solving large-scale problems involve approximations for the constraints of structural optimization problems and/or decomposition of the problem into multiple subproblems that can be solved in parallel. An area of game theory, equilibrium programming (also known as noncooperative game theory), can be used to unify these existing approaches from a theoretical point of view (considering the existence and optimality of solutions), and be used as a framework for the development of new methods for solving large-scale optimization problems. Equilibrium programming theory is described, and existing design techniques such as fully stressed design and constraint approximations are shown to fit within its framework. Two new structural design formulations are also derived. The first new formulation is another approximation technique which is a general updating scheme for the sensitivity derivatives of design constraints. The second new formulation uses a substructure-based decomposition of the structure for analysis and sensitivity calculations. Significant computational benefits of the new formulations compared with a conventional method are demonstrated.

Combining constraint satisfaction and local improvement algorithms to construct anaesthetists' rotas

NASA Technical Reports Server (NTRS)

Smith, Barbara M.; Bennett, Sean

1992-01-01

A system is described which was built to compile weekly rotas for the anaesthetists in a large hospital. The rota compilation problem is an optimization problem (the number of tasks which cannot be assigned to an anaesthetist must be minimized) and was formulated as a constraint satisfaction problem (CSP). The forward checking algorithm is used to find a feasible rota, but because of the size of the problem, it cannot find an optimal (or even a good enough) solution in an acceptable time. Instead, an algorithm was devised which makes local improvements to a feasible solution. The algorithm makes use of the constraints as expressed in the CSP to ensure that feasibility is maintained, and produces very good rotas which are being used by the hospital involved in the project. It is argued that formulation as a constraint satisfaction problem may be a good approach to solving discrete optimization problems, even if the resulting CSP is too large to be solved exactly in an acceptable time. A CSP algorithm may be able to produce a feasible solution which can then be improved, giving a good, if not provably optimal, solution.

Solving large-scale fixed cost integer linear programming models for grid-based location problems with heuristic techniques

NASA Astrophysics Data System (ADS)

Noor-E-Alam, Md.; Doucette, John

2015-08-01

Grid-based location problems (GBLPs) can be used to solve location problems in business, engineering, resource exploitation, and even in the field of medical sciences. To solve these decision problems, an integer linear programming (ILP) model is designed and developed to provide the optimal solution for GBLPs considering fixed cost criteria. Preliminary results show that the ILP model is efficient in solving small to moderate-sized problems. However, this ILP model becomes intractable in solving large-scale instances. Therefore, a decomposition heuristic is proposed to solve these large-scale GBLPs, which demonstrates significant reduction of solution runtimes. To benchmark the proposed heuristic, results are compared with the exact solution via ILP. The experimental results show that the proposed method significantly outperforms the exact method in runtime with minimal (and in most cases, no) loss of optimality.

Optimizing Value and Avoiding Problems in Building Schools.

ERIC Educational Resources Information Center

Brevard County School Board, Cocoa, FL.

This report describes school design and construction delivery processes used by the School Board of Brevard County (Cocoa, Florida) that help optimize value, avoid problems, and eliminate the cost of maintaining a large facility staff. The project phases are examined from project definition through design to construction. Project delivery…

Algorithms for Mathematical Programming with Emphasis on Bi-level Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goldfarb, Donald; Iyengar, Garud

2014-05-22

The research supported by this grant was focused primarily on first-order methods for solving large scale and structured convex optimization problems and convex relaxations of nonconvex problems. These include optimal gradient methods, operator and variable splitting methods, alternating direction augmented Lagrangian methods, and block coordinate descent methods.

Asymptotic analysis of SPTA-based algorithms for no-wait flow shop scheduling problem with release dates.

PubMed

Ren, Tao; Zhang, Chuan; Lin, Lin; Guo, Meiting; Xie, Xionghang

2014-01-01

We address the scheduling problem for a no-wait flow shop to optimize total completion time with release dates. With the tool of asymptotic analysis, we prove that the objective values of two SPTA-based algorithms converge to the optimal value for sufficiently large-sized problems. To further enhance the performance of the SPTA-based algorithms, an improvement scheme based on local search is provided for moderate scale problems. New lower bound is presented for evaluating the asymptotic optimality of the algorithms. Numerical simulations demonstrate the effectiveness of the proposed algorithms.

Asymptotic Analysis of SPTA-Based Algorithms for No-Wait Flow Shop Scheduling Problem with Release Dates

PubMed Central

Ren, Tao; Zhang, Chuan; Lin, Lin; Guo, Meiting; Xie, Xionghang

2014-01-01

We address the scheduling problem for a no-wait flow shop to optimize total completion time with release dates. With the tool of asymptotic analysis, we prove that the objective values of two SPTA-based algorithms converge to the optimal value for sufficiently large-sized problems. To further enhance the performance of the SPTA-based algorithms, an improvement scheme based on local search is provided for moderate scale problems. New lower bound is presented for evaluating the asymptotic optimality of the algorithms. Numerical simulations demonstrate the effectiveness of the proposed algorithms. PMID:24764774

Simultaneous optimization of loading pattern and burnable poison placement for PWRs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alim, F.; Ivanov, K.; Yilmaz, S.

2006-07-01

To solve in-core fuel management optimization problem, GARCO-PSU (Genetic Algorithm Reactor Core Optimization - Pennsylvania State Univ.) is developed. This code is applicable for all types and geometry of PWR core structures with unlimited number of fuel assembly (FA) types in the inventory. For this reason an innovative genetic algorithm is developed with modifying the classical representation of the genotype. In-core fuel management heuristic rules are introduced into GARCO. The core re-load design optimization has two parts, loading pattern (LP) optimization and burnable poison (BP) placement optimization. These parts depend on each other, but it is difficult to solve themore » combined problem due to its large size. Separating the problem into two parts provides a practical way to solve the problem. However, the result of this method does not reflect the real optimal solution. GARCO-PSU achieves to solve LP optimization and BP placement optimization simultaneously in an efficient manner. (authors)« less

Simultaneous analysis and design

NASA Technical Reports Server (NTRS)

Haftka, R. T.

1984-01-01

Optimization techniques are increasingly being used for performing nonlinear structural analysis. The development of element by element (EBE) preconditioned conjugate gradient (CG) techniques is expected to extend this trend to linear analysis. Under these circumstances the structural design problem can be viewed as a nested optimization problem. There are computational benefits to treating this nested problem as a large single optimization problem. The response variables (such as displacements) and the structural parameters are all treated as design variables in a unified formulation which performs simultaneously the design and analysis. Two examples are used for demonstration. A seventy-two bar truss is optimized subject to linear stress constraints and a wing box structure is optimized subject to nonlinear collapse constraints. Both examples show substantial computational savings with the unified approach as compared to the traditional nested approach.

Multimode resource-constrained multiple project scheduling problem under fuzzy random environment and its application to a large scale hydropower construction project.

PubMed

Xu, Jiuping; Feng, Cuiying

2014-01-01

This paper presents an extension of the multimode resource-constrained project scheduling problem for a large scale construction project where multiple parallel projects and a fuzzy random environment are considered. By taking into account the most typical goals in project management, a cost/weighted makespan/quality trade-off optimization model is constructed. To deal with the uncertainties, a hybrid crisp approach is used to transform the fuzzy random parameters into fuzzy variables that are subsequently defuzzified using an expected value operator with an optimistic-pessimistic index. Then a combinatorial-priority-based hybrid particle swarm optimization algorithm is developed to solve the proposed model, where the combinatorial particle swarm optimization and priority-based particle swarm optimization are designed to assign modes to activities and to schedule activities, respectively. Finally, the results and analysis of a practical example at a large scale hydropower construction project are presented to demonstrate the practicality and efficiency of the proposed model and optimization method.

Multimode Resource-Constrained Multiple Project Scheduling Problem under Fuzzy Random Environment and Its Application to a Large Scale Hydropower Construction Project

PubMed Central

Xu, Jiuping

2014-01-01

This paper presents an extension of the multimode resource-constrained project scheduling problem for a large scale construction project where multiple parallel projects and a fuzzy random environment are considered. By taking into account the most typical goals in project management, a cost/weighted makespan/quality trade-off optimization model is constructed. To deal with the uncertainties, a hybrid crisp approach is used to transform the fuzzy random parameters into fuzzy variables that are subsequently defuzzified using an expected value operator with an optimistic-pessimistic index. Then a combinatorial-priority-based hybrid particle swarm optimization algorithm is developed to solve the proposed model, where the combinatorial particle swarm optimization and priority-based particle swarm optimization are designed to assign modes to activities and to schedule activities, respectively. Finally, the results and analysis of a practical example at a large scale hydropower construction project are presented to demonstrate the practicality and efficiency of the proposed model and optimization method. PMID:24550708

Research on the precise positioning of customers in large data environment

NASA Astrophysics Data System (ADS)

Zhou, Xu; He, Lili

2018-04-01

Customer positioning has always been a problem that enterprises focus on. In this paper, FCM clustering algorithm is used to cluster customer groups. However, due to the traditional FCM clustering algorithm, which is susceptible to the influence of the initial clustering center and easy to fall into the local optimal problem, the short board of FCM is solved by the gray optimization algorithm (GWO) to achieve efficient and accurate handling of a large number of retailer data.

An optimal control strategy for hybrid actuator systems: Application to an artificial muscle with electric motor assist.

PubMed

Ishihara, Koji; Morimoto, Jun

2018-03-01

Humans use multiple muscles to generate such joint movements as an elbow motion. With multiple lightweight and compliant actuators, joint movements can also be efficiently generated. Similarly, robots can use multiple actuators to efficiently generate a one degree of freedom movement. For this movement, the desired joint torque must be properly distributed to each actuator. One approach to cope with this torque distribution problem is an optimal control method. However, solving the optimal control problem at each control time step has not been deemed a practical approach due to its large computational burden. In this paper, we propose a computationally efficient method to derive an optimal control strategy for a hybrid actuation system composed of multiple actuators, where each actuator has different dynamical properties. We investigated a singularly perturbed system of the hybrid actuator model that subdivided the original large-scale control problem into smaller subproblems so that the optimal control outputs for each actuator can be derived at each control time step and applied our proposed method to our pneumatic-electric hybrid actuator system. Our method derived a torque distribution strategy for the hybrid actuator by dealing with the difficulty of solving real-time optimal control problems. Copyright © 2017 The Author(s). Published by Elsevier Ltd.. All rights reserved.

A modular approach to large-scale design optimization of aerospace systems

NASA Astrophysics Data System (ADS)

Hwang, John T.

Gradient-based optimization and the adjoint method form a synergistic combination that enables the efficient solution of large-scale optimization problems. Though the gradient-based approach struggles with non-smooth or multi-modal problems, the capability to efficiently optimize up to tens of thousands of design variables provides a valuable design tool for exploring complex tradeoffs and finding unintuitive designs. However, the widespread adoption of gradient-based optimization is limited by the implementation challenges for computing derivatives efficiently and accurately, particularly in multidisciplinary and shape design problems. This thesis addresses these difficulties in two ways. First, to deal with the heterogeneity and integration challenges of multidisciplinary problems, this thesis presents a computational modeling framework that solves multidisciplinary systems and computes their derivatives in a semi-automated fashion. This framework is built upon a new mathematical formulation developed in this thesis that expresses any computational model as a system of algebraic equations and unifies all methods for computing derivatives using a single equation. The framework is applied to two engineering problems: the optimization of a nanosatellite with 7 disciplines and over 25,000 design variables; and simultaneous allocation and mission optimization for commercial aircraft involving 330 design variables, 12 of which are integer variables handled using the branch-and-bound method. In both cases, the framework makes large-scale optimization possible by reducing the implementation effort and code complexity. The second half of this thesis presents a differentiable parametrization of aircraft geometries and structures for high-fidelity shape optimization. Existing geometry parametrizations are not differentiable, or they are limited in the types of shape changes they allow. This is addressed by a novel parametrization that smoothly interpolates aircraft components, providing differentiability. An unstructured quadrilateral mesh generation algorithm is also developed to automate the creation of detailed meshes for aircraft structures, and a mesh convergence study is performed to verify that the quality of the mesh is maintained as it is refined. As a demonstration, high-fidelity aerostructural analysis is performed for two unconventional configurations with detailed structures included, and aerodynamic shape optimization is applied to the truss-braced wing, which finds and eliminates a shock in the region bounded by the struts and the wing.

Comparison of Genetic Algorithm, Particle Swarm Optimization and Biogeography-based Optimization for Feature Selection to Classify Clusters of Microcalcifications

NASA Astrophysics Data System (ADS)

Khehra, Baljit Singh; Pharwaha, Amar Partap Singh

2017-04-01

Ductal carcinoma in situ (DCIS) is one type of breast cancer. Clusters of microcalcifications (MCCs) are symptoms of DCIS that are recognized by mammography. Selection of robust features vector is the process of selecting an optimal subset of features from a large number of available features in a given problem domain after the feature extraction and before any classification scheme. Feature selection reduces the feature space that improves the performance of classifier and decreases the computational burden imposed by using many features on classifier. Selection of an optimal subset of features from a large number of available features in a given problem domain is a difficult search problem. For n features, the total numbers of possible subsets of features are 2n. Thus, selection of an optimal subset of features problem belongs to the category of NP-hard problems. In this paper, an attempt is made to find the optimal subset of MCCs features from all possible subsets of features using genetic algorithm (GA), particle swarm optimization (PSO) and biogeography-based optimization (BBO). For simulation, a total of 380 benign and malignant MCCs samples have been selected from mammogram images of DDSM database. A total of 50 features extracted from benign and malignant MCCs samples are used in this study. In these algorithms, fitness function is correct classification rate of classifier. Support vector machine is used as a classifier. From experimental results, it is also observed that the performance of PSO-based and BBO-based algorithms to select an optimal subset of features for classifying MCCs as benign or malignant is better as compared to GA-based algorithm.

Optimal orbit transfer suitable for large flexible structures

NASA Technical Reports Server (NTRS)

Chatterjee, Alok K.

1989-01-01

The problem of continuous low-thrust planar orbit transfer of large flexible structures is formulated as an optimal control problem with terminal state constraints. The dynamics of the spacecraft motion are treated as a point-mass central force field problem; the thrust-acceleration magnitude is treated as an additional state variable; and the rate of change of thrust-acceleration is treated as a control variable. To ensure smooth transfer, essential for flexible structures, an additional quadratic term is appended to the time cost functional. This term penalizes any abrupt change in acceleration. Numerical results are presented for the special case of a planar transfer.

Solving LP Relaxations of Large-Scale Precedence Constrained Problems

NASA Astrophysics Data System (ADS)

Bienstock, Daniel; Zuckerberg, Mark

We describe new algorithms for solving linear programming relaxations of very large precedence constrained production scheduling problems. We present theory that motivates a new set of algorithmic ideas that can be employed on a wide range of problems; on data sets arising in the mining industry our algorithms prove effective on problems with many millions of variables and constraints, obtaining provably optimal solutions in a few minutes of computation.

Inverse problems in the design, modeling and testing of engineering systems

NASA Technical Reports Server (NTRS)

Alifanov, Oleg M.

1991-01-01

Formulations, classification, areas of application, and approaches to solving different inverse problems are considered for the design of structures, modeling, and experimental data processing. Problems in the practical implementation of theoretical-experimental methods based on solving inverse problems are analyzed in order to identify mathematical models of physical processes, aid in input data preparation for design parameter optimization, help in design parameter optimization itself, and to model experiments, large-scale tests, and real tests of engineering systems.

A General-Purpose Optimization Engine for Multi-Disciplinary Design Applications

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Hopkins, Dale A.; Berke, Laszlo

1996-01-01

A general purpose optimization tool for multidisciplinary applications, which in the literature is known as COMETBOARDS, is being developed at NASA Lewis Research Center. The modular organization of COMETBOARDS includes several analyzers and state-of-the-art optimization algorithms along with their cascading strategy. The code structure allows quick integration of new analyzers and optimizers. The COMETBOARDS code reads input information from a number of data files, formulates a design as a set of multidisciplinary nonlinear programming problems, and then solves the resulting problems. COMETBOARDS can be used to solve a large problem which can be defined through multiple disciplines, each of which can be further broken down into several subproblems. Alternatively, a small portion of a large problem can be optimized in an effort to improve an existing system. Some of the other unique features of COMETBOARDS include design variable formulation, constraint formulation, subproblem coupling strategy, global scaling technique, analysis approximation, use of either sequential or parallel computational modes, and so forth. The special features and unique strengths of COMETBOARDS assist convergence and reduce the amount of CPU time used to solve the difficult optimization problems of aerospace industries. COMETBOARDS has been successfully used to solve a number of problems, including structural design of space station components, design of nozzle components of an air-breathing engine, configuration design of subsonic and supersonic aircraft, mixed flow turbofan engines, wave rotor topped engines, and so forth. This paper introduces the COMETBOARDS design tool and its versatility, which is illustrated by citing examples from structures, aircraft design, and air-breathing propulsion engine design.

The mathematical statement for the solving of the problem of N-version software system design

NASA Astrophysics Data System (ADS)

Kovalev, I. V.; Kovalev, D. I.; Zelenkov, P. V.; Voroshilova, A. A.

2015-10-01

The N-version programming, as a methodology of the fault-tolerant software systems design, allows successful solving of the mentioned tasks. The use of N-version programming approach turns out to be effective, since the system is constructed out of several parallel executed versions of some software module. Those versions are written to meet the same specification but by different programmers. The problem of developing an optimal structure of N-version software system presents a kind of very complex optimization problem. This causes the use of deterministic optimization methods inappropriate for solving the stated problem. In this view, exploiting heuristic strategies looks more rational. In the field of pseudo-Boolean optimization theory, the so called method of varied probabilities (MVP) has been developed to solve problems with a large dimensionality.

Parameter optimization of differential evolution algorithm for automatic playlist generation problem

NASA Astrophysics Data System (ADS)

Alamag, Kaye Melina Natividad B.; Addawe, Joel M.

2017-11-01

With the digitalization of music, the number of collection of music increased largely and there is a need to create lists of music that filter the collection according to user preferences, thus giving rise to the Automatic Playlist Generation Problem (APGP). Previous attempts to solve this problem include the use of search and optimization algorithms. If a music database is very large, the algorithm to be used must be able to search the lists thoroughly taking into account the quality of the playlist given a set of user constraints. In this paper we perform an evolutionary meta-heuristic optimization algorithm, Differential Evolution (DE) using different combination of parameter values and select the best performing set when used to solve four standard test functions. Performance of the proposed algorithm is then compared with normal Genetic Algorithm (GA) and a hybrid GA with Tabu Search. Numerical simulations are carried out to show better results from Differential Evolution approach with the optimized parameter values.

A novel model-based evolutionary algorithm for multi-objective deformable image registration with content mismatch and large deformations: benchmarking efficiency and quality

NASA Astrophysics Data System (ADS)

Bouter, Anton; Alderliesten, Tanja; Bosman, Peter A. N.

2017-02-01

Taking a multi-objective optimization approach to deformable image registration has recently gained attention, because such an approach removes the requirement of manually tuning the weights of all the involved objectives. Especially for problems that require large complex deformations, this is a non-trivial task. From the resulting Pareto set of solutions one can then much more insightfully select a registration outcome that is most suitable for the problem at hand. To serve as an internal optimization engine, currently used multi-objective algorithms are competent, but rather inefficient. In this paper we largely improve upon this by introducing a multi-objective real-valued adaptation of the recently introduced Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) for discrete optimization. In this work, GOMEA is tailored specifically to the problem of deformable image registration to obtain substantially improved efficiency. This improvement is achieved by exploiting a key strength of GOMEA: iteratively improving small parts of solutions, allowing to faster exploit the impact of such updates on the objectives at hand through partial evaluations. We performed experiments on three registration problems. In particular, an artificial problem containing a disappearing structure, a pair of pre- and post-operative breast CT scans, and a pair of breast MRI scans acquired in prone and supine position were considered. Results show that compared to the previously used evolutionary algorithm, GOMEA obtains a speed-up of up to a factor of 1600 on the tested registration problems while achieving registration outcomes of similar quality.

Mixed Integer Programming and Heuristic Scheduling for Space Communication Networks

NASA Technical Reports Server (NTRS)

Lee, Charles H.; Cheung, Kar-Ming

2012-01-01

In this paper, we propose to solve the constrained optimization problem in two phases. The first phase uses heuristic methods such as the ant colony method, particle swarming optimization, and genetic algorithm to seek a near optimal solution among a list of feasible initial populations. The final optimal solution can be found by using the solution of the first phase as the initial condition to the SQP algorithm. We demonstrate the above problem formulation and optimization schemes with a large-scale network that includes the DSN ground stations and a number of spacecraft of deep space missions.

A time-domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems

NASA Astrophysics Data System (ADS)

Heinkenschloss, Matthias

2005-01-01

We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.

Parallel-vector computation for structural analysis and nonlinear unconstrained optimization problems

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.

1990-01-01

Practical engineering application can often be formulated in the form of a constrained optimization problem. There are several solution algorithms for solving a constrained optimization problem. One approach is to convert a constrained problem into a series of unconstrained problems. Furthermore, unconstrained solution algorithms can be used as part of the constrained solution algorithms. Structural optimization is an iterative process where one starts with an initial design, a finite element structure analysis is then performed to calculate the response of the system (such as displacements, stresses, eigenvalues, etc.). Based upon the sensitivity information on the objective and constraint functions, an optimizer such as ADS or IDESIGN, can be used to find the new, improved design. For the structural analysis phase, the equation solver for the system of simultaneous, linear equations plays a key role since it is needed for either static, or eigenvalue, or dynamic analysis. For practical, large-scale structural analysis-synthesis applications, computational time can be excessively large. Thus, it is necessary to have a new structural analysis-synthesis code which employs new solution algorithms to exploit both parallel and vector capabilities offered by modern, high performance computers such as the Convex, Cray-2 and Cray-YMP computers. The objective of this research project is, therefore, to incorporate the latest development in the parallel-vector equation solver, PVSOLVE into the widely popular finite-element production code, such as the SAP-4. Furthermore, several nonlinear unconstrained optimization subroutines have also been developed and tested under a parallel computer environment. The unconstrained optimization subroutines are not only useful in their own right, but they can also be incorporated into a more popular constrained optimization code, such as ADS.

Exploring quantum computing application to satellite data assimilation

NASA Astrophysics Data System (ADS)

Cheung, S.; Zhang, S. Q.

2015-12-01

This is an exploring work on potential application of quantum computing to a scientific data optimization problem. On classical computational platforms, the physical domain of a satellite data assimilation problem is represented by a discrete variable transform, and classical minimization algorithms are employed to find optimal solution of the analysis cost function. The computation becomes intensive and time-consuming when the problem involves large number of variables and data. The new quantum computer opens a very different approach both in conceptual programming and in hardware architecture for solving optimization problem. In order to explore if we can utilize the quantum computing machine architecture, we formulate a satellite data assimilation experimental case in the form of quadratic programming optimization problem. We find a transformation of the problem to map it into Quadratic Unconstrained Binary Optimization (QUBO) framework. Binary Wavelet Transform (BWT) will be applied to the data assimilation variables for its invertible decomposition and all calculations in BWT are performed by Boolean operations. The transformed problem will be experimented as to solve for a solution of QUBO instances defined on Chimera graphs of the quantum computer.

A hybrid binary particle swarm optimization for large capacitated multi item multi level lot sizing (CMIMLLS) problem

NASA Astrophysics Data System (ADS)

Mishra, S. K.; Sahithi, V. V. D.; Rao, C. S. P.

2016-09-01

The lot sizing problem deals with finding optimal order quantities which minimizes the ordering and holding cost of product mix. when multiple items at multiple levels with all capacity restrictions are considered, the lot sizing problem become NP hard. Many heuristics were developed in the past have inevitably failed due to size, computational complexity and time. However the authors were successful in the development of PSO based technique namely iterative improvement binary particles swarm technique to address very large capacitated multi-item multi level lot sizing (CMIMLLS) problem. First binary particle Swarm Optimization algorithm is used to find a solution in a reasonable time and iterative improvement local search mechanism is employed to improvise the solution obtained by BPSO algorithm. This hybrid mechanism of using local search on the global solution is found to improve the quality of solutions with respect to time thus IIBPSO method is found best and show excellent results.

Exact solution for the optimal neuronal layout problem.

PubMed

Chklovskii, Dmitri B

2004-10-01

Evolution perfected brain design by maximizing its functionality while minimizing costs associated with building and maintaining it. Assumption that brain functionality is specified by neuronal connectivity, implemented by costly biological wiring, leads to the following optimal design problem. For a given neuronal connectivity, find a spatial layout of neurons that minimizes the wiring cost. Unfortunately, this problem is difficult to solve because the number of possible layouts is often astronomically large. We argue that the wiring cost may scale as wire length squared, reducing the optimal layout problem to a constrained minimization of a quadratic form. For biologically plausible constraints, this problem has exact analytical solutions, which give reasonable approximations to actual layouts in the brain. These solutions make the inverse problem of inferring neuronal connectivity from neuronal layout more tractable.

Dynamic optimization of chemical processes using ant colony framework.

PubMed

Rajesh, J; Gupta, K; Kusumakar, H S; Jayaraman, V K; Kulkarni, B D

2001-11-01

Ant colony framework is illustrated by considering dynamic optimization of six important bench marking examples. This new computational tool is simple to implement and can tackle problems with state as well as terminal constraints in a straightforward fashion. It requires fewer grid points to reach the global optimum at relatively very low computational effort. The examples with varying degree of complexities, analyzed here, illustrate its potential for solving a large class of process optimization problems in chemical engineering.

Final Report---Optimization Under Nonconvexity and Uncertainty: Algorithms and Software

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jeff Linderoth

2011-11-06

the goal of this work was to develop new algorithmic techniques for solving large-scale numerical optimization problems, focusing on problems classes that have proven to be among the most challenging for practitioners: those involving uncertainty and those involving nonconvexity. This research advanced the state-of-the-art in solving mixed integer linear programs containing symmetry, mixed integer nonlinear programs, and stochastic optimization problems. The focus of the work done in the continuation was on Mixed Integer Nonlinear Programs (MINLP)s and Mixed Integer Linear Programs (MILP)s, especially those containing a great deal of symmetry.

Distributed Parallel Processing and Dynamic Load Balancing Techniques for Multidisciplinary High Speed Aircraft Design

NASA Technical Reports Server (NTRS)

Krasteva, Denitza T.

1998-01-01

Multidisciplinary design optimization (MDO) for large-scale engineering problems poses many challenges (e.g., the design of an efficient concurrent paradigm for global optimization based on disciplinary analyses, expensive computations over vast data sets, etc.) This work focuses on the application of distributed schemes for massively parallel architectures to MDO problems, as a tool for reducing computation time and solving larger problems. The specific problem considered here is configuration optimization of a high speed civil transport (HSCT), and the efficient parallelization of the embedded paradigm for reasonable design space identification. Two distributed dynamic load balancing techniques (random polling and global round robin with message combining) and two necessary termination detection schemes (global task count and token passing) were implemented and evaluated in terms of effectiveness and scalability to large problem sizes and a thousand processors. The effect of certain parameters on execution time was also inspected. Empirical results demonstrated stable performance and effectiveness for all schemes, and the parametric study showed that the selected algorithmic parameters have a negligible effect on performance.

Distributed Method to Optimal Profile Descent

NASA Astrophysics Data System (ADS)

Kim, Geun I.

Current ground automation tools for Optimal Profile Descent (OPD) procedures utilize path stretching and speed profile change to maintain proper merging and spacing requirements at high traffic terminal area. However, low predictability of aircraft's vertical profile and path deviation during decent add uncertainty to computing estimated time of arrival, a key information that enables the ground control center to manage airspace traffic effectively. This paper uses an OPD procedure that is based on a constant flight path angle to increase the predictability of the vertical profile and defines an OPD optimization problem that uses both path stretching and speed profile change while largely maintaining the original OPD procedure. This problem minimizes the cumulative cost of performing OPD procedures for a group of aircraft by assigning a time cost function to each aircraft and a separation cost function to a pair of aircraft. The OPD optimization problem is then solved in a decentralized manner using dual decomposition techniques under inter-aircraft ADS-B mechanism. This method divides the optimization problem into more manageable sub-problems which are then distributed to the group of aircraft. Each aircraft solves its assigned sub-problem and communicate the solutions to other aircraft in an iterative process until an optimal solution is achieved thus decentralizing the computation of the optimization problem.

Decentralized Optimal Dispatch of Photovoltaic Inverters in Residential Distribution Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall'Anese, Emiliano; Dhople, Sairaj V.; Johnson, Brian B.

Summary form only given. Decentralized methods for computing optimal real and reactive power setpoints for residential photovoltaic (PV) inverters are developed in this paper. It is known that conventional PV inverter controllers, which are designed to extract maximum power at unity power factor, cannot address secondary performance objectives such as voltage regulation and network loss minimization. Optimal power flow techniques can be utilized to select which inverters will provide ancillary services, and to compute their optimal real and reactive power setpoints according to well-defined performance criteria and economic objectives. Leveraging advances in sparsity-promoting regularization techniques and semidefinite relaxation, this papermore » shows how such problems can be solved with reduced computational burden and optimality guarantees. To enable large-scale implementation, a novel algorithmic framework is introduced - based on the so-called alternating direction method of multipliers - by which optimal power flow-type problems in this setting can be systematically decomposed into sub-problems that can be solved in a decentralized fashion by the utility and customer-owned PV systems with limited exchanges of information. Since the computational burden is shared among multiple devices and the requirement of all-to-all communication can be circumvented, the proposed optimization approach scales favorably to large distribution networks.« less

OPTIMIZING THROUGH CO-EVOLUTIONARY AVALANCHES

DOE Office of Scientific and Technical Information (OSTI.GOV)

S. BOETTCHER; A. PERCUS

2000-08-01

We explore a new general-purpose heuristic for finding high-quality solutions to hard optimization problems. The method, called extremal optimization, is inspired by ''self-organized critically,'' a concept introduced to describe emergent complexity in many physical systems. In contrast to Genetic Algorithms which operate on an entire ''gene-pool'' of possible solutions, extremal optimization successively replaces extremely undesirable elements of a sub-optimal solution with new, random ones. Large fluctuations, called ''avalanches,'' ensue that efficiently explore many local optima. Drawing upon models used to simulate far-from-equilibrium dynamics, extremal optimization complements approximation methods inspired by equilibrium statistical physics, such as simulated annealing. With only onemore » adjustable parameter, its performance has proved competitive with more elaborate methods, especially near phase transitions. Those phase transitions are found in the parameter space of most optimization problems, and have recently been conjectured to be the origin of some of the hardest instances in computational complexity. We will demonstrate how extremal optimization can be implemented for a variety of combinatorial optimization problems. We believe that extremal optimization will be a useful tool in the investigation of phase transitions in combinatorial optimization problems, hence valuable in elucidating the origin of computational complexity.« less

Optimization-based additive decomposition of weakly coercive problems with applications

DOE PAGES

Bochev, Pavel B.; Ridzal, Denis

2016-01-27

In this study, we present an abstract mathematical framework for an optimization-based additive decomposition of a large class of variational problems into a collection of concurrent subproblems. The framework replaces a given monolithic problem by an equivalent constrained optimization formulation in which the subproblems define the optimization constraints and the objective is to minimize the mismatch between their solutions. The significance of this reformulation stems from the fact that one can solve the resulting optimality system by an iterative process involving only solutions of the subproblems. Consequently, assuming that stable numerical methods and efficient solvers are available for every subproblem,more » our reformulation leads to robust and efficient numerical algorithms for a given monolithic problem by breaking it into subproblems that can be handled more easily. An application of the framework to the Oseen equations illustrates its potential.« less

Multi-GPU implementation of a VMAT treatment plan optimization algorithm.

PubMed

Tian, Zhen; Peng, Fei; Folkerts, Michael; Tan, Jun; Jia, Xun; Jiang, Steve B

2015-06-01

Volumetric modulated arc therapy (VMAT) optimization is a computationally challenging problem due to its large data size, high degrees of freedom, and many hardware constraints. High-performance graphics processing units (GPUs) have been used to speed up the computations. However, GPU's relatively small memory size cannot handle cases with a large dose-deposition coefficient (DDC) matrix in cases of, e.g., those with a large target size, multiple targets, multiple arcs, and/or small beamlet size. The main purpose of this paper is to report an implementation of a column-generation-based VMAT algorithm, previously developed in the authors' group, on a multi-GPU platform to solve the memory limitation problem. While the column-generation-based VMAT algorithm has been previously developed, the GPU implementation details have not been reported. Hence, another purpose is to present detailed techniques employed for GPU implementation. The authors also would like to utilize this particular problem as an example problem to study the feasibility of using a multi-GPU platform to solve large-scale problems in medical physics. The column-generation approach generates VMAT apertures sequentially by solving a pricing problem (PP) and a master problem (MP) iteratively. In the authors' method, the sparse DDC matrix is first stored on a CPU in coordinate list format (COO). On the GPU side, this matrix is split into four submatrices according to beam angles, which are stored on four GPUs in compressed sparse row format. Computation of beamlet price, the first step in PP, is accomplished using multi-GPUs. A fast inter-GPU data transfer scheme is accomplished using peer-to-peer access. The remaining steps of PP and MP problems are implemented on CPU or a single GPU due to their modest problem scale and computational loads. Barzilai and Borwein algorithm with a subspace step scheme is adopted here to solve the MP problem. A head and neck (H&N) cancer case is then used to validate the authors' method. The authors also compare their multi-GPU implementation with three different single GPU implementation strategies, i.e., truncating DDC matrix (S1), repeatedly transferring DDC matrix between CPU and GPU (S2), and porting computations involving DDC matrix to CPU (S3), in terms of both plan quality and computational efficiency. Two more H&N patient cases and three prostate cases are used to demonstrate the advantages of the authors' method. The authors' multi-GPU implementation can finish the optimization process within ∼ 1 min for the H&N patient case. S1 leads to an inferior plan quality although its total time was 10 s shorter than the multi-GPU implementation due to the reduced matrix size. S2 and S3 yield the same plan quality as the multi-GPU implementation but take ∼4 and ∼6 min, respectively. High computational efficiency was consistently achieved for the other five patient cases tested, with VMAT plans of clinically acceptable quality obtained within 23-46 s. Conversely, to obtain clinically comparable or acceptable plans for all six of these VMAT cases that the authors have tested in this paper, the optimization time needed in a commercial TPS system on CPU was found to be in an order of several minutes. The results demonstrate that the multi-GPU implementation of the authors' column-generation-based VMAT optimization can handle the large-scale VMAT optimization problem efficiently without sacrificing plan quality. The authors' study may serve as an example to shed some light on other large-scale medical physics problems that require multi-GPU techniques.

Introducing the MCHF/OVRP/SDMP: Multicapacitated/Heterogeneous Fleet/Open Vehicle Routing Problems with Split Deliveries and Multiproducts

PubMed Central

Yilmaz Eroglu, Duygu; Caglar Gencosman, Burcu; Cavdur, Fatih; Ozmutlu, H. Cenk

2014-01-01

In this paper, we analyze a real-world OVRP problem for a production company. Considering real-world constrains, we classify our problem as multicapacitated/heterogeneous fleet/open vehicle routing problem with split deliveries and multiproduct (MCHF/OVRP/SDMP) which is a novel classification of an OVRP. We have developed a mixed integer programming (MIP) model for the problem and generated test problems in different size (10–90 customers) considering real-world parameters. Although MIP is able to find optimal solutions of small size (10 customers) problems, when the number of customers increases, the problem gets harder to solve, and thus MIP could not find optimal solutions for problems that contain more than 10 customers. Moreover, MIP fails to find any feasible solution of large-scale problems (50–90 customers) within time limits (7200 seconds). Therefore, we have developed a genetic algorithm (GA) based solution approach for large-scale problems. The experimental results show that the GA based approach reaches successful solutions with 9.66% gap in 392.8 s on average instead of 7200 s for the problems that contain 10–50 customers. For large-scale problems (50–90 customers), GA reaches feasible solutions of problems within time limits. In conclusion, for the real-world applications, GA is preferable rather than MIP to reach feasible solutions in short time periods. PMID:25045735

Quantum Heterogeneous Computing for Satellite Positioning Optimization

NASA Astrophysics Data System (ADS)

Bass, G.; Kumar, V.; Dulny, J., III

2016-12-01

Hard optimization problems occur in many fields of academic study and practical situations. We present results in which quantum heterogeneous computing is used to solve a real-world optimization problem: satellite positioning. Optimization problems like this can scale very rapidly with problem size, and become unsolvable with traditional brute-force methods. Typically, such problems have been approximately solved with heuristic approaches; however, these methods can take a long time to calculate and are not guaranteed to find optimal solutions. Quantum computing offers the possibility of producing significant speed-up and improved solution quality. There are now commercially available quantum annealing (QA) devices that are designed to solve difficult optimization problems. These devices have 1000+ quantum bits, but they have significant hardware size and connectivity limitations. We present a novel heterogeneous computing stack that combines QA and classical machine learning and allows the use of QA on problems larger than the quantum hardware could solve in isolation. We begin by analyzing the satellite positioning problem with a heuristic solver, the genetic algorithm. The classical computer's comparatively large available memory can explore the full problem space and converge to a solution relatively close to the true optimum. The QA device can then evolve directly to the optimal solution within this more limited space. Preliminary experiments, using the Quantum Monte Carlo (QMC) algorithm to simulate QA hardware, have produced promising results. Working with problem instances with known global minima, we find a solution within 8% in a matter of seconds, and within 5% in a few minutes. Future studies include replacing QMC with commercially available quantum hardware and exploring more problem sets and model parameters. Our results have important implications for how heterogeneous quantum computing can be used to solve difficult optimization problems in any field.

Formal and heuristic system decomposition methods in multidisciplinary synthesis. Ph.D. Thesis, 1991

NASA Technical Reports Server (NTRS)

Bloebaum, Christina L.

1991-01-01

The multidisciplinary interactions which exist in large scale engineering design problems provide a unique set of difficulties. These difficulties are associated primarily with unwieldy numbers of design variables and constraints, and with the interdependencies of the discipline analysis modules. Such obstacles require design techniques which account for the inherent disciplinary couplings in the analyses and optimizations. The objective of this work was to develop an efficient holistic design synthesis methodology that takes advantage of the synergistic nature of integrated design. A general decomposition approach for optimization of large engineering systems is presented. The method is particularly applicable for multidisciplinary design problems which are characterized by closely coupled interactions among discipline analyses. The advantage of subsystem modularity allows for implementation of specialized methods for analysis and optimization, computational efficiency, and the ability to incorporate human intervention and decision making in the form of an expert systems capability. The resulting approach is not a method applicable to only a specific situation, but rather, a methodology which can be used for a large class of engineering design problems in which the system is non-hierarchic in nature.

Approaches to eliminate waste and reduce cost for recycling glass.

PubMed

Chao, Chien-Wen; Liao, Ching-Jong

2011-12-01

In recent years, the issue of environmental protection has received considerable attention. This paper adds to the literature by investigating a scheduling problem in the manufacturing of a glass recycling factory in Taiwan. The objective is to minimize the sum of the total holding cost and loss cost. We first represent the problem as an integer programming (IP) model, and then develop two heuristics based on the IP model to find near-optimal solutions for the problem. To validate the proposed heuristics, comparisons between optimal solutions from the IP model and solutions from the current method are conducted. The comparisons involve two problem sizes, small and large, where the small problems range from 15 to 45 jobs, and the large problems from 50 to 100 jobs. Finally, a genetic algorithm is applied to evaluate the proposed heuristics. Computational experiments show that the proposed heuristics can find good solutions in a reasonable time for the considered problem. Copyright © 2011 Elsevier Ltd. All rights reserved.

Two-machine flow shop scheduling integrated with preventive maintenance planning

NASA Astrophysics Data System (ADS)

Wang, Shijin; Liu, Ming

2016-02-01

This paper investigates an integrated optimisation problem of production scheduling and preventive maintenance (PM) in a two-machine flow shop with time to failure of each machine subject to a Weibull probability distribution. The objective is to find the optimal job sequence and the optimal PM decisions before each job such that the expected makespan is minimised. To investigate the value of integrated scheduling solution, computational experiments on small-scale problems with different configurations are conducted with total enumeration method, and the results are compared with those of scheduling without maintenance but with machine degradation, and individual job scheduling combined with independent PM planning. Then, for large-scale problems, four genetic algorithm (GA) based heuristics are proposed. The numerical results with several large problem sizes and different configurations indicate the potential benefits of integrated scheduling solution and the results also show that proposed GA-based heuristics are efficient for the integrated problem.

Formulation for Simultaneous Aerodynamic Analysis and Design Optimization

NASA Technical Reports Server (NTRS)

Hou, G. W.; Taylor, A. C., III; Mani, S. V.; Newman, P. A.

1993-01-01

An efficient approach for simultaneous aerodynamic analysis and design optimization is presented. This approach does not require the performance of many flow analyses at each design optimization step, which can be an expensive procedure. Thus, this approach brings us one step closer to meeting the challenge of incorporating computational fluid dynamic codes into gradient-based optimization techniques for aerodynamic design. An adjoint-variable method is introduced to nullify the effect of the increased number of design variables in the problem formulation. The method has been successfully tested on one-dimensional nozzle flow problems, including a sample problem with a normal shock. Implementations of the above algorithm are also presented that incorporate Newton iterations to secure a high-quality flow solution at the end of the design process. Implementations with iterative flow solvers are possible and will be required for large, multidimensional flow problems.

Fast-SNP: a fast matrix pre-processing algorithm for efficient loopless flux optimization of metabolic models

PubMed Central

Saa, Pedro A.; Nielsen, Lars K.

2016-01-01

Motivation: Computation of steady-state flux solutions in large metabolic models is routinely performed using flux balance analysis based on a simple LP (Linear Programming) formulation. A minimal requirement for thermodynamic feasibility of the flux solution is the absence of internal loops, which are enforced using ‘loopless constraints’. The resulting loopless flux problem is a substantially harder MILP (Mixed Integer Linear Programming) problem, which is computationally expensive for large metabolic models. Results: We developed a pre-processing algorithm that significantly reduces the size of the original loopless problem into an easier and equivalent MILP problem. The pre-processing step employs a fast matrix sparsification algorithm—Fast- sparse null-space pursuit (SNP)—inspired by recent results on SNP. By finding a reduced feasible ‘loop-law’ matrix subject to known directionalities, Fast-SNP considerably improves the computational efficiency in several metabolic models running different loopless optimization problems. Furthermore, analysis of the topology encoded in the reduced loop matrix enabled identification of key directional constraints for the potential permanent elimination of infeasible loops in the underlying model. Overall, Fast-SNP is an effective and simple algorithm for efficient formulation of loop-law constraints, making loopless flux optimization feasible and numerically tractable at large scale. Availability and Implementation: Source code for MATLAB including examples is freely available for download at http://www.aibn.uq.edu.au/cssb-resources under Software. Optimization uses Gurobi, CPLEX or GLPK (the latter is included with the algorithm). Contact: lars.nielsen@uq.edu.au Supplementary information: Supplementary data are available at Bioinformatics online. PMID:27559155

Parallel Optimization of Polynomials for Large-scale Problems in Stability and Control

NASA Astrophysics Data System (ADS)

Kamyar, Reza

In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems --- in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) --- whose solutions converge to the exact solution of the NP-hard problem. However, the computational and memory complexity of these LPs and SDPs grow exponentially with the progress of the sequence - meaning that improving the accuracy of the solutions requires solving SDPs with tens of thousands of decision variables and constraints. Setting up and solving such problems is a significant challenge. The existing optimization algorithms and software are only designed to use desktop computers or small cluster computers --- machines which do not have sufficient memory for solving such large SDPs. Moreover, the speed-up of these algorithms does not scale beyond dozens of processors. This in fact is the reason we seek parallel algorithms for setting-up and solving large SDPs on large cluster- and/or super-computers. We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to efficiently utilize hundreds and potentially thousands of processors, and analyze systems with 100+ dimensional state-space. Furthermore, we extend our algorithms to analyze robust stability over more complicated geometries such as hypercubes and arbitrary convex polytopes. Our algorithms can be readily extended to address a wide variety of problems in control such as Hinfinity synthesis for systems with parametric uncertainty and computing control Lyapunov functions.

A parallel metaheuristic for large mixed-integer dynamic optimization problems, with applications in computational biology

PubMed Central

Henriques, David; González, Patricia; Doallo, Ramón; Saez-Rodriguez, Julio; Banga, Julio R.

2017-01-01

Background We consider a general class of global optimization problems dealing with nonlinear dynamic models. Although this class is relevant to many areas of science and engineering, here we are interested in applying this framework to the reverse engineering problem in computational systems biology, which yields very large mixed-integer dynamic optimization (MIDO) problems. In particular, we consider the framework of logic-based ordinary differential equations (ODEs). Methods We present saCeSS2, a parallel method for the solution of this class of problems. This method is based on an parallel cooperative scatter search metaheuristic, with new mechanisms of self-adaptation and specific extensions to handle large mixed-integer problems. We have paid special attention to the avoidance of convergence stagnation using adaptive cooperation strategies tailored to this class of problems. Results We illustrate its performance with a set of three very challenging case studies from the domain of dynamic modelling of cell signaling. The simpler case study considers a synthetic signaling pathway and has 84 continuous and 34 binary decision variables. A second case study considers the dynamic modeling of signaling in liver cancer using high-throughput data, and has 135 continuous and 109 binaries decision variables. The third case study is an extremely difficult problem related with breast cancer, involving 690 continuous and 138 binary decision variables. We report computational results obtained in different infrastructures, including a local cluster, a large supercomputer and a public cloud platform. Interestingly, the results show how the cooperation of individual parallel searches modifies the systemic properties of the sequential algorithm, achieving superlinear speedups compared to an individual search (e.g. speedups of 15 with 10 cores), and significantly improving (above a 60%) the performance with respect to a non-cooperative parallel scheme. The scalability of the method is also good (tests were performed using up to 300 cores). Conclusions These results demonstrate that saCeSS2 can be used to successfully reverse engineer large dynamic models of complex biological pathways. Further, these results open up new possibilities for other MIDO-based large-scale applications in the life sciences such as metabolic engineering, synthetic biology, drug scheduling. PMID:28813442

A parallel metaheuristic for large mixed-integer dynamic optimization problems, with applications in computational biology.

PubMed

Penas, David R; Henriques, David; González, Patricia; Doallo, Ramón; Saez-Rodriguez, Julio; Banga, Julio R

2017-01-01

We consider a general class of global optimization problems dealing with nonlinear dynamic models. Although this class is relevant to many areas of science and engineering, here we are interested in applying this framework to the reverse engineering problem in computational systems biology, which yields very large mixed-integer dynamic optimization (MIDO) problems. In particular, we consider the framework of logic-based ordinary differential equations (ODEs). We present saCeSS2, a parallel method for the solution of this class of problems. This method is based on an parallel cooperative scatter search metaheuristic, with new mechanisms of self-adaptation and specific extensions to handle large mixed-integer problems. We have paid special attention to the avoidance of convergence stagnation using adaptive cooperation strategies tailored to this class of problems. We illustrate its performance with a set of three very challenging case studies from the domain of dynamic modelling of cell signaling. The simpler case study considers a synthetic signaling pathway and has 84 continuous and 34 binary decision variables. A second case study considers the dynamic modeling of signaling in liver cancer using high-throughput data, and has 135 continuous and 109 binaries decision variables. The third case study is an extremely difficult problem related with breast cancer, involving 690 continuous and 138 binary decision variables. We report computational results obtained in different infrastructures, including a local cluster, a large supercomputer and a public cloud platform. Interestingly, the results show how the cooperation of individual parallel searches modifies the systemic properties of the sequential algorithm, achieving superlinear speedups compared to an individual search (e.g. speedups of 15 with 10 cores), and significantly improving (above a 60%) the performance with respect to a non-cooperative parallel scheme. The scalability of the method is also good (tests were performed using up to 300 cores). These results demonstrate that saCeSS2 can be used to successfully reverse engineer large dynamic models of complex biological pathways. Further, these results open up new possibilities for other MIDO-based large-scale applications in the life sciences such as metabolic engineering, synthetic biology, drug scheduling.

Evaluation of Methods for Multidisciplinary Design Optimization (MDO). Part 2

NASA Technical Reports Server (NTRS)

Kodiyalam, Srinivas; Yuan, Charles; Sobieski, Jaroslaw (Technical Monitor)

2000-01-01

A new MDO method, BLISS, and two different variants of the method, BLISS/RS and BLISS/S, have been implemented using iSIGHT's scripting language and evaluated in this report on multidisciplinary problems. All of these methods are based on decomposing a modular system optimization system into several subtasks optimization, that may be executed concurrently, and the system optimization that coordinates the subtasks optimization. The BLISS method and its variants are well suited for exploiting the concurrent processing capabilities in a multiprocessor machine. Several steps, including the local sensitivity analysis, local optimization, response surfaces construction and updates are all ideally suited for concurrent processing. Needless to mention, such algorithms that can effectively exploit the concurrent processing capabilities of the compute servers will be a key requirement for solving large-scale industrial design problems, such as the automotive vehicle problem detailed in Section 3.4.

Design of shared unit-dose drug distribution network using multi-level particle swarm optimization.

PubMed

Chen, Linjie; Monteiro, Thibaud; Wang, Tao; Marcon, Eric

2018-03-01

Unit-dose drug distribution systems provide optimal choices in terms of medication security and efficiency for organizing the drug-use process in large hospitals. As small hospitals have to share such automatic systems for economic reasons, the structure of their logistic organization becomes a very sensitive issue. In the research reported here, we develop a generalized multi-level optimization method - multi-level particle swarm optimization (MLPSO) - to design a shared unit-dose drug distribution network. Structurally, the problem studied can be considered as a type of capacitated location-routing problem (CLRP) with new constraints related to specific production planning. This kind of problem implies that a multi-level optimization should be performed in order to minimize logistic operating costs. Our results show that with the proposed algorithm, a more suitable modeling framework, as well as computational time savings and better optimization performance are obtained than that reported in the literature on this subject.

Optimal Budget Allocation for Sample Average Approximation

DTIC Science & Technology

2011-06-01

an optimization algorithm applied to the sample average problem. We examine the convergence rate of the estimator as the computing budget tends to...regime for the optimization algorithm . 1 Introduction Sample average approximation (SAA) is a frequently used approach to solving stochastic programs...appealing due to its simplicity and the fact that a large number of standard optimization algorithms are often available to optimize the resulting sample

Information Based Numerical Practice.

DTIC Science & Technology

1987-02-01

characterization by comparative computational studies of various benchmark problems. See e.g. [MacNeal, Harder (1985)], [Robinson, Blackham (1981)] any...FOR NONADAPTIVE METHODS 2.1. THE QUADRATURE FORMULA The simplest example studied in detail in the literature is the problem of the optimal quadrature...formulae and the functional analytic prerequisites for the study of optimal formulae, we refer to the large monography (808 p) of [Sobolev (1974)]. Let us

Graph Design via Convex Optimization: Online and Distributed Perspectives

NASA Astrophysics Data System (ADS)

Meng, De

Network and graph have long been natural abstraction of relations in a variety of applications, e.g. transportation, power system, social network, communication, electrical circuit, etc. As a large number of computation and optimization problems are naturally defined on graphs, graph structures not only enable important properties of these problems, but also leads to highly efficient distributed and online algorithms. For example, graph separability enables the parallelism for computation and operation as well as limits the size of local problems. More interestingly, graphs can be defined and constructed in order to take best advantage of those problem properties. This dissertation focuses on graph structure and design in newly proposed optimization problems, which establish a bridge between graph properties and optimization problem properties. We first study a new optimization problem called Geodesic Distance Maximization Problem (GDMP). Given a graph with fixed edge weights, finding the shortest path, also known as the geodesic, between two nodes is a well-studied network flow problem. We introduce the Geodesic Distance Maximization Problem (GDMP): the problem of finding the edge weights that maximize the length of the geodesic subject to convex constraints on the weights. We show that GDMP is a convex optimization problem for a wide class of flow costs, and provide a physical interpretation using the dual. We present applications of the GDMP in various fields, including optical lens design, network interdiction, and resource allocation in the control of forest fires. We develop an Alternating Direction Method of Multipliers (ADMM) by exploiting specific problem structures to solve large-scale GDMP, and demonstrate its effectiveness in numerical examples. We then turn our attention to distributed optimization on graph with only local communication. Distributed optimization arises in a variety of applications, e.g. distributed tracking and localization, estimation problems in sensor networks, multi-agent coordination. Distributed optimization aims to optimize a global objective function formed by summation of coupled local functions over a graph via only local communication and computation. We developed a weighted proximal ADMM for distributed optimization using graph structure. This fully distributed, single-loop algorithm allows simultaneous updates and can be viewed as a generalization of existing algorithms. More importantly, we achieve faster convergence by jointly designing graph weights and algorithm parameters. Finally, we propose a new problem on networks called Online Network Formation Problem: starting with a base graph and a set of candidate edges, at each round of the game, player one first chooses a candidate edge and reveals it to player two, then player two decides whether to accept it; player two can only accept limited number of edges and make online decisions with the goal to achieve the best properties of the synthesized network. The network properties considered include the number of spanning trees, algebraic connectivity and total effective resistance. These network formation games arise in a variety of cooperative multiagent systems. We propose a primal-dual algorithm framework for the general online network formation game, and analyze the algorithm performance by the competitive ratio and regret.

D-Optimal Experimental Design for Contaminant Source Identification

NASA Astrophysics Data System (ADS)

Sai Baba, A. K.; Alexanderian, A.

2016-12-01

Contaminant source identification seeks to estimate the release history of a conservative solute given point concentration measurements at some time after the release. This can be mathematically expressed as an inverse problem, with a linear observation operator or a parameter-to-observation map, which we tackle using a Bayesian approach. Acquisition of experimental data can be laborious and expensive. The goal is to control the experimental parameters - in our case, the sparsity of the sensors, to maximize the information gain subject to some physical or budget constraints. This is known as optimal experimental design (OED). D-optimal experimental design seeks to maximize the expected information gain, and has long been considered the gold standard in the statistics community. Our goal is to develop scalable methods for D-optimal experimental designs involving large-scale PDE constrained problems with high-dimensional parameter fields. A major challenge for the OED, is that a nonlinear optimization algorithm for the D-optimality criterion requires repeated evaluation of objective function and gradient involving the determinant of large and dense matrices - this cost can be prohibitively expensive for applications of interest. We propose novel randomized matrix techniques that bring down the computational costs of the objective function and gradient evaluations by several orders of magnitude compared to the naive approach. The effect of randomized estimators on the accuracy and the convergence of the optimization solver will be discussed. The features and benefits of our new approach will be demonstrated on a challenging model problem from contaminant source identification involving the inference of the initial condition from spatio-temporal observations in a time-dependent advection-diffusion problem.

The Modified HZ Conjugate Gradient Algorithm for Large-Scale Nonsmooth Optimization.

PubMed

Yuan, Gonglin; Sheng, Zhou; Liu, Wenjie

2016-01-01

In this paper, the Hager and Zhang (HZ) conjugate gradient (CG) method and the modified HZ (MHZ) CG method are presented for large-scale nonsmooth convex minimization. Under some mild conditions, convergent results of the proposed methods are established. Numerical results show that the presented methods can be better efficiency for large-scale nonsmooth problems, and several problems are tested (with the maximum dimensions to 100,000 variables).

Maximizing algebraic connectivity in air transportation networks

NASA Astrophysics Data System (ADS)

Wei, Peng

In air transportation networks the robustness of a network regarding node and link failures is a key factor for its design. An experiment based on the real air transportation network is performed to show that the algebraic connectivity is a good measure for network robustness. Three optimization problems of algebraic connectivity maximization are then formulated in order to find the most robust network design under different constraints. The algebraic connectivity maximization problem with flight routes addition or deletion is first formulated. Three methods to optimize and analyze the network algebraic connectivity are proposed. The Modified Greedy Perturbation Algorithm (MGP) provides a sub-optimal solution in a fast iterative manner. The Weighted Tabu Search (WTS) is designed to offer a near optimal solution with longer running time. The relaxed semi-definite programming (SDP) is used to set a performance upper bound and three rounding techniques are discussed to find the feasible solution. The simulation results present the trade-off among the three methods. The case study on two air transportation networks of Virgin America and Southwest Airlines show that the developed methods can be applied in real world large scale networks. The algebraic connectivity maximization problem is extended by adding the leg number constraint, which considers the traveler's tolerance for the total connecting stops. The Binary Semi-Definite Programming (BSDP) with cutting plane method provides the optimal solution. The tabu search and 2-opt search heuristics can find the optimal solution in small scale networks and the near optimal solution in large scale networks. The third algebraic connectivity maximization problem with operating cost constraint is formulated. When the total operating cost budget is given, the number of the edges to be added is not fixed. Each edge weight needs to be calculated instead of being pre-determined. It is illustrated that the edge addition and the weight assignment can not be studied separately for the problem with operating cost constraint. Therefore a relaxed SDP method with golden section search is developed to solve both at the same time. The cluster decomposition is utilized to solve large scale networks.

New bounding and decomposition approaches for MILP investment problems: Multi-area transmission and generation planning under policy constraints

DOE PAGES

Munoz, F. D.; Hobbs, B. F.; Watson, J. -P.

2016-02-01

A novel two-phase bounding and decomposition approach to compute optimal and near-optimal solutions to large-scale mixed-integer investment planning problems is proposed and it considers a large number of operating subproblems, each of which is a convex optimization. Our motivating application is the planning of power transmission and generation in which policy constraints are designed to incentivize high amounts of intermittent generation in electric power systems. The bounding phase exploits Jensen’s inequality to define a lower bound, which we extend to stochastic programs that use expected-value constraints to enforce policy objectives. The decomposition phase, in which the bounds are tightened, improvesmore » upon the standard Benders’ algorithm by accelerating the convergence of the bounds. The lower bound is tightened by using a Jensen’s inequality-based approach to introduce an auxiliary lower bound into the Benders master problem. Upper bounds for both phases are computed using a sub-sampling approach executed on a parallel computer system. Numerical results show that only the bounding phase is necessary if loose optimality gaps are acceptable. But, the decomposition phase is required to attain optimality gaps. Moreover, use of both phases performs better, in terms of convergence speed, than attempting to solve the problem using just the bounding phase or regular Benders decomposition separately.« less

New bounding and decomposition approaches for MILP investment problems: Multi-area transmission and generation planning under policy constraints

DOE Office of Scientific and Technical Information (OSTI.GOV)

Munoz, F. D.; Hobbs, B. F.; Watson, J. -P.

A novel two-phase bounding and decomposition approach to compute optimal and near-optimal solutions to large-scale mixed-integer investment planning problems is proposed and it considers a large number of operating subproblems, each of which is a convex optimization. Our motivating application is the planning of power transmission and generation in which policy constraints are designed to incentivize high amounts of intermittent generation in electric power systems. The bounding phase exploits Jensen’s inequality to define a lower bound, which we extend to stochastic programs that use expected-value constraints to enforce policy objectives. The decomposition phase, in which the bounds are tightened, improvesmore » upon the standard Benders’ algorithm by accelerating the convergence of the bounds. The lower bound is tightened by using a Jensen’s inequality-based approach to introduce an auxiliary lower bound into the Benders master problem. Upper bounds for both phases are computed using a sub-sampling approach executed on a parallel computer system. Numerical results show that only the bounding phase is necessary if loose optimality gaps are acceptable. But, the decomposition phase is required to attain optimality gaps. Moreover, use of both phases performs better, in terms of convergence speed, than attempting to solve the problem using just the bounding phase or regular Benders decomposition separately.« less

Influence maximization in complex networks through optimal percolation

NASA Astrophysics Data System (ADS)

Morone, Flaviano; Makse, Hernan; CUNY Collaboration; CUNY Collaboration

The whole frame of interconnections in complex networks hinges on a specific set of structural nodes, much smaller than the total size, which, if activated, would cause the spread of information to the whole network, or, if immunized, would prevent the diffusion of a large scale epidemic. Localizing this optimal, that is, minimal, set of structural nodes, called influencers, is one of the most important problems in network science. Here we map the problem onto optimal percolation in random networks to identify the minimal set of influencers, which arises by minimizing the energy of a many-body system, where the form of the interactions is fixed by the non-backtracking matrix of the network. Big data analyses reveal that the set of optimal influencers is much smaller than the one predicted by previous heuristic centralities. Remarkably, a large number of previously neglected weakly connected nodes emerges among the optimal influencers. Reference: F. Morone, H. A. Makse, Nature 524,65-68 (2015)

Optimizing a realistic large-scale frequency assignment problem using a new parallel evolutionary approach

NASA Astrophysics Data System (ADS)

Chaves-González, José M.; Vega-Rodríguez, Miguel A.; Gómez-Pulido, Juan A.; Sánchez-Pérez, Juan M.

2011-08-01

This article analyses the use of a novel parallel evolutionary strategy to solve complex optimization problems. The work developed here has been focused on a relevant real-world problem from the telecommunication domain to verify the effectiveness of the approach. The problem, known as frequency assignment problem (FAP), basically consists of assigning a very small number of frequencies to a very large set of transceivers used in a cellular phone network. Real data FAP instances are very difficult to solve due to the NP-hard nature of the problem, therefore using an efficient parallel approach which makes the most of different evolutionary strategies can be considered as a good way to obtain high-quality solutions in short periods of time. Specifically, a parallel hyper-heuristic based on several meta-heuristics has been developed. After a complete experimental evaluation, results prove that the proposed approach obtains very high-quality solutions for the FAP and beats any other result published.

A Numerical Comparison of Barrier and Modified Barrier Methods for Large-Scale Bound-Constrained Optimization

NASA Technical Reports Server (NTRS)

Nash, Stephen G.; Polyak, R.; Sofer, Ariela

1994-01-01

When a classical barrier method is applied to the solution of a nonlinear programming problem with inequality constraints, the Hessian matrix of the barrier function becomes increasingly ill-conditioned as the solution is approached. As a result, it may be desirable to consider alternative numerical algorithms. We compare the performance of two methods motivated by barrier functions. The first is a stabilized form of the classical barrier method, where a numerically stable approximation to the Newton direction is used when the barrier parameter is small. The second is a modified barrier method where a barrier function is applied to a shifted form of the problem, and the resulting barrier terms are scaled by estimates of the optimal Lagrange multipliers. The condition number of the Hessian matrix of the resulting modified barrier function remains bounded as the solution to the constrained optimization problem is approached. Both of these techniques can be used in the context of a truncated-Newton method, and hence can be applied to large problems, as well as on parallel computers. In this paper, both techniques are applied to problems with bound constraints and we compare their practical behavior.

Large-Scale Optimization for Bayesian Inference in Complex Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Willcox, Karen; Marzouk, Youssef

2013-11-12

The SAGUARO (Scalable Algorithms for Groundwater Uncertainty Analysis and Robust Optimization) Project focused on the development of scalable numerical algorithms for large-scale Bayesian inversion in complex systems that capitalize on advances in large-scale simulation-based optimization and inversion methods. The project was a collaborative effort among MIT, the University of Texas at Austin, Georgia Institute of Technology, and Sandia National Laboratories. The research was directed in three complementary areas: efficient approximations of the Hessian operator, reductions in complexity of forward simulations via stochastic spectral approximations and model reduction, and employing large-scale optimization concepts to accelerate sampling. The MIT--Sandia component of themore » SAGUARO Project addressed the intractability of conventional sampling methods for large-scale statistical inverse problems by devising reduced-order models that are faithful to the full-order model over a wide range of parameter values; sampling then employs the reduced model rather than the full model, resulting in very large computational savings. Results indicate little effect on the computed posterior distribution. On the other hand, in the Texas--Georgia Tech component of the project, we retain the full-order model, but exploit inverse problem structure (adjoint-based gradients and partial Hessian information of the parameter-to-observation map) to implicitly extract lower dimensional information on the posterior distribution; this greatly speeds up sampling methods, so that fewer sampling points are needed. We can think of these two approaches as ``reduce then sample'' and ``sample then reduce.'' In fact, these two approaches are complementary, and can be used in conjunction with each other. Moreover, they both exploit deterministic inverse problem structure, in the form of adjoint-based gradient and Hessian information of the underlying parameter-to-observation map, to achieve their speedups.« less

Advanced design for orbital debris removal in support of solar system exploration

NASA Technical Reports Server (NTRS)

1991-01-01

The development of an Autonomous Space Processor for Orbital Debris (ASPOD) is the ultimate goal. The craft will process, in situ, orbital debris using resources available in low Earth orbit (LEO). The serious problem of orbital debris is briefly described and the nature of the large debris population is outlined. This year, focus was on development of a versatile robotic manipulator to augment an existing robotic arm; incorporation of remote operation of robotic arms; and formulation of optimal (time and energy) trajectory planning algorithms for coordinating robotic arms. The mechanical design of the new arm is described in detail. The versatile work envelope is explained showing the flexibility of the new design. Several telemetry communication systems are described which will enable the remote operation of the robotic arms. The trajectory planning algorithms are fully developed for both the time-optimal and energy-optimal problem. The optimal problem is solved using phase plane techniques while the energy optimal problem is solved using dynamics programming.

Autonomous space processor for orbital debris

NASA Technical Reports Server (NTRS)

Ramohalli, Kumar; Marine, Micky; Colvin, James; Crockett, Richard; Sword, Lee; Putz, Jennifer; Woelfle, Sheri

1991-01-01

The development of an Autonomous Space Processor for Orbital Debris (ASPOD) was the goal. The nature of this craft, which will process, in situ, orbital debris using resources available in low Earth orbit (LEO) is explained. The serious problem of orbital debris is briefly described and the nature of the large debris population is outlined. The focus was on the development of a versatile robotic manipulator to augment an existing robotic arm, the incorporation of remote operation of the robotic arms, and the formulation of optimal (time and energy) trajectory planning algorithms for coordinated robotic arms. The mechanical design of the new arm is described in detail. The work envelope is explained showing the flexibility of the new design. Several telemetry communication systems are described which will enable the remote operation of the robotic arms. The trajectory planning algorithms are fully developed for both the time optimal and energy optimal problems. The time optimal problem is solved using phase plane techniques while the energy optimal problem is solved using dynamic programming.

Cloud-based large-scale air traffic flow optimization

NASA Astrophysics Data System (ADS)

Cao, Yi

The ever-increasing traffic demand makes the efficient use of airspace an imperative mission, and this paper presents an effort in response to this call. Firstly, a new aggregate model, called Link Transmission Model (LTM), is proposed, which models the nationwide traffic as a network of flight routes identified by origin-destination pairs. The traversal time of a flight route is assumed to be the mode of distribution of historical flight records, and the mode is estimated by using Kernel Density Estimation. As this simplification abstracts away physical trajectory details, the complexity of modeling is drastically decreased, resulting in efficient traffic forecasting. The predicative capability of LTM is validated against recorded traffic data. Secondly, a nationwide traffic flow optimization problem with airport and en route capacity constraints is formulated based on LTM. The optimization problem aims at alleviating traffic congestions with minimal global delays. This problem is intractable due to millions of variables. A dual decomposition method is applied to decompose the large-scale problem such that the subproblems are solvable. However, the whole problem is still computational expensive to solve since each subproblem is an smaller integer programming problem that pursues integer solutions. Solving an integer programing problem is known to be far more time-consuming than solving its linear relaxation. In addition, sequential execution on a standalone computer leads to linear runtime increase when the problem size increases. To address the computational efficiency problem, a parallel computing framework is designed which accommodates concurrent executions via multithreading programming. The multithreaded version is compared with its monolithic version to show decreased runtime. Finally, an open-source cloud computing framework, Hadoop MapReduce, is employed for better scalability and reliability. This framework is an "off-the-shelf" parallel computing model that can be used for both offline historical traffic data analysis and online traffic flow optimization. It provides an efficient and robust platform for easy deployment and implementation. A small cloud consisting of five workstations was configured and used to demonstrate the advantages of cloud computing in dealing with large-scale parallelizable traffic problems.

Thermal energy storage to minimize cost and improve efficiency of a polygeneration district energy system in a real-time electricity market

DOE Office of Scientific and Technical Information (OSTI.GOV)

Powell, Kody M.; Kim, Jong Suk; Cole, Wesley J.

2016-10-01

District energy systems can produce low-cost utilities for large energy networks, but can also be a resource for the electric grid by their ability to ramp production or to store thermal energy by responding to real-time market signals. In this work, dynamic optimization exploits the flexibility of thermal energy storage by determining optimal times to store and extract excess energy. This concept is applied to a polygeneration distributed energy system with combined heat and power, district heating, district cooling, and chilled water thermal energy storage. The system is a university campus responsible for meeting the energy needs of tens ofmore » thousands of people. The objective for the dynamic optimization problem is to minimize cost over a 24-h period while meeting multiple loads in real time. The paper presents a novel algorithm to solve this dynamic optimization problem with energy storage by decomposing the problem into multiple static mixed-integer nonlinear programming (MINLP) problems. Another innovative feature of this work is the study of a large, complex energy network which includes the interrelations of a wide variety of energy technologies. Results indicate that a cost savings of 16.5% is realized when the system can participate in the wholesale electricity market.« less

Bicriteria Network Optimization Problem using Priority-based Genetic Algorithm

NASA Astrophysics Data System (ADS)

Gen, Mitsuo; Lin, Lin; Cheng, Runwei

Network optimization is being an increasingly important and fundamental issue in the fields such as engineering, computer science, operations research, transportation, telecommunication, decision support systems, manufacturing, and airline scheduling. In many applications, however, there are several criteria associated with traversing each edge of a network. For example, cost and flow measures are both important in the networks. As a result, there has been recent interest in solving Bicriteria Network Optimization Problem. The Bicriteria Network Optimization Problem is known a NP-hard. The efficient set of paths may be very large, possibly exponential in size. Thus the computational effort required to solve it can increase exponentially with the problem size in the worst case. In this paper, we propose a genetic algorithm (GA) approach used a priority-based chromosome for solving the bicriteria network optimization problem including maximum flow (MXF) model and minimum cost flow (MCF) model. The objective is to find the set of Pareto optimal solutions that give possible maximum flow with minimum cost. This paper also combines Adaptive Weight Approach (AWA) that utilizes some useful information from the current population to readjust weights for obtaining a search pressure toward a positive ideal point. Computer simulations show the several numerical experiments by using some difficult-to-solve network design problems, and show the effectiveness of the proposed method.

Large-angle slewing maneuvers for flexible spacecraft

NASA Technical Reports Server (NTRS)

Chun, Hon M.; Turner, James D.

1988-01-01

A new class of closed-form solutions for finite-time linear-quadratic optimal control problems is presented. The solutions involve Potter's solution for the differential matrix Riccati equation, which assumes the form of a steady-state plus transient term. Illustrative examples are presented which show that the new solutions are more computationally efficient than alternative solutions based on the state transition matrix. As an application of the closed-form solutions, the neighboring extremal path problem is presented for a spacecraft retargeting maneuver where a perturbed plant with off-nominal boundary conditions now follows a neighboring optimal trajectory. The perturbation feedback approach is further applied to three-dimensional slewing maneuvers of large flexible spacecraft. For this problem, the nominal solution is the optimal three-dimensional rigid body slew. The perturbation feedback then limits the deviations from this nominal solution due to the flexible body effects. The use of frequency shaping in both the nominal and perturbation feedback formulations reduces the excitation of high-frequency unmodeled modes. A modified Kalman filter is presented for estimating the plant states.

A Scalable, Parallel Approach for Multi-Point, High-Fidelity Aerostructural Optimization of Aircraft Configurations

NASA Astrophysics Data System (ADS)

Kenway, Gaetan K. W.

This thesis presents new tools and techniques developed to address the challenging problem of high-fidelity aerostructural optimization with respect to large numbers of design variables. A new mesh-movement scheme is developed that is both computationally efficient and sufficiently robust to accommodate large geometric design changes and aerostructural deformations. A fully coupled Newton-Krylov method is presented that accelerates the convergence of aerostructural systems and provides a 20% performance improvement over the traditional nonlinear block Gauss-Seidel approach and can handle more exible structures. A coupled adjoint method is used that efficiently computes derivatives for a gradient-based optimization algorithm. The implementation uses only machine accurate derivative techniques and is verified to yield fully consistent derivatives by comparing against the complex step method. The fully-coupled large-scale coupled adjoint solution method is shown to have 30% better performance than the segregated approach. The parallel scalability of the coupled adjoint technique is demonstrated on an Euler Computational Fluid Dynamics (CFD) model with more than 80 million state variables coupled to a detailed structural finite-element model of the wing with more than 1 million degrees of freedom. Multi-point high-fidelity aerostructural optimizations of a long-range wide-body, transonic transport aircraft configuration are performed using the developed techniques. The aerostructural analysis employs Euler CFD with a 2 million cell mesh and a structural finite element model with 300 000 DOF. Two design optimization problems are solved: one where takeoff gross weight is minimized, and another where fuel burn is minimized. Each optimization uses a multi-point formulation with 5 cruise conditions and 2 maneuver conditions. The optimization problems have 476 design variables are optimal results are obtained within 36 hours of wall time using 435 processors. The TOGW minimization results in a 4.2% reduction in TOGW with a 6.6% fuel burn reduction, while the fuel burn optimization resulted in a 11.2% fuel burn reduction with no change to the takeoff gross weight.

Fuel management optimization using genetic algorithms and code independence

DOE Office of Scientific and Technical Information (OSTI.GOV)

DeChaine, M.D.; Feltus, M.A.

1994-12-31

Fuel management optimization is a hard problem for traditional optimization techniques. Loading pattern optimization is a large combinatorial problem without analytical derivative information. Therefore, methods designed for continuous functions, such as linear programming, do not always work well. Genetic algorithms (GAs) address these problems and, therefore, appear ideal for fuel management optimization. They do not require derivative information and work well with combinatorial. functions. The GAs are a stochastic method based on concepts from biological genetics. They take a group of candidate solutions, called the population, and use selection, crossover, and mutation operators to create the next generation of bettermore » solutions. The selection operator is a {open_quotes}survival-of-the-fittest{close_quotes} operation and chooses the solutions for the next generation. The crossover operator is analogous to biological mating, where children inherit a mixture of traits from their parents, and the mutation operator makes small random changes to the solutions.« less

Finite element analysis and genetic algorithm optimization design for the actuator placement on a large adaptive structure

NASA Astrophysics Data System (ADS)

Sheng, Lizeng

The dissertation focuses on one of the major research needs in the area of adaptive/intelligent/smart structures, the development and application of finite element analysis and genetic algorithms for optimal design of large-scale adaptive structures. We first review some basic concepts in finite element method and genetic algorithms, along with the research on smart structures. Then we propose a solution methodology for solving a critical problem in the design of a next generation of large-scale adaptive structures---optimal placements of a large number of actuators to control thermal deformations. After briefly reviewing the three most frequently used general approaches to derive a finite element formulation, the dissertation presents techniques associated with general shell finite element analysis using flat triangular laminated composite elements. The element used here has three nodes and eighteen degrees of freedom and is obtained by combining a triangular membrane element and a triangular plate bending element. The element includes the coupling effect between membrane deformation and bending deformation. The membrane element is derived from the linear strain triangular element using Cook's transformation. The discrete Kirchhoff triangular (DKT) element is used as the plate bending element. For completeness, a complete derivation of the DKT is presented. Geometrically nonlinear finite element formulation is derived for the analysis of adaptive structures under the combined thermal and electrical loads. Next, we solve the optimization problems of placing a large number of piezoelectric actuators to control thermal distortions in a large mirror in the presence of four different thermal loads. We then extend this to a multi-objective optimization problem of determining only one set of piezoelectric actuator locations that can be used to control the deformation in the same mirror under the action of any one of the four thermal loads. A series of genetic algorithms, GA Version 1, 2 and 3, were developed to find the optimal locations of piezoelectric actuators from the order of 1021 ˜ 1056 candidate placements. Introducing a variable population approach, we improve the flexibility of selection operation in genetic algorithms. Incorporating mutation and hill climbing into micro-genetic algorithms, we are able to develop a more efficient genetic algorithm. Through extensive numerical experiments, we find that the design search space for the optimal placements of a large number of actuators is highly multi-modal and that the most distinct nature of genetic algorithms is their robustness. They give results that are random but with only a slight variability. The genetic algorithms can be used to get adequate solution using a limited number of evaluations. To get the highest quality solution, multiple runs including different random seed generators are necessary. The investigation time can be significantly reduced using a very coarse grain parallel computing. Overall, the methodology of using finite element analysis and genetic algorithm optimization provides a robust solution approach for the challenging problem of optimal placements of a large number of actuators in the design of next generation of adaptive structures.

On Reverse Stackelberg Game and Optimal Mean Field Control for a Large Population of Thermostatically Controlled Loads

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Sen; Zhang, Wei; Lian, Jianming

This paper studies a multi-stage pricing problem for a large population of thermostatically controlled loads. The problem is formulated as a reverse Stackelberg game that involves a mean field game in the hierarchy of decision making. In particular, in the higher level, a coordinator needs to design a pricing function to motivate individual agents to maximize the social welfare. In the lower level, the individual utility maximization problem of each agent forms a mean field game coupled through the pricing function that depends on the average of the population control/state. We derive the solution to the reverse Stackelberg game bymore » connecting it to a team problem and the competitive equilibrium, and we show that this solution corresponds to the optimal mean field control that maximizes the social welfare. Realistic simulations are presented to validate the proposed methods.« less

Ant colony optimization for solving university facility layout problem

NASA Astrophysics Data System (ADS)

Mohd Jani, Nurul Hafiza; Mohd Radzi, Nor Haizan; Ngadiman, Mohd Salihin

2013-04-01

Quadratic Assignment Problems (QAP) is classified as the NP hard problem. It has been used to model a lot of problem in several areas such as operational research, combinatorial data analysis and also parallel and distributed computing, optimization problem such as graph portioning and Travel Salesman Problem (TSP). In the literature, researcher use exact algorithm, heuristics algorithm and metaheuristic approaches to solve QAP problem. QAP is largely applied in facility layout problem (FLP). In this paper we used QAP to model university facility layout problem. There are 8 facilities that need to be assigned to 8 locations. Hence we have modeled a QAP problem with n ≤ 10 and developed an Ant Colony Optimization (ACO) algorithm to solve the university facility layout problem. The objective is to assign n facilities to n locations such that the minimum product of flows and distances is obtained. Flow is the movement from one to another facility, whereas distance is the distance between one locations of a facility to other facilities locations. The objective of the QAP is to obtain minimum total walking (flow) of lecturers from one destination to another (distance).

Modal Test/Analysis Correlation of Space Station Structures Using Nonlinear Sensitivity

NASA Technical Reports Server (NTRS)

Gupta, Viney K.; Newell, James F.; Berke, Laszlo; Armand, Sasan

1992-01-01

The modal correlation problem is formulated as a constrained optimization problem for validation of finite element models (FEM's). For large-scale structural applications, a pragmatic procedure for substructuring, model verification, and system integration is described to achieve effective modal correlation. The space station substructure FEM's are reduced using Lanczos vectors and integrated into a system FEM using Craig-Bampton component modal synthesis. The optimization code is interfaced with MSC/NASTRAN to solve the problem of modal test/analysis correlation; that is, the problem of validating FEM's for launch and on-orbit coupled loads analysis against experimentally observed frequencies and mode shapes. An iterative perturbation algorithm is derived and implemented to update nonlinear sensitivity (derivatives of eigenvalues and eigenvectors) during optimizer iterations, which reduced the number of finite element analyses.

Modal test/analysis correlation of Space Station structures using nonlinear sensitivity

NASA Technical Reports Server (NTRS)

Gupta, Viney K.; Newell, James F.; Berke, Laszlo; Armand, Sasan

1992-01-01

The modal correlation problem is formulated as a constrained optimization problem for validation of finite element models (FEM's). For large-scale structural applications, a pragmatic procedure for substructuring, model verification, and system integration is described to achieve effective modal correlations. The space station substructure FEM's are reduced using Lanczos vectors and integrated into a system FEM using Craig-Bampton component modal synthesis. The optimization code is interfaced with MSC/NASTRAN to solve the problem of modal test/analysis correlation; that is, the problem of validating FEM's for launch and on-orbit coupled loads analysis against experimentally observed frequencies and mode shapes. An iterative perturbation algorithm is derived and implemented to update nonlinear sensitivity (derivatives of eigenvalues and eigenvectors) during optimizer iterations, which reduced the number of finite element analyses.

Statistical physics of hard combinatorial optimization: Vertex cover problem

NASA Astrophysics Data System (ADS)

Zhao, Jin-Hua; Zhou, Hai-Jun

2014-07-01

Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years, the replica-symmetry-breaking mean field theory of spin glasses and the associated message-passing algorithms have greatly deepened our understanding of typical-case computation complexity. In this paper, we use the vertex cover problem, a basic nondeterministic-polynomial (NP)-complete combinatorial optimization problem of wide application, as an example to introduce the statistical physical methods and algorithms. We do not go into the technical details but emphasize mainly the intuitive physical meanings of the message-passing equations. A nonfamiliar reader shall be able to understand to a large extent the physics behind the mean field approaches and to adjust the mean field methods in solving other optimization problems.

Numerical Optimization Algorithms and Software for Systems Biology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saunders, Michael

2013-02-02

The basic aims of this work are: to develop reliable algorithms for solving optimization problems involving large stoi- chiometric matrices; to investigate cyclic dependency between metabolic and macromolecular biosynthetic networks; and to quantify the significance of thermodynamic constraints on prokaryotic metabolism.

Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chang, Justin; Karra, Satish; Nakshatrala, Kalyana B.

It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. Recently, optimization-based methodologies that satisfy maximum principles and the non-negative constraint for steady-state and transient diffusion-type equations have been proposed. To date, these methodologies have been tested only on small-scale academic problems. The purpose of this paper is to systematically study the performance of the non-negative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, usedmore » for the parallel environment and optimization solvers. For large-scale problems, it is important for computational scientists to understand the computational performance of current algorithms available in these scientific libraries. The numerical experiments are conducted on the state-of-the-art HPC systems, and a single-core performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems.« less

Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies

DOE PAGES

Chang, Justin; Karra, Satish; Nakshatrala, Kalyana B.

2016-07-26

It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. Recently, optimization-based methodologies that satisfy maximum principles and the non-negative constraint for steady-state and transient diffusion-type equations have been proposed. To date, these methodologies have been tested only on small-scale academic problems. The purpose of this paper is to systematically study the performance of the non-negative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, usedmore » for the parallel environment and optimization solvers. For large-scale problems, it is important for computational scientists to understand the computational performance of current algorithms available in these scientific libraries. The numerical experiments are conducted on the state-of-the-art HPC systems, and a single-core performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems.« less

Optimized method for manufacturing large aspheric surfaces

NASA Astrophysics Data System (ADS)

Zhou, Xusheng; Li, Shengyi; Dai, Yifan; Xie, Xuhui

2007-12-01

Aspheric optics are being used more and more widely in modern optical systems, due to their ability of correcting aberrations, enhancing image quality, enlarging the field of view and extending the range of effect, while reducing the weight and volume of the system. With optical technology development, we have more pressing requirement to large-aperture and high-precision aspheric surfaces. The original computer controlled optical surfacing (CCOS) technique cannot meet the challenge of precision and machining efficiency. This problem has been thought highly of by researchers. Aiming at the problem of original polishing process, an optimized method for manufacturing large aspheric surfaces is put forward. Subsurface damage (SSD), full aperture errors and full band of frequency errors are all in control of this method. Lesser SSD depth can be gained by using little hardness tool and small abrasive grains in grinding process. For full aperture errors control, edge effects can be controlled by using smaller tools and amendment model with material removal function. For full band of frequency errors control, low frequency errors can be corrected with the optimized material removal function, while medium-high frequency errors by using uniform removing principle. With this optimized method, the accuracy of a K9 glass paraboloid mirror can reach rms 0.055 waves (where a wave is 0.6328μm) in a short time. The results show that the optimized method can guide large aspheric surface manufacturing effectively.

Effect of local minima on adiabatic quantum optimization.

PubMed

Amin, M H S

2008-04-04

We present a perturbative method to estimate the spectral gap for adiabatic quantum optimization, based on the structure of the energy levels in the problem Hamiltonian. We show that, for problems that have an exponentially large number of local minima close to the global minimum, the gap becomes exponentially small making the computation time exponentially long. The quantum advantage of adiabatic quantum computation may then be accessed only via the local adiabatic evolution, which requires phase coherence throughout the evolution and knowledge of the spectrum. Such problems, therefore, are not suitable for adiabatic quantum computation.

A New Coarsening Operator for the Optimal Preconditioning of the Dual and Primal Domain Decomposition Methods: Application to Problems with Severe Coefficient Jumps

NASA Technical Reports Server (NTRS)

Farhat, Charbel; Rixen, Daniel

1996-01-01

We present an optimal preconditioning algorithm that is equally applicable to the dual (FETI) and primal (Balancing) Schur complement domain decomposition methods, and which successfully addresses the problems of subdomain heterogeneities including the effects of large jumps of coefficients. The proposed preconditioner is derived from energy principles and embeds a new coarsening operator that propagates the error globally and accelerates convergence. The resulting iterative solver is illustrated with the solution of highly heterogeneous elasticity problems.

Heuristics for Multiobjective Optimization of Two-Sided Assembly Line Systems

PubMed Central

Jawahar, N.; Ponnambalam, S. G.; Sivakumar, K.; Thangadurai, V.

2014-01-01

Products such as cars, trucks, and heavy machinery are assembled by two-sided assembly line. Assembly line balancing has significant impacts on the performance and productivity of flow line manufacturing systems and is an active research area for several decades. This paper addresses the line balancing problem of a two-sided assembly line in which the tasks are to be assigned at L side or R side or any one side (addressed as E). Two objectives, minimum number of workstations and minimum unbalance time among workstations, have been considered for balancing the assembly line. There are two approaches to solve multiobjective optimization problem: first approach combines all the objectives into a single composite function or moves all but one objective to the constraint set; second approach determines the Pareto optimal solution set. This paper proposes two heuristics to evolve optimal Pareto front for the TALBP under consideration: Enumerative Heuristic Algorithm (EHA) to handle problems of small and medium size and Simulated Annealing Algorithm (SAA) for large-sized problems. The proposed approaches are illustrated with example problems and their performances are compared with a set of test problems. PMID:24790568

The Role of the Goal in Solving Hard Computational Problems: Do People Really Optimize?

ERIC Educational Resources Information Center

Carruthers, Sarah; Stege, Ulrike; Masson, Michael E. J.

2018-01-01

The role that the mental, or internal, representation plays when people are solving hard computational problems has largely been overlooked to date, despite the reality that this internal representation drives problem solving. In this work we investigate how performance on versions of two hard computational problems differs based on what internal…

Solving Large-Scale Inverse Magnetostatic Problems using the Adjoint Method

PubMed Central

Bruckner, Florian; Abert, Claas; Wautischer, Gregor; Huber, Christian; Vogler, Christoph; Hinze, Michael; Suess, Dieter

2017-01-01

An efficient algorithm for the reconstruction of the magnetization state within magnetic components is presented. The occurring inverse magnetostatic problem is solved by means of an adjoint approach, based on the Fredkin-Koehler method for the solution of the forward problem. Due to the use of hybrid FEM-BEM coupling combined with matrix compression techniques the resulting algorithm is well suited for large-scale problems. Furthermore the reconstruction of the magnetization state within a permanent magnet as well as an optimal design application are demonstrated. PMID:28098851

Six-Degree-of-Freedom Trajectory Optimization Utilizing a Two-Timescale Collocation Architecture

NASA Technical Reports Server (NTRS)

Desai, Prasun N.; Conway, Bruce A.

2005-01-01

Six-degree-of-freedom (6DOF) trajectory optimization of a reentry vehicle is solved using a two-timescale collocation methodology. This class of 6DOF trajectory problems are characterized by two distinct timescales in their governing equations, where a subset of the states have high-frequency dynamics (the rotational equations of motion) while the remaining states (the translational equations of motion) vary comparatively slowly. With conventional collocation methods, the 6DOF problem size becomes extraordinarily large and difficult to solve. Utilizing the two-timescale collocation architecture, the problem size is reduced significantly. The converged solution shows a realistic landing profile and captures the appropriate high-frequency rotational dynamics. A large reduction in the overall problem size (by 55%) is attained with the two-timescale architecture as compared to the conventional single-timescale collocation method. Consequently, optimum 6DOF trajectory problems can now be solved efficiently using collocation, which was not previously possible for a system with two distinct timescales in the governing states.

SfM with MRFs: discrete-continuous optimization for large-scale structure from motion.

PubMed

Crandall, David J; Owens, Andrew; Snavely, Noah; Huttenlocher, Daniel P

2013-12-01

Recent work in structure from motion (SfM) has built 3D models from large collections of images downloaded from the Internet. Many approaches to this problem use incremental algorithms that solve progressively larger bundle adjustment problems. These incremental techniques scale poorly as the image collection grows, and can suffer from drift or local minima. We present an alternative framework for SfM based on finding a coarse initial solution using hybrid discrete-continuous optimization and then improving that solution using bundle adjustment. The initial optimization step uses a discrete Markov random field (MRF) formulation, coupled with a continuous Levenberg-Marquardt refinement. The formulation naturally incorporates various sources of information about both the cameras and points, including noisy geotags and vanishing point (VP) estimates. We test our method on several large-scale photo collections, including one with measured camera positions, and show that it produces models that are similar to or better than those produced by incremental bundle adjustment, but more robustly and in a fraction of the time.

Development and Application of the Collaborative Optimization Architecture in a Multidisciplinary Design Environment

NASA Technical Reports Server (NTRS)

Braun, R. D.; Kroo, I. M.

1995-01-01

Collaborative optimization is a design architecture applicable in any multidisciplinary analysis environment but specifically intended for large-scale distributed analysis applications. In this approach, a complex problem is hierarchically de- composed along disciplinary boundaries into a number of subproblems which are brought into multidisciplinary agreement by a system-level coordination process. When applied to problems in a multidisciplinary design environment, this scheme has several advantages over traditional solution strategies. These advantageous features include reducing the amount of information transferred between disciplines, the removal of large iteration-loops, allowing the use of different subspace optimizers among the various analysis groups, an analysis framework which is easily parallelized and can operate on heterogenous equipment, and a structural framework that is well-suited for conventional disciplinary organizations. In this article, the collaborative architecture is developed and its mathematical foundation is presented. An example application is also presented which highlights the potential of this method for use in large-scale design applications.

Optimal Limited Contingency Planning

NASA Technical Reports Server (NTRS)

Meuleau, Nicolas; Smith, David E.

2003-01-01

For a given problem, the optimal Markov policy over a finite horizon is a conditional plan containing a potentially large number of branches. However, there are applications where it is desirable to strictly limit the number of decision points and branches in a plan. This raises the question of how one goes about finding optimal plans containing only a limited number of branches. In this paper, we present an any-time algorithm for optimal k-contingency planning. It is the first optimal algorithm for limited contingency planning that is not an explicit enumeration of possible contingent plans. By modelling the problem as a partially observable Markov decision process, it implements the Bellman optimality principle and prunes the solution space. We present experimental results of applying this algorithm to some simple test cases.

Energy-modeled flight in a wind field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Feldman, M.A.; Cliff, E.M.

Optimal shaping of aerospace trajectories has provided the motivation for much modern study of optimization theory and algorithms. Current industrial practice favors approaches where the continuous-time optimal control problem is transcribed to a finite-dimensional nonlinear programming problem (NLP) by a discretization process. Two such formulations are implemented in the POST and the OTIS codes. In the present paper we use a discretization that is specially adapted to the flight problem of interest. Among the unique aspects of the present discretization are: a least-squares formulation for certain kinematic constraints; the use of an energy ideas to enforce Newton`s Laws; and, themore » inclusion of large magnitude horizontal winds. In the next section we shall provide a description of the flight problem and its NLP representation. Following this we provide some details of the constraint formulation. Finally, we present an overview of the NLP problem.« less

Control and structural optimization for maneuvering large spacecraft

NASA Technical Reports Server (NTRS)

Chun, H. M.; Turner, J. D.; Yu, C. C.

1990-01-01

Presented here are the results of an advanced control design as well as a discussion of the requirements for automating both the structures and control design efforts for maneuvering a large spacecraft. The advanced control application addresses a general three dimensional slewing problem, and is applied to a large geostationary platform. The platform consists of two flexible antennas attached to the ends of a flexible truss. The control strategy involves an open-loop rigid body control profile which is derived from a nonlinear optimal control problem and provides the main control effort. A perturbation feedback control reduces the response due to the flexibility of the structure. Results are shown which demonstrate the usefulness of the approach. Software issues are considered for developing an integrated structures and control design environment.

Large Scale Multi-area Static/Dynamic Economic Dispatch using Nature Inspired Optimization

NASA Astrophysics Data System (ADS)

Pandit, Manjaree; Jain, Kalpana; Dubey, Hari Mohan; Singh, Rameshwar

2017-04-01

Economic dispatch (ED) ensures that the generation allocation to the power units is carried out such that the total fuel cost is minimized and all the operating equality/inequality constraints are satisfied. Classical ED does not take transmission constraints into consideration, but in the present restructured power systems the tie-line limits play a very important role in deciding operational policies. ED is a dynamic problem which is performed on-line in the central load dispatch centre with changing load scenarios. The dynamic multi-area ED (MAED) problem is more complex due to the additional tie-line, ramp-rate and area-wise power balance constraints. Nature inspired (NI) heuristic optimization methods are gaining popularity over the traditional methods for complex problems. This work presents the modified particle swarm optimization (PSO) based techniques where parameter automation is effectively used for improving the search efficiency by avoiding stagnation to a sub-optimal result. This work validates the performance of the PSO variants with traditional solver GAMS for single as well as multi-area economic dispatch (MAED) on three test cases of a large 140-unit standard test system having complex constraints.

Multi-GPU implementation of a VMAT treatment plan optimization algorithm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tian, Zhen, E-mail: Zhen.Tian@UTSouthwestern.edu, E-mail: Xun.Jia@UTSouthwestern.edu, E-mail: Steve.Jiang@UTSouthwestern.edu; Folkerts, Michael; Tan, Jun

Purpose: Volumetric modulated arc therapy (VMAT) optimization is a computationally challenging problem due to its large data size, high degrees of freedom, and many hardware constraints. High-performance graphics processing units (GPUs) have been used to speed up the computations. However, GPU’s relatively small memory size cannot handle cases with a large dose-deposition coefficient (DDC) matrix in cases of, e.g., those with a large target size, multiple targets, multiple arcs, and/or small beamlet size. The main purpose of this paper is to report an implementation of a column-generation-based VMAT algorithm, previously developed in the authors’ group, on a multi-GPU platform tomore » solve the memory limitation problem. While the column-generation-based VMAT algorithm has been previously developed, the GPU implementation details have not been reported. Hence, another purpose is to present detailed techniques employed for GPU implementation. The authors also would like to utilize this particular problem as an example problem to study the feasibility of using a multi-GPU platform to solve large-scale problems in medical physics. Methods: The column-generation approach generates VMAT apertures sequentially by solving a pricing problem (PP) and a master problem (MP) iteratively. In the authors’ method, the sparse DDC matrix is first stored on a CPU in coordinate list format (COO). On the GPU side, this matrix is split into four submatrices according to beam angles, which are stored on four GPUs in compressed sparse row format. Computation of beamlet price, the first step in PP, is accomplished using multi-GPUs. A fast inter-GPU data transfer scheme is accomplished using peer-to-peer access. The remaining steps of PP and MP problems are implemented on CPU or a single GPU due to their modest problem scale and computational loads. Barzilai and Borwein algorithm with a subspace step scheme is adopted here to solve the MP problem. A head and neck (H and N) cancer case is then used to validate the authors’ method. The authors also compare their multi-GPU implementation with three different single GPU implementation strategies, i.e., truncating DDC matrix (S1), repeatedly transferring DDC matrix between CPU and GPU (S2), and porting computations involving DDC matrix to CPU (S3), in terms of both plan quality and computational efficiency. Two more H and N patient cases and three prostate cases are used to demonstrate the advantages of the authors’ method. Results: The authors’ multi-GPU implementation can finish the optimization process within ∼1 min for the H and N patient case. S1 leads to an inferior plan quality although its total time was 10 s shorter than the multi-GPU implementation due to the reduced matrix size. S2 and S3 yield the same plan quality as the multi-GPU implementation but take ∼4 and ∼6 min, respectively. High computational efficiency was consistently achieved for the other five patient cases tested, with VMAT plans of clinically acceptable quality obtained within 23–46 s. Conversely, to obtain clinically comparable or acceptable plans for all six of these VMAT cases that the authors have tested in this paper, the optimization time needed in a commercial TPS system on CPU was found to be in an order of several minutes. Conclusions: The results demonstrate that the multi-GPU implementation of the authors’ column-generation-based VMAT optimization can handle the large-scale VMAT optimization problem efficiently without sacrificing plan quality. The authors’ study may serve as an example to shed some light on other large-scale medical physics problems that require multi-GPU techniques.« less

A majorized Newton-CG augmented Lagrangian-based finite element method for 3D restoration of geological models

NASA Astrophysics Data System (ADS)

Tang, Peipei; Wang, Chengjing; Dai, Xiaoxia

2016-04-01

In this paper, we propose a majorized Newton-CG augmented Lagrangian-based finite element method for 3D elastic frictionless contact problems. In this scheme, we discretize the restoration problem via the finite element method and reformulate it to a constrained optimization problem. Then we apply the majorized Newton-CG augmented Lagrangian method to solve the optimization problem, which is very suitable for the ill-conditioned case. Numerical results demonstrate that the proposed method is a very efficient algorithm for various large-scale 3D restorations of geological models, especially for the restoration of geological models with complicated faults.

Markovian Search Games in Heterogeneous Spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Griffin, Christopher H

2009-01-01

We consider how to search for a mobile evader in a large heterogeneous region when sensors are used for detection. Sensors are modeled using probability of detection. Due to environmental effects, this probability will not be constant over the entire region. We map this problem to a graph search problem and, even though deterministic graph search is NP-complete, we derive a tractable, optimal, probabilistic search strategy. We do this by defining the problem as a differential game played on a Markov chain. We prove that this strategy is optimal in the sense of Nash. Simulations of an example problem illustratemore » our approach and verify our claims.« less

Neural Network Solves "Traveling-Salesman" Problem

NASA Technical Reports Server (NTRS)

Thakoor, Anilkumar P.; Moopenn, Alexander W.

1990-01-01

Experimental electronic neural network solves "traveling-salesman" problem. Plans round trip of minimum distance among N cities, visiting every city once and only once (without backtracking). This problem is paradigm of many problems of global optimization (e.g., routing or allocation of resources) occuring in industry, business, and government. Applied to large number of cities (or resources), circuits of this kind expected to solve problem faster and more cheaply.

Fuzzy Adaptive Decentralized Optimal Control for Strict Feedback Nonlinear Large-Scale Systems.

PubMed

Sun, Kangkang; Sui, Shuai; Tong, Shaocheng

2018-04-01

This paper considers the optimal decentralized fuzzy adaptive control design problem for a class of interconnected large-scale nonlinear systems in strict feedback form and with unknown nonlinear functions. The fuzzy logic systems are introduced to learn the unknown dynamics and cost functions, respectively, and a state estimator is developed. By applying the state estimator and the backstepping recursive design algorithm, a decentralized feedforward controller is established. By using the backstepping decentralized feedforward control scheme, the considered interconnected large-scale nonlinear system in strict feedback form is changed into an equivalent affine large-scale nonlinear system. Subsequently, an optimal decentralized fuzzy adaptive control scheme is constructed. The whole optimal decentralized fuzzy adaptive controller is composed of a decentralized feedforward control and an optimal decentralized control. It is proved that the developed optimal decentralized controller can ensure that all the variables of the control system are uniformly ultimately bounded, and the cost functions are the smallest. Two simulation examples are provided to illustrate the validity of the developed optimal decentralized fuzzy adaptive control scheme.

Multicriteria hierarchical iterative interactive algorithm for organizing operational modes of large heat supply systems

NASA Astrophysics Data System (ADS)

Korotkova, T. I.; Popova, V. I.

2017-11-01

The generalized mathematical model of decision-making in the problem of planning and mode selection providing required heat loads in a large heat supply system is considered. The system is multilevel, decomposed into levels of main and distribution heating networks with intermediate control stages. Evaluation of the effectiveness, reliability and safety of such a complex system is carried out immediately according to several indicators, in particular pressure, flow, temperature. This global multicriteria optimization problem with constraints is decomposed into a number of local optimization problems and the coordination problem. An agreed solution of local problems provides a solution to the global multicriterion problem of decision making in a complex system. The choice of the optimum operational mode of operation of a complex heat supply system is made on the basis of the iterative coordination process, which converges to the coordinated solution of local optimization tasks. The interactive principle of multicriteria task decision-making includes, in particular, periodic adjustment adjustments, if necessary, guaranteeing optimal safety, reliability and efficiency of the system as a whole in the process of operation. The degree of accuracy of the solution, for example, the degree of deviation of the internal air temperature from the required value, can also be changed interactively. This allows to carry out adjustment activities in the best way and to improve the quality of heat supply to consumers. At the same time, an energy-saving task is being solved to determine the minimum required values of heads at sources and pumping stations.

Improved mine blast algorithm for optimal cost design of water distribution systems

NASA Astrophysics Data System (ADS)

Sadollah, Ali; Guen Yoo, Do; Kim, Joong Hoon

2015-12-01

The design of water distribution systems is a large class of combinatorial, nonlinear optimization problems with complex constraints such as conservation of mass and energy equations. Since feasible solutions are often extremely complex, traditional optimization techniques are insufficient. Recently, metaheuristic algorithms have been applied to this class of problems because they are highly efficient. In this article, a recently developed optimizer called the mine blast algorithm (MBA) is considered. The MBA is improved and coupled with the hydraulic simulator EPANET to find the optimal cost design for water distribution systems. The performance of the improved mine blast algorithm (IMBA) is demonstrated using the well-known Hanoi, New York tunnels and Balerma benchmark networks. Optimization results obtained using IMBA are compared to those using MBA and other optimizers in terms of their minimum construction costs and convergence rates. For the complex Balerma network, IMBA offers the cheapest network design compared to other optimization algorithms.

Theory and computation of optimal low- and medium-thrust transfers

NASA Technical Reports Server (NTRS)

Chuang, C.-H.

1994-01-01

This report describes the current state of development of methods for calculating optimal orbital transfers with large numbers of burns. Reported on first is the homotopy-motivated and so-called direction correction method. So far this method has been partially tested with one solver; the final step has yet to be implemented. Second is the patched transfer method. This method is rooted in some simplifying approximations made on the original optimal control problem. The transfer is broken up into single-burn segments, each single-burn solved as a predictor step and the whole problem then solved with a corrector step.

Stiffness optimization of non-linear elastic structures

DOE PAGES

Wallin, Mathias; Ivarsson, Niklas; Tortorelli, Daniel

2017-11-13

Our paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. And for the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed bymore » using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. We formulate a well-posed topology optimization problem by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.« less

Stiffness optimization of non-linear elastic structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wallin, Mathias; Ivarsson, Niklas; Tortorelli, Daniel

Our paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. And for the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed bymore » using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. We formulate a well-posed topology optimization problem by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.« less

An Optimizing Space Data-Communications Scheduling Method and Algorithm with Interference Mitigation, Generalized for a Broad Class of Optimization Problems

NASA Technical Reports Server (NTRS)

Rash, James L.

2010-01-01

NASA's space data-communications infrastructure, the Space Network and the Ground Network, provide scheduled (as well as some limited types of unscheduled) data-communications services to user spacecraft via orbiting relay satellites and ground stations. An implementation of the methods and algorithms disclosed herein will be a system that produces globally optimized schedules with not only optimized service delivery by the space data-communications infrastructure but also optimized satisfaction of all user requirements and prescribed constraints, including radio frequency interference (RFI) constraints. Evolutionary search, a class of probabilistic strategies for searching large solution spaces, constitutes the essential technology in this disclosure. Also disclosed are methods and algorithms for optimizing the execution efficiency of the schedule-generation algorithm itself. The scheduling methods and algorithms as presented are adaptable to accommodate the complexity of scheduling the civilian and/or military data-communications infrastructure. Finally, the problem itself, and the methods and algorithms, are generalized and specified formally, with applicability to a very broad class of combinatorial optimization problems.

A new hybrid meta-heuristic algorithm for optimal design of large-scale dome structures

NASA Astrophysics Data System (ADS)

Kaveh, A.; Ilchi Ghazaan, M.

2018-02-01

In this article a hybrid algorithm based on a vibrating particles system (VPS) algorithm, multi-design variable configuration (Multi-DVC) cascade optimization, and an upper bound strategy (UBS) is presented for global optimization of large-scale dome truss structures. The new algorithm is called MDVC-UVPS in which the VPS algorithm acts as the main engine of the algorithm. The VPS algorithm is one of the most recent multi-agent meta-heuristic algorithms mimicking the mechanisms of damped free vibration of single degree of freedom systems. In order to handle a large number of variables, cascade sizing optimization utilizing a series of DVCs is used. Moreover, the UBS is utilized to reduce the computational time. Various dome truss examples are studied to demonstrate the effectiveness and robustness of the proposed method, as compared to some existing structural optimization techniques. The results indicate that the MDVC-UVPS technique is a powerful search and optimization method for optimizing structural engineering problems.

Combining local search with co-evolution in a remarkably simple way

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boettcher, S.; Percus, A.

2000-05-01

The authors explore a new general-purpose heuristic for finding high-quality solutions to hard optimization problem. The method, called extremal optimization, is inspired by self-organized criticality, a concept introduced to describe emergent complexity in physical systems. In contrast to genetic algorithms, which operate on an entire gene-pool of possible solutions, extremal optimization successively replaces extremely undesirable elements of a single sub-optimal solution with new, random ones. Large fluctuations, or avalanches, ensue that efficiently explore many local optima. Drawing upon models used to simulate far-from-equilibrium dynamics, extremal optimization complements heuristics inspired by equilibrium statistical physics, such as simulated annealing. With only onemore » adjustable parameter, its performance has proved competitive with more elaborate methods, especially near phase transitions. Phase transitions are found in many combinatorial optimization problems, and have been conjectured to occur in the region of parameter space containing the hardest instances. We demonstrate how extremal optimization can be implemented for a variety of hard optimization problems. We believe that this will be a useful tool in the investigation of phase transitions in combinatorial optimization, thereby helping to elucidate the origin of computational complexity.« less

Hybrid Nested Partitions and Math Programming Framework for Large-scale Combinatorial Optimization

DTIC Science & Technology

2010-03-31

optimization problems: 1) exact algorithms and 2) metaheuristic algorithms . This project will integrate concepts from these two technologies to develop...optimal solutions within an acceptable amount of computation time, and 2) metaheuristic algorithms such as genetic algorithms , tabu search, and the...integer programming decomposition approaches, such as Dantzig Wolfe decomposition and Lagrangian relaxation, and metaheuristics such as the Nested

Theory and computation of optimal low- and medium-thrust transfers

NASA Technical Reports Server (NTRS)

Chuang, C.-H.

1994-01-01

This report presents two numerical methods considered for the computation of fuel-optimal, low-thrust orbit transfers in large numbers of burns. The origins of these methods are observations made with the extremal solutions of transfers in small numbers of burns; there seems to exist a trend such that the longer the time allowed to perform an optimal transfer the less fuel that is used. These longer transfers are obviously of interest since they require a motor of low thrust; however, we also find a trend that the longer the time allowed to perform the optimal transfer the more burns are required to satisfy optimality. Unfortunately, this usually increases the difficulty of computation. Both of the methods described use small-numbered burn solutions to determine solutions in large numbers of burns. One method is a homotopy method that corrects for problems that arise when a solution requires a new burn or coast arc for optimality. The other method is to simply patch together long transfers from smaller ones. An orbit correction problem is solved to develop this method. This method may also lead to a good guidance law for transfer orbits with long transfer times.

Optimal estimation and scheduling in aquifer management using the rapid feedback control method

NASA Astrophysics Data System (ADS)

Ghorbanidehno, Hojat; Kokkinaki, Amalia; Kitanidis, Peter K.; Darve, Eric

2017-12-01

Management of water resources systems often involves a large number of parameters, as in the case of large, spatially heterogeneous aquifers, and a large number of "noisy" observations, as in the case of pressure observation in wells. Optimizing the operation of such systems requires both searching among many possible solutions and utilizing new information as it becomes available. However, the computational cost of this task increases rapidly with the size of the problem to the extent that textbook optimization methods are practically impossible to apply. In this paper, we present a new computationally efficient technique as a practical alternative for optimally operating large-scale dynamical systems. The proposed method, which we term Rapid Feedback Controller (RFC), provides a practical approach for combined monitoring, parameter estimation, uncertainty quantification, and optimal control for linear and nonlinear systems with a quadratic cost function. For illustration, we consider the case of a weakly nonlinear uncertain dynamical system with a quadratic objective function, specifically a two-dimensional heterogeneous aquifer management problem. To validate our method, we compare our results with the linear quadratic Gaussian (LQG) method, which is the basic approach for feedback control. We show that the computational cost of the RFC scales only linearly with the number of unknowns, a great improvement compared to the basic LQG control with a computational cost that scales quadratically. We demonstrate that the RFC method can obtain the optimal control values at a greatly reduced computational cost compared to the conventional LQG algorithm with small and controllable losses in the accuracy of the state and parameter estimation.

Hybrid Pareto artificial bee colony algorithm for multi-objective single machine group scheduling problem with sequence-dependent setup times and learning effects.

PubMed

Yue, Lei; Guan, Zailin; Saif, Ullah; Zhang, Fei; Wang, Hao

2016-01-01

Group scheduling is significant for efficient and cost effective production system. However, there exist setup times between the groups, which require to decrease it by sequencing groups in an efficient way. Current research is focused on a sequence dependent group scheduling problem with an aim to minimize the makespan in addition to minimize the total weighted tardiness simultaneously. In most of the production scheduling problems, the processing time of jobs is assumed as fixed. However, the actual processing time of jobs may be reduced due to "learning effect". The integration of sequence dependent group scheduling problem with learning effects has been rarely considered in literature. Therefore, current research considers a single machine group scheduling problem with sequence dependent setup times and learning effects simultaneously. A novel hybrid Pareto artificial bee colony algorithm (HPABC) with some steps of genetic algorithm is proposed for current problem to get Pareto solutions. Furthermore, five different sizes of test problems (small, small medium, medium, large medium, large) are tested using proposed HPABC. Taguchi method is used to tune the effective parameters of the proposed HPABC for each problem category. The performance of HPABC is compared with three famous multi objective optimization algorithms, improved strength Pareto evolutionary algorithm (SPEA2), non-dominated sorting genetic algorithm II (NSGAII) and particle swarm optimization algorithm (PSO). Results indicate that HPABC outperforms SPEA2, NSGAII and PSO and gives better Pareto optimal solutions in terms of diversity and quality for almost all the instances of the different sizes of problems.

A feasible DY conjugate gradient method for linear equality constraints

NASA Astrophysics Data System (ADS)

LI, Can

2017-09-01

In this paper, we propose a feasible conjugate gradient method for solving linear equality constrained optimization problem. The method is an extension of the Dai-Yuan conjugate gradient method proposed by Dai and Yuan to linear equality constrained optimization problem. It can be applied to solve large linear equality constrained problem due to lower storage requirement. An attractive property of the method is that the generated direction is always feasible and descent direction. Under mild conditions, the global convergence of the proposed method with exact line search is established. Numerical experiments are also given which show the efficiency of the method.

Portable parallel portfolio optimization in the Aurora Financial Management System

NASA Astrophysics Data System (ADS)

Laure, Erwin; Moritsch, Hans

2001-07-01

Financial planning problems are formulated as large scale, stochastic, multiperiod, tree structured optimization problems. An efficient technique for solving this kind of problems is the nested Benders decomposition method. In this paper we present a parallel, portable, asynchronous implementation of this technique. To achieve our portability goals we elected the programming language Java for our implementation and used a high level Java based framework, called OpusJava, for expressing the parallelism potential as well as synchronization constraints. Our implementation is embedded within a modular decision support tool for portfolio and asset liability management, the Aurora Financial Management System.

Handling Practicalities in Agricultural Policy Optimization for Water Quality Improvements

EPA Science Inventory

Bilevel and multi-objective optimization methods are often useful to spatially target agri-environmental policy throughout a watershed. This type of problem is complex and is comprised of a number of practicalities: (i) a large number of decision variables, (ii) at least two inte...

A reduced successive quadratic programming strategy for errors-in-variables estimation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tjoa, I.-B.; Biegler, L. T.; Carnegie-Mellon Univ.

Parameter estimation problems in process engineering represent a special class of nonlinear optimization problems, because the maximum likelihood structure of the objective function can be exploited. Within this class, the errors in variables method (EVM) is particularly interesting. Here we seek a weighted least-squares fit to the measurements with an underdetermined process model. Thus, both the number of variables and degrees of freedom available for optimization increase linearly with the number of data sets. Large optimization problems of this type can be particularly challenging and expensive to solve because, for general-purpose nonlinear programming (NLP) algorithms, the computational effort increases atmore » least quadratically with problem size. In this study we develop a tailored NLP strategy for EVM problems. The method is based on a reduced Hessian approach to successive quadratic programming (SQP), but with the decomposition performed separately for each data set. This leads to the elimination of all variables but the model parameters, which are determined by a QP coordination step. In this way the computational effort remains linear in the number of data sets. Moreover, unlike previous approaches to the EVM problem, global and superlinear properties of the SQP algorithm apply naturally. Also, the method directly incorporates inequality constraints on the model parameters (although not on the fitted variables). This approach is demonstrated on five example problems with up to 102 degrees of freedom. Compared to general-purpose NLP algorithms, large improvements in computational performance are observed.« less

Efficient hybrid evolutionary algorithm for optimization of a strip coiling process

NASA Astrophysics Data System (ADS)

Pholdee, Nantiwat; Park, Won-Woong; Kim, Dong-Kyu; Im, Yong-Taek; Bureerat, Sujin; Kwon, Hyuck-Cheol; Chun, Myung-Sik

2015-04-01

This article proposes an efficient metaheuristic based on hybridization of teaching-learning-based optimization and differential evolution for optimization to improve the flatness of a strip during a strip coiling process. Differential evolution operators were integrated into the teaching-learning-based optimization with a Latin hypercube sampling technique for generation of an initial population. The objective function was introduced to reduce axial inhomogeneity of the stress distribution and the maximum compressive stress calculated by Love's elastic solution within the thin strip, which may cause an irregular surface profile of the strip during the strip coiling process. The hybrid optimizer and several well-established evolutionary algorithms (EAs) were used to solve the optimization problem. The comparative studies show that the proposed hybrid algorithm outperformed other EAs in terms of convergence rate and consistency. It was found that the proposed hybrid approach was powerful for process optimization, especially with a large-scale design problem.

Comparing genetic algorithm and particle swarm optimization for solving capacitated vehicle routing problem

NASA Astrophysics Data System (ADS)

Iswari, T.; Asih, A. M. S.

2018-04-01

In the logistics system, transportation plays an important role to connect every element in the supply chain, but it can produces the greatest cost. Therefore, it is important to make the transportation costs as minimum as possible. Reducing the transportation cost can be done in several ways. One of the ways to minimizing the transportation cost is by optimizing the routing of its vehicles. It refers to Vehicle Routing Problem (VRP). The most common type of VRP is Capacitated Vehicle Routing Problem (CVRP). In CVRP, the vehicles have their own capacity and the total demands from the customer should not exceed the capacity of the vehicle. CVRP belongs to the class of NP-hard problems. These NP-hard problems make it more complex to solve such that exact algorithms become highly time-consuming with the increases in problem sizes. Thus, for large-scale problem instances, as typically found in industrial applications, finding an optimal solution is not practicable. Therefore, this paper uses two kinds of metaheuristics approach to solving CVRP. Those are Genetic Algorithm and Particle Swarm Optimization. This paper compares the results of both algorithms and see the performance of each algorithm. The results show that both algorithms perform well in solving CVRP but still needs to be improved. From algorithm testing and numerical example, Genetic Algorithm yields a better solution than Particle Swarm Optimization in total distance travelled.

Energy-efficient approach to minimizing the energy consumption in an extended job-shop scheduling problem

NASA Astrophysics Data System (ADS)

Tang, Dunbing; Dai, Min

2015-09-01

The traditional production planning and scheduling problems consider performance indicators like time, cost and quality as optimization objectives in manufacturing processes. However, environmentally-friendly factors like energy consumption of production have not been completely taken into consideration. Against this background, this paper addresses an approach to modify a given schedule generated by a production planning and scheduling system in a job shop floor, where machine tools can work at different cutting speeds. It can adjust the cutting speeds of the operations while keeping the original assignment and processing sequence of operations of each job fixed in order to obtain energy savings. First, the proposed approach, based on a mixed integer programming mathematical model, changes the total idle time of the given schedule to minimize energy consumption in the job shop floor while accepting the optimal solution of the scheduling objective, makespan. Then, a genetic-simulated annealing algorithm is used to explore the optimal solution due to the fact that the problem is strongly NP-hard. Finally, the effectiveness of the approach is performed smalland large-size instances, respectively. The experimental results show that the approach can save 5%-10% of the average energy consumption while accepting the optimal solution of the makespan in small-size instances. In addition, the average maximum energy saving ratio can reach to 13%. And it can save approximately 1%-4% of the average energy consumption and approximately 2.4% of the average maximum energy while accepting the near-optimal solution of the makespan in large-size instances. The proposed research provides an interesting point to explore an energy-aware schedule optimization for a traditional production planning and scheduling problem.

The application of nonlinear programming and collocation to optimal aeroassisted orbital transfers

NASA Astrophysics Data System (ADS)

Shi, Y. Y.; Nelson, R. L.; Young, D. H.; Gill, P. E.; Murray, W.; Saunders, M. A.

1992-01-01

Sequential quadratic programming (SQP) and collocation of the differential equations of motion were applied to optimal aeroassisted orbital transfers. The Optimal Trajectory by Implicit Simulation (OTIS) computer program codes with updated nonlinear programming code (NZSOL) were used as a testbed for the SQP nonlinear programming (NLP) algorithms. The state-of-the-art sparse SQP method is considered to be effective for solving large problems with a sparse matrix. Sparse optimizers are characterized in terms of memory requirements and computational efficiency. For the OTIS problems, less than 10 percent of the Jacobian matrix elements are nonzero. The SQP method encompasses two phases: finding an initial feasible point by minimizing the sum of infeasibilities and minimizing the quadratic objective function within the feasible region. The orbital transfer problem under consideration involves the transfer from a high energy orbit to a low energy orbit.

Enabling Controlling Complex Networks with Local Topological Information.

PubMed

Li, Guoqi; Deng, Lei; Xiao, Gaoxi; Tang, Pei; Wen, Changyun; Hu, Wuhua; Pei, Jing; Shi, Luping; Stanley, H Eugene

2018-03-15

Complex networks characterize the nature of internal/external interactions in real-world systems including social, economic, biological, ecological, and technological networks. Two issues keep as obstacles to fulfilling control of large-scale networks: structural controllability which describes the ability to guide a dynamical system from any initial state to any desired final state in finite time, with a suitable choice of inputs; and optimal control, which is a typical control approach to minimize the cost for driving the network to a predefined state with a given number of control inputs. For large complex networks without global information of network topology, both problems remain essentially open. Here we combine graph theory and control theory for tackling the two problems in one go, using only local network topology information. For the structural controllability problem, a distributed local-game matching method is proposed, where every node plays a simple Bayesian game with local information and local interactions with adjacent nodes, ensuring a suboptimal solution at a linear complexity. Starring from any structural controllability solution, a minimizing longest control path method can efficiently reach a good solution for the optimal control in large networks. Our results provide solutions for distributed complex network control and demonstrate a way to link the structural controllability and optimal control together.

Use of the Collaborative Optimization Architecture for Launch Vehicle Design

NASA Technical Reports Server (NTRS)

Braun, R. D.; Moore, A. A.; Kroo, I. M.

1996-01-01

Collaborative optimization is a new design architecture specifically created for large-scale distributed-analysis applications. In this approach, problem is decomposed into a user-defined number of subspace optimization problems that are driven towards interdisciplinary compatibility and the appropriate solution by a system-level coordination process. This decentralized design strategy allows domain-specific issues to be accommodated by disciplinary analysts, while requiring interdisciplinary decisions to be reached by consensus. The present investigation focuses on application of the collaborative optimization architecture to the multidisciplinary design of a single-stage-to-orbit launch vehicle. Vehicle design, trajectory, and cost issues are directly modeled. Posed to suit the collaborative architecture, the design problem is characterized by 5 design variables and 16 constraints. Numerous collaborative solutions are obtained. Comparison of these solutions demonstrates the influence which an priori ascent-abort criterion has on development cost. Similarly, objective-function selection is discussed, demonstrating the difference between minimum weight and minimum cost concepts. The operational advantages of the collaborative optimization

Simultaneous multislice refocusing via time optimal control.

PubMed

Rund, Armin; Aigner, Christoph Stefan; Kunisch, Karl; Stollberger, Rudolf

2018-02-09

Joint design of minimum duration RF pulses and slice-selective gradient shapes for MRI via time optimal control with strict physical constraints, and its application to simultaneous multislice imaging. The minimization of the pulse duration is cast as a time optimal control problem with inequality constraints describing the refocusing quality and physical constraints. It is solved with a bilevel method, where the pulse length is minimized in the upper level, and the constraints are satisfied in the lower level. To address the inherent nonconvexity of the optimization problem, the upper level is enhanced with new heuristics for finding a near global optimizer based on a second optimization problem. A large set of optimized examples shows an average temporal reduction of 87.1% for double diffusion and 74% for turbo spin echo pulses compared to power independent number of slices pulses. The optimized results are validated on a 3T scanner with phantom measurements. The presented design method computes minimum duration RF pulse and slice-selective gradient shapes subject to physical constraints. The shorter pulse duration can be used to decrease the effective echo time in existing echo-planar imaging or echo spacing in turbo spin echo sequences. © 2018 International Society for Magnetic Resonance in Medicine.

Capacitated vehicle-routing problem model for scheduled solid waste collection and route optimization using PSO algorithm.

PubMed

Hannan, M A; Akhtar, Mahmuda; Begum, R A; Basri, H; Hussain, A; Scavino, Edgar

2018-01-01

Waste collection widely depends on the route optimization problem that involves a large amount of expenditure in terms of capital, labor, and variable operational costs. Thus, the more waste collection route is optimized, the more reduction in different costs and environmental effect will be. This study proposes a modified particle swarm optimization (PSO) algorithm in a capacitated vehicle-routing problem (CVRP) model to determine the best waste collection and route optimization solutions. In this study, threshold waste level (TWL) and scheduling concepts are applied in the PSO-based CVRP model under different datasets. The obtained results from different datasets show that the proposed algorithmic CVRP model provides the best waste collection and route optimization in terms of travel distance, total waste, waste collection efficiency, and tightness at 70-75% of TWL. The obtained results for 1 week scheduling show that 70% of TWL performs better than all node consideration in terms of collected waste, distance, tightness, efficiency, fuel consumption, and cost. The proposed optimized model can serve as a valuable tool for waste collection and route optimization toward reducing socioeconomic and environmental impacts. Copyright © 2017 Elsevier Ltd. All rights reserved.

Fast Gaussian kernel learning for classification tasks based on specially structured global optimization.

PubMed

Zhong, Shangping; Chen, Tianshun; He, Fengying; Niu, Yuzhen

2014-09-01

For a practical pattern classification task solved by kernel methods, the computing time is mainly spent on kernel learning (or training). However, the current kernel learning approaches are based on local optimization techniques, and hard to have good time performances, especially for large datasets. Thus the existing algorithms cannot be easily extended to large-scale tasks. In this paper, we present a fast Gaussian kernel learning method by solving a specially structured global optimization (SSGO) problem. We optimize the Gaussian kernel function by using the formulated kernel target alignment criterion, which is a difference of increasing (d.i.) functions. Through using a power-transformation based convexification method, the objective criterion can be represented as a difference of convex (d.c.) functions with a fixed power-transformation parameter. And the objective programming problem can then be converted to a SSGO problem: globally minimizing a concave function over a convex set. The SSGO problem is classical and has good solvability. Thus, to find the global optimal solution efficiently, we can adopt the improved Hoffman's outer approximation method, which need not repeat the searching procedure with different starting points to locate the best local minimum. Also, the proposed method can be proven to converge to the global solution for any classification task. We evaluate the proposed method on twenty benchmark datasets, and compare it with four other Gaussian kernel learning methods. Experimental results show that the proposed method stably achieves both good time-efficiency performance and good classification performance. Copyright © 2014 Elsevier Ltd. All rights reserved.

Co-optimizing Generation and Transmission Expansion with Wind Power in Large-Scale Power Grids Implementation in the US Eastern Interconnection

DOE PAGES

You, Shutang; Hadley, Stanton W.; Shankar, Mallikarjun; ...

2016-01-12

This paper studies the generation and transmission expansion co-optimization problem with a high wind power penetration rate in the US Eastern Interconnection (EI) power grid. In this paper, the generation and transmission expansion problem for the EI system is modeled as a mixed-integer programming (MIP) problem. Our paper also analyzed a time series generation method to capture the variation and correlation of both load and wind power across regions. The obtained series can be easily introduced into the expansion planning problem and then solved through existing MIP solvers. Simulation results show that the proposed planning model and series generation methodmore » can improve the expansion result significantly through modeling more detailed information of wind and load variation among regions in the US EI system. Moreover, the improved expansion plan that combines generation and transmission will aid system planners and policy makers to maximize the social welfare in large-scale power grids.« less

Fast optimal wavefront reconstruction for multi-conjugate adaptive optics using the Fourier domain preconditioned conjugate gradient algorithm.

PubMed

Vogel, Curtis R; Yang, Qiang

2006-08-21

We present two different implementations of the Fourier domain preconditioned conjugate gradient algorithm (FD-PCG) to efficiently solve the large structured linear systems that arise in optimal volume turbulence estimation, or tomography, for multi-conjugate adaptive optics (MCAO). We describe how to deal with several critical technical issues, including the cone coordinate transformation problem and sensor subaperture grid spacing. We also extend the FD-PCG approach to handle the deformable mirror fitting problem for MCAO.

Focusing on the golden ball metaheuristic: an extended study on a wider set of problems.

PubMed

Osaba, E; Diaz, F; Carballedo, R; Onieva, E; Perallos, A

2014-01-01

Nowadays, the development of new metaheuristics for solving optimization problems is a topic of interest in the scientific community. In the literature, a large number of techniques of this kind can be found. Anyway, there are many recently proposed techniques, such as the artificial bee colony and imperialist competitive algorithm. This paper is focused on one recently published technique, the one called Golden Ball (GB). The GB is a multiple-population metaheuristic based on soccer concepts. Although it was designed to solve combinatorial optimization problems, until now, it has only been tested with two simple routing problems: the traveling salesman problem and the capacitated vehicle routing problem. In this paper, the GB is applied to four different combinatorial optimization problems. Two of them are routing problems, which are more complex than the previously used ones: the asymmetric traveling salesman problem and the vehicle routing problem with backhauls. Additionally, one constraint satisfaction problem (the n-queen problem) and one combinatorial design problem (the one-dimensional bin packing problem) have also been used. The outcomes obtained by GB are compared with the ones got by two different genetic algorithms and two distributed genetic algorithms. Additionally, two statistical tests are conducted to compare these results.

Focusing on the Golden Ball Metaheuristic: An Extended Study on a Wider Set of Problems

PubMed Central

Osaba, E.; Diaz, F.; Carballedo, R.; Onieva, E.; Perallos, A.

2014-01-01

Nowadays, the development of new metaheuristics for solving optimization problems is a topic of interest in the scientific community. In the literature, a large number of techniques of this kind can be found. Anyway, there are many recently proposed techniques, such as the artificial bee colony and imperialist competitive algorithm. This paper is focused on one recently published technique, the one called Golden Ball (GB). The GB is a multiple-population metaheuristic based on soccer concepts. Although it was designed to solve combinatorial optimization problems, until now, it has only been tested with two simple routing problems: the traveling salesman problem and the capacitated vehicle routing problem. In this paper, the GB is applied to four different combinatorial optimization problems. Two of them are routing problems, which are more complex than the previously used ones: the asymmetric traveling salesman problem and the vehicle routing problem with backhauls. Additionally, one constraint satisfaction problem (the n-queen problem) and one combinatorial design problem (the one-dimensional bin packing problem) have also been used. The outcomes obtained by GB are compared with the ones got by two different genetic algorithms and two distributed genetic algorithms. Additionally, two statistical tests are conducted to compare these results. PMID:25165742

Recent experience in simultaneous control-structure optimization

NASA Technical Reports Server (NTRS)

Salama, M.; Ramaker, R.; Milman, M.

1989-01-01

To show the feasibility of simultaneous optimization as design procedure, low order problems were used in conjunction with simple control formulations. The numerical results indicate that simultaneous optimization is not only feasible, but also advantageous. Such advantages come at the expense of introducing complexities beyond those encountered in structure optimization alone, or control optimization alone. Examples include: larger design parameter space, optimization may combine continuous and combinatoric variables, and the combined objective function may be nonconvex. Future extensions to include large order problems, more complex objective functions and constraints, and more sophisticated control formulations will require further research to ensure that the additional complexities do not outweigh the advantages of simultaneous optimization. Some areas requiring more efficient tools than currently available include: multiobjective criteria and nonconvex optimization. Efficient techniques to deal with optimization over combinatoric and continuous variables, and with truncation issues for structure and control parameters of both the model space as well as the design space need to be developed.

Symmetric tridiagonal structure preserving finite element model updating problem for the quadratic model

NASA Astrophysics Data System (ADS)

Rakshit, Suman; Khare, Swanand R.; Datta, Biswa Nath

2018-07-01

One of the most important yet difficult aspect of the Finite Element Model Updating Problem is to preserve the finite element inherited structures in the updated model. Finite element matrices are in general symmetric, positive definite (or semi-definite) and banded (tridiagonal, diagonal, penta-diagonal, etc.). Though a large number of papers have been published in recent years on various aspects of solutions of this problem, papers dealing with structure preservation almost do not exist. A novel optimization based approach that preserves the symmetric tridiagonal structures of the stiffness and damping matrices is proposed in this paper. An analytical expression for the global minimum solution of the associated optimization problem along with the results of numerical experiments obtained by both the analytical expressions and by an appropriate numerical optimization algorithm are presented. The results of numerical experiments support the validity of the proposed method.

Evolutionary optimization methods for accelerator design

NASA Astrophysics Data System (ADS)

Poklonskiy, Alexey A.

Many problems from the fields of accelerator physics and beam theory can be formulated as optimization problems and, as such, solved using optimization methods. Despite growing efficiency of the optimization methods, the adoption of modern optimization techniques in these fields is rather limited. Evolutionary Algorithms (EAs) form a relatively new and actively developed optimization methods family. They possess many attractive features such as: ease of the implementation, modest requirements on the objective function, a good tolerance to noise, robustness, and the ability to perform a global search efficiently. In this work we study the application of EAs to problems from accelerator physics and beam theory. We review the most commonly used methods of unconstrained optimization and describe the GATool, evolutionary algorithm and the software package, used in this work, in detail. Then we use a set of test problems to assess its performance in terms of computational resources, quality of the obtained result, and the tradeoff between them. We justify the choice of GATool as a heuristic method to generate cutoff values for the COSY-GO rigorous global optimization package for the COSY Infinity scientific computing package. We design the model of their mutual interaction and demonstrate that the quality of the result obtained by GATool increases as the information about the search domain is refined, which supports the usefulness of this model. We Giscuss GATool's performance on the problems suffering from static and dynamic noise and study useful strategies of GATool parameter tuning for these and other difficult problems. We review the challenges of constrained optimization with EAs and methods commonly used to overcome them. We describe REPA, a new constrained optimization method based on repairing, in exquisite detail, including the properties of its two repairing techniques: REFIND and REPROPT. We assess REPROPT's performance on the standard constrained optimization test problems for EA with a variety of different configurations and suggest optimal default parameter values based on the results. Then we study the performance of the REPA method on the same set of test problems and compare the obtained results with those of several commonly used constrained optimization methods with EA. Based on the obtained results, particularly on the outstanding performance of REPA on test problem that presents significant difficulty for other reviewed EAs, we conclude that the proposed method is useful and competitive. We discuss REPA parameter tuning for difficult problems and critically review some of the problems from the de-facto standard test problem set for the constrained optimization with EA. In order to demonstrate the practical usefulness of the developed method, we study several problems of accelerator design and demonstrate how they can be solved with EAs. These problems include a simple accelerator design problem (design a quadrupole triplet to be stigmatically imaging, find all possible solutions), a complex real-life accelerator design problem (an optimization of the front end section for the future neutrino factory), and a problem of the normal form defect function optimization which is used to rigorously estimate the stability of the beam dynamics in circular accelerators. The positive results we obtained suggest that the application of EAs to problems from accelerator theory can be very beneficial and has large potential. The developed optimization scenarios and tools can be used to approach similar problems.

Optimal structural design of the midship of a VLCC based on the strategy integrating SVM and GA

NASA Astrophysics Data System (ADS)

Sun, Li; Wang, Deyu

2012-03-01

In this paper a hybrid process of modeling and optimization, which integrates a support vector machine (SVM) and genetic algorithm (GA), was introduced to reduce the high time cost in structural optimization of ships. SVM, which is rooted in statistical learning theory and an approximate implementation of the method of structural risk minimization, can provide a good generalization performance in metamodeling the input-output relationship of real problems and consequently cuts down on high time cost in the analysis of real problems, such as FEM analysis. The GA, as a powerful optimization technique, possesses remarkable advantages for the problems that can hardly be optimized with common gradient-based optimization methods, which makes it suitable for optimizing models built by SVM. Based on the SVM-GA strategy, optimization of structural scantlings in the midship of a very large crude carrier (VLCC) ship was carried out according to the direct strength assessment method in common structural rules (CSR), which eventually demonstrates the high efficiency of SVM-GA in optimizing the ship structural scantlings under heavy computational complexity. The time cost of this optimization with SVM-GA has been sharply reduced, many more loops have been processed within a small amount of time and the design has been improved remarkably.

An EGO-like optimization framework for sensor placement optimization in modal analysis

NASA Astrophysics Data System (ADS)

Morlier, Joseph; Basile, Aniello; Chiplunkar, Ankit; Charlotte, Miguel

2018-07-01

In aircraft design, ground/flight vibration tests are conducted to extract aircraft’s modal parameters (natural frequencies, damping ratios and mode shapes) also known as the modal basis. The main problem in aircraft modal identification is the large number of sensors needed, which increases operational time and costs. The goal of this paper is to minimize the number of sensors by optimizing their locations in order to reconstruct a truncated modal basis of N mode shapes with a high level of accuracy in the reconstruction. There are several methods to solve sensors placement optimization (SPO) problems, but for this case an original approach has been established based on an iterative process for mode shapes reconstruction through an adaptive Kriging metamodeling approach so called efficient global optimization (EGO)-SPO. The main idea in this publication is to solve an optimization problem where the sensors locations are variables and the objective function is defined by maximizing the trace of criteria so called AutoMAC. The results on a 2D wing demonstrate a reduction of sensors by 30% using our EGO-SPO strategy.

Constrained multi-objective optimization of storage ring lattices

NASA Astrophysics Data System (ADS)

Husain, Riyasat; Ghodke, A. D.

2018-03-01

The storage ring lattice optimization is a class of constrained multi-objective optimization problem, where in addition to low beam emittance, a large dynamic aperture for good injection efficiency and improved beam lifetime are also desirable. The convergence and computation times are of great concern for the optimization algorithms, as various objectives are to be optimized and a number of accelerator parameters to be varied over a large span with several constraints. In this paper, a study of storage ring lattice optimization using differential evolution is presented. The optimization results are compared with two most widely used optimization techniques in accelerators-genetic algorithm and particle swarm optimization. It is found that the differential evolution produces a better Pareto optimal front in reasonable computation time between two conflicting objectives-beam emittance and dispersion function in the straight section. The differential evolution was used, extensively, for the optimization of linear and nonlinear lattices of Indus-2 for exploring various operational modes within the magnet power supply capabilities.

A learning approach to the bandwidth multicolouring problem

NASA Astrophysics Data System (ADS)

Akbari Torkestani, Javad

2016-05-01

In this article, a generalisation of the vertex colouring problem known as bandwidth multicolouring problem (BMCP), in which a set of colours is assigned to each vertex such that the difference between the colours, assigned to each vertex and its neighbours, is by no means less than a predefined threshold, is considered. It is shown that the proposed method can be applied to solve the bandwidth colouring problem (BCP) as well. BMCP is known to be NP-hard in graph theory, and so a large number of approximation solutions, as well as exact algorithms, have been proposed to solve it. In this article, two learning automata-based approximation algorithms are proposed for estimating a near-optimal solution to the BMCP. We show, for the first proposed algorithm, that by choosing a proper learning rate, the algorithm finds the optimal solution with a probability close enough to unity. Moreover, we compute the worst-case time complexity of the first algorithm for finding a 1/(1-ɛ) optimal solution to the given problem. The main advantage of this method is that a trade-off between the running time of algorithm and the colour set size (colouring optimality) can be made, by a proper choice of the learning rate also. Finally, it is shown that the running time of the proposed algorithm is independent of the graph size, and so it is a scalable algorithm for large graphs. The second proposed algorithm is compared with some well-known colouring algorithms and the results show the efficiency of the proposed algorithm in terms of the colour set size and running time of algorithm.

A globally convergent LCL method for nonlinear optimization.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Friedlander, M. P.; Saunders, M. A.; Mathematics and Computer Science

2005-01-01

For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods solve a sequence of subproblems of the form 'minimize an augmented Lagrangian function subject to linearized constraints.' Such methods converge rapidly near a solution but may not be reliable from arbitrary starting points. Nevertheless, the well-known software package MINOS has proved effective on many large problems. Its success motivates us to derive a related LCL algorithm that possesses three important properties: it is globally convergent, the subproblem constraints are always feasible, and the subproblems may be solved inexactly. The new algorithm has been implemented in Matlab, with an optionmore » to use either MINOS or SNOPT (Fortran codes) to solve the linearly constrained subproblems. Only first derivatives are required. We present numerical results on a subset of the COPS, HS, and CUTE test problems, which include many large examples. The results demonstrate the robustness and efficiency of the stabilized LCL procedure.« less

A study of the use of linear programming techniques to improve the performance in design optimization problems

NASA Technical Reports Server (NTRS)

Young, Katherine C.; Sobieszczanski-Sobieski, Jaroslaw

1988-01-01

This project has two objectives. The first is to determine whether linear programming techniques can improve performance when handling design optimization problems with a large number of design variables and constraints relative to the feasible directions algorithm. The second purpose is to determine whether using the Kreisselmeier-Steinhauser (KS) function to replace the constraints with one constraint will reduce the cost of total optimization. Comparisons are made using solutions obtained with linear and non-linear methods. The results indicate that there is no cost saving using the linear method or in using the KS function to replace constraints.

Improved Fractal Space Filling Curves Hybrid Optimization Algorithm for Vehicle Routing Problem.

PubMed

Yue, Yi-xiang; Zhang, Tong; Yue, Qun-xing

2015-01-01

Vehicle Routing Problem (VRP) is one of the key issues in optimization of modern logistics system. In this paper, a modified VRP model with hard time window is established and a Hybrid Optimization Algorithm (HOA) based on Fractal Space Filling Curves (SFC) method and Genetic Algorithm (GA) is introduced. By incorporating the proposed algorithm, SFC method can find an initial and feasible solution very fast; GA is used to improve the initial solution. Thereafter, experimental software was developed and a large number of experimental computations from Solomon's benchmark have been studied. The experimental results demonstrate the feasibility and effectiveness of the HOA.

Algorithm For Optimal Control Of Large Structures

NASA Technical Reports Server (NTRS)

Salama, Moktar A.; Garba, John A..; Utku, Senol

1989-01-01

Cost of computation appears competitive with other methods. Problem to compute optimal control of forced response of structure with n degrees of freedom identified in terms of smaller number, r, of vibrational modes. Article begins with Hamilton-Jacobi formulation of mechanics and use of quadratic cost functional. Complexity reduced by alternative approach in which quadratic cost functional expressed in terms of control variables only. Leads to iterative solution of second-order time-integral matrix Volterra equation of second kind containing optimal control vector. Cost of algorithm, measured in terms of number of computations required, is of order of, or less than, cost of prior algoritms applied to similar problems.

Improved Fractal Space Filling Curves Hybrid Optimization Algorithm for Vehicle Routing Problem

PubMed Central

Yue, Yi-xiang; Zhang, Tong; Yue, Qun-xing

2015-01-01

Vehicle Routing Problem (VRP) is one of the key issues in optimization of modern logistics system. In this paper, a modified VRP model with hard time window is established and a Hybrid Optimization Algorithm (HOA) based on Fractal Space Filling Curves (SFC) method and Genetic Algorithm (GA) is introduced. By incorporating the proposed algorithm, SFC method can find an initial and feasible solution very fast; GA is used to improve the initial solution. Thereafter, experimental software was developed and a large number of experimental computations from Solomon's benchmark have been studied. The experimental results demonstrate the feasibility and effectiveness of the HOA. PMID:26167171

Optimizing spread dynamics on graphs by message passing

NASA Astrophysics Data System (ADS)

Altarelli, F.; Braunstein, A.; Dall'Asta, L.; Zecchina, R.

2013-09-01

Cascade processes are responsible for many important phenomena in natural and social sciences. Simple models of irreversible dynamics on graphs, in which nodes activate depending on the state of their neighbors, have been successfully applied to describe cascades in a large variety of contexts. Over the past decades, much effort has been devoted to understanding the typical behavior of the cascades arising from initial conditions extracted at random from some given ensemble. However, the problem of optimizing the trajectory of the system, i.e. of identifying appropriate initial conditions to maximize (or minimize) the final number of active nodes, is still considered to be practically intractable, with the only exception being models that satisfy a sort of diminishing returns property called submodularity. Submodular models can be approximately solved by means of greedy strategies, but by definition they lack cooperative characteristics which are fundamental in many real systems. Here we introduce an efficient algorithm based on statistical physics for the optimization of trajectories in cascade processes on graphs. We show that for a wide class of irreversible dynamics, even in the absence of submodularity, the spread optimization problem can be solved efficiently on large networks. Analytic and algorithmic results on random graphs are complemented by the solution of the spread maximization problem on a real-world network (the Epinions consumer reviews network).

Optimization of Angular-Momentum Biases of Reaction Wheels

NASA Technical Reports Server (NTRS)

Lee, Clifford; Lee, Allan

2008-01-01

RBOT [RWA Bias Optimization Tool (wherein RWA signifies Reaction Wheel Assembly )] is a computer program designed for computing angular momentum biases for reaction wheels used for providing spacecraft pointing in various directions as required for scientific observations. RBOT is currently deployed to support the Cassini mission to prevent operation of reaction wheels at unsafely high speeds while minimizing time in undesirable low-speed range, where elasto-hydrodynamic lubrication films in bearings become ineffective, leading to premature bearing failure. The problem is formulated as a constrained optimization problem in which maximum wheel speed limit is a hard constraint and a cost functional that increases as speed decreases below a low-speed threshold. The optimization problem is solved using a parametric search routine known as the Nelder-Mead simplex algorithm. To increase computational efficiency for extended operation involving large quantity of data, the algorithm is designed to (1) use large time increments during intervals when spacecraft attitudes or rates of rotation are nearly stationary, (2) use sinusoidal-approximation sampling to model repeated long periods of Earth-point rolling maneuvers to reduce computational loads, and (3) utilize an efficient equation to obtain wheel-rate profiles as functions of initial wheel biases based on conservation of angular momentum (in an inertial frame) using pre-computed terms.

Robust Optimal Adaptive Control Method with Large Adaptive Gain

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.

2009-01-01

In the presence of large uncertainties, a control system needs to be able to adapt rapidly to regain performance. Fast adaptation is referred to the implementation of adaptive control with a large adaptive gain to reduce the tracking error rapidly. However, a large adaptive gain can lead to high-frequency oscillations which can adversely affect robustness of an adaptive control law. A new adaptive control modification is presented that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. The modification is based on the minimization of the Y2 norm of the tracking error, which is formulated as an optimal control problem. The optimality condition is used to derive the modification using the gradient method. The optimal control modification results in a stable adaptation and allows a large adaptive gain to be used for better tracking while providing sufficient stability robustness. Simulations were conducted for a damaged generic transport aircraft with both standard adaptive control and the adaptive optimal control modification technique. The results demonstrate the effectiveness of the proposed modification in tracking a reference model while maintaining a sufficient time delay margin.

Minimization of energy and surface roughness of the products machined by milling

NASA Astrophysics Data System (ADS)

Belloufi, A.; Abdelkrim, M.; Bouakba, M.; Rezgui, I.

2017-08-01

Metal cutting represents a large portion in the manufacturing industries, which makes this process the largest consumer of energy. Energy consumption is an indirect source of carbon footprint, we know that CO2 emissions come from the production of energy. Therefore high energy consumption requires a large production, which leads to high cost and a large amount of CO2 emissions. At this day, a lot of researches done on the Metal cutting, but the environmental problems of the processes are rarely discussed. The right selection of cutting parameters is an effective method to reduce energy consumption because of the direct relationship between energy consumption and cutting parameters in machining processes. Therefore, one of the objectives of this research is to propose an optimization strategy suitable for machining processes (milling) to achieve the optimum cutting conditions based on the criterion of the energy consumed during the milling. In this paper the problem of energy consumed in milling is solved by an optimization method chosen. The optimization is done according to the different requirements in the process of roughing and finishing under various technological constraints.

A multi-product green supply chain under government supervision with price and demand uncertainty

NASA Astrophysics Data System (ADS)

Hafezalkotob, Ashkan; Zamani, Soma

2018-05-01

In this paper, a bi-level game-theoretic model is proposed to investigate the effects of governmental financial intervention on green supply chain. This problem is formulated as a bi-level program for a green supply chain that produces various products with different environmental pollution levels. The problem is also regard uncertainties in market demand and sale price of raw materials and products. The model is further transformed into a single-level nonlinear programming problem by replacing the lower-level optimization problem with its Karush-Kuhn-Tucker optimality conditions. Genetic algorithm is applied as a solution methodology to solve nonlinear programming model. Finally, to investigate the validity of the proposed method, the computational results obtained through genetic algorithm are compared with global optimal solution attained by enumerative method. Analytical results indicate that the proposed GA offers better solutions in large size problems. Also, we conclude that financial intervention by government consists of green taxation and subsidization is an effective method to stabilize green supply chain members' performance.

Generating Data Flow Programs from Nonprocedural Specifications.

DTIC Science & Technology

1983-03-01

With the I-structures, Gajski points out, it is difficult to know ahead of time the optimal memory allocation scheme to pertition large arrays. amory...contention problems may occur for frequently accessed elements stored in the sam memory module. Gajski observes that these are the same problem which

On Improving Efficiency of Differential Evolution for Aerodynamic Shape Optimization Applications

NASA Technical Reports Server (NTRS)

Madavan, Nateri K.

2004-01-01

Differential Evolution (DE) is a simple and robust evolutionary strategy that has been provEn effective in determining the global optimum for several difficult optimization problems. Although DE offers several advantages over traditional optimization approaches, its use in applications such as aerodynamic shape optimization where the objective function evaluations are computationally expensive is limited by the large number of function evaluations often required. In this paper various approaches for improving the efficiency of DE are reviewed and discussed. Several approaches that have proven effective for other evolutionary algorithms are modified and implemented in a DE-based aerodynamic shape optimization method that uses a Navier-Stokes solver for the objective function evaluations. Parallelization techniques on distributed computers are used to reduce turnaround times. Results are presented for standard test optimization problems and for the inverse design of a turbine airfoil. The efficiency improvements achieved by the different approaches are evaluated and compared.

A modified generalized extremal optimization algorithm for the quay crane scheduling problem with interference constraints

NASA Astrophysics Data System (ADS)

Guo, Peng; Cheng, Wenming; Wang, Yi

2014-10-01

The quay crane scheduling problem (QCSP) determines the handling sequence of tasks at ship bays by a set of cranes assigned to a container vessel such that the vessel's service time is minimized. A number of heuristics or meta-heuristics have been proposed to obtain the near-optimal solutions to overcome the NP-hardness of the problem. In this article, the idea of generalized extremal optimization (GEO) is adapted to solve the QCSP with respect to various interference constraints. The resulting GEO is termed the modified GEO. A randomized searching method for neighbouring task-to-QC assignments to an incumbent task-to-QC assignment is developed in executing the modified GEO. In addition, a unidirectional search decoding scheme is employed to transform a task-to-QC assignment to an active quay crane schedule. The effectiveness of the developed GEO is tested on a suite of benchmark problems introduced by K.H. Kim and Y.M. Park in 2004 (European Journal of Operational Research, Vol. 156, No. 3). Compared with other well-known existing approaches, the experiment results show that the proposed modified GEO is capable of obtaining the optimal or near-optimal solution in a reasonable time, especially for large-sized problems.

Dynamic optimization of distributed biological systems using robust and efficient numerical techniques.

PubMed

Vilas, Carlos; Balsa-Canto, Eva; García, Maria-Sonia G; Banga, Julio R; Alonso, Antonio A

2012-07-02

Systems biology allows the analysis of biological systems behavior under different conditions through in silico experimentation. The possibility of perturbing biological systems in different manners calls for the design of perturbations to achieve particular goals. Examples would include, the design of a chemical stimulation to maximize the amplitude of a given cellular signal or to achieve a desired pattern in pattern formation systems, etc. Such design problems can be mathematically formulated as dynamic optimization problems which are particularly challenging when the system is described by partial differential equations.This work addresses the numerical solution of such dynamic optimization problems for spatially distributed biological systems. The usual nonlinear and large scale nature of the mathematical models related to this class of systems and the presence of constraints on the optimization problems, impose a number of difficulties, such as the presence of suboptimal solutions, which call for robust and efficient numerical techniques. Here, the use of a control vector parameterization approach combined with efficient and robust hybrid global optimization methods and a reduced order model methodology is proposed. The capabilities of this strategy are illustrated considering the solution of a two challenging problems: bacterial chemotaxis and the FitzHugh-Nagumo model. In the process of chemotaxis the objective was to efficiently compute the time-varying optimal concentration of chemotractant in one of the spatial boundaries in order to achieve predefined cell distribution profiles. Results are in agreement with those previously published in the literature. The FitzHugh-Nagumo problem is also efficiently solved and it illustrates very well how dynamic optimization may be used to force a system to evolve from an undesired to a desired pattern with a reduced number of actuators. The presented methodology can be used for the efficient dynamic optimization of generic distributed biological systems.

[Research on non-rigid registration of multi-modal medical image based on Demons algorithm].

PubMed

Hao, Peibo; Chen, Zhen; Jiang, Shaofeng; Wang, Yang

2014-02-01

Non-rigid medical image registration is a popular subject in the research areas of the medical image and has an important clinical value. In this paper we put forward an improved algorithm of Demons, together with the conservation of gray model and local structure tensor conservation model, to construct a new energy function processing multi-modal registration problem. We then applied the L-BFGS algorithm to optimize the energy function and solve complex three-dimensional data optimization problem. And finally we used the multi-scale hierarchical refinement ideas to solve large deformation registration. The experimental results showed that the proposed algorithm for large de formation and multi-modal three-dimensional medical image registration had good effects.

Optimization in the utility maximization framework for conservation planning: a comparison of solution procedures in a study of multifunctional agriculture

PubMed Central

Stoms, David M.; Davis, Frank W.

2014-01-01

Quantitative methods of spatial conservation prioritization have traditionally been applied to issues in conservation biology and reserve design, though their use in other types of natural resource management is growing. The utility maximization problem is one form of a covering problem where multiple criteria can represent the expected social benefits of conservation action. This approach allows flexibility with a problem formulation that is more general than typical reserve design problems, though the solution methods are very similar. However, few studies have addressed optimization in utility maximization problems for conservation planning, and the effect of solution procedure is largely unquantified. Therefore, this study mapped five criteria describing elements of multifunctional agriculture to determine a hypothetical conservation resource allocation plan for agricultural land conservation in the Central Valley of CA, USA. We compared solution procedures within the utility maximization framework to determine the difference between an open source integer programming approach and a greedy heuristic, and find gains from optimization of up to 12%. We also model land availability for conservation action as a stochastic process and determine the decline in total utility compared to the globally optimal set using both solution algorithms. Our results are comparable to other studies illustrating the benefits of optimization for different conservation planning problems, and highlight the importance of maximizing the effectiveness of limited funding for conservation and natural resource management. PMID:25538868

Optimization in the utility maximization framework for conservation planning: a comparison of solution procedures in a study of multifunctional agriculture

USGS Publications Warehouse

Kreitler, Jason R.; Stoms, David M.; Davis, Frank W.

2014-01-01

Quantitative methods of spatial conservation prioritization have traditionally been applied to issues in conservation biology and reserve design, though their use in other types of natural resource management is growing. The utility maximization problem is one form of a covering problem where multiple criteria can represent the expected social benefits of conservation action. This approach allows flexibility with a problem formulation that is more general than typical reserve design problems, though the solution methods are very similar. However, few studies have addressed optimization in utility maximization problems for conservation planning, and the effect of solution procedure is largely unquantified. Therefore, this study mapped five criteria describing elements of multifunctional agriculture to determine a hypothetical conservation resource allocation plan for agricultural land conservation in the Central Valley of CA, USA. We compared solution procedures within the utility maximization framework to determine the difference between an open source integer programming approach and a greedy heuristic, and find gains from optimization of up to 12%. We also model land availability for conservation action as a stochastic process and determine the decline in total utility compared to the globally optimal set using both solution algorithms. Our results are comparable to other studies illustrating the benefits of optimization for different conservation planning problems, and highlight the importance of maximizing the effectiveness of limited funding for conservation and natural resource management.

A staggered-grid finite-difference scheme optimized in the time–space domain for modeling scalar-wave propagation in geophysical problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tan, Sirui, E-mail: siruitan@hotmail.com; Huang, Lianjie, E-mail: ljh@lanl.gov

For modeling scalar-wave propagation in geophysical problems using finite-difference schemes, optimizing the coefficients of the finite-difference operators can reduce numerical dispersion. Most optimized finite-difference schemes for modeling seismic-wave propagation suppress only spatial but not temporal dispersion errors. We develop a novel optimized finite-difference scheme for numerical scalar-wave modeling to control dispersion errors not only in space but also in time. Our optimized scheme is based on a new stencil that contains a few more grid points than the standard stencil. We design an objective function for minimizing relative errors of phase velocities of waves propagating in all directions within amore » given range of wavenumbers. Dispersion analysis and numerical examples demonstrate that our optimized finite-difference scheme is computationally up to 2.5 times faster than the optimized schemes using the standard stencil to achieve the similar modeling accuracy for a given 2D or 3D problem. Compared with the high-order finite-difference scheme using the same new stencil, our optimized scheme reduces 50 percent of the computational cost to achieve the similar modeling accuracy. This new optimized finite-difference scheme is particularly useful for large-scale 3D scalar-wave modeling and inversion.« less

Maximum Margin Clustering of Hyperspectral Data

NASA Astrophysics Data System (ADS)

Niazmardi, S.; Safari, A.; Homayouni, S.

2013-09-01

In recent decades, large margin methods such as Support Vector Machines (SVMs) are supposed to be the state-of-the-art of supervised learning methods for classification of hyperspectral data. However, the results of these algorithms mainly depend on the quality and quantity of available training data. To tackle down the problems associated with the training data, the researcher put effort into extending the capability of large margin algorithms for unsupervised learning. One of the recent proposed algorithms is Maximum Margin Clustering (MMC). The MMC is an unsupervised SVMs algorithm that simultaneously estimates both the labels and the hyperplane parameters. Nevertheless, the optimization of the MMC algorithm is a non-convex problem. Most of the existing MMC methods rely on the reformulating and the relaxing of the non-convex optimization problem as semi-definite programs (SDP), which are computationally very expensive and only can handle small data sets. Moreover, most of these algorithms are two-class classification, which cannot be used for classification of remotely sensed data. In this paper, a new MMC algorithm is used that solve the original non-convex problem using Alternative Optimization method. This algorithm is also extended for multi-class classification and its performance is evaluated. The results of the proposed algorithm show that the algorithm has acceptable results for hyperspectral data clustering.

Optimal control in adaptive optics modeling of nonlinear systems

NASA Astrophysics Data System (ADS)

Herrmann, J.

The problem of using an adaptive optics system to correct for nonlinear effects like thermal blooming is addressed using a model containing nonlinear lenses through which Gaussian beams are propagated. The best correction of this nonlinear system can be formulated as a deterministic open loop optimal control problem. This treatment gives a limit for the best possible correction. Aspects of adaptive control and servo systems are not included at this stage. An attempt is made to determine that control in the transmitter plane which minimizes the time averaged area or maximizes the fluence in the target plane. The standard minimization procedure leads to a two-point-boundary-value problem, which is ill-conditioned in the case. The optimal control problem was solved using an iterative gradient technique. An instantaneous correction is introduced and compared with the optimal correction. The results of the calculations show that for short times or weak nonlinearities the instantaneous correction is close to the optimal correction, but that for long times and strong nonlinearities a large difference develops between the two types of correction. For these cases the steady state correction becomes better than the instantaneous correction and approaches the optimum correction.

Regularizing portfolio optimization

NASA Astrophysics Data System (ADS)

Still, Susanne; Kondor, Imre

2010-07-01

The optimization of large portfolios displays an inherent instability due to estimation error. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in effect, very far from optimal with respect to the average risk. In this paper, we approach the problem from the point of view of statistical learning theory. The occurrence of the instability is intimately related to over-fitting, which can be avoided using known regularization methods. We show how regularized portfolio optimization with the expected shortfall as a risk measure is related to support vector regression. The budget constraint dictates a modification. We present the resulting optimization problem and discuss the solution. The L2 norm of the weight vector is used as a regularizer, which corresponds to a diversification 'pressure'. This means that diversification, besides counteracting downward fluctuations in some assets by upward fluctuations in others, is also crucial because it improves the stability of the solution. The approach we provide here allows for the simultaneous treatment of optimization and diversification in one framework that enables the investor to trade off between the two, depending on the size of the available dataset.

Helping the decision maker effectively promote various experts' views into various optimal solutions to China's institutional problem of health care provider selection through the organization of a pilot health care provider research system.

PubMed

Tang, Liyang

2013-04-04

The main aim of China's Health Care System Reform was to help the decision maker find the optimal solution to China's institutional problem of health care provider selection. A pilot health care provider research system was recently organized in China's health care system, and it could efficiently collect the data for determining the optimal solution to China's institutional problem of health care provider selection from various experts, then the purpose of this study was to apply the optimal implementation methodology to help the decision maker effectively promote various experts' views into various optimal solutions to this problem under the support of this pilot system. After the general framework of China's institutional problem of health care provider selection was established, this study collaborated with the National Bureau of Statistics of China to commission a large-scale 2009 to 2010 national expert survey (n = 3,914) through the organization of a pilot health care provider research system for the first time in China, and the analytic network process (ANP) implementation methodology was adopted to analyze the dataset from this survey. The market-oriented health care provider approach was the optimal solution to China's institutional problem of health care provider selection from the doctors' point of view; the traditional government's regulation-oriented health care provider approach was the optimal solution to China's institutional problem of health care provider selection from the pharmacists' point of view, the hospital administrators' point of view, and the point of view of health officials in health administration departments; the public private partnership (PPP) approach was the optimal solution to China's institutional problem of health care provider selection from the nurses' point of view, the point of view of officials in medical insurance agencies, and the health care researchers' point of view. The data collected through a pilot health care provider research system in the 2009 to 2010 national expert survey could help the decision maker effectively promote various experts' views into various optimal solutions to China's institutional problem of health care provider selection.

Dynamic Flow Management Problems in Air Transportation

NASA Technical Reports Server (NTRS)

Patterson, Sarah Stock

1997-01-01

In 1995, over six hundred thousand licensed pilots flew nearly thirty-five million flights into over eighteen thousand U.S. airports, logging more than 519 billion passenger miles. Since demand for air travel has increased by more than 50% in the last decade while capacity has stagnated, congestion is a problem of undeniable practical significance. In this thesis, we will develop optimization techniques that reduce the impact of congestion on the national airspace. We start by determining the optimal release times for flights into the airspace and the optimal speed adjustment while airborne taking into account the capacitated airspace. This is called the Air Traffic Flow Management Problem (TFMP). We address the complexity, showing that it is NP-hard. We build an integer programming formulation that is quite strong as some of the proposed inequalities are facet defining for the convex hull of solutions. For practical problems, the solutions of the LP relaxation of the TFMP are very often integral. In essence, we reduce the problem to efficiently solving large scale linear programming problems. Thus, the computation times are reasonably small for large scale, practical problems involving thousands of flights. Next, we address the problem of determining how to reroute aircraft in the airspace system when faced with dynamically changing weather conditions. This is called the Air Traffic Flow Management Rerouting Problem (TFMRP) We present an integrated mathematical programming approach for the TFMRP, which utilizes several methodologies, in order to minimize delay costs. In order to address the high dimensionality, we present an aggregate model, in which we formulate the TFMRP as a multicommodity, integer, dynamic network flow problem with certain side constraints. Using Lagrangian relaxation, we generate aggregate flows that are decomposed into a collection of flight paths using a randomized rounding heuristic. This collection of paths is used in a packing integer programming formulation, the solution of which generates feasible and near-optimal routes for individual flights. The algorithm, termed the Lagrangian Generation Algorithm, is used to solve practical problems in the southwestern portion of United States in which the solutions are within 1% of the corresponding lower bounds.

Annual Review of Research Under the Joint Service Electronics Program.

DTIC Science & Technology

1979-10-01

Contents: Quadratic Optimization Problems; Nonlinear Control; Nonlinear Fault Analysis; Qualitative Analysis of Large Scale Systems; Multidimensional System Theory ; Optical Noise; and Pattern Recognition.

An Optimization-Based Method for Feature Ranking in Nonlinear Regression Problems.

PubMed

Bravi, Luca; Piccialli, Veronica; Sciandrone, Marco

2017-04-01

In this paper, we consider the feature ranking problem, where, given a set of training instances, the task is to associate a score with the features in order to assess their relevance. Feature ranking is a very important tool for decision support systems, and may be used as an auxiliary step of feature selection to reduce the high dimensionality of real-world data. We focus on regression problems by assuming that the process underlying the generated data can be approximated by a continuous function (for instance, a feedforward neural network). We formally state the notion of relevance of a feature by introducing a minimum zero-norm inversion problem of a neural network, which is a nonsmooth, constrained optimization problem. We employ a concave approximation of the zero-norm function, and we define a smooth, global optimization problem to be solved in order to assess the relevance of the features. We present the new feature ranking method based on the solution of instances of the global optimization problem depending on the available training data. Computational experiments on both artificial and real data sets are performed, and point out that the proposed feature ranking method is a valid alternative to existing methods in terms of effectiveness. The obtained results also show that the method is costly in terms of CPU time, and this may be a limitation in the solution of large-dimensional problems.

An electromagnetism-like metaheuristic for open-shop problems with no buffer

NASA Astrophysics Data System (ADS)

Naderi, Bahman; Najafi, Esmaeil; Yazdani, Mehdi

2012-12-01

This paper considers open-shop scheduling with no intermediate buffer to minimize total tardiness. This problem occurs in many production settings, in the plastic molding, chemical, and food processing industries. The paper mathematically formulates the problem by a mixed integer linear program. The problem can be optimally solved by the model. The paper also develops a novel metaheuristic based on an electromagnetism algorithm to solve the large-sized problems. The paper conducts two computational experiments. The first includes small-sized instances by which the mathematical model and general performance of the proposed metaheuristic are evaluated. The second evaluates the metaheuristic for its performance to solve some large-sized instances. The results show that the model and algorithm are effective to deal with the problem.

Joint optimization of green vehicle scheduling and routing problem with time-varying speeds

PubMed Central

Zhang, Dezhi; Wang, Xin; Ni, Nan; Zhang, Zhuo

2018-01-01

Based on an analysis of the congestion effect and changes in the speed of vehicle flow during morning and evening peaks in a large- or medium-sized city, the piecewise function is used to capture the rules of the time-varying speed of vehicles, which are very important in modelling their fuel consumption and CO2 emission. A joint optimization model of the green vehicle scheduling and routing problem with time-varying speeds is presented in this study. Extra wages during nonworking periods and soft time-window constraints are considered. A heuristic algorithm based on the adaptive large neighborhood search algorithm is also presented. Finally, a numerical simulation example is provided to illustrate the optimization model and its algorithm. Results show that, (1) the shortest route is not necessarily the route that consumes the least energy, (2) the departure time influences the vehicle fuel consumption and CO2 emissions and the optimal departure time saves on fuel consumption and reduces CO2 emissions by up to 5.4%, and (3) extra driver wages have significant effects on routing and departure time slot decisions. PMID:29466370

Joint optimization of green vehicle scheduling and routing problem with time-varying speeds.

PubMed

Zhang, Dezhi; Wang, Xin; Li, Shuangyan; Ni, Nan; Zhang, Zhuo

2018-01-01

Based on an analysis of the congestion effect and changes in the speed of vehicle flow during morning and evening peaks in a large- or medium-sized city, the piecewise function is used to capture the rules of the time-varying speed of vehicles, which are very important in modelling their fuel consumption and CO2 emission. A joint optimization model of the green vehicle scheduling and routing problem with time-varying speeds is presented in this study. Extra wages during nonworking periods and soft time-window constraints are considered. A heuristic algorithm based on the adaptive large neighborhood search algorithm is also presented. Finally, a numerical simulation example is provided to illustrate the optimization model and its algorithm. Results show that, (1) the shortest route is not necessarily the route that consumes the least energy, (2) the departure time influences the vehicle fuel consumption and CO2 emissions and the optimal departure time saves on fuel consumption and reduces CO2 emissions by up to 5.4%, and (3) extra driver wages have significant effects on routing and departure time slot decisions.

A Grouping Particle Swarm Optimizer with Personal-Best-Position Guidance for Large Scale Optimization.

PubMed

Guo, Weian; Si, Chengyong; Xue, Yu; Mao, Yanfen; Wang, Lei; Wu, Qidi

2017-05-04

Particle Swarm Optimization (PSO) is a popular algorithm which is widely investigated and well implemented in many areas. However, the canonical PSO does not perform well in population diversity maintenance so that usually leads to a premature convergence or local optima. To address this issue, we propose a variant of PSO named Grouping PSO with Personal- Best-Position (Pbest) Guidance (GPSO-PG) which maintains the population diversity by preserving the diversity of exemplars. On one hand, we adopt uniform random allocation strategy to assign particles into different groups and in each group the losers will learn from the winner. On the other hand, we employ personal historical best position of each particle in social learning rather than the current global best particle. In this way, the exemplars diversity increases and the effect from the global best particle is eliminated. We test the proposed algorithm to the benchmarks in CEC 2008 and CEC 2010, which concern the large scale optimization problems (LSOPs). By comparing several current peer algorithms, GPSO-PG exhibits a competitive performance to maintain population diversity and obtains a satisfactory performance to the problems.

Maximum Entropy/Optimal Projection (MEOP) control design synthesis: Optimal quantification of the major design tradeoffs

NASA Technical Reports Server (NTRS)

Hyland, D. C.; Bernstein, D. S.

1987-01-01

The underlying philosophy and motivation of the optimal projection/maximum entropy (OP/ME) stochastic modeling and reduced control design methodology for high order systems with parameter uncertainties are discussed. The OP/ME design equations for reduced-order dynamic compensation including the effect of parameter uncertainties are reviewed. The application of the methodology to several Large Space Structures (LSS) problems of representative complexity is illustrated.

Solving Large Problems with a Small Working Memory

ERIC Educational Resources Information Center

Pizlo, Zygmunt; Stefanov, Emil

2013-01-01

We describe an important elaboration of our multiscale/multiresolution model for solving the Traveling Salesman Problem (TSP). Our previous model emulated the non-uniform distribution of receptors on the human retina and the shifts of visual attention. This model produced near-optimal solutions of TSP in linear time by performing hierarchical…

Exploration of the Maximum Entropy/Optimal Projection Approach to Control Design Synthesis for Large Space Structures.

DTIC Science & Technology

1985-02-01

Energy Analysis , a branch of dynamic modal analysis developed for analyzing acoustic vibration problems, its present stage of development embodies a...Maximum Entropy Stochastic Modelling and Reduced-Order Design Synthesis is a rigorous new approach to this class of problems. Inspired by Statistical

Non Linear Programming (NLP) Formulation for Quantitative Modeling of Protein Signal Transduction Pathways

PubMed Central

Morris, Melody K.; Saez-Rodriguez, Julio; Lauffenburger, Douglas A.; Alexopoulos, Leonidas G.

2012-01-01

Modeling of signal transduction pathways plays a major role in understanding cells' function and predicting cellular response. Mathematical formalisms based on a logic formalism are relatively simple but can describe how signals propagate from one protein to the next and have led to the construction of models that simulate the cells response to environmental or other perturbations. Constrained fuzzy logic was recently introduced to train models to cell specific data to result in quantitative pathway models of the specific cellular behavior. There are two major issues in this pathway optimization: i) excessive CPU time requirements and ii) loosely constrained optimization problem due to lack of data with respect to large signaling pathways. Herein, we address both issues: the former by reformulating the pathway optimization as a regular nonlinear optimization problem; and the latter by enhanced algorithms to pre/post-process the signaling network to remove parts that cannot be identified given the experimental conditions. As a case study, we tackle the construction of cell type specific pathways in normal and transformed hepatocytes using medium and large-scale functional phosphoproteomic datasets. The proposed Non Linear Programming (NLP) formulation allows for fast optimization of signaling topologies by combining the versatile nature of logic modeling with state of the art optimization algorithms. PMID:23226239

Non Linear Programming (NLP) formulation for quantitative modeling of protein signal transduction pathways.

PubMed

Mitsos, Alexander; Melas, Ioannis N; Morris, Melody K; Saez-Rodriguez, Julio; Lauffenburger, Douglas A; Alexopoulos, Leonidas G

2012-01-01

Modeling of signal transduction pathways plays a major role in understanding cells' function and predicting cellular response. Mathematical formalisms based on a logic formalism are relatively simple but can describe how signals propagate from one protein to the next and have led to the construction of models that simulate the cells response to environmental or other perturbations. Constrained fuzzy logic was recently introduced to train models to cell specific data to result in quantitative pathway models of the specific cellular behavior. There are two major issues in this pathway optimization: i) excessive CPU time requirements and ii) loosely constrained optimization problem due to lack of data with respect to large signaling pathways. Herein, we address both issues: the former by reformulating the pathway optimization as a regular nonlinear optimization problem; and the latter by enhanced algorithms to pre/post-process the signaling network to remove parts that cannot be identified given the experimental conditions. As a case study, we tackle the construction of cell type specific pathways in normal and transformed hepatocytes using medium and large-scale functional phosphoproteomic datasets. The proposed Non Linear Programming (NLP) formulation allows for fast optimization of signaling topologies by combining the versatile nature of logic modeling with state of the art optimization algorithms.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baker, Kyri; Toomey, Bridget

Evolving power systems with increasing levels of stochasticity call for a need to solve optimal power flow problems with large quantities of random variables. Weather forecasts, electricity prices, and shifting load patterns introduce higher levels of uncertainty and can yield optimization problems that are difficult to solve in an efficient manner. Solution methods for single chance constraints in optimal power flow problems have been considered in the literature, ensuring single constraints are satisfied with a prescribed probability; however, joint chance constraints, ensuring multiple constraints are simultaneously satisfied, have predominantly been solved via scenario-based approaches or by utilizing Boole's inequality asmore » an upper bound. In this paper, joint chance constraints are used to solve an AC optimal power flow problem while preventing overvoltages in distribution grids under high penetrations of photovoltaic systems. A tighter version of Boole's inequality is derived and used to provide a new upper bound on the joint chance constraint, and simulation results are shown demonstrating the benefit of the proposed upper bound. The new framework allows for a less conservative and more computationally efficient solution to considering joint chance constraints, specifically regarding preventing overvoltages.« less

Efficiency Improvements to the Displacement Based Multilevel Structural Optimization Algorithm

NASA Technical Reports Server (NTRS)

Plunkett, C. L.; Striz, A. G.; Sobieszczanski-Sobieski, J.

2001-01-01

Multilevel Structural Optimization (MSO) continues to be an area of research interest in engineering optimization. In the present project, the weight optimization of beams and trusses using Displacement based Multilevel Structural Optimization (DMSO), a member of the MSO set of methodologies, is investigated. In the DMSO approach, the optimization task is subdivided into a single system and multiple subsystems level optimizations. The system level optimization minimizes the load unbalance resulting from the use of displacement functions to approximate the structural displacements. The function coefficients are then the design variables. Alternately, the system level optimization can be solved using the displacements themselves as design variables, as was shown in previous research. Both approaches ensure that the calculated loads match the applied loads. In the subsystems level, the weight of the structure is minimized using the element dimensions as design variables. The approach is expected to be very efficient for large structures, since parallel computing can be utilized in the different levels of the problem. In this paper, the method is applied to a one-dimensional beam and a large three-dimensional truss. The beam was tested to study possible simplifications to the system level optimization. In previous research, polynomials were used to approximate the global nodal displacements. The number of coefficients of the polynomials equally matched the number of degrees of freedom of the problem. Here it was desired to see if it is possible to only match a subset of the degrees of freedom in the system level. This would lead to a simplification of the system level, with a resulting increase in overall efficiency. However, the methods tested for this type of system level simplification did not yield positive results. The large truss was utilized to test further improvements in the efficiency of DMSO. In previous work, parallel processing was applied to the subsystems level, where the derivative verification feature of the optimizer NPSOL had been utilized in the optimizations. This resulted in large runtimes. In this paper, the optimizations were repeated without using the derivative verification, and the results are compared to those from the previous work. Also, the optimizations were run on both, a network of SUN workstations using the MPICH implementation of the Message Passing Interface (MPI) and on the faster Beowulf cluster at ICASE, NASA Langley Research Center, using the LAM implementation of UP]. The results on both systems were consistent and showed that it is not necessary to verify the derivatives and that this gives a large increase in efficiency of the DMSO algorithm.

Discrete optimal control approach to a four-dimensional guidance problem near terminal areas

NASA Technical Reports Server (NTRS)

Nagarajan, N.

1974-01-01

Description of a computer-oriented technique to generate the necessary control inputs to guide an aircraft in a given time from a given initial state to a prescribed final state subject to the constraints on airspeed, acceleration, and pitch and bank angles of the aircraft. A discrete-time mathematical model requiring five state variables and three control variables is obtained, assuming steady wind and zero sideslip. The guidance problem is posed as a discrete nonlinear optimal control problem with a cost functional of Bolza form. A solution technique for the control problem is investigated, and numerical examples are presented. It is believed that this approach should prove to be useful in automated air traffic control schemes near large terminal areas.

Strategic planning for disaster recovery with stochastic last mile distribution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bent, Russell Whitford; Van Hentenryck, Pascal; Coffrin, Carleton

2010-01-01

This paper considers the single commodity allocation problem (SCAP) for disaster recovery, a fundamental problem faced by all populated areas. SCAPs are complex stochastic optimization problems that combine resource allocation, warehouse routing, and parallel fleet routing. Moreover, these problems must be solved under tight runtime constraints to be practical in real-world disaster situations. This paper formalizes the specification of SCAPs and introduces a novel multi-stage hybrid-optimization algorithm that utilizes the strengths of mixed integer programming, constraint programming, and large neighborhood search. The algorithm was validated on hurricane disaster scenarios generated by Los Alamos National Laboratory using state-of-the-art disaster simulation toolsmore » and is deployed to aid federal organizations in the US.« less

Metamodeling and the Critic-based approach to multi-level optimization.

PubMed

Werbos, Ludmilla; Kozma, Robert; Silva-Lugo, Rodrigo; Pazienza, Giovanni E; Werbos, Paul J

2012-08-01

Large-scale networks with hundreds of thousands of variables and constraints are becoming more and more common in logistics, communications, and distribution domains. Traditionally, the utility functions defined on such networks are optimized using some variation of Linear Programming, such as Mixed Integer Programming (MIP). Despite enormous progress both in hardware (multiprocessor systems and specialized processors) and software (Gurobi) we are reaching the limits of what these tools can handle in real time. Modern logistic problems, for example, call for expanding the problem both vertically (from one day up to several days) and horizontally (combining separate solution stages into an integrated model). The complexity of such integrated models calls for alternative methods of solution, such as Approximate Dynamic Programming (ADP), which provide a further increase in the performance necessary for the daily operation. In this paper, we present the theoretical basis and related experiments for solving the multistage decision problems based on the results obtained for shorter periods, as building blocks for the models and the solution, via Critic-Model-Action cycles, where various types of neural networks are combined with traditional MIP models in a unified optimization system. In this system architecture, fast and simple feed-forward networks are trained to reasonably initialize more complicated recurrent networks, which serve as approximators of the value function (Critic). The combination of interrelated neural networks and optimization modules allows for multiple queries for the same system, providing flexibility and optimizing performance for large-scale real-life problems. A MATLAB implementation of our solution procedure for a realistic set of data and constraints shows promising results, compared to the iterative MIP approach. Copyright © 2012 Elsevier Ltd. All rights reserved.

The damper placement problem for large flexible space structures

NASA Technical Reports Server (NTRS)

Kincaid, Rex K.

1992-01-01

The damper placement problem for large flexible space truss structures is formulated as a combinatorial optimization problem. The objective is to determine the p truss members of the structure to replace with active (or passive) dampers so that the modal damping ratio is as large as possible for all significant modes of vibration. Equivalently, given a strain energy matrix with rows indexed on the modes and the columns indexed on the truss members, we seek to find the set of p columns such that the smallest row sum, over the p columns, is maximized. We develop a tabu search heuristic for the damper placement problems on the Controls Structures Interaction (CSI) Phase 1 Evolutionary Model (10 modes and 1507 truss members). The resulting solutions are shown to be of high quality.

A tabu search evalutionary algorithm for multiobjective optimization: Application to a bi-criterion aircraft structural reliability problem

NASA Astrophysics Data System (ADS)

Long, Kim Chenming

Real-world engineering optimization problems often require the consideration of multiple conflicting and noncommensurate objectives, subject to nonconvex constraint regions in a high-dimensional decision space. Further challenges occur for combinatorial multiobjective problems in which the decision variables are not continuous. Traditional multiobjective optimization methods of operations research, such as weighting and epsilon constraint methods, are ill-suited to solving these complex, multiobjective problems. This has given rise to the application of a wide range of metaheuristic optimization algorithms, such as evolutionary, particle swarm, simulated annealing, and ant colony methods, to multiobjective optimization. Several multiobjective evolutionary algorithms have been developed, including the strength Pareto evolutionary algorithm (SPEA) and the non-dominated sorting genetic algorithm (NSGA), for determining the Pareto-optimal set of non-dominated solutions. Although numerous researchers have developed a wide range of multiobjective optimization algorithms, there is a continuing need to construct computationally efficient algorithms with an improved ability to converge to globally non-dominated solutions along the Pareto-optimal front for complex, large-scale, multiobjective engineering optimization problems. This is particularly important when the multiple objective functions and constraints of the real-world system cannot be expressed in explicit mathematical representations. This research presents a novel metaheuristic evolutionary algorithm for complex multiobjective optimization problems, which combines the metaheuristic tabu search algorithm with the evolutionary algorithm (TSEA), as embodied in genetic algorithms. TSEA is successfully applied to bicriteria (i.e., structural reliability and retrofit cost) optimization of the aircraft tail structure fatigue life, which increases its reliability by prolonging fatigue life. A comparison for this application of the proposed algorithm, TSEA, with several state-of-the-art multiobjective optimization algorithms reveals that TSEA outperforms these algorithms by providing retrofit solutions with greater reliability for the same costs (i.e., closer to the Pareto-optimal front) after the algorithms are executed for the same number of generations. This research also demonstrates that TSEA competes with and, in some situations, outperforms state-of-the-art multiobjective optimization algorithms such as NSGA II and SPEA 2 when applied to classic bicriteria test problems in the technical literature and other complex, sizable real-world applications. The successful implementation of TSEA contributes to the safety of aeronautical structures by providing a systematic way to guide aircraft structural retrofitting efforts, as well as a potentially useful algorithm for a wide range of multiobjective optimization problems in engineering and other fields.

MDTS: automatic complex materials design using Monte Carlo tree search.

PubMed

M Dieb, Thaer; Ju, Shenghong; Yoshizoe, Kazuki; Hou, Zhufeng; Shiomi, Junichiro; Tsuda, Koji

2017-01-01

Complex materials design is often represented as a black-box combinatorial optimization problem. In this paper, we present a novel python library called MDTS (Materials Design using Tree Search). Our algorithm employs a Monte Carlo tree search approach, which has shown exceptional performance in computer Go game. Unlike evolutionary algorithms that require user intervention to set parameters appropriately, MDTS has no tuning parameters and works autonomously in various problems. In comparison to a Bayesian optimization package, our algorithm showed competitive search efficiency and superior scalability. We succeeded in designing large Silicon-Germanium (Si-Ge) alloy structures that Bayesian optimization could not deal with due to excessive computational cost. MDTS is available at https://github.com/tsudalab/MDTS.

MDTS: automatic complex materials design using Monte Carlo tree search

NASA Astrophysics Data System (ADS)

Dieb, Thaer M.; Ju, Shenghong; Yoshizoe, Kazuki; Hou, Zhufeng; Shiomi, Junichiro; Tsuda, Koji

2017-12-01

Complex materials design is often represented as a black-box combinatorial optimization problem. In this paper, we present a novel python library called MDTS (Materials Design using Tree Search). Our algorithm employs a Monte Carlo tree search approach, which has shown exceptional performance in computer Go game. Unlike evolutionary algorithms that require user intervention to set parameters appropriately, MDTS has no tuning parameters and works autonomously in various problems. In comparison to a Bayesian optimization package, our algorithm showed competitive search efficiency and superior scalability. We succeeded in designing large Silicon-Germanium (Si-Ge) alloy structures that Bayesian optimization could not deal with due to excessive computational cost. MDTS is available at https://github.com/tsudalab/MDTS.

Identification of mutated driver pathways in cancer using a multi-objective optimization model.

PubMed

Zheng, Chun-Hou; Yang, Wu; Chong, Yan-Wen; Xia, Jun-Feng

2016-05-01

New-generation high-throughput technologies, including next-generation sequencing technology, have been extensively applied to solve biological problems. As a result, large cancer genomics projects such as the Cancer Genome Atlas (TCGA) and the International Cancer Genome Consortium are producing large amount of rich and diverse data in multiple cancer types. The identification of mutated driver genes and driver pathways from these data is a significant challenge. Genome aberrations in cancer cells can be divided into two types: random 'passenger mutation' and functional 'driver mutation'. In this paper, we introduced a Multi-objective Optimization model based on a Genetic Algorithm (MOGA) to solve the maximum weight submatrix problem, which can be employed to identify driver genes and driver pathways promoting cancer proliferation. The maximum weight submatrix problem defined to find mutated driver pathways is based on two specific properties, i.e., high coverage and high exclusivity. The multi-objective optimization model can adjust the trade-off between high coverage and high exclusivity. We proposed an integrative model by combining gene expression data and mutation data to improve the performance of the MOGA algorithm in a biological context. Copyright © 2016 Elsevier Ltd. All rights reserved.

Optimal sensor placement for leak location in water distribution networks using genetic algorithms.

PubMed

Casillas, Myrna V; Puig, Vicenç; Garza-Castañón, Luis E; Rosich, Albert

2013-11-04

This paper proposes a new sensor placement approach for leak location in water distribution networks (WDNs). The sensor placement problem is formulated as an integer optimization problem. The optimization criterion consists in minimizing the number of non-isolable leaks according to the isolability criteria introduced. Because of the large size and non-linear integer nature of the resulting optimization problem, genetic algorithms (GAs) are used as the solution approach. The obtained results are compared with a semi-exhaustive search method with higher computational effort, proving that GA allows one to find near-optimal solutions with less computational load. Moreover, three ways of increasing the robustness of the GA-based sensor placement method have been proposed using a time horizon analysis, a distance-based scoring and considering different leaks sizes. A great advantage of the proposed methodology is that it does not depend on the isolation method chosen by the user, as long as it is based on leak sensitivity analysis. Experiments in two networks allow us to evaluate the performance of the proposed approach.

Optimal Sensor Placement for Leak Location in Water Distribution Networks Using Genetic Algorithms

PubMed Central

Casillas, Myrna V.; Puig, Vicenç; Garza-Castañón, Luis E.; Rosich, Albert

2013-01-01

This paper proposes a new sensor placement approach for leak location in water distribution networks (WDNs). The sensor placement problem is formulated as an integer optimization problem. The optimization criterion consists in minimizing the number of non-isolable leaks according to the isolability criteria introduced. Because of the large size and non-linear integer nature of the resulting optimization problem, genetic algorithms (GAs) are used as the solution approach. The obtained results are compared with a semi-exhaustive search method with higher computational effort, proving that GA allows one to find near-optimal solutions with less computational load. Moreover, three ways of increasing the robustness of the GA-based sensor placement method have been proposed using a time horizon analysis, a distance-based scoring and considering different leaks sizes. A great advantage of the proposed methodology is that it does not depend on the isolation method chosen by the user, as long as it is based on leak sensitivity analysis. Experiments in two networks allow us to evaluate the performance of the proposed approach. PMID:24193099

Integrated optimization of location assignment and sequencing in multi-shuttle automated storage and retrieval systems under modified 2n-command cycle pattern

NASA Astrophysics Data System (ADS)

Yang, Peng; Peng, Yongfei; Ye, Bin; Miao, Lixin

2017-09-01

This article explores the integrated optimization problem of location assignment and sequencing in multi-shuttle automated storage/retrieval systems under the modified 2n-command cycle pattern. The decision of storage and retrieval (S/R) location assignment and S/R request sequencing are jointly considered. An integer quadratic programming model is formulated to describe this integrated optimization problem. The optimal travel cycles for multi-shuttle S/R machines can be obtained to process S/R requests in the storage and retrieval request order lists by solving the model. The small-sized instances are optimally solved using CPLEX. For large-sized problems, two tabu search algorithms are proposed, in which the first come, first served and nearest neighbour are used to generate initial solutions. Various numerical experiments are conducted to examine the heuristics' performance and the sensitivity of algorithm parameters. Furthermore, the experimental results are analysed from the viewpoint of practical application, and a parameter list for applying the proposed heuristics is recommended under different real-life scenarios.

L2-norm multiple kernel learning and its application to biomedical data fusion

PubMed Central

2010-01-01

Background This paper introduces the notion of optimizing different norms in the dual problem of support vector machines with multiple kernels. The selection of norms yields different extensions of multiple kernel learning (MKL) such as L∞, L1, and L2 MKL. In particular, L2 MKL is a novel method that leads to non-sparse optimal kernel coefficients, which is different from the sparse kernel coefficients optimized by the existing L∞ MKL method. In real biomedical applications, L2 MKL may have more advantages over sparse integration method for thoroughly combining complementary information in heterogeneous data sources. Results We provide a theoretical analysis of the relationship between the L2 optimization of kernels in the dual problem with the L2 coefficient regularization in the primal problem. Understanding the dual L2 problem grants a unified view on MKL and enables us to extend the L2 method to a wide range of machine learning problems. We implement L2 MKL for ranking and classification problems and compare its performance with the sparse L∞ and the averaging L1 MKL methods. The experiments are carried out on six real biomedical data sets and two large scale UCI data sets. L2 MKL yields better performance on most of the benchmark data sets. In particular, we propose a novel L2 MKL least squares support vector machine (LSSVM) algorithm, which is shown to be an efficient and promising classifier for large scale data sets processing. Conclusions This paper extends the statistical framework of genomic data fusion based on MKL. Allowing non-sparse weights on the data sources is an attractive option in settings where we believe most data sources to be relevant to the problem at hand and want to avoid a "winner-takes-all" effect seen in L∞ MKL, which can be detrimental to the performance in prospective studies. The notion of optimizing L2 kernels can be straightforwardly extended to ranking, classification, regression, and clustering algorithms. To tackle the computational burden of MKL, this paper proposes several novel LSSVM based MKL algorithms. Systematic comparison on real data sets shows that LSSVM MKL has comparable performance as the conventional SVM MKL algorithms. Moreover, large scale numerical experiments indicate that when cast as semi-infinite programming, LSSVM MKL can be solved more efficiently than SVM MKL. Availability The MATLAB code of algorithms implemented in this paper is downloadable from http://homes.esat.kuleuven.be/~sistawww/bioi/syu/l2lssvm.html. PMID:20529363

The reduced space Sequential Quadratic Programming (SQP) method for calculating the worst resonance response of nonlinear systems

NASA Astrophysics Data System (ADS)

Liao, Haitao; Wu, Wenwang; Fang, Daining

2018-07-01

A coupled approach combining the reduced space Sequential Quadratic Programming (SQP) method with the harmonic balance condensation technique for finding the worst resonance response is developed. The nonlinear equality constraints of the optimization problem are imposed on the condensed harmonic balance equations. Making use of the null space decomposition technique, the original optimization formulation in the full space is mathematically simplified, and solved in the reduced space by means of the reduced SQP method. The transformation matrix that maps the full space to the null space of the constrained optimization problem is constructed via the coordinate basis scheme. The removal of the nonlinear equality constraints is accomplished, resulting in a simple optimization problem subject to bound constraints. Moreover, second order correction technique is introduced to overcome Maratos effect. The combination application of the reduced SQP method and condensation technique permits a large reduction of the computational cost. Finally, the effectiveness and applicability of the proposed methodology is demonstrated by two numerical examples.

Discrete homotopy analysis for optimal trading execution with nonlinear transient market impact

NASA Astrophysics Data System (ADS)

Curato, Gianbiagio; Gatheral, Jim; Lillo, Fabrizio

2016-10-01

Optimal execution in financial markets is the problem of how to trade a large quantity of shares incrementally in time in order to minimize the expected cost. In this paper, we study the problem of the optimal execution in the presence of nonlinear transient market impact. Mathematically such problem is equivalent to solve a strongly nonlinear integral equation, which in our model is a weakly singular Urysohn equation of the first kind. We propose an approach based on Homotopy Analysis Method (HAM), whereby a well behaved initial trading strategy is continuously deformed to lower the expected execution cost. Specifically, we propose a discrete version of the HAM, i.e. the DHAM approach, in order to use the method when the integrals to compute have no closed form solution. We find that the optimal solution is front loaded for concave instantaneous impact even when the investor is risk neutral. More important we find that the expected cost of the DHAM strategy is significantly smaller than the cost of conventional strategies.

Generalized SMO algorithm for SVM-based multitask learning.

PubMed

Cai, Feng; Cherkassky, Vladimir

2012-06-01

Exploiting additional information to improve traditional inductive learning is an active research area in machine learning. In many supervised-learning applications, training data can be naturally separated into several groups, and incorporating this group information into learning may improve generalization. Recently, Vapnik proposed a general approach to formalizing such problems, known as "learning with structured data" and its support vector machine (SVM) based optimization formulation called SVM+. Liang and Cherkassky showed the connection between SVM+ and multitask learning (MTL) approaches in machine learning, and proposed an SVM-based formulation for MTL called SVM+MTL for classification. Training the SVM+MTL classifier requires the solution of a large quadratic programming optimization problem which scales as O(n(3)) with sample size n. So there is a need to develop computationally efficient algorithms for implementing SVM+MTL. This brief generalizes Platt's sequential minimal optimization (SMO) algorithm to the SVM+MTL setting. Empirical results show that, for typical SVM+MTL problems, the proposed generalized SMO achieves over 100 times speed-up, in comparison with general-purpose optimization routines.

Optimization in optical systems revisited: Beyond genetic algorithms

NASA Astrophysics Data System (ADS)

Gagnon, Denis; Dumont, Joey; Dubé, Louis

2013-05-01

Designing integrated photonic devices such as waveguides, beam-splitters and beam-shapers often requires optimization of a cost function over a large solution space. Metaheuristics - algorithms based on empirical rules for exploring the solution space - are specifically tailored to those problems. One of the most widely used metaheuristics is the standard genetic algorithm (SGA), based on the evolution of a population of candidate solutions. However, the stochastic nature of the SGA sometimes prevents access to the optimal solution. Our goal is to show that a parallel tabu search (PTS) algorithm is more suited to optimization problems in general, and to photonics in particular. PTS is based on several search processes using a pool of diversified initial solutions. To assess the performance of both algorithms (SGA and PTS), we consider an integrated photonics design problem, the generation of arbitrary beam profiles using a two-dimensional waveguide-based dielectric structure. The authors acknowledge financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC).

Hybrid Microgrid Configuration Optimization with Evolutionary Algorithms

NASA Astrophysics Data System (ADS)

Lopez, Nicolas

This dissertation explores the Renewable Energy Integration Problem, and proposes a Genetic Algorithm embedded with a Monte Carlo simulation to solve large instances of the problem that are impractical to solve via full enumeration. The Renewable Energy Integration Problem is defined as finding the optimum set of components to supply the electric demand to a hybrid microgrid. The components considered are solar panels, wind turbines, diesel generators, electric batteries, connections to the power grid and converters, which can be inverters and/or rectifiers. The methodology developed is explained as well as the combinatorial formulation. In addition, 2 case studies of a single objective optimization version of the problem are presented, in order to minimize cost and to minimize global warming potential (GWP) followed by a multi-objective implementation of the offered methodology, by utilizing a non-sorting Genetic Algorithm embedded with a monte Carlo Simulation. The method is validated by solving a small instance of the problem with known solution via a full enumeration algorithm developed by NREL in their software HOMER. The dissertation concludes that the evolutionary algorithms embedded with Monte Carlo simulation namely modified Genetic Algorithms are an efficient form of solving the problem, by finding approximate solutions in the case of single objective optimization, and by approximating the true Pareto front in the case of multiple objective optimization of the Renewable Energy Integration Problem.

Effective optimization using sample persistence: A case study on quantum annealers and various Monte Carlo optimization methods

NASA Astrophysics Data System (ADS)

Karimi, Hamed; Rosenberg, Gili; Katzgraber, Helmut G.

2017-10-01

We present and apply a general-purpose, multistart algorithm for improving the performance of low-energy samplers used for solving optimization problems. The algorithm iteratively fixes the value of a large portion of the variables to values that have a high probability of being optimal. The resulting problems are smaller and less connected, and samplers tend to give better low-energy samples for these problems. The algorithm is trivially parallelizable since each start in the multistart algorithm is independent, and could be applied to any heuristic solver that can be run multiple times to give a sample. We present results for several classes of hard problems solved using simulated annealing, path-integral quantum Monte Carlo, parallel tempering with isoenergetic cluster moves, and a quantum annealer, and show that the success metrics and the scaling are improved substantially. When combined with this algorithm, the quantum annealer's scaling was substantially improved for native Chimera graph problems. In addition, with this algorithm the scaling of the time to solution of the quantum annealer is comparable to the Hamze-de Freitas-Selby algorithm on the weak-strong cluster problems introduced by Boixo et al. Parallel tempering with isoenergetic cluster moves was able to consistently solve three-dimensional spin glass problems with 8000 variables when combined with our method, whereas without our method it could not solve any.

Solving quantum optimal control problems using Clebsch variables and Lin constraints

NASA Astrophysics Data System (ADS)

Delgado-Téllez, M.; Ibort, A.; Rodríguez de la Peña, T.

2018-01-01

Clebsch variables (and Lin constraints) are applied to the study of a class of optimal control problems for affine-controlled quantum systems. The optimal control problem will be modelled with controls defined on an auxiliary space where the dynamical group of the system acts freely. The reciprocity between both theories: the classical theory defined by the objective functional and the quantum system, is established by using a suitable version of Lagrange’s multipliers theorem and a geometrical interpretation of the constraints of the system as defining a subspace of horizontal curves in an associated bundle. It is shown how the solutions of the variational problem defined by the objective functional determine solutions of the quantum problem. Then a new way of obtaining explicit solutions for a family of optimal control problems for affine-controlled quantum systems (finite or infinite dimensional) is obtained. One of its main advantages, is the the use of Clebsch variables allows to compute such solutions from solutions of invariant problems that can often be computed explicitly. This procedure can be presented as an algorithm that can be applied to a large class of systems. Finally, some simple examples, spin control, a simple quantum Hamiltonian with an ‘Elroy beanie’ type classical model and a controlled one-dimensional quantum harmonic oscillator, illustrating the main features of the theory, will be discussed.

Implementing and Bounding a Cascade Heuristic for Large-Scale Optimization

DTIC Science & Technology

2017-06-01

solving the monolith, we develop a method for producing lower bounds to the optimal objective function value. To do this, we solve a new integer...as developing and analyzing methods for producing lower bounds to the optimal objective function value of the seminal problem monolith, which this...length of the window decreases, the end effects of the model typically increase (Zerr, 2016). There are four primary methods for correcting end

Inference of Vohradský's Models of Genetic Networks by Solving Two-Dimensional Function Optimization Problems

PubMed Central

Kimura, Shuhei; Sato, Masanao; Okada-Hatakeyama, Mariko

2013-01-01

The inference of a genetic network is a problem in which mutual interactions among genes are inferred from time-series of gene expression levels. While a number of models have been proposed to describe genetic networks, this study focuses on a mathematical model proposed by Vohradský. Because of its advantageous features, several researchers have proposed the inference methods based on Vohradský's model. When trying to analyze large-scale networks consisting of dozens of genes, however, these methods must solve high-dimensional non-linear function optimization problems. In order to resolve the difficulty of estimating the parameters of the Vohradský's model, this study proposes a new method that defines the problem as several two-dimensional function optimization problems. Through numerical experiments on artificial genetic network inference problems, we showed that, although the computation time of the proposed method is not the shortest, the method has the ability to estimate parameters of Vohradský's models more effectively with sufficiently short computation times. This study then applied the proposed method to an actual inference problem of the bacterial SOS DNA repair system, and succeeded in finding several reasonable regulations. PMID:24386175

A global stochastic programming approach for the optimal placement of gas detectors with nonuniform unavailabilities

DOE PAGES

Liu, Jianfeng; Laird, Carl Damon

2017-09-22

Optimal design of a gas detection systems is challenging because of the numerous sources of uncertainty, including weather and environmental conditions, leak location and characteristics, and process conditions. Rigorous CFD simulations of dispersion scenarios combined with stochastic programming techniques have been successfully applied to the problem of optimal gas detector placement; however, rigorous treatment of sensor failure and nonuniform unavailability has received less attention. To improve reliability of the design, this paper proposes a problem formulation that explicitly considers nonuniform unavailabilities and all backup detection levels. The resulting sensor placement problem is a large-scale mixed-integer nonlinear programming (MINLP) problem thatmore » requires a tailored solution approach for efficient solution. We have developed a multitree method which depends on iteratively solving a sequence of upper-bounding master problems and lower-bounding subproblems. The tailored global solution strategy is tested on a real data problem and the encouraging numerical results indicate that our solution framework is promising in solving sensor placement problems. This study was selected for the special issue in JLPPI from the 2016 International Symposium of the MKO Process Safety Center.« less

A global stochastic programming approach for the optimal placement of gas detectors with nonuniform unavailabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Jianfeng; Laird, Carl Damon

Optimal design of a gas detection systems is challenging because of the numerous sources of uncertainty, including weather and environmental conditions, leak location and characteristics, and process conditions. Rigorous CFD simulations of dispersion scenarios combined with stochastic programming techniques have been successfully applied to the problem of optimal gas detector placement; however, rigorous treatment of sensor failure and nonuniform unavailability has received less attention. To improve reliability of the design, this paper proposes a problem formulation that explicitly considers nonuniform unavailabilities and all backup detection levels. The resulting sensor placement problem is a large-scale mixed-integer nonlinear programming (MINLP) problem thatmore » requires a tailored solution approach for efficient solution. We have developed a multitree method which depends on iteratively solving a sequence of upper-bounding master problems and lower-bounding subproblems. The tailored global solution strategy is tested on a real data problem and the encouraging numerical results indicate that our solution framework is promising in solving sensor placement problems. This study was selected for the special issue in JLPPI from the 2016 International Symposium of the MKO Process Safety Center.« less

Reliable and efficient solution of genome-scale models of Metabolism and macromolecular Expression

DOE PAGES

Ma, Ding; Yang, Laurence; Fleming, Ronan M. T.; ...

2017-01-18

Currently, Constraint-Based Reconstruction and Analysis (COBRA) is the only methodology that permits integrated modeling of Metabolism and macromolecular Expression (ME) at genome-scale. Linear optimization computes steady-state flux solutions to ME models, but flux values are spread over many orders of magnitude. Data values also have greatly varying magnitudes. Furthermore, standard double-precision solvers may return inaccurate solutions or report that no solution exists. Exact simplex solvers based on rational arithmetic require a near-optimal warm start to be practical on large problems (current ME models have 70,000 constraints and variables and will grow larger). We also developed a quadrupleprecision version of ourmore » linear and nonlinear optimizer MINOS, and a solution procedure (DQQ) involving Double and Quad MINOS that achieves reliability and efficiency for ME models and other challenging problems tested here. DQQ will enable extensive use of large linear and nonlinear models in systems biology and other applications involving multiscale data.« less

Methodologies for optimal resource allocation to the national space program and new space utilizations. Volume 1: Technical description

NASA Technical Reports Server (NTRS)

1971-01-01

The optimal allocation of resources to the national space program over an extended time period requires the solution of a large combinatorial problem in which the program elements are interdependent. The computer model uses an accelerated search technique to solve this problem. The model contains a large number of options selectable by the user to provide flexible input and a broad range of output for use in sensitivity analyses of all entering elements. Examples of these options are budget smoothing under varied appropriation levels, entry of inflation and discount effects, and probabilistic output which provides quantified degrees of certainty that program costs will remain within planned budget. Criteria and related analytic procedures were established for identifying potential new space program directions. Used in combination with the optimal resource allocation model, new space applications can be analyzed in realistic perspective, including the advantage gain from existing space program plant and on-going programs such as the space transportation system.

Reliable and efficient solution of genome-scale models of Metabolism and macromolecular Expression

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ma, Ding; Yang, Laurence; Fleming, Ronan M. T.

Currently, Constraint-Based Reconstruction and Analysis (COBRA) is the only methodology that permits integrated modeling of Metabolism and macromolecular Expression (ME) at genome-scale. Linear optimization computes steady-state flux solutions to ME models, but flux values are spread over many orders of magnitude. Data values also have greatly varying magnitudes. Furthermore, standard double-precision solvers may return inaccurate solutions or report that no solution exists. Exact simplex solvers based on rational arithmetic require a near-optimal warm start to be practical on large problems (current ME models have 70,000 constraints and variables and will grow larger). We also developed a quadrupleprecision version of ourmore » linear and nonlinear optimizer MINOS, and a solution procedure (DQQ) involving Double and Quad MINOS that achieves reliability and efficiency for ME models and other challenging problems tested here. DQQ will enable extensive use of large linear and nonlinear models in systems biology and other applications involving multiscale data.« less

Diffusion Monte Carlo approach versus adiabatic computation for local Hamiltonians

NASA Astrophysics Data System (ADS)

Bringewatt, Jacob; Dorland, William; Jordan, Stephen P.; Mink, Alan

2018-02-01

Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real non-negative amplitudes and thus for whom destructive interference is not manifest. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path-integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k -SAT problems, use k -local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n -body interactions. Here we present a 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.

Multidisciplinary optimization of a controlled space structure using 150 design variables

NASA Technical Reports Server (NTRS)

James, Benjamin B.

1993-01-01

A controls-structures interaction design method is presented. The method coordinates standard finite-element structural analysis, multivariable controls, and nonlinear programming codes and allows simultaneous optimization of the structure and control system of a spacecraft. Global sensitivity equations are used to account for coupling between the disciplines. Use of global sensitivity equations helps solve optimization problems that have a large number of design variables and a high degree of coupling between disciplines. The preliminary design of a generic geostationary platform is used to demonstrate the multidisciplinary optimization method. Design problems using 15, 63, and 150 design variables to optimize truss member sizes and feedback gain values are solved and the results are presented. The goal is to reduce the total mass of the structure and the vibration control system while satisfying constraints on vibration decay rate. Incorporation of the nonnegligible mass of actuators causes an essential coupling between structural design variables and control design variables.

A Multi-Verse Optimizer with Levy Flights for Numerical Optimization and Its Application in Test Scheduling for Network-on-Chip.

PubMed

Hu, Cong; Li, Zhi; Zhou, Tian; Zhu, Aijun; Xu, Chuanpei

2016-01-01

We propose a new meta-heuristic algorithm named Levy flights multi-verse optimizer (LFMVO), which incorporates Levy flights into multi-verse optimizer (MVO) algorithm to solve numerical and engineering optimization problems. The Original MVO easily falls into stagnation when wormholes stochastically re-span a number of universes (solutions) around the best universe achieved over the course of iterations. Since Levy flights are superior in exploring unknown, large-scale search space, they are integrated into the previous best universe to force MVO out of stagnation. We test this method on three sets of 23 well-known benchmark test functions and an NP complete problem of test scheduling for Network-on-Chip (NoC). Experimental results prove that the proposed LFMVO is more competitive than its peers in both the quality of the resulting solutions and convergence speed.

A Multi-Verse Optimizer with Levy Flights for Numerical Optimization and Its Application in Test Scheduling for Network-on-Chip

PubMed Central

Hu, Cong; Li, Zhi; Zhou, Tian; Zhu, Aijun; Xu, Chuanpei

2016-01-01

We propose a new meta-heuristic algorithm named Levy flights multi-verse optimizer (LFMVO), which incorporates Levy flights into multi-verse optimizer (MVO) algorithm to solve numerical and engineering optimization problems. The Original MVO easily falls into stagnation when wormholes stochastically re-span a number of universes (solutions) around the best universe achieved over the course of iterations. Since Levy flights are superior in exploring unknown, large-scale search space, they are integrated into the previous best universe to force MVO out of stagnation. We test this method on three sets of 23 well-known benchmark test functions and an NP complete problem of test scheduling for Network-on-Chip (NoC). Experimental results prove that the proposed LFMVO is more competitive than its peers in both the quality of the resulting solutions and convergence speed. PMID:27926946

Ordinal optimization and its application to complex deterministic problems

NASA Astrophysics Data System (ADS)

Yang, Mike Shang-Yu

1998-10-01

We present in this thesis a new perspective to approach a general class of optimization problems characterized by large deterministic complexities. Many problems of real-world concerns today lack analyzable structures and almost always involve high level of difficulties and complexities in the evaluation process. Advances in computer technology allow us to build computer models to simulate the evaluation process through numerical means, but the burden of high complexities remains to tax the simulation with an exorbitant computing cost for each evaluation. Such a resource requirement makes local fine-tuning of a known design difficult under most circumstances, let alone global optimization. Kolmogorov equivalence of complexity and randomness in computation theory is introduced to resolve this difficulty by converting the complex deterministic model to a stochastic pseudo-model composed of a simple deterministic component and a white-noise like stochastic term. The resulting randomness is then dealt with by a noise-robust approach called Ordinal Optimization. Ordinal Optimization utilizes Goal Softening and Ordinal Comparison to achieve an efficient and quantifiable selection of designs in the initial search process. The approach is substantiated by a case study in the turbine blade manufacturing process. The problem involves the optimization of the manufacturing process of the integrally bladed rotor in the turbine engines of U.S. Air Force fighter jets. The intertwining interactions among the material, thermomechanical, and geometrical changes makes the current FEM approach prohibitively uneconomical in the optimization process. The generalized OO approach to complex deterministic problems is applied here with great success. Empirical results indicate a saving of nearly 95% in the computing cost.

Use of multilevel modeling for determining optimal parameters of heat supply systems

NASA Astrophysics Data System (ADS)

Stennikov, V. A.; Barakhtenko, E. A.; Sokolov, D. V.

2017-07-01

The problem of finding optimal parameters of a heat-supply system (HSS) is in ensuring the required throughput capacity of a heat network by determining pipeline diameters and characteristics and location of pumping stations. Effective methods for solving this problem, i.e., the method of stepwise optimization based on the concept of dynamic programming and the method of multicircuit optimization, were proposed in the context of the hydraulic circuit theory developed at Melentiev Energy Systems Institute (Siberian Branch, Russian Academy of Sciences). These methods enable us to determine optimal parameters of various types of piping systems due to flexible adaptability of the calculation procedure to intricate nonlinear mathematical models describing features of used equipment items and methods of their construction and operation. The new and most significant results achieved in developing methodological support and software for finding optimal parameters of complex heat supply systems are presented: a new procedure for solving the problem based on multilevel decomposition of a heat network model that makes it possible to proceed from the initial problem to a set of interrelated, less cumbersome subproblems with reduced dimensionality; a new algorithm implementing the method of multicircuit optimization and focused on the calculation of a hierarchical model of a heat supply system; the SOSNA software system for determining optimum parameters of intricate heat-supply systems and implementing the developed methodological foundation. The proposed procedure and algorithm enable us to solve engineering problems of finding the optimal parameters of multicircuit heat supply systems having large (real) dimensionality, and are applied in solving urgent problems related to the optimal development and reconstruction of these systems. The developed methodological foundation and software can be used for designing heat supply systems in the Central and the Admiralty regions in St. Petersburg, the city of Bratsk, and the Magistral'nyi settlement.

Local Approximation and Hierarchical Methods for Stochastic Optimization

NASA Astrophysics Data System (ADS)

Cheng, Bolong

In this thesis, we present local and hierarchical approximation methods for two classes of stochastic optimization problems: optimal learning and Markov decision processes. For the optimal learning problem class, we introduce a locally linear model with radial basis function for estimating the posterior mean of the unknown objective function. The method uses a compact representation of the function which avoids storing the entire history, as is typically required by nonparametric methods. We derive a knowledge gradient policy with the locally parametric model, which maximizes the expected value of information. We show the policy is asymptotically optimal in theory, and experimental works suggests that the method can reliably find the optimal solution on a range of test functions. For the Markov decision processes problem class, we are motivated by an application where we want to co-optimize a battery for multiple revenue, in particular energy arbitrage and frequency regulation. The nature of this problem requires the battery to make charging and discharging decisions at different time scales while accounting for the stochastic information such as load demand, electricity prices, and regulation signals. Computing the exact optimal policy becomes intractable due to the large state space and the number of time steps. We propose two methods to circumvent the computation bottleneck. First, we propose a nested MDP model that structure the co-optimization problem into smaller sub-problems with reduced state space. This new model allows us to understand how the battery behaves down to the two-second dynamics (that of the frequency regulation market). Second, we introduce a low-rank value function approximation for backward dynamic programming. This new method only requires computing the exact value function for a small subset of the state space and approximate the entire value function via low-rank matrix completion. We test these methods on historical price data from the PJM Interconnect and show that it outperforms the baseline approach used in the industry.

Optimizing Balanced Incomplete Block Designs for Educational Assessments

ERIC Educational Resources Information Center

van der Linden, Wim J.; Veldkamp, Bernard P.; Carlson, James E.

2004-01-01

A popular design in large-scale educational assessments as well as any other type of survey is the balanced incomplete block design. The design is based on an item pool split into a set of blocks of items that are assigned to sets of "assessment booklets." This article shows how the problem of calculating an optimal balanced incomplete block…

Non-adaptive and adaptive hybrid approaches for enhancing water quality management

NASA Astrophysics Data System (ADS)

Kalwij, Ineke M.; Peralta, Richard C.

2008-09-01

SummaryUsing optimization to help solve groundwater management problems cost-effectively is becoming increasingly important. Hybrid optimization approaches, that combine two or more optimization algorithms, will become valuable and common tools for addressing complex nonlinear hydrologic problems. Hybrid heuristic optimizers have capabilities far beyond those of a simple genetic algorithm (SGA), and are continuously improving. SGAs having only parent selection, crossover, and mutation are inefficient and rarely used for optimizing contaminant transport management. Even an advanced genetic algorithm (AGA) that includes elitism (to emphasize using the best strategies as parents) and healing (to help assure optimal strategy feasibility) is undesirably inefficient. Much more efficient than an AGA is the presented hybrid (AGCT), which adds comprehensive tabu search (TS) features to an AGA. TS mechanisms (TS probability, tabu list size, search coarseness and solution space size, and a TS threshold value) force the optimizer to search portions of the solution space that yield superior pumping strategies, and to avoid reproducing similar or inferior strategies. An AGCT characteristic is that TS control parameters are unchanging during optimization. However, TS parameter values that are ideal for optimization commencement can be undesirable when nearing assumed global optimality. The second presented hybrid, termed global converger (GC), is significantly better than the AGCT. GC includes AGCT plus feedback-driven auto-adaptive control that dynamically changes TS parameters during run-time. Before comparing AGCT and GC, we empirically derived scaled dimensionless TS control parameter guidelines by evaluating 50 sets of parameter values for a hypothetical optimization problem. For the hypothetical area, AGCT optimized both well locations and pumping rates. The parameters are useful starting values because using trial-and-error to identify an ideal combination of control parameter values for a new optimization problem can be time consuming. For comparison, AGA, AGCT, and GC are applied to optimize pumping rates for assumed well locations of a complex large-scale contaminant transport and remediation optimization problem at Blaine Naval Ammunition Depot (NAD). Both hybrid approaches converged more closely to the optimal solution than the non-hybrid AGA. GC averaged 18.79% better convergence than AGCT, and 31.9% than AGA, within the same computation time (12.5 days). AGCT averaged 13.1% better convergence than AGA. The GC can significantly reduce the burden of employing computationally intensive hydrologic simulation models within a limited time period and for real-world optimization problems. Although demonstrated for a groundwater quality problem, it is also applicable to other arenas, such as managing salt water intrusion and surface water contaminant loading.

Two-Dimensional Crystallography Introduced by the Sprinkler Watering Problem

ERIC Educational Resources Information Center

De Toro, Jose A.; Calvo, Gabriel F.; Muniz, Pablo

2012-01-01

The problem of optimizing the number of circular sprinklers watering large fields is used to introduce, from a purely elementary geometrical perspective, some basic concepts in crystallography and comment on a few size effects in condensed matter physics. We examine square and hexagonal lattices to build a function describing the, so-called, dry…

Optimal placement of multiple types of communicating sensors with availability and coverage redundancy constraints

NASA Astrophysics Data System (ADS)

Vecherin, Sergey N.; Wilson, D. Keith; Pettit, Chris L.

2010-04-01

Determination of an optimal configuration (numbers, types, and locations) of a sensor network is an important practical problem. In most applications, complex signal propagation effects and inhomogeneous coverage preferences lead to an optimal solution that is highly irregular and nonintuitive. The general optimization problem can be strictly formulated as a binary linear programming problem. Due to the combinatorial nature of this problem, however, its strict solution requires significant computational resources (NP-complete class of complexity) and is unobtainable for large spatial grids of candidate sensor locations. For this reason, a greedy algorithm for approximate solution was recently introduced [S. N. Vecherin, D. K. Wilson, and C. L. Pettit, "Optimal sensor placement with terrain-based constraints and signal propagation effects," Unattended Ground, Sea, and Air Sensor Technologies and Applications XI, SPIE Proc. Vol. 7333, paper 73330S (2009)]. Here further extensions to the developed algorithm are presented to include such practical needs and constraints as sensor availability, coverage by multiple sensors, and wireless communication of the sensor information. Both communication and detection are considered in a probabilistic framework. Communication signal and signature propagation effects are taken into account when calculating probabilities of communication and detection. Comparison of approximate and strict solutions on reduced-size problems suggests that the approximate algorithm yields quick and good solutions, which thus justifies using that algorithm for full-size problems. Examples of three-dimensional outdoor sensor placement are provided using a terrain-based software analysis tool.

Applications of Derandomization Theory in Coding

NASA Astrophysics Data System (ADS)

Cheraghchi, Mahdi

2011-07-01

Randomized techniques play a fundamental role in theoretical computer science and discrete mathematics, in particular for the design of efficient algorithms and construction of combinatorial objects. The basic goal in derandomization theory is to eliminate or reduce the need for randomness in such randomized constructions. In this thesis, we explore some applications of the fundamental notions in derandomization theory to problems outside the core of theoretical computer science, and in particular, certain problems related to coding theory. First, we consider the wiretap channel problem which involves a communication system in which an intruder can eavesdrop a limited portion of the transmissions, and construct efficient and information-theoretically optimal communication protocols for this model. Then we consider the combinatorial group testing problem. In this classical problem, one aims to determine a set of defective items within a large population by asking a number of queries, where each query reveals whether a defective item is present within a specified group of items. We use randomness condensers to explicitly construct optimal, or nearly optimal, group testing schemes for a setting where the query outcomes can be highly unreliable, as well as the threshold model where a query returns positive if the number of defectives pass a certain threshold. Finally, we design ensembles of error-correcting codes that achieve the information-theoretic capacity of a large class of communication channels, and then use the obtained ensembles for construction of explicit capacity achieving codes. [This is a shortened version of the actual abstract in the thesis.

Discrete-time neural network for fast solving large linear L1 estimation problems and its application to image restoration.

PubMed

Xia, Youshen; Sun, Changyin; Zheng, Wei Xing

2012-05-01

There is growing interest in solving linear L1 estimation problems for sparsity of the solution and robustness against non-Gaussian noise. This paper proposes a discrete-time neural network which can calculate large linear L1 estimation problems fast. The proposed neural network has a fixed computational step length and is proved to be globally convergent to an optimal solution. Then, the proposed neural network is efficiently applied to image restoration. Numerical results show that the proposed neural network is not only efficient in solving degenerate problems resulting from the nonunique solutions of the linear L1 estimation problems but also needs much less computational time than the related algorithms in solving both linear L1 estimation and image restoration problems.

A Genetic Algorithm for Flow Shop Scheduling with Assembly Operations to Minimize Makespan

NASA Astrophysics Data System (ADS)

Bhongade, A. S.; Khodke, P. M.

2014-04-01

Manufacturing systems, in which, several parts are processed through machining workstations and later assembled to form final products, is common. Though scheduling of such problems are solved using heuristics, available solution approaches can provide solution for only moderate sized problems due to large computation time required. In this work, scheduling approach is developed for such flow-shop manufacturing system having machining workstations followed by assembly workstations. The initial schedule is generated using Disjunctive method and genetic algorithm (GA) is applied further for generating schedule for large sized problems. GA is found to give near optimal solution based on the deviation of makespan from lower bound. The lower bound of makespan of such problem is estimated and percent deviation of makespan from lower bounds is used as a performance measure to evaluate the schedules. Computational experiments are conducted on problems developed using fractional factorial orthogonal array, varying the number of parts per product, number of products, and number of workstations (ranging upto 1,520 number of operations). A statistical analysis indicated the significance of all the three factors considered. It is concluded that GA method can obtain optimal makespan.

Design optimization of steel frames using an enhanced firefly algorithm

NASA Astrophysics Data System (ADS)

Carbas, Serdar

2016-12-01

Mathematical modelling of real-world-sized steel frames under the Load and Resistance Factor Design-American Institute of Steel Construction (LRFD-AISC) steel design code provisions, where the steel profiles for the members are selected from a table of steel sections, turns out to be a discrete nonlinear programming problem. Finding the optimum design of such design optimization problems using classical optimization techniques is difficult. Metaheuristic algorithms provide an alternative way of solving such problems. The firefly algorithm (FFA) belongs to the swarm intelligence group of metaheuristics. The standard FFA has the drawback of being caught up in local optima in large-sized steel frame design problems. This study attempts to enhance the performance of the FFA by suggesting two new expressions for the attractiveness and randomness parameters of the algorithm. Two real-world-sized design examples are designed by the enhanced FFA and its performance is compared with standard FFA as well as with particle swarm and cuckoo search algorithms.

DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers

NASA Astrophysics Data System (ADS)

Mokhtari, Aryan; Shi, Wei; Ling, Qing; Ribeiro, Alejandro

2016-10-01

This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with neighbors only. A decentralized version of the alternating directions method of multipliers (DADMM) is a common method for solving this category of problems. DADMM exhibits linear convergence rate to the optimal objective but its implementation requires solving a convex optimization problem at each iteration. This can be computationally costly and may result in large overall convergence times. The decentralized quadratically approximated ADMM algorithm (DQM), which minimizes a quadratic approximation of the objective function that DADMM minimizes at each iteration, is proposed here. The consequent reduction in computational time is shown to have minimal effect on convergence properties. Convergence still proceeds at a linear rate with a guaranteed constant that is asymptotically equivalent to the DADMM linear convergence rate constant. Numerical results demonstrate advantages of DQM relative to DADMM and other alternatives in a logistic regression problem.

Million city traveling salesman problem solution by divide and conquer clustering with adaptive resonance neural networks.

PubMed

Mulder, Samuel A; Wunsch, Donald C

2003-01-01

The Traveling Salesman Problem (TSP) is a very hard optimization problem in the field of operations research. It has been shown to be NP-complete, and is an often-used benchmark for new optimization techniques. One of the main challenges with this problem is that standard, non-AI heuristic approaches such as the Lin-Kernighan algorithm (LK) and the chained LK variant are currently very effective and in wide use for the common fully connected, Euclidean variant that is considered here. This paper presents an algorithm that uses adaptive resonance theory (ART) in combination with a variation of the Lin-Kernighan local optimization algorithm to solve very large instances of the TSP. The primary advantage of this algorithm over traditional LK and chained-LK approaches is the increased scalability and parallelism allowed by the divide-and-conquer clustering paradigm. Tours obtained by the algorithm are lower quality, but scaling is much better and there is a high potential for increasing performance using parallel hardware.

Open shop scheduling problem to minimize total weighted completion time

NASA Astrophysics Data System (ADS)

Bai, Danyu; Zhang, Zhihai; Zhang, Qiang; Tang, Mengqian

2017-01-01

A given number of jobs in an open shop scheduling environment must each be processed for given amounts of time on each of a given set of machines in an arbitrary sequence. This study aims to achieve a schedule that minimizes total weighted completion time. Owing to the strong NP-hardness of the problem, the weighted shortest processing time block (WSPTB) heuristic is presented to obtain approximate solutions for large-scale problems. Performance analysis proves the asymptotic optimality of the WSPTB heuristic in the sense of probability limits. The largest weight block rule is provided to seek optimal schedules in polynomial time for a special case. A hybrid discrete differential evolution algorithm is designed to obtain high-quality solutions for moderate-scale problems. Simulation experiments demonstrate the effectiveness of the proposed algorithms.

Applications of fuzzy theories to multi-objective system optimization

NASA Technical Reports Server (NTRS)

Rao, S. S.; Dhingra, A. K.

1991-01-01

Most of the computer aided design techniques developed so far deal with the optimization of a single objective function over the feasible design space. However, there often exist several engineering design problems which require a simultaneous consideration of several objective functions. This work presents several techniques of multiobjective optimization. In addition, a new formulation, based on fuzzy theories, is also introduced for the solution of multiobjective system optimization problems. The fuzzy formulation is useful in dealing with systems which are described imprecisely using fuzzy terms such as, 'sufficiently large', 'very strong', or 'satisfactory'. The proposed theory translates the imprecise linguistic statements and multiple objectives into equivalent crisp mathematical statements using fuzzy logic. The effectiveness of all the methodologies and theories presented is illustrated by formulating and solving two different engineering design problems. The first one involves the flight trajectory optimization and the main rotor design of helicopters. The second one is concerned with the integrated kinematic-dynamic synthesis of planar mechanisms. The use and effectiveness of nonlinear membership functions in fuzzy formulation is also demonstrated. The numerical results indicate that the fuzzy formulation could yield results which are qualitatively different from those provided by the crisp formulation. It is felt that the fuzzy formulation will handle real life design problems on a more rational basis.

Portable parallel stochastic optimization for the design of aeropropulsion components

NASA Technical Reports Server (NTRS)

Sues, Robert H.; Rhodes, G. S.

1994-01-01

This report presents the results of Phase 1 research to develop a methodology for performing large-scale Multi-disciplinary Stochastic Optimization (MSO) for the design of aerospace systems ranging from aeropropulsion components to complete aircraft configurations. The current research recognizes that such design optimization problems are computationally expensive, and require the use of either massively parallel or multiple-processor computers. The methodology also recognizes that many operational and performance parameters are uncertain, and that uncertainty must be considered explicitly to achieve optimum performance and cost. The objective of this Phase 1 research was to initialize the development of an MSO methodology that is portable to a wide variety of hardware platforms, while achieving efficient, large-scale parallelism when multiple processors are available. The first effort in the project was a literature review of available computer hardware, as well as review of portable, parallel programming environments. The first effort was to implement the MSO methodology for a problem using the portable parallel programming language, Parallel Virtual Machine (PVM). The third and final effort was to demonstrate the example on a variety of computers, including a distributed-memory multiprocessor, a distributed-memory network of workstations, and a single-processor workstation. Results indicate the MSO methodology can be well-applied towards large-scale aerospace design problems. Nearly perfect linear speedup was demonstrated for computation of optimization sensitivity coefficients on both a 128-node distributed-memory multiprocessor (the Intel iPSC/860) and a network of workstations (speedups of almost 19 times achieved for 20 workstations). Very high parallel efficiencies (75 percent for 31 processors and 60 percent for 50 processors) were also achieved for computation of aerodynamic influence coefficients on the Intel. Finally, the multi-level parallelization strategy that will be needed for large-scale MSO problems was demonstrated to be highly efficient. The same parallel code instructions were used on both platforms, demonstrating portability. There are many applications for which MSO can be applied, including NASA's High-Speed-Civil Transport, and advanced propulsion systems. The use of MSO will reduce design and development time and testing costs dramatically.

Collective Framework and Performance Optimizations to Open MPI for Cray XT Platforms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ladd, Joshua S; Gorentla Venkata, Manjunath; Shamis, Pavel

2011-01-01

The performance and scalability of collective operations plays a key role in the performance and scalability of many scientific applications. Within the Open MPI code base we have developed a general purpose hierarchical collective operations framework called Cheetah, and applied it at large scale on the Oak Ridge Leadership Computing Facility's Jaguar (OLCF) platform, obtaining better performance and scalability than the native MPI implementation. This paper discuss Cheetah's design and implementation, and optimizations to the framework for Cray XT 5 platforms. Our results show that the Cheetah's Broadcast and Barrier perform better than the native MPI implementation. For medium data,more » the Cheetah's Broadcast outperforms the native MPI implementation by 93% for 49,152 processes problem size. For small and large data, it out performs the native MPI implementation by 10% and 9%, respectively, at 24,576 processes problem size. The Cheetah's Barrier performs 10% better than the native MPI implementation for 12,288 processes problem size.« less

Multitrace/singletrace formulations and Domain Decomposition Methods for the solution of Helmholtz transmission problems for bounded composite scatterers

NASA Astrophysics Data System (ADS)

Jerez-Hanckes, Carlos; Pérez-Arancibia, Carlos; Turc, Catalin

2017-12-01

We present Nyström discretizations of multitrace/singletrace formulations and non-overlapping Domain Decomposition Methods (DDM) for the solution of Helmholtz transmission problems for bounded composite scatterers with piecewise constant material properties. We investigate the performance of DDM with both classical Robin and optimized transmission boundary conditions. The optimized transmission boundary conditions incorporate square root Fourier multiplier approximations of Dirichlet to Neumann operators. While the multitrace/singletrace formulations as well as the DDM that use classical Robin transmission conditions are not particularly well suited for Krylov subspace iterative solutions of high-contrast high-frequency Helmholtz transmission problems, we provide ample numerical evidence that DDM with optimized transmission conditions constitute efficient computational alternatives for these type of applications. In the case of large numbers of subdomains with different material properties, we show that the associated DDM linear system can be efficiently solved via hierarchical Schur complements elimination.

From Physics Model to Results: An Optimizing Framework for Cross-Architecture Code Generation

DOE PAGES

Blazewicz, Marek; Hinder, Ian; Koppelman, David M.; ...

2013-01-01

Starting from a high-level problem description in terms of partial differential equations using abstract tensor notation, the Chemora framework discretizes, optimizes, and generates complete high performance codes for a wide range of compute architectures. Chemora extends the capabilities of Cactus, facilitating the usage of large-scale CPU/GPU systems in an efficient manner for complex applications, without low-level code tuning. Chemora achieves parallelism through MPI and multi-threading, combining OpenMP and CUDA. Optimizations include high-level code transformations, efficient loop traversal strategies, dynamically selected data and instruction cache usage strategies, and JIT compilation of GPU code tailored to the problem characteristics. The discretization ismore » based on higher-order finite differences on multi-block domains. Chemora's capabilities are demonstrated by simulations of black hole collisions. This problem provides an acid test of the framework, as the Einstein equations contain hundreds of variables and thousands of terms.« less

Layout optimization with algebraic multigrid methods

NASA Technical Reports Server (NTRS)

Regler, Hans; Ruede, Ulrich

1993-01-01

Finding the optimal position for the individual cells (also called functional modules) on the chip surface is an important and difficult step in the design of integrated circuits. This paper deals with the problem of relative placement, that is the minimization of a quadratic functional with a large, sparse, positive definite system matrix. The basic optimization problem must be augmented by constraints to inhibit solutions where cells overlap. Besides classical iterative methods, based on conjugate gradients (CG), we show that algebraic multigrid methods (AMG) provide an interesting alternative. For moderately sized examples with about 10000 cells, AMG is already competitive with CG and is expected to be superior for larger problems. Besides the classical 'multiplicative' AMG algorithm where the levels are visited sequentially, we propose an 'additive' variant of AMG where levels may be treated in parallel and that is suitable as a preconditioner in the CG algorithm.

Optimization of memory use of fragment extension-based protein-ligand docking with an original fast minimum cost flow algorithm.

PubMed

Yanagisawa, Keisuke; Komine, Shunta; Kubota, Rikuto; Ohue, Masahito; Akiyama, Yutaka

2018-06-01

The need to accelerate large-scale protein-ligand docking in virtual screening against a huge compound database led researchers to propose a strategy that entails memorizing the evaluation result of the partial structure of a compound and reusing it to evaluate other compounds. However, the previous method required frequent disk accesses, resulting in insufficient acceleration. Thus, more efficient memory usage can be expected to lead to further acceleration, and optimal memory usage could be achieved by solving the minimum cost flow problem. In this research, we propose a fast algorithm for the minimum cost flow problem utilizing the characteristics of the graph generated for this problem as constraints. The proposed algorithm, which optimized memory usage, was approximately seven times faster compared to existing minimum cost flow algorithms. Copyright © 2018 The Authors. Published by Elsevier Ltd.. All rights reserved.

Solving geosteering inverse problems by stochastic Hybrid Monte Carlo method

DOE PAGES

Shen, Qiuyang; Wu, Xuqing; Chen, Jiefu; ...

2017-11-20

The inverse problems arise in almost all fields of science where the real-world parameters are extracted from a set of measured data. The geosteering inversion plays an essential role in the accurate prediction of oncoming strata as well as a reliable guidance to adjust the borehole position on the fly to reach one or more geological targets. This mathematical treatment is not easy to solve, which requires finding an optimum solution among a large solution space, especially when the problem is non-linear and non-convex. Nowadays, a new generation of logging-while-drilling (LWD) tools has emerged on the market. The so-called azimuthalmore » resistivity LWD tools have azimuthal sensitivity and a large depth of investigation. Hence, the associated inverse problems become much more difficult since the earth model to be inverted will have more detailed structures. The conventional deterministic methods are incapable to solve such a complicated inverse problem, where they suffer from the local minimum trap. Alternatively, stochastic optimizations are in general better at finding global optimal solutions and handling uncertainty quantification. In this article, we investigate the Hybrid Monte Carlo (HMC) based statistical inversion approach and suggest that HMC based inference is more efficient in dealing with the increased complexity and uncertainty faced by the geosteering problems.« less

Conditional nonlinear optimal perturbations based on the particle swarm optimization and their applications to the predictability problems

NASA Astrophysics Data System (ADS)

Zheng, Qin; Yang, Zubin; Sha, Jianxin; Yan, Jun

2017-02-01

In predictability problem research, the conditional nonlinear optimal perturbation (CNOP) describes the initial perturbation that satisfies a certain constraint condition and causes the largest prediction error at the prediction time. The CNOP has been successfully applied in estimation of the lower bound of maximum predictable time (LBMPT). Generally, CNOPs are calculated by a gradient descent algorithm based on the adjoint model, which is called ADJ-CNOP. This study, through the two-dimensional Ikeda model, investigates the impacts of the nonlinearity on ADJ-CNOP and the corresponding precision problems when using ADJ-CNOP to estimate the LBMPT. Our conclusions are that (1) when the initial perturbation is large or the prediction time is long, the strong nonlinearity of the dynamical model in the prediction variable will lead to failure of the ADJ-CNOP method, and (2) when the objective function has multiple extreme values, ADJ-CNOP has a large probability of producing local CNOPs, hence making a false estimation of the LBMPT. Furthermore, the particle swarm optimization (PSO) algorithm, one kind of intelligent algorithm, is introduced to solve this problem. The method using PSO to compute CNOP is called PSO-CNOP. The results of numerical experiments show that even with a large initial perturbation and long prediction time, or when the objective function has multiple extreme values, PSO-CNOP can always obtain the global CNOP. Since the PSO algorithm is a heuristic search algorithm based on the population, it can overcome the impact of nonlinearity and the disturbance from multiple extremes of the objective function. In addition, to check the estimation accuracy of the LBMPT presented by PSO-CNOP and ADJ-CNOP, we partition the constraint domain of initial perturbations into sufficiently fine grid meshes and take the LBMPT obtained by the filtering method as a benchmark. The result shows that the estimation presented by PSO-CNOP is closer to the true value than the one by ADJ-CNOP with the forecast time increasing.

Exact parallel algorithms for some members of the traveling salesman problem family

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pekny, J.F.

1989-01-01

The traveling salesman problem and its many generalizations comprise one of the best known combinatorial optimization problem families. Most members of the family are NP-complete problems so that exact algorithms require an unpredictable and sometimes large computational effort. Parallel computers offer hope for providing the power required to meet these demands. A major barrier to applying parallel computers is the lack of parallel algorithms. The contributions presented in this thesis center around new exact parallel algorithms for the asymmetric traveling salesman problem (ATSP), prize collecting traveling salesman problem (PCTSP), and resource constrained traveling salesman problem (RCTSP). The RCTSP is amore » particularly difficult member of the family since finding a feasible solution is an NP-complete problem. An exact sequential algorithm is also presented for the directed hamiltonian cycle problem (DHCP). The DHCP algorithm is superior to current heuristic approaches and represents the first exact method applicable to large graphs. Computational results presented for each of the algorithms demonstrates the effectiveness of combining efficient algorithms with parallel computing methods. Performance statistics are reported for randomly generated ATSPs with 7,500 cities, PCTSPs with 200 cities, RCTSPs with 200 cities, DHCPs with 3,500 vertices, and assignment problems of size 10,000. Sequential results were collected on a Sun 4/260 engineering workstation, while parallel results were collected using a 14 and 100 processor BBN Butterfly Plus computer. The computational results represent the largest instances ever solved to optimality on any type of computer.« less

Hybrid Quantum-Classical Approach to Quantum Optimal Control.

PubMed

Li, Jun; Yang, Xiaodong; Peng, Xinhua; Sun, Chang-Pu

2017-04-14

A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid quantum-classical scheme to tackle the quantum optimal control problem. We show that the most computationally demanding part of gradient-based algorithms, namely, computing the fitness function and its gradient for a control input, can be accomplished by the process of evolution and measurement on a quantum simulator. By posing queries to and receiving answers from the quantum simulator, classical computing devices update the control parameters until an optimal control solution is found. To demonstrate the quantum-classical scheme in experiment, we use a seven-qubit nuclear magnetic resonance system, on which we have succeeded in optimizing state preparation without involving classical computation of the large Hilbert space evolution.

Helping the decision maker effectively promote various experts’ views into various optimal solutions to China’s institutional problem of health care provider selection through the organization of a pilot health care provider research system

PubMed Central

2013-01-01

Background The main aim of China’s Health Care System Reform was to help the decision maker find the optimal solution to China’s institutional problem of health care provider selection. A pilot health care provider research system was recently organized in China’s health care system, and it could efficiently collect the data for determining the optimal solution to China’s institutional problem of health care provider selection from various experts, then the purpose of this study was to apply the optimal implementation methodology to help the decision maker effectively promote various experts’ views into various optimal solutions to this problem under the support of this pilot system. Methods After the general framework of China’s institutional problem of health care provider selection was established, this study collaborated with the National Bureau of Statistics of China to commission a large-scale 2009 to 2010 national expert survey (n = 3,914) through the organization of a pilot health care provider research system for the first time in China, and the analytic network process (ANP) implementation methodology was adopted to analyze the dataset from this survey. Results The market-oriented health care provider approach was the optimal solution to China’s institutional problem of health care provider selection from the doctors’ point of view; the traditional government’s regulation-oriented health care provider approach was the optimal solution to China’s institutional problem of health care provider selection from the pharmacists’ point of view, the hospital administrators’ point of view, and the point of view of health officials in health administration departments; the public private partnership (PPP) approach was the optimal solution to China’s institutional problem of health care provider selection from the nurses’ point of view, the point of view of officials in medical insurance agencies, and the health care researchers’ point of view. Conclusions The data collected through a pilot health care provider research system in the 2009 to 2010 national expert survey could help the decision maker effectively promote various experts’ views into various optimal solutions to China’s institutional problem of health care provider selection. PMID:23557082

The 2-D magnetotelluric inverse problem solved with optimization

NASA Astrophysics Data System (ADS)

van Beusekom, Ashley E.; Parker, Robert L.; Bank, Randolph E.; Gill, Philip E.; Constable, Steven

2011-02-01

The practical 2-D magnetotelluric inverse problem seeks to determine the shallow-Earth conductivity structure using finite and uncertain data collected on the ground surface. We present an approach based on using PLTMG (Piecewise Linear Triangular MultiGrid), a special-purpose code for optimization with second-order partial differential equation (PDE) constraints. At each frequency, the electromagnetic field and conductivity are treated as unknowns in an optimization problem in which the data misfit is minimized subject to constraints that include Maxwell's equations and the boundary conditions. Within this framework it is straightforward to accommodate upper and lower bounds or other conditions on the conductivity. In addition, as the underlying inverse problem is ill-posed, constraints may be used to apply various kinds of regularization. We discuss some of the advantages and difficulties associated with using PDE-constrained optimization as the basis for solving large-scale nonlinear geophysical inverse problems. Combined transverse electric and transverse magnetic complex admittances from the COPROD2 data are inverted. First, we invert penalizing size and roughness giving solutions that are similar to those found previously. In a second example, conventional regularization is replaced by a technique that imposes upper and lower bounds on the model. In both examples the data misfit is better than that obtained previously, without any increase in model complexity.

Design Optimization Toolkit: Users' Manual

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aguilo Valentin, Miguel Alejandro

The Design Optimization Toolkit (DOTk) is a stand-alone C++ software package intended to solve complex design optimization problems. DOTk software package provides a range of solution methods that are suited for gradient/nongradient-based optimization, large scale constrained optimization, and topology optimization. DOTk was design to have a flexible user interface to allow easy access to DOTk solution methods from external engineering software packages. This inherent flexibility makes DOTk barely intrusive to other engineering software packages. As part of this inherent flexibility, DOTk software package provides an easy-to-use MATLAB interface that enables users to call DOTk solution methods directly from the MATLABmore » command window.« less

Meshless methods in shape optimization of linear elastic and thermoelastic solids

NASA Astrophysics Data System (ADS)

Bobaru, Florin

This dissertation proposes a meshless approach to problems in shape optimization of elastic and thermoelastic solids. The Element-free Galerkin (EFG) method is used for this purpose. The ability of the EFG to avoid remeshing, that is normally done in a Finite Element approach to correct highly distorted meshes, is clearly demonstrated by several examples. The shape optimization example of a thermal cooling fin shows a dramatic improvement in the objective compared to a previous FEM analysis. More importantly, the new solution, displaying large shape changes contrasted to the initial design, was completely missed by the FEM analysis. The EFG formulation given here for shape optimization "uncovers" new solutions that are, apparently, unobtainable via a FEM approach. This is one of the main achievements of our work. The variational formulations for the analysis problem and for the sensitivity problems are obtained with a penalty method for imposing the displacement boundary conditions. The continuum formulation is general and this facilitates 2D and 3D with minor differences from one another. Also, transient thermoelastic problems can use the present development at each time step to solve shape optimization problems for time-dependent thermal problems. For the elasticity framework, displacement sensitivity is obtained in the EFG context. Excellent agreements with analytical solutions for some test problems are obtained. The shape optimization of a fillet is carried out in great detail, and results show significant improvement of the EFG solution over the FEM or the Boundary Element Method solutions. In our approach we avoid differentiating the complicated EFG shape functions, with respect to the shape design parameters, by using a particular discretization for sensitivity calculations. Displacement and temperature sensitivities are formulated for the shape optimization of a linear thermoelastic solid. Two important examples considered in this work, the optimization of a thermal fin and of a uniformly loaded thermoelastic beam, reveal new characteristics of the EFG method in shape optimization applications. Among other advantages of the EFG method over traditional FEM treatments of shape optimization problems, some of the most important ones are shown to be: elimination of post-processing for stress and strain recovery that directly gives more accurate results in critical positions (near the boundaries, for example) for shape optimization problems; nodes movement flexibility that permits new, better shapes (previously missed by an FEM analysis) to be discovered. Several new research directions that need further consideration are exposed.

Optimal parameter estimation with a fixed rate of abstention

NASA Astrophysics Data System (ADS)

Gendra, B.; Ronco-Bonvehi, E.; Calsamiglia, J.; Muñoz-Tapia, R.; Bagan, E.

2013-07-01

The problems of optimally estimating a phase, a direction, and the orientation of a Cartesian frame (or trihedron) with general pure states are addressed. Special emphasis is put on estimation schemes that allow for inconclusive answers or abstention. It is shown that such schemes enable drastic improvements, up to the extent of attaining the Heisenberg limit in some cases, and the required amount of abstention is quantified. A general mathematical framework to deal with the asymptotic limit of many qubits or large angular momentum is introduced and used to obtain analytical results for all the relevant cases under consideration. Parameter estimation with abstention is also formulated as a semidefinite programming problem, for which very efficient numerical optimization techniques exist.

Guaranteed Discrete Energy Optimization on Large Protein Design Problems.

PubMed

Simoncini, David; Allouche, David; de Givry, Simon; Delmas, Céline; Barbe, Sophie; Schiex, Thomas

2015-12-08

In Computational Protein Design (CPD), assuming a rigid backbone and amino-acid rotamer library, the problem of finding a sequence with an optimal conformation is NP-hard. In this paper, using Dunbrack's rotamer library and Talaris2014 decomposable energy function, we use an exact deterministic method combining branch and bound, arc consistency, and tree-decomposition to provenly identify the global minimum energy sequence-conformation on full-redesign problems, defining search spaces of size up to 10(234). This is achieved on a single core of a standard computing server, requiring a maximum of 66GB RAM. A variant of the algorithm is able to exhaustively enumerate all sequence-conformations within an energy threshold of the optimum. These proven optimal solutions are then used to evaluate the frequencies and amplitudes, in energy and sequence, at which an existing CPD-dedicated simulated annealing implementation may miss the optimum on these full redesign problems. The probability of finding an optimum drops close to 0 very quickly. In the worst case, despite 1,000 repeats, the annealing algorithm remained more than 1 Rosetta unit away from the optimum, leading to design sequences that could differ from the optimal sequence by more than 30% of their amino acids.

Final Technical Report: Sparse Grid Scenario Generation and Interior Algorithms for Stochastic Optimization in a Parallel Computing Environment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mehrotra, Sanjay

2016-09-07

The support from this grant resulted in seven published papers and a technical report. Two papers are published in SIAM J. on Optimization [87, 88]; two papers are published in IEEE Transactions on Power Systems [77, 78]; one paper is published in Smart Grid [79]; one paper is published in Computational Optimization and Applications [44] and one in INFORMS J. on Computing [67]). The works in [44, 67, 87, 88] were funded primarily by this DOE grant. The applied papers in [77, 78, 79] were also supported through a subcontract from the Argonne National Lab. We start by presenting ourmore » main research results on the scenario generation problem in Sections 1–2. We present our algorithmic results on interior point methods for convex optimization problems in Section 3. We describe a new ‘central’ cutting surface algorithm developed for solving large scale convex programming problems (as is the case with our proposed research) with semi-infinite number of constraints in Section 4. In Sections 5–6 we present our work on two application problems of interest to DOE.« less

Social Milieu Oriented Routing: A New Dimension to Enhance Network Security in WSNs.

PubMed

Liu, Lianggui; Chen, Li; Jia, Huiling

2016-02-19

In large-scale wireless sensor networks (WSNs), in order to enhance network security, it is crucial for a trustor node to perform social milieu oriented routing to a target a trustee node to carry out trust evaluation. This challenging social milieu oriented routing with more than one end-to-end Quality of Trust (QoT) constraint has proved to be NP-complete. Heuristic algorithms with polynomial and pseudo-polynomial-time complexities are often used to deal with this challenging problem. However, existing solutions cannot guarantee the efficiency of searching; that is, they can hardly avoid obtaining partial optimal solutions during a searching process. Quantum annealing (QA) uses delocalization and tunneling to avoid falling into local minima without sacrificing execution time. This has been proven a promising way to many optimization problems in recently published literatures. In this paper, for the first time, with the help of a novel approach, that is, configuration path-integral Monte Carlo (CPIMC) simulations, a QA-based optimal social trust path (QA_OSTP) selection algorithm is applied to the extraction of the optimal social trust path in large-scale WSNs. Extensive experiments have been conducted, and the experiment results demonstrate that QA_OSTP outperforms its heuristic opponents.

Final Report: Large-Scale Optimization for Bayesian Inference in Complex Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghattas, Omar

2013-10-15

The SAGUARO (Scalable Algorithms for Groundwater Uncertainty Analysis and Robust Optimiza- tion) Project focuses on the development of scalable numerical algorithms for large-scale Bayesian inversion in complex systems that capitalize on advances in large-scale simulation-based optimiza- tion and inversion methods. Our research is directed in three complementary areas: efficient approximations of the Hessian operator, reductions in complexity of forward simulations via stochastic spectral approximations and model reduction, and employing large-scale optimization concepts to accelerate sampling. Our efforts are integrated in the context of a challenging testbed problem that considers subsurface reacting flow and transport. The MIT component of the SAGUAROmore » Project addresses the intractability of conventional sampling methods for large-scale statistical inverse problems by devising reduced-order models that are faithful to the full-order model over a wide range of parameter values; sampling then employs the reduced model rather than the full model, resulting in very large computational savings. Results indicate little effect on the computed posterior distribution. On the other hand, in the Texas-Georgia Tech component of the project, we retain the full-order model, but exploit inverse problem structure (adjoint-based gradients and partial Hessian information of the parameter-to- observation map) to implicitly extract lower dimensional information on the posterior distribution; this greatly speeds up sampling methods, so that fewer sampling points are needed. We can think of these two approaches as "reduce then sample" and "sample then reduce." In fact, these two approaches are complementary, and can be used in conjunction with each other. Moreover, they both exploit deterministic inverse problem structure, in the form of adjoint-based gradient and Hessian information of the underlying parameter-to-observation map, to achieve their speedups.« less

The linear regulator problem for parabolic systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Kunisch, K.

1983-01-01

An approximation framework is presented for computation (in finite imensional spaces) of Riccati operators that can be guaranteed to converge to the Riccati operator in feedback controls for abstract evolution systems in a Hilbert space. It is shown how these results may be used in the linear optimal regulator problem for a large class of parabolic systems.

Distributed Optimization of Multi-Agent Systems: Framework, Local Optimizer, and Applications

NASA Astrophysics Data System (ADS)

Zu, Yue

Convex optimization problem can be solved in a centralized or distributed manner. Compared with centralized methods based on single-agent system, distributed algorithms rely on multi-agent systems with information exchanging among connected neighbors, which leads to great improvement on the system fault tolerance. Thus, a task within multi-agent system can be completed with presence of partial agent failures. By problem decomposition, a large-scale problem can be divided into a set of small-scale sub-problems that can be solved in sequence/parallel. Hence, the computational complexity is greatly reduced by distributed algorithm in multi-agent system. Moreover, distributed algorithm allows data collected and stored in a distributed fashion, which successfully overcomes the drawbacks of using multicast due to the bandwidth limitation. Distributed algorithm has been applied in solving a variety of real-world problems. Our research focuses on the framework and local optimizer design in practical engineering applications. In the first one, we propose a multi-sensor and multi-agent scheme for spatial motion estimation of a rigid body. Estimation performance is improved in terms of accuracy and convergence speed. Second, we develop a cyber-physical system and implement distributed computation devices to optimize the in-building evacuation path when hazard occurs. The proposed Bellman-Ford Dual-Subgradient path planning method relieves the congestion in corridor and the exit areas. At last, highway traffic flow is managed by adjusting speed limits to minimize the fuel consumption and travel time in the third project. Optimal control strategy is designed through both centralized and distributed algorithm based on convex problem formulation. Moreover, a hybrid control scheme is presented for highway network travel time minimization. Compared with no controlled case or conventional highway traffic control strategy, the proposed hybrid control strategy greatly reduces total travel time on test highway network.

Newton Methods for Large Scale Problems in Machine Learning

ERIC Educational Resources Information Center

Hansen, Samantha Leigh

2014-01-01

The focus of this thesis is on practical ways of designing optimization algorithms for minimizing large-scale nonlinear functions with applications in machine learning. Chapter 1 introduces the overarching ideas in the thesis. Chapters 2 and 3 are geared towards supervised machine learning applications that involve minimizing a sum of loss…

Hierarchical optimal control of large-scale nonlinear chemical processes.

PubMed

Ramezani, Mohammad Hossein; Sadati, Nasser

2009-01-01

In this paper, a new approach is presented for optimal control of large-scale chemical processes. In this approach, the chemical process is decomposed into smaller sub-systems at the first level, and a coordinator at the second level, for which a two-level hierarchical control strategy is designed. For this purpose, each sub-system in the first level can be solved separately, by using any conventional optimization algorithm. In the second level, the solutions obtained from the first level are coordinated using a new gradient-type strategy, which is updated by the error of the coordination vector. The proposed algorithm is used to solve the optimal control problem of a complex nonlinear chemical stirred tank reactor (CSTR), where its solution is also compared with the ones obtained using the centralized approach. The simulation results show the efficiency and the capability of the proposed hierarchical approach, in finding the optimal solution, over the centralized method.

Optimal Sensor Allocation for Fault Detection and Isolation

NASA Technical Reports Server (NTRS)

Azam, Mohammad; Pattipati, Krishna; Patterson-Hine, Ann

2004-01-01

Automatic fault diagnostic schemes rely on various types of sensors (e.g., temperature, pressure, vibration, etc) to measure the system parameters. Efficacy of a diagnostic scheme is largely dependent on the amount and quality of information available from these sensors. The reliability of sensors, as well as the weight, volume, power, and cost constraints, often makes it impractical to monitor a large number of system parameters. An optimized sensor allocation that maximizes the fault diagnosibility, subject to specified weight, volume, power, and cost constraints is required. Use of optimal sensor allocation strategies during the design phase can ensure better diagnostics at a reduced cost for a system incorporating a high degree of built-in testing. In this paper, we propose an approach that employs multiple fault diagnosis (MFD) and optimization techniques for optimal sensor placement for fault detection and isolation (FDI) in complex systems. Keywords: sensor allocation, multiple fault diagnosis, Lagrangian relaxation, approximate belief revision, multidimensional knapsack problem.

A guide to multi-objective optimization for ecological problems with an application to cackling goose management

USGS Publications Warehouse

Williams, Perry J.; Kendall, William L.

2017-01-01

Choices in ecological research and management are the result of balancing multiple, often competing, objectives. Multi-objective optimization (MOO) is a formal decision-theoretic framework for solving multiple objective problems. MOO is used extensively in other fields including engineering, economics, and operations research. However, its application for solving ecological problems has been sparse, perhaps due to a lack of widespread understanding. Thus, our objective was to provide an accessible primer on MOO, including a review of methods common in other fields, a review of their application in ecology, and a demonstration to an applied resource management problem.A large class of methods for solving MOO problems can be separated into two strategies: modelling preferences pre-optimization (the a priori strategy), or modelling preferences post-optimization (the a posteriori strategy). The a priori strategy requires describing preferences among objectives without knowledge of how preferences affect the resulting decision. In the a posteriori strategy, the decision maker simultaneously considers a set of solutions (the Pareto optimal set) and makes a choice based on the trade-offs observed in the set. We describe several methods for modelling preferences pre-optimization, including: the bounded objective function method, the lexicographic method, and the weighted-sum method. We discuss modelling preferences post-optimization through examination of the Pareto optimal set. We applied each MOO strategy to the natural resource management problem of selecting a population target for cackling goose (Branta hutchinsii minima) abundance. Cackling geese provide food security to Native Alaskan subsistence hunters in the goose's nesting area, but depredate crops on private agricultural fields in wintering areas. We developed objective functions to represent the competing objectives related to the cackling goose population target and identified an optimal solution first using the a priori strategy, and then by examining trade-offs in the Pareto set using the a posteriori strategy. We used four approaches for selecting a final solution within the a posteriori strategy; the most common optimal solution, the most robust optimal solution, and two solutions based on maximizing a restricted portion of the Pareto set. We discuss MOO with respect to natural resource management, but MOO is sufficiently general to cover any ecological problem that contains multiple competing objectives that can be quantified using objective functions.

3D Data Acquisition Platform for Human Activity Understanding

DTIC Science & Technology

2016-03-02

address fundamental research problems of representation and invariant description of3D data, human motion modeling and applications of human activity analysis, and computational optimization of large-scale 3D data.

3D Data Acquisition Platform for Human Activity Understanding

DTIC Science & Technology

2016-03-02

address fundamental research problems of representation and invariant description of 3D data, human motion modeling and applications of human activity analysis, and computational optimization of large-scale 3D data.

Adaptive Flight Control Design with Optimal Control Modification on an F-18 Aircraft Model

NASA Technical Reports Server (NTRS)

Burken, John J.; Nguyen, Nhan T.; Griffin, Brian J.

2010-01-01

In the presence of large uncertainties, a control system needs to be able to adapt rapidly to regain performance. Fast adaptation is referred to as the implementation of adaptive control with a large adaptive gain to reduce the tracking error rapidly; however, a large adaptive gain can lead to high-frequency oscillations which can adversely affect the robustness of an adaptive control law. A new adaptive control modification is presented that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. The modification is based on the minimization of the Y2 norm of the tracking error, which is formulated as an optimal control problem. The optimality condition is used to derive the modification using the gradient method. The optimal control modification results in a stable adaptation and allows a large adaptive gain to be used for better tracking while providing sufficient robustness. A damping term (v) is added in the modification to increase damping as needed. Simulations were conducted on a damaged F-18 aircraft (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) with both the standard baseline dynamic inversion controller and the adaptive optimal control modification technique. The results demonstrate the effectiveness of the proposed modification in tracking a reference model.

Global Detection of Live Virtual Machine Migration Based on Cellular Neural Networks

PubMed Central

Xie, Kang; Yang, Yixian; Zhang, Ling; Jing, Maohua; Xin, Yang; Li, Zhongxian

2014-01-01

In order to meet the demands of operation monitoring of large scale, autoscaling, and heterogeneous virtual resources in the existing cloud computing, a new method of live virtual machine (VM) migration detection algorithm based on the cellular neural networks (CNNs), is presented. Through analyzing the detection process, the parameter relationship of CNN is mapped as an optimization problem, in which improved particle swarm optimization algorithm based on bubble sort is used to solve the problem. Experimental results demonstrate that the proposed method can display the VM migration processing intuitively. Compared with the best fit heuristic algorithm, this approach reduces the processing time, and emerging evidence has indicated that this new approach is affordable to parallelism and analog very large scale integration (VLSI) implementation allowing the VM migration detection to be performed better. PMID:24959631

Global detection of live virtual machine migration based on cellular neural networks.

PubMed

Xie, Kang; Yang, Yixian; Zhang, Ling; Jing, Maohua; Xin, Yang; Li, Zhongxian

2014-01-01

In order to meet the demands of operation monitoring of large scale, autoscaling, and heterogeneous virtual resources in the existing cloud computing, a new method of live virtual machine (VM) migration detection algorithm based on the cellular neural networks (CNNs), is presented. Through analyzing the detection process, the parameter relationship of CNN is mapped as an optimization problem, in which improved particle swarm optimization algorithm based on bubble sort is used to solve the problem. Experimental results demonstrate that the proposed method can display the VM migration processing intuitively. Compared with the best fit heuristic algorithm, this approach reduces the processing time, and emerging evidence has indicated that this new approach is affordable to parallelism and analog very large scale integration (VLSI) implementation allowing the VM migration detection to be performed better.

The dynamics and control of large flexible space structures - 13

NASA Technical Reports Server (NTRS)

Bainum, Peter M.; Li, Feiyue; Xu, Jianke

1990-01-01

The optimal control of three-dimensional large angle maneuvers and vibrations of a Shuttle-mast-reflector system is considered. The nonlinear equations of motion are formulated by using Lagrange's formula, with the mast modeled as a continuous beam subject to three-dimensional deformations. Pontryagin's Maximum Principle is applied to the slewing problem, to derive the necessary conditions for the optimal controls, which are bounded by given saturation levels. The resulting two point boundary value problem is then solved by using the quasilinearization algorithm and the method of particular solutions. The study of the large angle maneuvering of the Shuttle-beam-reflector spacecraft in the plane of a circular earth orbit is extended to consider the effects of the structural offset connection, the axial shortening, and the gravitational torque on the slewing motion. Finally the effect of additional design parameters (such as related to additional payload requirement) on the linear quadratic regulator based design of an orbiting control/structural system is examined.

Cooperative Coevolution with Formula-Based Variable Grouping for Large-Scale Global Optimization.

PubMed

Wang, Yuping; Liu, Haiyan; Wei, Fei; Zong, Tingting; Li, Xiaodong

2017-08-09

For a large-scale global optimization (LSGO) problem, divide-and-conquer is usually considered an effective strategy to decompose the problem into smaller subproblems, each of which can then be solved individually. Among these decomposition methods, variable grouping is shown to be promising in recent years. Existing variable grouping methods usually assume the problem to be black-box (i.e., assuming that an analytical model of the objective function is unknown), and they attempt to learn appropriate variable grouping that would allow for a better decomposition of the problem. In such cases, these variable grouping methods do not make a direct use of the formula of the objective function. However, it can be argued that many real-world problems are white-box problems, that is, the formulas of objective functions are often known a priori. These formulas of the objective functions provide rich information which can then be used to design an effective variable group method. In this article, a formula-based grouping strategy (FBG) for white-box problems is first proposed. It groups variables directly via the formula of an objective function which usually consists of a finite number of operations (i.e., four arithmetic operations "[Formula: see text]", "[Formula: see text]", "[Formula: see text]", "[Formula: see text]" and composite operations of basic elementary functions). In FBG, the operations are classified into two classes: one resulting in nonseparable variables, and the other resulting in separable variables. In FBG, variables can be automatically grouped into a suitable number of non-interacting subcomponents, with variables in each subcomponent being interdependent. FBG can easily be applied to any white-box problem and can be integrated into a cooperative coevolution framework. Based on FBG, a novel cooperative coevolution algorithm with formula-based variable grouping (so-called CCF) is proposed in this article for decomposing a large-scale white-box problem into several smaller subproblems and optimizing them respectively. To further enhance the efficiency of CCF, a new local search scheme is designed to improve the solution quality. To verify the efficiency of CCF, experiments are conducted on the standard LSGO benchmark suites of CEC'2008, CEC'2010, CEC'2013, and a real-world problem. Our results suggest that the performance of CCF is very competitive when compared with those of the state-of-the-art LSGO algorithms.

A cooperative strategy for parameter estimation in large scale systems biology models.

PubMed

Villaverde, Alejandro F; Egea, Jose A; Banga, Julio R

2012-06-22

Mathematical models play a key role in systems biology: they summarize the currently available knowledge in a way that allows to make experimentally verifiable predictions. Model calibration consists of finding the parameters that give the best fit to a set of experimental data, which entails minimizing a cost function that measures the goodness of this fit. Most mathematical models in systems biology present three characteristics which make this problem very difficult to solve: they are highly non-linear, they have a large number of parameters to be estimated, and the information content of the available experimental data is frequently scarce. Hence, there is a need for global optimization methods capable of solving this problem efficiently. A new approach for parameter estimation of large scale models, called Cooperative Enhanced Scatter Search (CeSS), is presented. Its key feature is the cooperation between different programs ("threads") that run in parallel in different processors. Each thread implements a state of the art metaheuristic, the enhanced Scatter Search algorithm (eSS). Cooperation, meaning information sharing between threads, modifies the systemic properties of the algorithm and allows to speed up performance. Two parameter estimation problems involving models related with the central carbon metabolism of E. coli which include different regulatory levels (metabolic and transcriptional) are used as case studies. The performance and capabilities of the method are also evaluated using benchmark problems of large-scale global optimization, with excellent results. The cooperative CeSS strategy is a general purpose technique that can be applied to any model calibration problem. Its capability has been demonstrated by calibrating two large-scale models of different characteristics, improving the performance of previously existing methods in both cases. The cooperative metaheuristic presented here can be easily extended to incorporate other global and local search solvers and specific structural information for particular classes of problems.

A cooperative strategy for parameter estimation in large scale systems biology models

PubMed Central

2012-01-01

Background Mathematical models play a key role in systems biology: they summarize the currently available knowledge in a way that allows to make experimentally verifiable predictions. Model calibration consists of finding the parameters that give the best fit to a set of experimental data, which entails minimizing a cost function that measures the goodness of this fit. Most mathematical models in systems biology present three characteristics which make this problem very difficult to solve: they are highly non-linear, they have a large number of parameters to be estimated, and the information content of the available experimental data is frequently scarce. Hence, there is a need for global optimization methods capable of solving this problem efficiently. Results A new approach for parameter estimation of large scale models, called Cooperative Enhanced Scatter Search (CeSS), is presented. Its key feature is the cooperation between different programs (“threads”) that run in parallel in different processors. Each thread implements a state of the art metaheuristic, the enhanced Scatter Search algorithm (eSS). Cooperation, meaning information sharing between threads, modifies the systemic properties of the algorithm and allows to speed up performance. Two parameter estimation problems involving models related with the central carbon metabolism of E. coli which include different regulatory levels (metabolic and transcriptional) are used as case studies. The performance and capabilities of the method are also evaluated using benchmark problems of large-scale global optimization, with excellent results. Conclusions The cooperative CeSS strategy is a general purpose technique that can be applied to any model calibration problem. Its capability has been demonstrated by calibrating two large-scale models of different characteristics, improving the performance of previously existing methods in both cases. The cooperative metaheuristic presented here can be easily extended to incorporate other global and local search solvers and specific structural information for particular classes of problems. PMID:22727112

An inverse problem strategy based on forward model evaluations: Gradient-based optimization without adjoint solves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aguilo Valentin, Miguel Alejandro

2016-07-01

This study presents a new nonlinear programming formulation for the solution of inverse problems. First, a general inverse problem formulation based on the compliance error functional is presented. The proposed error functional enables the computation of the Lagrange multipliers, and thus the first order derivative information, at the expense of just one model evaluation. Therefore, the calculation of the Lagrange multipliers does not require the solution of the computationally intensive adjoint problem. This leads to significant speedups for large-scale, gradient-based inverse problems.

Fuel consumption optimization for smart hybrid electric vehicle during a car-following process

NASA Astrophysics Data System (ADS)

Li, Liang; Wang, Xiangyu; Song, Jian

2017-03-01

Hybrid electric vehicles (HEVs) provide large potential to save energy and reduce emission, and smart vehicles bring out great convenience and safety for drivers. By combining these two technologies, vehicles may achieve excellent performances in terms of dynamic, economy, environmental friendliness, safety, and comfort. Hence, a smart hybrid electric vehicle (s-HEV) is selected as a platform in this paper to study a car-following process with optimizing the fuel consumption. The whole process is a multi-objective optimal problem, whose optimal solution is not just adding an energy management strategy (EMS) to an adaptive cruise control (ACC), but a deep fusion of these two methods. The problem has more restricted conditions, optimal objectives, and system states, which may result in larger computing burden. Therefore, a novel fuel consumption optimization algorithm based on model predictive control (MPC) is proposed and some search skills are adopted in receding horizon optimization to reduce computing burden. Simulations are carried out and the results indicate that the fuel consumption of proposed method is lower than that of the ACC+EMS method on the condition of ensuring car-following performances.

GA-optimization for rapid prototype system demonstration

NASA Technical Reports Server (NTRS)

Kim, Jinwoo; Zeigler, Bernard P.

1994-01-01

An application of the Genetic Algorithm (GA) is discussed. A novel scheme of Hierarchical GA was developed to solve complicated engineering problems which require optimization of a large number of parameters with high precision. High level GAs search for few parameters which are much more sensitive to the system performance. Low level GAs search in more detail and employ a greater number of parameters for further optimization. Therefore, the complexity of the search is decreased and the computing resources are used more efficiently.

An efficient implementation of 3D high-resolution imaging for large-scale seismic data with GPU/CPU heterogeneous parallel computing

NASA Astrophysics Data System (ADS)

Xu, Jincheng; Liu, Wei; Wang, Jin; Liu, Linong; Zhang, Jianfeng

2018-02-01

De-absorption pre-stack time migration (QPSTM) compensates for the absorption and dispersion of seismic waves by introducing an effective Q parameter, thereby making it an effective tool for 3D, high-resolution imaging of seismic data. Although the optimal aperture obtained via stationary-phase migration reduces the computational cost of 3D QPSTM and yields 3D stationary-phase QPSTM, the associated computational efficiency is still the main problem in the processing of 3D, high-resolution images for real large-scale seismic data. In the current paper, we proposed a division method for large-scale, 3D seismic data to optimize the performance of stationary-phase QPSTM on clusters of graphics processing units (GPU). Then, we designed an imaging point parallel strategy to achieve an optimal parallel computing performance. Afterward, we adopted an asynchronous double buffering scheme for multi-stream to perform the GPU/CPU parallel computing. Moreover, several key optimization strategies of computation and storage based on the compute unified device architecture (CUDA) were adopted to accelerate the 3D stationary-phase QPSTM algorithm. Compared with the initial GPU code, the implementation of the key optimization steps, including thread optimization, shared memory optimization, register optimization and special function units (SFU), greatly improved the efficiency. A numerical example employing real large-scale, 3D seismic data showed that our scheme is nearly 80 times faster than the CPU-QPSTM algorithm. Our GPU/CPU heterogeneous parallel computing framework significant reduces the computational cost and facilitates 3D high-resolution imaging for large-scale seismic data.

A frozen Gaussian approximation-based multi-level particle swarm optimization for seismic inversion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Jinglai, E-mail: jinglaili@sjtu.edu.cn; Lin, Guang, E-mail: lin491@purdue.edu; Computational Sciences and Mathematics Division, Pacific Northwest National Laboratory, Richland, WA 99352

2015-09-01

In this paper, we propose a frozen Gaussian approximation (FGA)-based multi-level particle swarm optimization (MLPSO) method for seismic inversion of high-frequency wave data. The method addresses two challenges in it: First, the optimization problem is highly non-convex, which makes hard for gradient-based methods to reach global minima. This is tackled by MLPSO which can escape from undesired local minima. Second, the character of high-frequency of seismic waves requires a large number of grid points in direct computational methods, and thus renders an extremely high computational demand on the simulation of each sample in MLPSO. We overcome this difficulty by threemore » steps: First, we use FGA to compute high-frequency wave propagation based on asymptotic analysis on phase plane; Then we design a constrained full waveform inversion problem to prevent the optimization search getting into regions of velocity where FGA is not accurate; Last, we solve the constrained optimization problem by MLPSO that employs FGA solvers with different fidelity. The performance of the proposed method is demonstrated by a two-dimensional full-waveform inversion example of the smoothed Marmousi model.« less

A surrogate-based metaheuristic global search method for beam angle selection in radiation treatment planning.

PubMed

Zhang, H H; Gao, S; Chen, W; Shi, L; D'Souza, W D; Meyer, R R

2013-03-21

An important element of radiation treatment planning for cancer therapy is the selection of beam angles (out of all possible coplanar and non-coplanar angles in relation to the patient) in order to maximize the delivery of radiation to the tumor site and minimize radiation damage to nearby organs-at-risk. This category of combinatorial optimization problem is particularly difficult because direct evaluation of the quality of treatment corresponding to any proposed selection of beams requires the solution of a large-scale dose optimization problem involving many thousands of variables that represent doses delivered to volume elements (voxels) in the patient. However, if the quality of angle sets can be accurately estimated without expensive computation, a large number of angle sets can be considered, increasing the likelihood of identifying a very high quality set. Using a computationally efficient surrogate beam set evaluation procedure based on single-beam data extracted from plans employing equallyspaced beams (eplans), we have developed a global search metaheuristic process based on the nested partitions framework for this combinatorial optimization problem. The surrogate scoring mechanism allows us to assess thousands of beam set samples within a clinically acceptable time frame. Tests on difficult clinical cases demonstrate that the beam sets obtained via our method are of superior quality.

A surrogate-based metaheuristic global search method for beam angle selection in radiation treatment planning

PubMed Central

Zhang, H H; Gao, S; Chen, W; Shi, L; D’Souza, W D; Meyer, R R

2013-01-01

An important element of radiation treatment planning for cancer therapy is the selection of beam angles (out of all possible coplanar and non-coplanar angles in relation to the patient) in order to maximize the delivery of radiation to the tumor site and minimize radiation damage to nearby organs-at-risk. This category of combinatorial optimization problem is particularly difficult because direct evaluation of the quality of treatment corresponding to any proposed selection of beams requires the solution of a large-scale dose optimization problem involving many thousands of variables that represent doses delivered to volume elements (voxels) in the patient. However, if the quality of angle sets can be accurately estimated without expensive computation, a large number of angle sets can be considered, increasing the likelihood of identifying a very high quality set. Using a computationally efficient surrogate beam set evaluation procedure based on single-beam data extracted from plans employing equally-spaced beams (eplans), we have developed a global search metaheuristic process based on the Nested Partitions framework for this combinatorial optimization problem. The surrogate scoring mechanism allows us to assess thousands of beam set samples within a clinically acceptable time frame. Tests on difficult clinical cases demonstrate that the beam sets obtained via our method are superior quality. PMID:23459411

Data mining for water resource management part 2 - methods and approaches to solving contemporary problems

USGS Publications Warehouse

Roehl, Edwin A.; Conrads, Paul

2010-01-01

This is the second of two papers that describe how data mining can aid natural-resource managers with the difficult problem of controlling the interactions between hydrologic and man-made systems. Data mining is a new science that assists scientists in converting large databases into knowledge, and is uniquely able to leverage the large amounts of real-time, multivariate data now being collected for hydrologic systems. Part 1 gives a high-level overview of data mining, and describes several applications that have addressed major water resource issues in South Carolina. This Part 2 paper describes how various data mining methods are integrated to produce predictive models for controlling surface- and groundwater hydraulics and quality. The methods include: - signal processing to remove noise and decompose complex signals into simpler components; - time series clustering that optimally groups hundreds of signals into "classes" that behave similarly for data reduction and (or) divide-and-conquer problem solving; - classification which optimally matches new data to behavioral classes; - artificial neural networks which optimally fit multivariate data to create predictive models; - model response surface visualization that greatly aids in understanding data and physical processes; and, - decision support systems that integrate data, models, and graphics into a single package that is easy to use.

Design optimization of large-size format edge-lit light guide units

NASA Astrophysics Data System (ADS)

Hastanin, J.; Lenaerts, C.; Fleury-Frenette, K.

2016-04-01

In this paper, we present an original method of dot pattern generation dedicated to large-size format light guide plate (LGP) design optimization, such as photo-bioreactors, the number of dots greatly exceeds the maximum allowable number of optical objects supported by most common ray-tracing software. In the proposed method, in order to simplify the computational problem, the original optical system is replaced by an equivalent one. Accordingly, an original dot pattern is splitted into multiple small sections, inside which the dot size variation is less than the ink dots printing typical resolution. Then, these sections are replaced by equivalent cells with continuous diffusing film. After that, we adjust the TIS (Total Integrated Scatter) two-dimensional distribution over the grid of equivalent cells, using an iterative optimization procedure. Finally, the obtained optimal TIS distribution is converted into the dot size distribution by applying an appropriate conversion rule. An original semi-empirical equation dedicated to rectangular large-size LGPs is proposed for the initial guess of TIS distribution. It allows significantly reduce the total time needed to dot pattern optimization.

Parameter estimation in large-scale systems biology models: a parallel and self-adaptive cooperative strategy.

PubMed

Penas, David R; González, Patricia; Egea, Jose A; Doallo, Ramón; Banga, Julio R

2017-01-21

The development of large-scale kinetic models is one of the current key issues in computational systems biology and bioinformatics. Here we consider the problem of parameter estimation in nonlinear dynamic models. Global optimization methods can be used to solve this type of problems but the associated computational cost is very large. Moreover, many of these methods need the tuning of a number of adjustable search parameters, requiring a number of initial exploratory runs and therefore further increasing the computation times. Here we present a novel parallel method, self-adaptive cooperative enhanced scatter search (saCeSS), to accelerate the solution of this class of problems. The method is based on the scatter search optimization metaheuristic and incorporates several key new mechanisms: (i) asynchronous cooperation between parallel processes, (ii) coarse and fine-grained parallelism, and (iii) self-tuning strategies. The performance and robustness of saCeSS is illustrated by solving a set of challenging parameter estimation problems, including medium and large-scale kinetic models of the bacterium E. coli, bakerés yeast S. cerevisiae, the vinegar fly D. melanogaster, Chinese Hamster Ovary cells, and a generic signal transduction network. The results consistently show that saCeSS is a robust and efficient method, allowing very significant reduction of computation times with respect to several previous state of the art methods (from days to minutes, in several cases) even when only a small number of processors is used. The new parallel cooperative method presented here allows the solution of medium and large scale parameter estimation problems in reasonable computation times and with small hardware requirements. Further, the method includes self-tuning mechanisms which facilitate its use by non-experts. We believe that this new method can play a key role in the development of large-scale and even whole-cell dynamic models.

Pricing and location decisions in multi-objective facility location problem with M/M/m/k queuing systems

NASA Astrophysics Data System (ADS)

Tavakkoli-Moghaddam, Reza; Vazifeh-Noshafagh, Samira; Taleizadeh, Ata Allah; Hajipour, Vahid; Mahmoudi, Amin

2017-01-01

This article presents a new multi-objective model for a facility location problem with congestion and pricing policies. This model considers situations in which immobile service facilities are congested by a stochastic demand following M/M/m/k queues. The presented model belongs to the class of mixed-integer nonlinear programming models and NP-hard problems. To solve such a hard model, a new multi-objective optimization algorithm based on a vibration theory, namely multi-objective vibration damping optimization (MOVDO), is developed. In order to tune the algorithms parameters, the Taguchi approach using a response metric is implemented. The computational results are compared with those of the non-dominated ranking genetic algorithm and non-dominated sorting genetic algorithm. The outputs demonstrate the robustness of the proposed MOVDO in large-sized problems.

Optimal time points sampling in pathway modelling.

PubMed

Hu, Shiyan

2004-01-01

Modelling cellular dynamics based on experimental data is at the heart of system biology. Considerable progress has been made to dynamic pathway modelling as well as the related parameter estimation. However, few of them gives consideration for the issue of optimal sampling time selection for parameter estimation. Time course experiments in molecular biology rarely produce large and accurate data sets and the experiments involved are usually time consuming and expensive. Therefore, to approximate parameters for models with only few available sampling data is of significant practical value. For signal transduction, the sampling intervals are usually not evenly distributed and are based on heuristics. In the paper, we investigate an approach to guide the process of selecting time points in an optimal way to minimize the variance of parameter estimates. In the method, we first formulate the problem to a nonlinear constrained optimization problem by maximum likelihood estimation. We then modify and apply a quantum-inspired evolutionary algorithm, which combines the advantages of both quantum computing and evolutionary computing, to solve the optimization problem. The new algorithm does not suffer from the morass of selecting good initial values and being stuck into local optimum as usually accompanied with the conventional numerical optimization techniques. The simulation results indicate the soundness of the new method.

Optimal Paths in Gliding Flight

NASA Astrophysics Data System (ADS)

Wolek, Artur

Underwater gliders are robust and long endurance ocean sampling platforms that are increasingly being deployed in coastal regions. This new environment is characterized by shallow waters and significant currents that can challenge the mobility of these efficient (but traditionally slow moving) vehicles. This dissertation aims to improve the performance of shallow water underwater gliders through path planning. The path planning problem is formulated for a dynamic particle (or "kinematic car") model. The objective is to identify the path which satisfies specified boundary conditions and minimizes a particular cost. Several cost functions are considered. The problem is addressed using optimal control theory. The length scales of interest for path planning are within a few turn radii. First, an approach is developed for planning minimum-time paths, for a fixed speed glider, that are sub-optimal but are guaranteed to be feasible in the presence of unknown time-varying currents. Next the minimum-time problem for a glider with speed controls, that may vary between the stall speed and the maximum speed, is solved. Last, optimal paths that minimize change in depth (equivalently, maximize range) are investigated. Recognizing that path planning alone cannot overcome all of the challenges associated with significant currents and shallow waters, the design of a novel underwater glider with improved capabilities is explored. A glider with a pneumatic buoyancy engine (allowing large, rapid buoyancy changes) and a cylindrical moving mass mechanism (generating large pitch and roll moments) is designed, manufactured, and tested to demonstrate potential improvements in speed and maneuverability.

Optimal four-impulse rendezvous between coplanar elliptical orbits

NASA Astrophysics Data System (ADS)

Wang, JianXia; Baoyin, HeXi; Li, JunFeng; Sun, FuChun

2011-04-01

Rendezvous in circular or near circular orbits has been investigated in great detail, while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored. Among the various optimization methods proposed for fuel optimal orbital rendezvous, Lawden's primer vector theory is favored by many researchers with its clear physical concept and simplicity in solution. Prussing has applied the primer vector optimization theory to minimum-fuel, multiple-impulse, time-fixed orbital rendezvous in a near circular orbit and achieved great success. Extending Prussing's work, this paper will employ the primer vector theory to study trajectory optimization problems of arbitrary eccentricity elliptical orbit rendezvous. Based on linearized equations of relative motion on elliptical reference orbit (referred to as T-H equations), the primer vector theory is used to deal with time-fixed multiple-impulse optimal rendezvous between two coplanar, coaxial elliptical orbits with arbitrary large eccentricity. A parameter adjustment method is developed for the prime vector to satisfy the Lawden's necessary condition for the optimal solution. Finally, the optimal multiple-impulse rendezvous solution including the time, direction and magnitudes of the impulse is obtained by solving the two-point boundary value problem. The rendezvous error of the linearized equation is also analyzed. The simulation results confirmed the analyzed results that the rendezvous error is small for the small eccentricity case and is large for the higher eccentricity. For better rendezvous accuracy of high eccentricity orbits, a combined method of multiplier penalty function with the simplex search method is used for local optimization. The simplex search method is sensitive to the initial values of optimization variables, but the simulation results show that initial values with the primer vector theory, and the local optimization algorithm can improve the rendezvous accuracy effectively with fast convergence, because the optimal results obtained by the primer vector theory are already very close to the actual optimal solution. If the initial values are taken randomly, it is difficult to converge to the optimal solution.

Rapid indirect trajectory optimization on highly parallel computing architectures

NASA Astrophysics Data System (ADS)

Antony, Thomas

Trajectory optimization is a field which can benefit greatly from the advantages offered by parallel computing. The current state-of-the-art in trajectory optimization focuses on the use of direct optimization methods, such as the pseudo-spectral method. These methods are favored due to their ease of implementation and large convergence regions while indirect methods have largely been ignored in the literature in the past decade except for specific applications in astrodynamics. It has been shown that the shortcomings conventionally associated with indirect methods can be overcome by the use of a continuation method in which complex trajectory solutions are obtained by solving a sequence of progressively difficult optimization problems. High performance computing hardware is trending towards more parallel architectures as opposed to powerful single-core processors. Graphics Processing Units (GPU), which were originally developed for 3D graphics rendering have gained popularity in the past decade as high-performance, programmable parallel processors. The Compute Unified Device Architecture (CUDA) framework, a parallel computing architecture and programming model developed by NVIDIA, is one of the most widely used platforms in GPU computing. GPUs have been applied to a wide range of fields that require the solution of complex, computationally demanding problems. A GPU-accelerated indirect trajectory optimization methodology which uses the multiple shooting method and continuation is developed using the CUDA platform. The various algorithmic optimizations used to exploit the parallelism inherent in the indirect shooting method are described. The resulting rapid optimal control framework enables the construction of high quality optimal trajectories that satisfy problem-specific constraints and fully satisfy the necessary conditions of optimality. The benefits of the framework are highlighted by construction of maximum terminal velocity trajectories for a hypothetical long range weapon system. The techniques used to construct an initial guess from an analytic near-ballistic trajectory and the methods used to formulate the necessary conditions of optimality in a manner that is transparent to the designer are discussed. Various hypothetical mission scenarios that enforce different combinations of initial, terminal, interior point and path constraints demonstrate the rapid construction of complex trajectories without requiring any a-priori insight into the structure of the solutions. Trajectory problems of this kind were previously considered impractical to solve using indirect methods. The performance of the GPU-accelerated solver is found to be 2x--4x faster than MATLAB's bvp4c, even while running on GPU hardware that is five years behind the state-of-the-art.

A DAG Scheduling Scheme on Heterogeneous Computing Systems Using Tuple-Based Chemical Reaction Optimization

PubMed Central

Jiang, Yuyi; Shao, Zhiqing; Guo, Yi

2014-01-01

A complex computing problem can be solved efficiently on a system with multiple computing nodes by dividing its implementation code into several parallel processing modules or tasks that can be formulated as directed acyclic graph (DAG) problems. The DAG jobs may be mapped to and scheduled on the computing nodes to minimize the total execution time. Searching an optimal DAG scheduling solution is considered to be NP-complete. This paper proposed a tuple molecular structure-based chemical reaction optimization (TMSCRO) method for DAG scheduling on heterogeneous computing systems, based on a very recently proposed metaheuristic method, chemical reaction optimization (CRO). Comparing with other CRO-based algorithms for DAG scheduling, the design of tuple reaction molecular structure and four elementary reaction operators of TMSCRO is more reasonable. TMSCRO also applies the concept of constrained critical paths (CCPs), constrained-critical-path directed acyclic graph (CCPDAG) and super molecule for accelerating convergence. In this paper, we have also conducted simulation experiments to verify the effectiveness and efficiency of TMSCRO upon a large set of randomly generated graphs and the graphs for real world problems. PMID:25143977

A DAG scheduling scheme on heterogeneous computing systems using tuple-based chemical reaction optimization.

PubMed

Jiang, Yuyi; Shao, Zhiqing; Guo, Yi

2014-01-01

A complex computing problem can be solved efficiently on a system with multiple computing nodes by dividing its implementation code into several parallel processing modules or tasks that can be formulated as directed acyclic graph (DAG) problems. The DAG jobs may be mapped to and scheduled on the computing nodes to minimize the total execution time. Searching an optimal DAG scheduling solution is considered to be NP-complete. This paper proposed a tuple molecular structure-based chemical reaction optimization (TMSCRO) method for DAG scheduling on heterogeneous computing systems, based on a very recently proposed metaheuristic method, chemical reaction optimization (CRO). Comparing with other CRO-based algorithms for DAG scheduling, the design of tuple reaction molecular structure and four elementary reaction operators of TMSCRO is more reasonable. TMSCRO also applies the concept of constrained critical paths (CCPs), constrained-critical-path directed acyclic graph (CCPDAG) and super molecule for accelerating convergence. In this paper, we have also conducted simulation experiments to verify the effectiveness and efficiency of TMSCRO upon a large set of randomly generated graphs and the graphs for real world problems.

Active vibration mitigation of distributed parameter, smart-type structures using Pseudo-Feedback Optimal Control (PFOC)

NASA Technical Reports Server (NTRS)

Patten, W. N.; Robertshaw, H. H.; Pierpont, D.; Wynn, R. H.

1989-01-01

A new, near-optimal feedback control technique is introduced that is shown to provide excellent vibration attenuation for those distributed parameter systems that are often encountered in the areas of aeroservoelasticity and large space systems. The technique relies on a novel solution methodology for the classical optimal control problem. Specifically, the quadratic regulator control problem for a flexible vibrating structure is first cast in a weak functional form that admits an approximate solution. The necessary conditions (first-order) are then solved via a time finite-element method. The procedure produces a low dimensional, algebraic parameterization of the optimal control problem that provides a rigorous basis for a discrete controller with a first-order like hold output. Simulation has shown that the algorithm can successfully control a wide variety of plant forms including multi-input/multi-output systems and systems exhibiting significant nonlinearities. In order to firmly establish the efficacy of the algorithm, a laboratory control experiment was implemented to provide planar (bending) vibration attenuation of a highly flexible beam (with a first clamped-free mode of approximately 0.5 Hz).

Perform - A performance optimizing computer program for dynamic systems subject to transient loadings

NASA Technical Reports Server (NTRS)

Pilkey, W. D.; Wang, B. P.; Yoo, Y.; Clark, B.

1973-01-01

A description and applications of a computer capability for determining the ultimate optimal behavior of a dynamically loaded structural-mechanical system are presented. This capability provides characteristics of the theoretically best, or limiting, design concept according to response criteria dictated by design requirements. Equations of motion of the system in first or second order form include incompletely specified elements whose characteristics are determined in the optimization of one or more performance indices subject to the response criteria in the form of constraints. The system is subject to deterministic transient inputs, and the computer capability is designed to operate with a large linear programming on-the-shelf software package which performs the desired optimization. The report contains user-oriented program documentation in engineering, problem-oriented form. Applications cover a wide variety of dynamics problems including those associated with such diverse configurations as a missile-silo system, impacting freight cars, and an aircraft ride control system.

A parallel adaptive quantum genetic algorithm for the controllability of arbitrary networks.

PubMed

Li, Yuhong; Gong, Guanghong; Li, Ni

2018-01-01

In this paper, we propose a novel algorithm-parallel adaptive quantum genetic algorithm-which can rapidly determine the minimum control nodes of arbitrary networks with both control nodes and state nodes. The corresponding network can be fully controlled with the obtained control scheme. We transformed the network controllability issue into a combinational optimization problem based on the Popov-Belevitch-Hautus rank condition. A set of canonical networks and a list of real-world networks were experimented. Comparison results demonstrated that the algorithm was more ideal to optimize the controllability of networks, especially those larger-size networks. We demonstrated subsequently that there were links between the optimal control nodes and some network statistical characteristics. The proposed algorithm provides an effective approach to improve the controllability optimization of large networks or even extra-large networks with hundreds of thousands nodes.

A comparison of quality and utilization problems in large and small group practices.

PubMed

Gleason, S C; Richards, M J; Quinnell, J E

1995-12-01

Physicians practicing in large, multispecialty medical groups share an organizational culture that differs from that of physicians in small or independent practices. Since 1980, there has been a sharp increase in the size of multispecialty group practice organizations, in part because of increased efficiencies of large group practices. The greater number of physicians and support personnel in a large group practice also requires a relatively more sophisticated management structure. The efficiencies, conveniences, and management structure of a large group practice provide an optimal environment to practice medicine. However, a search of the literature found no data linking a large group practice environment to practice outcomes. The purpose of the study reported in this article was to determine if physicians in large practices have fewer quality and utilization problems than physicians in small or independent practices.

Multicast Routing and Wavelength Assignment with Shared Protection in Multi-Fiber WDM Mesh Networks: Optimal and Heuristic Solutions

NASA Astrophysics Data System (ADS)

Woradit, Kampol; Guyot, Matthieu; Vanichchanunt, Pisit; Saengudomlert, Poompat; Wuttisittikulkij, Lunchakorn

While the problem of multicast routing and wavelength assignment (MC-RWA) in optical wavelength division multiplexing (WDM) networks has been investigated, relatively few researchers have considered network survivability for multicasting. This paper provides an optimization framework to solve the MC-RWA problem in a multi-fiber WDM network that can recover from a single-link failure with shared protection. Using the light-tree (LT) concept to support multicast sessions, we consider two protection strategies that try to reduce service disruptions after a link failure. The first strategy, called light-tree reconfiguration (LTR) protection, computes a new multicast LT for each session affected by the failure. The second strategy, called optical branch reconfiguration (OBR) protection, tries to restore a logical connection between two adjacent multicast members disconnected by the failure. To solve the MC-RWA problem optimally, we propose an integer linear programming (ILP) formulation that minimizes the total number of fibers required for both working and backup traffic. The ILP formulation takes into account joint routing of working and backup traffic, the wavelength continuity constraint, and the limited splitting degree of multicast-capable optical cross-connects (MC-OXCs). After showing some numerical results for optimal solutions, we propose heuristic algorithms that reduce the computational complexity and make the problem solvable for large networks. Numerical results suggest that the proposed heuristic yields efficient solutions compared to optimal solutions obtained from exact optimization.

BioPreDyn-bench: a suite of benchmark problems for dynamic modelling in systems biology.

PubMed

Villaverde, Alejandro F; Henriques, David; Smallbone, Kieran; Bongard, Sophia; Schmid, Joachim; Cicin-Sain, Damjan; Crombach, Anton; Saez-Rodriguez, Julio; Mauch, Klaus; Balsa-Canto, Eva; Mendes, Pedro; Jaeger, Johannes; Banga, Julio R

2015-02-20

Dynamic modelling is one of the cornerstones of systems biology. Many research efforts are currently being invested in the development and exploitation of large-scale kinetic models. The associated problems of parameter estimation (model calibration) and optimal experimental design are particularly challenging. The community has already developed many methods and software packages which aim to facilitate these tasks. However, there is a lack of suitable benchmark problems which allow a fair and systematic evaluation and comparison of these contributions. Here we present BioPreDyn-bench, a set of challenging parameter estimation problems which aspire to serve as reference test cases in this area. This set comprises six problems including medium and large-scale kinetic models of the bacterium E. coli, baker's yeast S. cerevisiae, the vinegar fly D. melanogaster, Chinese Hamster Ovary cells, and a generic signal transduction network. The level of description includes metabolism, transcription, signal transduction, and development. For each problem we provide (i) a basic description and formulation, (ii) implementations ready-to-run in several formats, (iii) computational results obtained with specific solvers, (iv) a basic analysis and interpretation. This suite of benchmark problems can be readily used to evaluate and compare parameter estimation methods. Further, it can also be used to build test problems for sensitivity and identifiability analysis, model reduction and optimal experimental design methods. The suite, including codes and documentation, can be freely downloaded from the BioPreDyn-bench website, https://sites.google.com/site/biopredynbenchmarks/ .

A brief historical introduction to Euler's formula for polyhedra, topology, graph theory and networks

NASA Astrophysics Data System (ADS)

Debnath, Lokenath

2010-09-01

This article is essentially devoted to a brief historical introduction to Euler's formula for polyhedra, topology, theory of graphs and networks with many examples from the real-world. Celebrated Königsberg seven-bridge problem and some of the basic properties of graphs and networks for some understanding of the macroscopic behaviour of real physical systems are included. We also mention some important and modern applications of graph theory or network problems from transportation to telecommunications. Graphs or networks are effectively used as powerful tools in industrial, electrical and civil engineering, communication networks in the planning of business and industry. Graph theory and combinatorics can be used to understand the changes that occur in many large and complex scientific, technical and medical systems. With the advent of fast large computers and the ubiquitous Internet consisting of a very large network of computers, large-scale complex optimization problems can be modelled in terms of graphs or networks and then solved by algorithms available in graph theory. Many large and more complex combinatorial problems dealing with the possible arrangements of situations of various kinds, and computing the number and properties of such arrangements can be formulated in terms of networks. The Knight's tour problem, Hamilton's tour problem, problem of magic squares, the Euler Graeco-Latin squares problem and their modern developments in the twentieth century are also included.

Ultra low power CMOS technology

NASA Technical Reports Server (NTRS)

Burr, J.; Peterson, A.

1991-01-01

This paper discusses the motivation, opportunities, and problems associated with implementing digital logic at very low voltages, including the challenge of making use of the available real estate in 3D multichip modules, energy requirements of very large neural networks, energy optimization metrics and their impact on system design, modeling problems, circuit design constraints, possible fabrication process modifications to improve performance, and barriers to practical implementation.

Optimal radiotherapy dose schedules under parametric uncertainty

NASA Astrophysics Data System (ADS)

Badri, Hamidreza; Watanabe, Yoichi; Leder, Kevin

2016-01-01

We consider the effects of parameter uncertainty on the optimal radiation schedule in the context of the linear-quadratic model. Our interest arises from the observation that if inter-patient variability in normal and tumor tissue radiosensitivity or sparing factor of the organs-at-risk (OAR) are not accounted for during radiation scheduling, the performance of the therapy may be strongly degraded or the OAR may receive a substantially larger dose than the allowable threshold. This paper proposes a stochastic radiation scheduling concept to incorporate inter-patient variability into the scheduling optimization problem. Our method is based on a probabilistic approach, where the model parameters are given by a set of random variables. Our probabilistic formulation ensures that our constraints are satisfied with a given probability, and that our objective function achieves a desired level with a stated probability. We used a variable transformation to reduce the resulting optimization problem to two dimensions. We showed that the optimal solution lies on the boundary of the feasible region and we implemented a branch and bound algorithm to find the global optimal solution. We demonstrated how the configuration of optimal schedules in the presence of uncertainty compares to optimal schedules in the absence of uncertainty (conventional schedule). We observed that in order to protect against the possibility of the model parameters falling into a region where the conventional schedule is no longer feasible, it is required to avoid extremal solutions, i.e. a single large dose or very large total dose delivered over a long period. Finally, we performed numerical experiments in the setting of head and neck tumors including several normal tissues to reveal the effect of parameter uncertainty on optimal schedules and to evaluate the sensitivity of the solutions to the choice of key model parameters.

Multilevel algorithms for nonlinear optimization

NASA Technical Reports Server (NTRS)

Alexandrov, Natalia; Dennis, J. E., Jr.

1994-01-01

Multidisciplinary design optimization (MDO) gives rise to nonlinear optimization problems characterized by a large number of constraints that naturally occur in blocks. We propose a class of multilevel optimization methods motivated by the structure and number of constraints and by the expense of the derivative computations for MDO. The algorithms are an extension to the nonlinear programming problem of the successful class of local Brown-Brent algorithms for nonlinear equations. Our extensions allow the user to partition constraints into arbitrary blocks to fit the application, and they separately process each block and the objective function, restricted to certain subspaces. The methods use trust regions as a globalization strategy, and they have been shown to be globally convergent under reasonable assumptions. The multilevel algorithms can be applied to all classes of MDO formulations. Multilevel algorithms for solving nonlinear systems of equations are a special case of the multilevel optimization methods. In this case, they can be viewed as a trust-region globalization of the Brown-Brent class.

Optimal design of composite upper covers of lateral wings with the effect of rib attachment to stiffener webs

NASA Astrophysics Data System (ADS)

Barkanov, E.; Eglītis, E.; Almeida, F.; Bowering, M. C.; Watson, G.

2013-07-01

The present investigation is devoted to the development of new optimal design concepts that exploit the full potential of advanced composite materials in the upper covers of aircraft lateral wings. A finite-element simulation of three-rib-bay laminated composite panels with T-stiffeners and a stiffener pitch of 200 mm is carried out using ANSYS to investigate the effect of rib attachment to stiffener webs on the performance of stiffened panels in terms of their buckling behavior and in relation to skin and stiffener lay-ups, stiffener height, and root width. Due to the large dimension of numerical problems to be solved, an optimization methodology is developed employing the method of experimental design and the response surface technique. Minimal-weight optimization problems were solved for four load levels with account of manufacturing, repairability, and damage tolerance requirements. The optimal results were verified successfully by using the ANSYS and ABAQUS shared-node models.

Multidisciplinary optimization of controlled space structures with global sensitivity equations

NASA Technical Reports Server (NTRS)

Padula, Sharon L.; James, Benjamin B.; Graves, Philip C.; Woodard, Stanley E.

1991-01-01

A new method for the preliminary design of controlled space structures is presented. The method coordinates standard finite element structural analysis, multivariable controls, and nonlinear programming codes and allows simultaneous optimization of the structures and control systems of a spacecraft. Global sensitivity equations are a key feature of this method. The preliminary design of a generic geostationary platform is used to demonstrate the multidisciplinary optimization method. Fifteen design variables are used to optimize truss member sizes and feedback gain values. The goal is to reduce the total mass of the structure and the vibration control system while satisfying constraints on vibration decay rate. Incorporating the nonnegligible mass of actuators causes an essential coupling between structural design variables and control design variables. The solution of the demonstration problem is an important step toward a comprehensive preliminary design capability for structures and control systems. Use of global sensitivity equations helps solve optimization problems that have a large number of design variables and a high degree of coupling between disciplines.

Efficient Planning of Wind-Optimal Routes in North Atlantic Oceanic Airspace

NASA Technical Reports Server (NTRS)

Rodionova, Olga; Sridhar, Banavar

2017-01-01

The North Atlantic oceanic airspace (NAT) is crossed daily by more than a thousand flights, which are greatly affected by strong jet stream air currents. Several studies devoted to generating wind-optimal (WO) aircraft trajectories in the NAT demonstrated great efficiency of such an approach for individual flights. However, because of the large separation norms imposed in the NAT, previously proposed WO trajectories induce a large number of potential conflicts. Much work has been done on strategic conflict detection and resolution (CDR) in the NAT. The work presented here extends previous methods and attempts to take advantage of the NAT traffic structure to simplify the problem and improve the results of CDR. Four approaches are studied in this work: 1) subdividing the existing CDR problem into sub-problems of smaller sizes, which are easier to handle; 2) more efficient data reorganization within the considered time period; 3) problem localization, i.e. concentrating the resolution effort in the most conflicted regions; 4) applying CDR to the pre-tactical decision horizon (a couple of hours in advance). Obtained results show that these methods efficiently resolve potential conflicts at the strategic and pre-tactical levels by keeping the resulting trajectories close to the initial WO ones.

Applications of Optimal Building Energy System Selection and Operation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marnay, Chris; Stadler, Michael; Siddiqui, Afzal

2011-04-01

Berkeley Lab has been developing the Distributed Energy Resources Customer Adoption Model (DER-CAM) for several years. Given load curves for energy services requirements in a building microgrid (u grid), fuel costs and other economic inputs, and a menu of available technologies, DER-CAM finds the optimum equipment fleet and its optimum operating schedule using a mixed integer linear programming approach. This capability is being applied using a software as a service (SaaS) model. Optimisation problems are set up on a Berkeley Lab server and clients can execute their jobs as needed, typically daily. The evolution of this approach is demonstrated bymore » description of three ongoing projects. The first is a public access web site focused on solar photovoltaic generation and battery viability at large commercial and industrial customer sites. The second is a building CO2 emissions reduction operations problem for a University of California, Davis student dining hall for which potential investments are also considered. And the third, is both a battery selection problem and a rolling operating schedule problem for a large County Jail. Together these examples show that optimization of building u grid design and operation can be effectively achieved using SaaS.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

None, None

The Second SIAM Conference on Computational Science and Engineering was held in San Diego from February 10-12, 2003. Total conference attendance was 553. This is a 23% increase in attendance over the first conference. The focus of this conference was to draw attention to the tremendous range of major computational efforts on large problems in science and engineering, to promote the interdisciplinary culture required to meet these large-scale challenges, and to encourage the training of the next generation of computational scientists. Computational Science & Engineering (CS&E) is now widely accepted, along with theory and experiment, as a crucial third modemore » of scientific investigation and engineering design. Aerospace, automotive, biological, chemical, semiconductor, and other industrial sectors now rely on simulation for technical decision support. For federal agencies also, CS&E has become an essential support for decisions on resources, transportation, and defense. CS&E is, by nature, interdisciplinary. It grows out of physical applications and it depends on computer architecture, but at its heart are powerful numerical algorithms and sophisticated computer science techniques. From an applied mathematics perspective, much of CS&E has involved analysis, but the future surely includes optimization and design, especially in the presence of uncertainty. Another mathematical frontier is the assimilation of very large data sets through such techniques as adaptive multi-resolution, automated feature search, and low-dimensional parameterization. The themes of the 2003 conference included, but were not limited to: Advanced Discretization Methods; Computational Biology and Bioinformatics; Computational Chemistry and Chemical Engineering; Computational Earth and Atmospheric Sciences; Computational Electromagnetics; Computational Fluid Dynamics; Computational Medicine and Bioengineering; Computational Physics and Astrophysics; Computational Solid Mechanics and Materials; CS&E Education; Meshing and Adaptivity; Multiscale and Multiphysics Problems; Numerical Algorithms for CS&E; Discrete and Combinatorial Algorithms for CS&E; Inverse Problems; Optimal Design, Optimal Control, and Inverse Problems; Parallel and Distributed Computing; Problem-Solving Environments; Software and Wddleware Systems; Uncertainty Estimation and Sensitivity Analysis; and Visualization and Computer Graphics.« less

Parallel evolutionary computation in bioinformatics applications.

PubMed

Pinho, Jorge; Sobral, João Luis; Rocha, Miguel

2013-05-01

A large number of optimization problems within the field of Bioinformatics require methods able to handle its inherent complexity (e.g. NP-hard problems) and also demand increased computational efforts. In this context, the use of parallel architectures is a necessity. In this work, we propose ParJECoLi, a Java based library that offers a large set of metaheuristic methods (such as Evolutionary Algorithms) and also addresses the issue of its efficient execution on a wide range of parallel architectures. The proposed approach focuses on the easiness of use, making the adaptation to distinct parallel environments (multicore, cluster, grid) transparent to the user. Indeed, this work shows how the development of the optimization library can proceed independently of its adaptation for several architectures, making use of Aspect-Oriented Programming. The pluggable nature of parallelism related modules allows the user to easily configure its environment, adding parallelism modules to the base source code when needed. The performance of the platform is validated with two case studies within biological model optimization. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

Reformulation of the covering and quantizer problems as ground states of interacting particles.

PubMed

Torquato, S

2010-11-01

It is known that the sphere-packing problem and the number-variance problem (closely related to an optimization problem in number theory) can be posed as energy minimizations associated with an infinite number of point particles in d-dimensional Euclidean space R(d) interacting via certain repulsive pair potentials. We reformulate the covering and quantizer problems as the determination of the ground states of interacting particles in R(d) that generally involve single-body, two-body, three-body, and higher-body interactions. This is done by linking the covering and quantizer problems to certain optimization problems involving the "void" nearest-neighbor functions that arise in the theory of random media and statistical mechanics. These reformulations, which again exemplify the deep interplay between geometry and physics, allow one now to employ theoretical and numerical optimization techniques to analyze and solve these energy minimization problems. The covering and quantizer problems have relevance in numerous applications, including wireless communication network layouts, the search of high-dimensional data parameter spaces, stereotactic radiation therapy, data compression, digital communications, meshing of space for numerical analysis, and coding and cryptography, among other examples. In the first three space dimensions, the best known solutions of the sphere-packing and number-variance problems (or their "dual" solutions) are directly related to those of the covering and quantizer problems, but such relationships may or may not exist for d≥4 , depending on the peculiarities of the dimensions involved. Our reformulation sheds light on the reasons for these similarities and differences. We also show that disordered saturated sphere packings provide relatively thin (economical) coverings and may yield thinner coverings than the best known lattice coverings in sufficiently large dimensions. In the case of the quantizer problem, we derive improved upper bounds on the quantizer error using sphere-packing solutions, which are generally substantially sharper than an existing upper bound in low to moderately large dimensions. We also demonstrate that disordered saturated sphere packings yield relatively good quantizers. Finally, we remark on possible applications of our results for the detection of gravitational waves.

Reformulation of the covering and quantizer problems as ground states of interacting particles

NASA Astrophysics Data System (ADS)

Torquato, S.

2010-11-01

It is known that the sphere-packing problem and the number-variance problem (closely related to an optimization problem in number theory) can be posed as energy minimizations associated with an infinite number of point particles in d -dimensional Euclidean space Rd interacting via certain repulsive pair potentials. We reformulate the covering and quantizer problems as the determination of the ground states of interacting particles in Rd that generally involve single-body, two-body, three-body, and higher-body interactions. This is done by linking the covering and quantizer problems to certain optimization problems involving the “void” nearest-neighbor functions that arise in the theory of random media and statistical mechanics. These reformulations, which again exemplify the deep interplay between geometry and physics, allow one now to employ theoretical and numerical optimization techniques to analyze and solve these energy minimization problems. The covering and quantizer problems have relevance in numerous applications, including wireless communication network layouts, the search of high-dimensional data parameter spaces, stereotactic radiation therapy, data compression, digital communications, meshing of space for numerical analysis, and coding and cryptography, among other examples. In the first three space dimensions, the best known solutions of the sphere-packing and number-variance problems (or their “dual” solutions) are directly related to those of the covering and quantizer problems, but such relationships may or may not exist for d≥4 , depending on the peculiarities of the dimensions involved. Our reformulation sheds light on the reasons for these similarities and differences. We also show that disordered saturated sphere packings provide relatively thin (economical) coverings and may yield thinner coverings than the best known lattice coverings in sufficiently large dimensions. In the case of the quantizer problem, we derive improved upper bounds on the quantizer error using sphere-packing solutions, which are generally substantially sharper than an existing upper bound in low to moderately large dimensions. We also demonstrate that disordered saturated sphere packings yield relatively good quantizers. Finally, we remark on possible applications of our results for the detection of gravitational waves.

A subgradient approach for constrained binary optimization via quantum adiabatic evolution

NASA Astrophysics Data System (ADS)

Karimi, Sahar; Ronagh, Pooya

2017-08-01

Outer approximation method has been proposed for solving the Lagrangian dual of a constrained binary quadratic programming problem via quantum adiabatic evolution in the literature. This should be an efficient prescription for solving the Lagrangian dual problem in the presence of an ideally noise-free quantum adiabatic system. However, current implementations of quantum annealing systems demand methods that are efficient at handling possible sources of noise. In this paper, we consider a subgradient method for finding an optimal primal-dual pair for the Lagrangian dual of a constrained binary polynomial programming problem. We then study the quadratic stable set (QSS) problem as a case study. We see that this method applied to the QSS problem can be viewed as an instance-dependent penalty-term approach that avoids large penalty coefficients. Finally, we report our experimental results of using the D-Wave 2X quantum annealer and conclude that our approach helps this quantum processor to succeed more often in solving these problems compared to the usual penalty-term approaches.

Extremal Optimization for Quadratic Unconstrained Binary Problems

NASA Astrophysics Data System (ADS)

Boettcher, S.

We present an implementation of τ-EO for quadratic unconstrained binary optimization (QUBO) problems. To this end, we transform modify QUBO from its conventional Boolean presentation into a spin glass with a random external field on each site. These fields tend to be rather large compared to the typical coupling, presenting EO with a challenging two-scale problem, exploring smaller differences in couplings effectively while sufficiently aligning with those strong external fields. However, we also find a simple solution to that problem that indicates that those external fields apparently tilt the energy landscape to a such a degree such that global minima become more easy to find than those of spin glasses without (or very small) fields. We explore the impact of the weight distribution of the QUBO formulation in the operations research literature and analyze their meaning in a spin-glass language. This is significant because QUBO problems are considered among the main contenders for NP-hard problems that could be solved efficiently on a quantum computer such as D-Wave.

Parallel computing for probabilistic fatigue analysis

NASA Technical Reports Server (NTRS)

Sues, Robert H.; Lua, Yuan J.; Smith, Mark D.

1993-01-01

This paper presents the results of Phase I research to investigate the most effective parallel processing software strategies and hardware configurations for probabilistic structural analysis. We investigate the efficiency of both shared and distributed-memory architectures via a probabilistic fatigue life analysis problem. We also present a parallel programming approach, the virtual shared-memory paradigm, that is applicable across both types of hardware. Using this approach, problems can be solved on a variety of parallel configurations, including networks of single or multiprocessor workstations. We conclude that it is possible to effectively parallelize probabilistic fatigue analysis codes; however, special strategies will be needed to achieve large-scale parallelism to keep large number of processors busy and to treat problems with the large memory requirements encountered in practice. We also conclude that distributed-memory architecture is preferable to shared-memory for achieving large scale parallelism; however, in the future, the currently emerging hybrid-memory architectures will likely be optimal.

Genetic algorithms and their use in Geophysical Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Parker, Paul B.

1999-04-01

Genetic algorithms (GAs), global optimization methods that mimic Darwinian evolution are well suited to the nonlinear inverse problems of geophysics. A standard genetic algorithm selects the best or ''fittest'' models from a ''population'' and then applies operators such as crossover and mutation in order to combine the most successful characteristics of each model and produce fitter models. More sophisticated operators have been developed, but the standard GA usually provides a robust and efficient search. Although the choice of parameter settings such as crossover and mutation rate may depend largely on the type of problem being solved, numerous results show thatmore » certain parameter settings produce optimal performance for a wide range of problems and difficulties. In particular, a low (about half of the inverse of the population size) mutation rate is crucial for optimal results, but the choice of crossover method and rate do not seem to affect performance appreciably. Optimal efficiency is usually achieved with smaller (< 50) populations. Lastly, tournament selection appears to be the best choice of selection methods due to its simplicity and its autoscaling properties. However, if a proportional selection method is used such as roulette wheel selection, fitness scaling is a necessity, and a high scaling factor (> 2.0) should be used for the best performance. Three case studies are presented in which genetic algorithms are used to invert for crustal parameters. The first is an inversion for basement depth at Yucca mountain using gravity data, the second an inversion for velocity structure in the crust of the south island of New Zealand using receiver functions derived from teleseismic events, and the third is a similar receiver function inversion for crustal velocities beneath the Mendocino Triple Junction region of Northern California. The inversions demonstrate that genetic algorithms are effective in solving problems with reasonably large numbers of free parameters and with computationally expensive objective function calculations. More sophisticated techniques are presented for special problems. Niching and island model algorithms are introduced as methods to find multiple, distinct solutions to the nonunique problems that are typically seen in geophysics. Finally, hybrid algorithms are investigated as a way to improve the efficiency of the standard genetic algorithm.« less

Genetic algorithms and their use in geophysical problems

NASA Astrophysics Data System (ADS)

Parker, Paul Bradley

Genetic algorithms (GAs), global optimization methods that mimic Darwinian evolution are well suited to the nonlinear inverse problems of geophysics. A standard genetic algorithm selects the best or "fittest" models from a "population" and then applies operators such as crossover and mutation in order to combine the most successful characteristics of each model and produce fitter models. More sophisticated operators have been developed, but the standard GA usually provides a robust and efficient search. Although the choice of parameter settings such as crossover and mutation rate may depend largely on the type of problem being solved, numerous results show that certain parameter settings produce optimal performance for a wide range of problems and difficulties. In particular, a low (about half of the inverse of the population size) mutation rate is crucial for optimal results, but the choice of crossover method and rate do not seem to affect performance appreciably. Also, optimal efficiency is usually achieved with smaller (<50) populations. Lastly, tournament selection appears to be the best choice of selection methods due to its simplicity and its autoscaling properties. However, if a proportional selection method is used such as roulette wheel selection, fitness scaling is a necessity, and a high scaling factor (>2.0) should be used for the best performance. Three case studies are presented in which genetic algorithms are used to invert for crustal parameters. The first is an inversion for basement depth at Yucca mountain using gravity data, the second an inversion for velocity structure in the crust of the south island of New Zealand using receiver functions derived from teleseismic events, and the third is a similar receiver function inversion for crustal velocities beneath the Mendocino Triple Junction region of Northern California. The inversions demonstrate that genetic algorithms are effective in solving problems with reasonably large numbers of free parameters and with computationally expensive objective function calculations. More sophisticated techniques are presented for special problems. Niching and island model algorithms are introduced as methods to find multiple, distinct solutions to the nonunique problems that are typically seen in geophysics. Finally, hybrid algorithms are investigated as a way to improve the efficiency of the standard genetic algorithm.

An optimization-based approach for facility energy management with uncertainties, and, Power portfolio optimization in deregulated electricity markets with risk management

NASA Astrophysics Data System (ADS)

Xu, Jun

Topic 1. An Optimization-Based Approach for Facility Energy Management with Uncertainties. Effective energy management for facilities is becoming increasingly important in view of the rising energy costs, the government mandate on the reduction of energy consumption, and the human comfort requirements. This part of dissertation presents a daily energy management formulation and the corresponding solution methodology for HVAC systems. The problem is to minimize the energy and demand costs through the control of HVAC units while satisfying human comfort, system dynamics, load limit constraints, and other requirements. The problem is difficult in view of the fact that the system is nonlinear, time-varying, building-dependent, and uncertain; and that the direct control of a large number of HVAC components is difficult. In this work, HVAC setpoints are the control variables developed on top of a Direct Digital Control (DDC) system. A method that combines Lagrangian relaxation, neural networks, stochastic dynamic programming, and heuristics is developed to predict the system dynamics and uncontrollable load, and to optimize the setpoints. Numerical testing and prototype implementation results show that our method can effectively reduce total costs, manage uncertainties, and shed the load, is computationally efficient. Furthermore, it is significantly better than existing methods. Topic 2. Power Portfolio Optimization in Deregulated Electricity Markets with Risk Management. In a deregulated electric power system, multiple markets of different time scales exist with various power supply instruments. A load serving entity (LSE) has multiple choices from these instruments to meet its load obligations. In view of the large amount of power involved, the complex market structure, risks in such volatile markets, stringent constraints to be satisfied, and the long time horizon, a power portfolio optimization problem is of critical importance but difficulty for an LSE to serve the load, maximize its profit, and manage risks. In this topic, a mid-term power portfolio optimization problem with risk management is presented. Key instruments are considered, risk terms based on semi-variances of spot market transactions are introduced, and penalties on load obligation violations are added to the objective function to improve algorithm convergence and constraint satisfaction. To overcome the inseparability of the resulting problem, a surrogate optimization framework is developed enabling a decomposition and coordination approach. Numerical testing results show that our method effectively provides decisions for various instruments to maximize profit, manage risks, and is computationally efficient.

The Shortlist Method for fast computation of the Earth Mover's Distance and finding optimal solutions to transportation problems.

PubMed

Gottschlich, Carsten; Schuhmacher, Dominic

2014-01-01

Finding solutions to the classical transportation problem is of great importance, since this optimization problem arises in many engineering and computer science applications. Especially the Earth Mover's Distance is used in a plethora of applications ranging from content-based image retrieval, shape matching, fingerprint recognition, object tracking and phishing web page detection to computing color differences in linguistics and biology. Our starting point is the well-known revised simplex algorithm, which iteratively improves a feasible solution to optimality. The Shortlist Method that we propose substantially reduces the number of candidates inspected for improving the solution, while at the same time balancing the number of pivots required. Tests on simulated benchmarks demonstrate a considerable reduction in computation time for the new method as compared to the usual revised simplex algorithm implemented with state-of-the-art initialization and pivot strategies. As a consequence, the Shortlist Method facilitates the computation of large scale transportation problems in viable time. In addition we describe a novel method for finding an initial feasible solution which we coin Modified Russell's Method.

The Shortlist Method for Fast Computation of the Earth Mover's Distance and Finding Optimal Solutions to Transportation Problems

PubMed Central

Gottschlich, Carsten; Schuhmacher, Dominic

2014-01-01

Finding solutions to the classical transportation problem is of great importance, since this optimization problem arises in many engineering and computer science applications. Especially the Earth Mover's Distance is used in a plethora of applications ranging from content-based image retrieval, shape matching, fingerprint recognition, object tracking and phishing web page detection to computing color differences in linguistics and biology. Our starting point is the well-known revised simplex algorithm, which iteratively improves a feasible solution to optimality. The Shortlist Method that we propose substantially reduces the number of candidates inspected for improving the solution, while at the same time balancing the number of pivots required. Tests on simulated benchmarks demonstrate a considerable reduction in computation time for the new method as compared to the usual revised simplex algorithm implemented with state-of-the-art initialization and pivot strategies. As a consequence, the Shortlist Method facilitates the computation of large scale transportation problems in viable time. In addition we describe a novel method for finding an initial feasible solution which we coin Modified Russell's Method. PMID:25310106

Optimal network modification for spectral radius dependent phase transitions

NASA Astrophysics Data System (ADS)

Rosen, Yonatan; Kirsch, Lior; Louzoun, Yoram

2016-09-01

The dynamics of contact processes on networks is often determined by the spectral radius of the networks adjacency matrices. A decrease of the spectral radius can prevent the outbreak of an epidemic, or impact the synchronization among systems of coupled oscillators. The spectral radius is thus tightly linked to network dynamics and function. As such, finding the minimal change in network structure necessary to reach the intended spectral radius is important theoretically and practically. Given contemporary big data resources such as large scale communication or social networks, this problem should be solved with a low runtime complexity. We introduce a novel method for the minimal decrease in weights of edges required to reach a given spectral radius. The problem is formulated as a convex optimization problem, where a global optimum is guaranteed. The method can be easily adjusted to an efficient discrete removal of edges. We introduce a variant of the method which finds optimal decrease with a focus on weights of vertices. The proposed algorithm is exceptionally scalable, solving the problem for real networks of tens of millions of edges in a short time.

Permutation flow-shop scheduling problem to optimize a quadratic objective function

NASA Astrophysics Data System (ADS)

Ren, Tao; Zhao, Peng; Zhang, Da; Liu, Bingqian; Yuan, Huawei; Bai, Danyu

2017-09-01

A flow-shop scheduling model enables appropriate sequencing for each job and for processing on a set of machines in compliance with identical processing orders. The objective is to achieve a feasible schedule for optimizing a given criterion. Permutation is a special setting of the model in which the processing order of the jobs on the machines is identical for each subsequent step of processing. This article addresses the permutation flow-shop scheduling problem to minimize the criterion of total weighted quadratic completion time. With a probability hypothesis, the asymptotic optimality of the weighted shortest processing time schedule under a consistency condition (WSPT-CC) is proven for sufficiently large-scale problems. However, the worst case performance ratio of the WSPT-CC schedule is the square of the number of machines in certain situations. A discrete differential evolution algorithm, where a new crossover method with multiple-point insertion is used to improve the final outcome, is presented to obtain high-quality solutions for moderate-scale problems. A sequence-independent lower bound is designed for pruning in a branch-and-bound algorithm for small-scale problems. A set of random experiments demonstrates the performance of the lower bound and the effectiveness of the proposed algorithms.

A Simple Label Switching Algorithm for Semisupervised Structural SVMs.

PubMed

Balamurugan, P; Shevade, Shirish; Sundararajan, S

2015-10-01

In structured output learning, obtaining labeled data for real-world applications is usually costly, while unlabeled examples are available in abundance. Semisupervised structured classification deals with a small number of labeled examples and a large number of unlabeled structured data. In this work, we consider semisupervised structural support vector machines with domain constraints. The optimization problem, which in general is not convex, contains the loss terms associated with the labeled and unlabeled examples, along with the domain constraints. We propose a simple optimization approach that alternates between solving a supervised learning problem and a constraint matching problem. Solving the constraint matching problem is difficult for structured prediction, and we propose an efficient and effective label switching method to solve it. The alternating optimization is carried out within a deterministic annealing framework, which helps in effective constraint matching and avoiding poor local minima, which are not very useful. The algorithm is simple and easy to implement. Further, it is suitable for any structured output learning problem where exact inference is available. Experiments on benchmark sequence labeling data sets and a natural language parsing data set show that the proposed approach, though simple, achieves comparable generalization performance.

An Optimizing Space Data-Communications Scheduling Method and Algorithm with Interference Mitigation, Generalized for a Broad Class of Optimization Problems

NASA Technical Reports Server (NTRS)

Rash, James

2014-01-01

NASA's space data-communications infrastructure-the Space Network and the Ground Network-provide scheduled (as well as some limited types of unscheduled) data-communications services to user spacecraft. The Space Network operates several orbiting geostationary platforms (the Tracking and Data Relay Satellite System (TDRSS)), each with its own servicedelivery antennas onboard. The Ground Network operates service-delivery antennas at ground stations located around the world. Together, these networks enable data transfer between user spacecraft and their mission control centers on Earth. Scheduling data-communications events for spacecraft that use the NASA communications infrastructure-the relay satellites and the ground stations-can be accomplished today with software having an operational heritage dating from the 1980s or earlier. An implementation of the scheduling methods and algorithms disclosed and formally specified herein will produce globally optimized schedules with not only optimized service delivery by the space data-communications infrastructure but also optimized satisfaction of all user requirements and prescribed constraints, including radio frequency interference (RFI) constraints. Evolutionary algorithms, a class of probabilistic strategies for searching large solution spaces, is the essential technology invoked and exploited in this disclosure. Also disclosed are secondary methods and algorithms for optimizing the execution efficiency of the schedule-generation algorithms themselves. The scheduling methods and algorithms as presented are adaptable to accommodate the complexity of scheduling the civilian and/or military data-communications infrastructure within the expected range of future users and space- or ground-based service-delivery assets. Finally, the problem itself, and the methods and algorithms, are generalized and specified formally. The generalized methods and algorithms are applicable to a very broad class of combinatorial-optimization problems that encompasses, among many others, the problem of generating optimal space-data communications schedules.

Phenomenological theory of collective decision-making

NASA Astrophysics Data System (ADS)

Zafeiris, Anna; Koman, Zsombor; Mones, Enys; Vicsek, Tamás

2017-08-01

An essential task of groups is to provide efficient solutions for the complex problems they face. Indeed, considerable efforts have been devoted to the question of collective decision-making related to problems involving a single dominant feature. Here we introduce a quantitative formalism for finding the optimal distribution of the group members' competences in the more typical case when the underlying problem is complex, i.e., multidimensional. Thus, we consider teams that are aiming at obtaining the best possible answer to a problem having a number of independent sub-problems. Our approach is based on a generic scheme for the process of evaluating the proposed solutions (i.e., negotiation). We demonstrate that the best performing groups have at least one specialist for each sub-problem - but a far less intuitive result is that finding the optimal solution by the interacting group members requires that the specialists also have some insight into the sub-problems beyond their unique field(s). We present empirical results obtained by using a large-scale database of citations being in good agreement with the above theory. The framework we have developed can easily be adapted to a variety of realistic situations since taking into account the weights of the sub-problems, the opinions or the relations of the group is straightforward. Consequently, our method can be used in several contexts, especially when the optimal composition of a group of decision-makers is designed.

SU-E-T-395: Multi-GPU-Based VMAT Treatment Plan Optimization Using a Column-Generation Approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tian, Z; Shi, F; Jia, X

Purpose: GPU has been employed to speed up VMAT optimizations from hours to minutes. However, its limited memory capacity makes it difficult to handle cases with a huge dose-deposition-coefficient (DDC) matrix, e.g. those with a large target size, multiple arcs, small beam angle intervals and/or small beamlet size. We propose multi-GPU-based VMAT optimization to solve this memory issue to make GPU-based VMAT more practical for clinical use. Methods: Our column-generation-based method generates apertures sequentially by iteratively searching for an optimal feasible aperture (referred as pricing problem, PP) and optimizing aperture intensities (referred as master problem, MP). The PP requires accessmore » to the large DDC matrix, which is implemented on a multi-GPU system. Each GPU stores a DDC sub-matrix corresponding to one fraction of beam angles and is only responsible for calculation related to those angles. Broadcast and parallel reduction schemes are adopted for inter-GPU data transfer. MP is a relatively small-scale problem and is implemented on one GPU. One headand- neck cancer case was used for test. Three different strategies for VMAT optimization on single GPU were also implemented for comparison: (S1) truncating DDC matrix to ignore its small value entries for optimization; (S2) transferring DDC matrix part by part to GPU during optimizations whenever needed; (S3) moving DDC matrix related calculation onto CPU. Results: Our multi-GPU-based implementation reaches a good plan within 1 minute. Although S1 was 10 seconds faster than our method, the obtained plan quality is worse. Both S2 and S3 handle the full DDC matrix and hence yield the same plan as in our method. However, the computation time is longer, namely 4 minutes and 30 minutes, respectively. Conclusion: Our multi-GPU-based VMAT optimization can effectively solve the limited memory issue with good plan quality and high efficiency, making GPUbased ultra-fast VMAT planning practical for real clinical use.« less

Application of high-performance computing to numerical simulation of human movement

NASA Technical Reports Server (NTRS)

Anderson, F. C.; Ziegler, J. M.; Pandy, M. G.; Whalen, R. T.

1995-01-01

We have examined the feasibility of using massively-parallel and vector-processing supercomputers to solve large-scale optimization problems for human movement. Specifically, we compared the computational expense of determining the optimal controls for the single support phase of gait using a conventional serial machine (SGI Iris 4D25), a MIMD parallel machine (Intel iPSC/860), and a parallel-vector-processing machine (Cray Y-MP 8/864). With the human body modeled as a 14 degree-of-freedom linkage actuated by 46 musculotendinous units, computation of the optimal controls for gait could take up to 3 months of CPU time on the Iris. Both the Cray and the Intel are able to reduce this time to practical levels. The optimal solution for gait can be found with about 77 hours of CPU on the Cray and with about 88 hours of CPU on the Intel. Although the overall speeds of the Cray and the Intel were found to be similar, the unique capabilities of each machine are better suited to different portions of the computational algorithm used. The Intel was best suited to computing the derivatives of the performance criterion and the constraints whereas the Cray was best suited to parameter optimization of the controls. These results suggest that the ideal computer architecture for solving very large-scale optimal control problems is a hybrid system in which a vector-processing machine is integrated into the communication network of a MIMD parallel machine.

Solving large scale unit dilemma in electricity system by applying commutative law

NASA Astrophysics Data System (ADS)

Legino, Supriadi; Arianto, Rakhmat

2018-03-01

The conventional system, pooling resources with large centralized power plant interconnected as a network. provides a lot of advantages compare to the isolated one include optimizing efficiency and reliability. However, such a large plant need a huge capital. In addition, more problems emerged to hinder the construction of big power plant as well as its associated transmission lines. By applying commutative law of math, ab = ba, for all a,b €-R, the problem associated with conventional system as depicted above, can be reduced. The idea of having small unit but many power plants, namely “Listrik Kerakyatan,” abbreviated as LK provides both social and environmental benefit that could be capitalized by using proper assumption. This study compares the cost and benefit of LK to those of conventional system, using simulation method to prove that LK offers alternative solution to answer many problems associated with the large system. Commutative Law of Algebra can be used as a simple mathematical model to analyze whether the LK system as an eco-friendly distributed generation can be applied to solve various problems associated with a large scale conventional system. The result of simulation shows that LK provides more value if its plants operate in less than 11 hours as peaker power plant or load follower power plant to improve load curve balance of the power system. The result of simulation indicates that the investment cost of LK plant should be optimized in order to minimize the plant investment cost. This study indicates that the benefit of economies of scale principle does not always apply to every condition, particularly if the portion of intangible cost and benefit is relatively high.

Environment-Aware Production Scheduling for Paint Shops in Automobile Manufacturing: A Multi-Objective Optimization Approach

PubMed Central

Zhang, Rui

2017-01-01

The traditional way of scheduling production processes often focuses on profit-driven goals (such as cycle time or material cost) while tending to overlook the negative impacts of manufacturing activities on the environment in the form of carbon emissions and other undesirable by-products. To bridge the gap, this paper investigates an environment-aware production scheduling problem that arises from a typical paint shop in the automobile manufacturing industry. In the studied problem, an objective function is defined to minimize the emission of chemical pollutants caused by the cleaning of painting devices which must be performed each time before a color change occurs. Meanwhile, minimization of due date violations in the downstream assembly shop is also considered because the two shops are interrelated and connected by a limited-capacity buffer. First, we have developed a mixed-integer programming formulation to describe this bi-objective optimization problem. Then, to solve problems of practical size, we have proposed a novel multi-objective particle swarm optimization (MOPSO) algorithm characterized by problem-specific improvement strategies. A branch-and-bound algorithm is designed for accurately assessing the most promising solutions. Finally, extensive computational experiments have shown that the proposed MOPSO is able to match the solution quality of an exact solver on small instances and outperform two state-of-the-art multi-objective optimizers in literature on large instances with up to 200 cars. PMID:29295603

Environment-Aware Production Schedulingfor Paint Shops in Automobile Manufacturing: A Multi-Objective Optimization Approach.

PubMed

Zhang, Rui

2017-12-25

The traditional way of scheduling production processes often focuses on profit-driven goals (such as cycle time or material cost) while tending to overlook the negative impacts of manufacturing activities on the environment in the form of carbon emissions and other undesirable by-products. To bridge the gap, this paper investigates an environment-aware production scheduling problem that arises from a typical paint shop in the automobile manufacturing industry. In the studied problem, an objective function is defined to minimize the emission of chemical pollutants caused by the cleaning of painting devices which must be performed each time before a color change occurs. Meanwhile, minimization of due date violations in the downstream assembly shop is also considered because the two shops are interrelated and connected by a limited-capacity buffer. First, we have developed a mixed-integer programming formulation to describe this bi-objective optimization problem. Then, to solve problems of practical size, we have proposed a novel multi-objective particle swarm optimization (MOPSO) algorithm characterized by problem-specific improvement strategies. A branch-and-bound algorithm is designed for accurately assessing the most promising solutions. Finally, extensive computational experiments have shown that the proposed MOPSO is able to match the solution quality of an exact solver on small instances and outperform two state-of-the-art multi-objective optimizers in literature on large instances with up to 200 cars.

Machine Learning Techniques in Optimal Design

NASA Technical Reports Server (NTRS)

Cerbone, Giuseppe

1992-01-01

Many important applications can be formalized as constrained optimization tasks. For example, we are studying the engineering domain of two-dimensional (2-D) structural design. In this task, the goal is to design a structure of minimum weight that bears a set of loads. A solution to a design problem in which there is a single load (L) and two stationary support points (S1 and S2) consists of four members, E1, E2, E3, and E4 that connect the load to the support points is discussed. In principle, optimal solutions to problems of this kind can be found by numerical optimization techniques. However, in practice [Vanderplaats, 1984] these methods are slow and they can produce different local solutions whose quality (ratio to the global optimum) varies with the choice of starting points. Hence, their applicability to real-world problems is severely restricted. To overcome these limitations, we propose to augment numerical optimization by first performing a symbolic compilation stage to produce: (a) objective functions that are faster to evaluate and that depend less on the choice of the starting point and (b) selection rules that associate problem instances to a set of recommended solutions. These goals are accomplished by successive specializations of the problem class and of the associated objective functions. In the end, this process reduces the problem to a collection of independent functions that are fast to evaluate, that can be differentiated symbolically, and that represent smaller regions of the overall search space. However, the specialization process can produce a large number of sub-problems. This is overcome by deriving inductively selection rules which associate problems to small sets of specialized independent sub-problems. Each set of candidate solutions is chosen to minimize a cost function which expresses the tradeoff between the quality of the solution that can be obtained from the sub-problem and the time it takes to produce it. The overall solution to the problem, is then obtained by solving in parallel each of the sub-problems in the set and computing the one with the minimum cost. In addition to speeding up the optimization process, our use of learning methods also relieves the expert from the burden of identifying rules that exactly pinpoint optimal candidate sub-problems. In real engineering tasks it is usually too costly to the engineers to derive such rules. Therefore, this paper also contributes to a further step towards the solution of the knowledge acquisition bottleneck [Feigenbaum, 1977] which has somewhat impaired the construction of rulebased expert systems.

Studies in Software Cost Model Behavior: Do We Really Understand Cost Model Performance?

NASA Technical Reports Server (NTRS)

Lum, Karen; Hihn, Jairus; Menzies, Tim

2006-01-01

While there exists extensive literature on software cost estimation techniques, industry practice continues to rely upon standard regression-based algorithms. These software effort models are typically calibrated or tuned to local conditions using local data. This paper cautions that current approaches to model calibration often produce sub-optimal models because of the large variance problem inherent in cost data and by including far more effort multipliers than the data supports. Building optimal models requires that a wider range of models be considered while correctly calibrating these models requires rejection rules that prune variables and records and use multiple criteria for evaluating model performance. The main contribution of this paper is to document a standard method that integrates formal model identification, estimation, and validation. It also documents what we call the large variance problem that is a leading cause of cost model brittleness or instability.

An Adjoint-Based Approach to Study a Flexible Flapping Wing in Pitching-Rolling Motion

NASA Astrophysics Data System (ADS)

Jia, Kun; Wei, Mingjun; Xu, Min; Li, Chengyu; Dong, Haibo

2017-11-01

Flapping-wing aerodynamics, with advantages in agility, efficiency, and hovering capability, has been the choice of many flyers in nature. However, the study of bio-inspired flapping-wing propulsion is often hindered by the problem's large control space with different wing kinematics and deformation. The adjoint-based approach reduces largely the computational cost to a feasible level by solving an inverse problem. Facing the complication from moving boundaries, non-cylindrical calculus provides an easy extension of traditional adjoint-based approach to handle the optimization involving moving boundaries. The improved adjoint method with non-cylindrical calculus for boundary treatment is first applied on a rigid pitching-rolling plate, then extended to a flexible one with active deformation to further increase its propulsion efficiency. The comparison of flow dynamics with the initial and optimal kinematics and deformation provides a unique opportunity to understand the flapping-wing mechanism. Supported by AFOSR and ARL.

Meta-control of combustion performance with a data mining approach

NASA Astrophysics Data System (ADS)

Song, Zhe

Large scale combustion process is complex and proposes challenges of optimizing its performance. Traditional approaches based on thermal dynamics have limitations on finding optimal operational regions due to time-shift nature of the process. Recent advances in information technology enable people collect large volumes of process data easily and continuously. The collected process data contains rich information about the process and, to some extent, represents a digital copy of the process over time. Although large volumes of data exist in industrial combustion processes, they are not fully utilized to the level where the process can be optimized. Data mining is an emerging science which finds patterns or models from large data sets. It has found many successful applications in business marketing, medical and manufacturing domains The focus of this dissertation is on applying data mining to industrial combustion processes, and ultimately optimizing the combustion performance. However the philosophy, methods and frameworks discussed in this research can also be applied to other industrial processes. Optimizing an industrial combustion process has two major challenges. One is the underlying process model changes over time and obtaining an accurate process model is nontrivial. The other is that a process model with high fidelity is usually highly nonlinear, solving the optimization problem needs efficient heuristics. This dissertation is set to solve these two major challenges. The major contribution of this 4-year research is the data-driven solution to optimize the combustion process, where process model or knowledge is identified based on the process data, then optimization is executed by evolutionary algorithms to search for optimal operating regions.

Optimization and Control of Agent-Based Models in Biology: A Perspective.

PubMed

An, G; Fitzpatrick, B G; Christley, S; Federico, P; Kanarek, A; Neilan, R Miller; Oremland, M; Salinas, R; Laubenbacher, R; Lenhart, S

2017-01-01

Agent-based models (ABMs) have become an increasingly important mode of inquiry for the life sciences. They are particularly valuable for systems that are not understood well enough to build an equation-based model. These advantages, however, are counterbalanced by the difficulty of analyzing and using ABMs, due to the lack of the type of mathematical tools available for more traditional models, which leaves simulation as the primary approach. As models become large, simulation becomes challenging. This paper proposes a novel approach to two mathematical aspects of ABMs, optimization and control, and it presents a few first steps outlining how one might carry out this approach. Rather than viewing the ABM as a model, it is to be viewed as a surrogate for the actual system. For a given optimization or control problem (which may change over time), the surrogate system is modeled instead, using data from the ABM and a modeling framework for which ready-made mathematical tools exist, such as differential equations, or for which control strategies can explored more easily. Once the optimization problem is solved for the model of the surrogate, it is then lifted to the surrogate and tested. The final step is to lift the optimization solution from the surrogate system to the actual system. This program is illustrated with published work, using two relatively simple ABMs as a demonstration, Sugarscape and a consumer-resource ABM. Specific techniques discussed include dimension reduction and approximation of an ABM by difference equations as well systems of PDEs, related to certain specific control objectives. This demonstration illustrates the very challenging mathematical problems that need to be solved before this approach can be realistically applied to complex and large ABMs, current and future. The paper outlines a research program to address them.

Dynamic programming methods for concurrent design and dynamic allocation of vehicles embedded in a system-of-systems

NASA Astrophysics Data System (ADS)

Nusawardhana

2007-12-01

Recent developments indicate a changing perspective on how systems or vehicles should be designed. Such transition comes from the way decision makers in defense related agencies address complex problems. Complex problems are now often posed in terms of the capabilities desired, rather than in terms of requirements for a single systems. As a result, the way to provide a set of capabilities is through a collection of several individual, independent systems. This collection of individual independent systems is often referred to as a "System of Systems'' (SoS). Because of the independent nature of the constituent systems in an SoS, approaches to design an SoS, and more specifically, approaches to design a new system as a member of an SoS, will likely be different than the traditional design approaches for complex, monolithic (meaning the constituent parts have no ability for independent operation) systems. Because a system of system evolves over time, this simultaneous system design and resource allocation problem should be investigated in a dynamic context. Such dynamic optimization problems are similar to conventional control problems. However, this research considers problems which not only seek optimizing policies but also seek the proper system or vehicle to operate under these policies. This thesis presents a framework and a set of analytical tools to solve a class of SoS problems that involves the simultaneous design of a new system and allocation of the new system along with existing systems. Such a class of problems belongs to the problems of concurrent design and control of a new systems with solutions consisting of both optimal system design and optimal control strategy. Rigorous mathematical arguments show that the proposed framework solves the concurrent design and control problems. Many results exist for dynamic optimization problems of linear systems. In contrary, results on optimal nonlinear dynamic optimization problems are rare. The proposed framework is equipped with the set of analytical tools to solve several cases of nonlinear optimal control problems: continuous- and discrete-time nonlinear problems with applications on both optimal regulation and tracking. These tools are useful when mathematical descriptions of dynamic systems are available. In the absence of such a mathematical model, it is often necessary to derive a solution based on computer simulation. For this case, a set of parameterized decision may constitute a solution. This thesis presents a method to adjust these parameters based on the principle of stochastic approximation simultaneous perturbation using continuous measurements. The set of tools developed here mostly employs the methods of exact dynamic programming. However, due to the complexity of SoS problems, this research also develops suboptimal solution approaches, collectively recognized as approximate dynamic programming solutions, for large scale problems. The thesis presents, explores, and solves problems from an airline industry, in which a new aircraft is to be designed and allocated along with an existing fleet of aircraft. Because the life cycle of an aircraft is on the order of 10 to 20 years, this problem is to be addressed dynamically so that the new aircraft design is the best design for the fleet over a given time horizon.

Conceptual design and multidisciplinary optimization of in-plane morphing wing structures

NASA Astrophysics Data System (ADS)

Inoyama, Daisaku; Sanders, Brian P.; Joo, James J.

2006-03-01

In this paper, the topology optimization methodology for the synthesis of distributed actuation system with specific applications to the morphing air vehicle is discussed. The main emphasis is placed on the topology optimization problem formulations and the development of computational modeling concepts. For demonstration purposes, the inplane morphing wing model is presented. The analysis model is developed to meet several important criteria: It must allow large rigid-body displacements, as well as variation in planform area, with minimum strain on structural members while retaining acceptable numerical stability for finite element analysis. Preliminary work has indicated that addressed modeling concept meets the criteria and may be suitable for the purpose. Topology optimization is performed on the ground structure based on this modeling concept with design variables that control the system configuration. In other words, states of each element in the model are design variables and they are to be determined through optimization process. In effect, the optimization process assigns morphing members as 'soft' elements, non-morphing load-bearing members as 'stiff' elements, and non-existent members as 'voids.' In addition, the optimization process determines the location and relative force intensities of distributed actuators, which is represented computationally as equal and opposite nodal forces with soft axial stiffness. Several different optimization problem formulations are investigated to understand their potential benefits in solution quality, as well as meaningfulness of formulation itself. Sample in-plane morphing problems are solved to demonstrate the potential capability of the methodology introduced in this paper.

Intelligent Support System of Steel Technical Preparation in an Arc Furnace: Functional Scheme of Interactive Builder of the Multi Objective Optimization Problem

NASA Astrophysics Data System (ADS)

Logunova, O. S.; Sibileva, N. S.

2017-12-01

The purpose of the study is to increase the efficiency of the steelmaking process in large capacity arc furnace on the basis of implementation a new decision-making system about the composition of charge materials. The authors proposed an interactive builder for the formation of the optimization problem, taking into account the requirements of the customer, normative documents and stocks of charge materials in the warehouse. To implement the interactive builder, the sets of deterministic and stochastic model components are developed, as well as a list of preferences of criteria and constraints.

Optimal File-Distribution in Heterogeneous and Asymmetric Storage Networks

NASA Astrophysics Data System (ADS)

Langner, Tobias; Schindelhauer, Christian; Souza, Alexander

We consider an optimisation problem which is motivated from storage virtualisation in the Internet. While storage networks make use of dedicated hardware to provide homogeneous bandwidth between servers and clients, in the Internet, connections between storage servers and clients are heterogeneous and often asymmetric with respect to upload and download. Thus, for a large file, the question arises how it should be fragmented and distributed among the servers to grant "optimal" access to the contents. We concentrate on the transfer time of a file, which is the time needed for one upload and a sequence of n downloads, using a set of m servers with heterogeneous bandwidths. We assume that fragments of the file can be transferred in parallel to and from multiple servers. This model yields a distribution problem that examines the question of how these fragments should be distributed onto those servers in order to minimise the transfer time. We present an algorithm, called FlowScaling, that finds an optimal solution within running time {O}(m log m). We formulate the distribution problem as a maximum flow problem, which involves a function that states whether a solution with a given transfer time bound exists. This function is then used with a scaling argument to determine an optimal solution within the claimed time complexity.

DOMe: A deduplication optimization method for the NewSQL database backups

PubMed Central

Wang, Longxiang; Zhu, Zhengdong; Zhang, Xingjun; Wang, Yinfeng

2017-01-01

Reducing duplicated data of database backups is an important application scenario for data deduplication technology. NewSQL is an emerging database system and is now being used more and more widely. NewSQL systems need to improve data reliability by periodically backing up in-memory data, resulting in a lot of duplicated data. The traditional deduplication method is not optimized for the NewSQL server system and cannot take full advantage of hardware resources to optimize deduplication performance. A recent research pointed out that the future NewSQL server will have thousands of CPU cores, large DRAM and huge NVRAM. Therefore, how to utilize these hardware resources to optimize the performance of data deduplication is an important issue. To solve this problem, we propose a deduplication optimization method (DOMe) for NewSQL system backup. To take advantage of the large number of CPU cores in the NewSQL server to optimize deduplication performance, DOMe parallelizes the deduplication method based on the fork-join framework. The fingerprint index, which is the key data structure in the deduplication process, is implemented as pure in-memory hash table, which makes full use of the large DRAM in NewSQL system, eliminating the performance bottleneck problem of fingerprint index existing in traditional deduplication method. The H-store is used as a typical NewSQL database system to implement DOMe method. DOMe is experimentally analyzed by two representative backup data. The experimental results show that: 1) DOMe can reduce the duplicated NewSQL backup data. 2) DOMe significantly improves deduplication performance by parallelizing CDC algorithms. In the case of the theoretical speedup ratio of the server is 20.8, the speedup ratio of DOMe can achieve up to 18; 3) DOMe improved the deduplication throughput by 1.5 times through the pure in-memory index optimization method. PMID:29049307

Task-driven dictionary learning.

PubMed

Mairal, Julien; Bach, Francis; Ponce, Jean

2012-04-01

Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience, and signal processing. For signals such as natural images that admit such sparse representations, it is now well established that these models are well suited to restoration tasks. In this context, learning the dictionary amounts to solving a large-scale matrix factorization problem, which can be done efficiently with classical optimization tools. The same approach has also been used for learning features from data for other purposes, e.g., image classification, but tuning the dictionary in a supervised way for these tasks has proven to be more difficult. In this paper, we present a general formulation for supervised dictionary learning adapted to a wide variety of tasks, and present an efficient algorithm for solving the corresponding optimization problem. Experiments on handwritten digit classification, digital art identification, nonlinear inverse image problems, and compressed sensing demonstrate that our approach is effective in large-scale settings, and is well suited to supervised and semi-supervised classification, as well as regression tasks for data that admit sparse representations.

Distance Metric Learning via Iterated Support Vector Machines.

PubMed

Zuo, Wangmeng; Wang, Faqiang; Zhang, David; Lin, Liang; Huang, Yuchi; Meng, Deyu; Zhang, Lei

2017-07-11

Distance metric learning aims to learn from the given training data a valid distance metric, with which the similarity between data samples can be more effectively evaluated for classification. Metric learning is often formulated as a convex or nonconvex optimization problem, while most existing methods are based on customized optimizers and become inefficient for large scale problems. In this paper, we formulate metric learning as a kernel classification problem with the positive semi-definite constraint, and solve it by iterated training of support vector machines (SVMs). The new formulation is easy to implement and efficient in training with the off-the-shelf SVM solvers. Two novel metric learning models, namely Positive-semidefinite Constrained Metric Learning (PCML) and Nonnegative-coefficient Constrained Metric Learning (NCML), are developed. Both PCML and NCML can guarantee the global optimality of their solutions. Experiments are conducted on general classification, face verification and person re-identification to evaluate our methods. Compared with the state-of-the-art approaches, our methods can achieve comparable classification accuracy and are efficient in training.

Unequal-area, fixed-shape facility layout problems using the firefly algorithm

NASA Astrophysics Data System (ADS)

Ingole, Supriya; Singh, Dinesh

2017-07-01

In manufacturing industries, the facility layout design is a very important task, as it is concerned with the overall manufacturing cost and profit of the industry. The facility layout problem (FLP) is solved by arranging the departments or facilities of known dimensions on the available floor space. The objective of this article is to implement the firefly algorithm (FA) for solving unequal-area, fixed-shape FLPs and optimizing the costs of total material handling and transportation between the facilities. The FA is a nature-inspired algorithm and can be used for combinatorial optimization problems. Benchmark problems from the previous literature are solved using the FA. To check its effectiveness, it is implemented to solve large-sized FLPs. Computational results obtained using the FA show that the algorithm is less time consuming and the total layout costs for FLPs are better than the best results achieved so far.

Numerical optimization in Hilbert space using inexact function and gradient evaluations

NASA Technical Reports Server (NTRS)

Carter, Richard G.

1989-01-01

Trust region algorithms provide a robust iterative technique for solving non-convex unstrained optimization problems, but in many instances it is prohibitively expensive to compute high accuracy function and gradient values for the method. Of particular interest are inverse and parameter estimation problems, since function and gradient evaluations involve numerically solving large systems of differential equations. A global convergence theory is presented for trust region algorithms in which neither function nor gradient values are known exactly. The theory is formulated in a Hilbert space setting so that it can be applied to variational problems as well as the finite dimensional problems normally seen in trust region literature. The conditions concerning allowable error are remarkably relaxed: relative errors in the gradient error condition is automatically satisfied if the error is orthogonal to the gradient approximation. A technique for estimating gradient error and improving the approximation is also presented.

A new impedance accounting for short- and long-range effects in mixed substructured formulations of nonlinear problems

NASA Astrophysics Data System (ADS)

Negrello, Camille; Gosselet, Pierre; Rey, Christian

2018-05-01

An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents the advantage to be eligible for the research of an optimal interface parameter (often called impedance) which can increase the convergence rate. The optimal value for this parameter is often too expensive to be computed exactly in practice: an approximate version has to be sought for, along with a compromise between efficiency and computational cost. In the context of parallel algorithms for solving nonlinear structural mechanical problems, we propose a new heuristic for the impedance which combines short and long range effects at a low computational cost.

High-performance image reconstruction in fluorescence tomography on desktop computers and graphics hardware.

PubMed

Freiberger, Manuel; Egger, Herbert; Liebmann, Manfred; Scharfetter, Hermann

2011-11-01

Image reconstruction in fluorescence optical tomography is a three-dimensional nonlinear ill-posed problem governed by a system of partial differential equations. In this paper we demonstrate that a combination of state of the art numerical algorithms and a careful hardware optimized implementation allows to solve this large-scale inverse problem in a few seconds on standard desktop PCs with modern graphics hardware. In particular, we present methods to solve not only the forward but also the non-linear inverse problem by massively parallel programming on graphics processors. A comparison of optimized CPU and GPU implementations shows that the reconstruction can be accelerated by factors of about 15 through the use of the graphics hardware without compromising the accuracy in the reconstructed images.

Compiling Planning into Quantum Optimization Problems: A Comparative Study

DTIC Science & Technology

2015-06-07

and Sipser, M. 2000. Quantum computation by adiabatic evolution. arXiv:quant- ph/0001106. Fikes, R. E., and Nilsson, N. J. 1972. STRIPS: A new...become available: quantum annealing. Quantum annealing is one of the most accessible quantum algorithms for a computer sci- ence audience not versed...in quantum computing because of its close ties to classical optimization algorithms such as simulated annealing. While large-scale universal quantum

Algorithms for Data Intensive Applications on Intelligent and Smart Memories

DTIC Science & Technology

2003-03-01

editors). Parallel Algorithms and Architectures. North Holland, 1986. [8] P. Diniz . USC ISI, Personal Communication, March, 2001. [9] M. Frigo, C. E ...hierarchy as well as the Translation Lookaside Buer TLB aect the e ectiveness of cache friendly optimizations These penalties vary among...processors and cause large variations in the e ectiveness of cache performance optimizations The area of graph problems is fundamental in a wide variety of

Kolkata Paise Restaurant Problem: An Introduction

NASA Astrophysics Data System (ADS)

Ghosh, Asim; Biswas, Soumyajyoti; Chatterjee, Arnab; Chakrabarti, Anindya Sundar; Naskar, Tapan; Mitra, Manipushpak; Chakrabarti, Bikas K.

We discuss several stochastic optimization strategies in games with many players having large number of choices (Kolkata Paise Restaurant Problem) and two choices (minority game problem). It is seen that a stochastic crowd avoiding strategy gives very efficient utilization in KPR problem. A slightly modified strategy in the minority game problem gives full utilization but the dynamics stops after reaching full efficiency, thereby making the utilization helpful for only about half of the population (those in minority). We further discuss the ways in which the dynamics may be continued and the utilization becomes effective for all the agents keeping fluctuation arbitrarily small.

Robustness of mission plans for unmanned aircraft

NASA Astrophysics Data System (ADS)

Niendorf, Moritz

This thesis studies the robustness of optimal mission plans for unmanned aircraft. Mission planning typically involves tactical planning and path planning. Tactical planning refers to task scheduling and in multi aircraft scenarios also includes establishing a communication topology. Path planning refers to computing a feasible and collision-free trajectory. For a prototypical mission planning problem, the traveling salesman problem on a weighted graph, the robustness of an optimal tour is analyzed with respect to changes to the edge costs. Specifically, the stability region of an optimal tour is obtained, i.e., the set of all edge cost perturbations for which that tour is optimal. The exact stability region of solutions to variants of the traveling salesman problems is obtained from a linear programming relaxation of an auxiliary problem. Edge cost tolerances and edge criticalities are derived from the stability region. For Euclidean traveling salesman problems, robustness with respect to perturbations to vertex locations is considered and safe radii and vertex criticalities are introduced. For weighted-sum multi-objective problems, stability regions with respect to changes in the objectives, weights, and simultaneous changes are given. Most critical weight perturbations are derived. Computing exact stability regions is intractable for large instances. Therefore, tractable approximations are desirable. The stability region of solutions to relaxations of the traveling salesman problem give under approximations and sets of tours give over approximations. The application of these results to the two-neighborhood and the minimum 1-tree relaxation are discussed. Bounds on edge cost tolerances and approximate criticalities are obtainable likewise. A minimum spanning tree is an optimal communication topology for minimizing the cumulative transmission power in multi aircraft missions. The stability region of a minimum spanning tree is given and tolerances, stability balls, and criticalities are derived. This analysis is extended to Euclidean minimum spanning trees. This thesis aims at enabling increased mission performance by providing means of assessing the robustness and optimality of a mission and methods for identifying critical elements. Examples of the application to mission planning in contested environments, cargo aircraft mission planning, multi-objective mission planning, and planning optimal communication topologies for teams of unmanned aircraft are given.

Resonator reset in circuit QED by optimal control for large open quantum systems

NASA Astrophysics Data System (ADS)

Boutin, Samuel; Andersen, Christian Kraglund; Venkatraman, Jayameenakshi; Ferris, Andrew J.; Blais, Alexandre

2017-10-01

We study an implementation of the open GRAPE (gradient ascent pulse engineering) algorithm well suited for large open quantum systems. While typical implementations of optimal control algorithms for open quantum systems rely on explicit matrix exponential calculations, our implementation avoids these operations, leading to a polynomial speedup of the open GRAPE algorithm in cases of interest. This speedup, as well as the reduced memory requirements of our implementation, are illustrated by comparison to a standard implementation of open GRAPE. As a practical example, we apply this open-system optimization method to active reset of a readout resonator in circuit QED. In this problem, the shape of a microwave pulse is optimized such as to empty the cavity from measurement photons as fast as possible. Using our open GRAPE implementation, we obtain pulse shapes, leading to a reset time over 4 times faster than passive reset.

A novel adaptive Cuckoo search for optimal query plan generation.

PubMed

Gomathi, Ramalingam; Sharmila, Dhandapani

2014-01-01

The emergence of multiple web pages day by day leads to the development of the semantic web technology. A World Wide Web Consortium (W3C) standard for storing semantic web data is the resource description framework (RDF). To enhance the efficiency in the execution time for querying large RDF graphs, the evolving metaheuristic algorithms become an alternate to the traditional query optimization methods. This paper focuses on the problem of query optimization of semantic web data. An efficient algorithm called adaptive Cuckoo search (ACS) for querying and generating optimal query plan for large RDF graphs is designed in this research. Experiments were conducted on different datasets with varying number of predicates. The experimental results have exposed that the proposed approach has provided significant results in terms of query execution time. The extent to which the algorithm is efficient is tested and the results are documented.

Design, economic and system considerations of large wind-driven generators

NASA Technical Reports Server (NTRS)

Jorgensen, G. E.; Lotker, M.; Meier, R. C.; Brierley, D.

1976-01-01

The increased search for alternative energy sources has lead to renewed interest and studies of large wind-driven generators. This paper presents the results and considerations of such an investigation. The paper emphasizes the concept selection of wind-driven generators, system optimization, control system design, safety aspects, economic viability on electric utility systems and potential electric system interfacing problems.

Optimal placement of excitations and sensors for verification of large dynamical systems

NASA Technical Reports Server (NTRS)

Salama, M.; Rose, T.; Garba, J.

1987-01-01

The computationally difficult problem of the optimal placement of excitations and sensors to maximize the observed measurements is studied within the framework of combinatorial optimization, and is solved numerically using a variation of the simulated annealing heuristic algorithm. Results of numerical experiments including a square plate and a 960 degrees-of-freedom Control of Flexible Structure (COFS) truss structure, are presented. Though the algorithm produces suboptimal solutions, its generality and simplicity allow the treatment of complex dynamical systems which would otherwise be difficult to handle.

UCAV path planning in the presence of radar-guided surface-to-air missile threats

NASA Astrophysics Data System (ADS)

Zeitz, Frederick H., III

This dissertation addresses the problem of path planning for unmanned combat aerial vehicles (UCAVs) in the presence of radar-guided surface-to-air missiles (SAMs). The radars, collocated with SAM launch sites, operate within the structure of an Integrated Air Defense System (IADS) that permits communication and cooperation between individual radars. The problem is formulated in the framework of the interaction between three sub-systems: the aircraft, the IADS, and the missile. The main features of this integrated model are: The aircraft radar cross section (RCS) depends explicitly on both the aspect and bank angles; hence, the RCS and aircraft dynamics are coupled. The probabilistic nature of IADS tracking is accounted for; namely, the probability that the aircraft has been continuously tracked by the IADS depends on the aircraft RCS and range from the perspective of each radar within the IADS. Finally, the requirement to maintain tracking prior to missile launch and during missile flyout are also modeled. Based on this model, the problem of UCAV path planning is formulated as a minimax optimal control problem, with the aircraft bank angle serving as control. Necessary conditions of optimality for this minimax problem are derived. Based on these necessary conditions, properties of the optimal paths are derived. These properties are used to discretize the dynamic optimization problem into a finite-dimensional, nonlinear programming problem that can be solved numerically. Properties of the optimal paths are also used to initialize the numerical procedure. A homotopy method is proposed to solve the finite-dimensional, nonlinear programming problem, and a heuristic method is proposed to improve the discretization during the homotopy process. Based upon the properties of numerical solutions, a method is proposed for parameterizing and storing information for later recall in flight to permit rapid replanning in response to changing threats. Illustrative examples are presented that confirm the standard flying tactics of "denying range, aspect, and aim," by yielding flight paths that "weave" to avoid long exposures of aspects with large RCS.

People efficiently explore the solution space of the computationally intractable traveling salesman problem to find near-optimal tours.

PubMed

Acuña, Daniel E; Parada, Víctor

2010-07-29

Humans need to solve computationally intractable problems such as visual search, categorization, and simultaneous learning and acting, yet an increasing body of evidence suggests that their solutions to instantiations of these problems are near optimal. Computational complexity advances an explanation to this apparent paradox: (1) only a small portion of instances of such problems are actually hard, and (2) successful heuristics exploit structural properties of the typical instance to selectively improve parts that are likely to be sub-optimal. We hypothesize that these two ideas largely account for the good performance of humans on computationally hard problems. We tested part of this hypothesis by studying the solutions of 28 participants to 28 instances of the Euclidean Traveling Salesman Problem (TSP). Participants were provided feedback on the cost of their solutions and were allowed unlimited solution attempts (trials). We found a significant improvement between the first and last trials and that solutions are significantly different from random tours that follow the convex hull and do not have self-crossings. More importantly, we found that participants modified their current better solutions in such a way that edges belonging to the optimal solution ("good" edges) were significantly more likely to stay than other edges ("bad" edges), a hallmark of structural exploitation. We found, however, that more trials harmed the participants' ability to tell good from bad edges, suggesting that after too many trials the participants "ran out of ideas." In sum, we provide the first demonstration of significant performance improvement on the TSP under repetition and feedback and evidence that human problem-solving may exploit the structure of hard problems paralleling behavior of state-of-the-art heuristics.

People Efficiently Explore the Solution Space of the Computationally Intractable Traveling Salesman Problem to Find Near-Optimal Tours

PubMed Central

Acuña, Daniel E.; Parada, Víctor

2010-01-01

Humans need to solve computationally intractable problems such as visual search, categorization, and simultaneous learning and acting, yet an increasing body of evidence suggests that their solutions to instantiations of these problems are near optimal. Computational complexity advances an explanation to this apparent paradox: (1) only a small portion of instances of such problems are actually hard, and (2) successful heuristics exploit structural properties of the typical instance to selectively improve parts that are likely to be sub-optimal. We hypothesize that these two ideas largely account for the good performance of humans on computationally hard problems. We tested part of this hypothesis by studying the solutions of 28 participants to 28 instances of the Euclidean Traveling Salesman Problem (TSP). Participants were provided feedback on the cost of their solutions and were allowed unlimited solution attempts (trials). We found a significant improvement between the first and last trials and that solutions are significantly different from random tours that follow the convex hull and do not have self-crossings. More importantly, we found that participants modified their current better solutions in such a way that edges belonging to the optimal solution (“good” edges) were significantly more likely to stay than other edges (“bad” edges), a hallmark of structural exploitation. We found, however, that more trials harmed the participants' ability to tell good from bad edges, suggesting that after too many trials the participants “ran out of ideas.” In sum, we provide the first demonstration of significant performance improvement on the TSP under repetition and feedback and evidence that human problem-solving may exploit the structure of hard problems paralleling behavior of state-of-the-art heuristics. PMID:20686597

A variable-gain output feedback control design methodology

NASA Technical Reports Server (NTRS)

Halyo, Nesim; Moerder, Daniel D.; Broussard, John R.; Taylor, Deborah B.

1989-01-01

A digital control system design technique is developed in which the control system gain matrix varies with the plant operating point parameters. The design technique is obtained by formulating the problem as an optimal stochastic output feedback control law with variable gains. This approach provides a control theory framework within which the operating range of a control law can be significantly extended. Furthermore, the approach avoids the major shortcomings of the conventional gain-scheduling techniques. The optimal variable gain output feedback control problem is solved by embedding the Multi-Configuration Control (MCC) problem, previously solved at ICS. An algorithm to compute the optimal variable gain output feedback control gain matrices is developed. The algorithm is a modified version of the MCC algorithm improved so as to handle the large dimensionality which arises particularly in variable-gain control problems. The design methodology developed is applied to a reconfigurable aircraft control problem. A variable-gain output feedback control problem was formulated to design a flight control law for an AFTI F-16 aircraft which can automatically reconfigure its control strategy to accommodate failures in the horizontal tail control surface. Simulations of the closed-loop reconfigurable system show that the approach produces a control design which can accommodate such failures with relative ease. The technique can be applied to many other problems including sensor failure accommodation, mode switching control laws and super agility.

Rational decisions, random matrices and spin glasses

NASA Astrophysics Data System (ADS)

Galluccio, Stefano; Bouchaud, Jean-Philippe; Potters, Marc

We consider the problem of rational decision making in the presence of nonlinear constraints. By using tools borrowed from spin glass and random matrix theory, we focus on the portfolio optimisation problem. We show that the number of optimal solutions is generally exponentially large, and each of them is fragile: rationality is in this case of limited use. In addition, this problem is related to spin glasses with Lévy-like (long-ranged) couplings, for which we show that the ground state is not exponentially degenerate.

Multidisciplinary Optimization Methods for Aircraft Preliminary Design

NASA Technical Reports Server (NTRS)

Kroo, Ilan; Altus, Steve; Braun, Robert; Gage, Peter; Sobieski, Ian

1994-01-01

This paper describes a research program aimed at improved methods for multidisciplinary design and optimization of large-scale aeronautical systems. The research involves new approaches to system decomposition, interdisciplinary communication, and methods of exploiting coarse-grained parallelism for analysis and optimization. A new architecture, that involves a tight coupling between optimization and analysis, is intended to improve efficiency while simplifying the structure of multidisciplinary, computation-intensive design problems involving many analysis disciplines and perhaps hundreds of design variables. Work in two areas is described here: system decomposition using compatibility constraints to simplify the analysis structure and take advantage of coarse-grained parallelism; and collaborative optimization, a decomposition of the optimization process to permit parallel design and to simplify interdisciplinary communication requirements.

Boosting quantum annealer performance via sample persistence

NASA Astrophysics Data System (ADS)

Karimi, Hamed; Rosenberg, Gili

2017-07-01

We propose a novel method for reducing the number of variables in quadratic unconstrained binary optimization problems, using a quantum annealer (or any sampler) to fix the value of a large portion of the variables to values that have a high probability of being optimal. The resulting problems are usually much easier for the quantum annealer to solve, due to their being smaller and consisting of disconnected components. This approach significantly increases the success rate and number of observations of the best known energy value in samples obtained from the quantum annealer, when compared with calling the quantum annealer without using it, even when using fewer annealing cycles. Use of the method results in a considerable improvement in success metrics even for problems with high-precision couplers and biases, which are more challenging for the quantum annealer to solve. The results are further enhanced by applying the method iteratively and combining it with classical pre-processing. We present results for both Chimera graph-structured problems and embedded problems from a real-world application.

Large scale nonlinear programming for the optimization of spacecraft trajectories

NASA Astrophysics Data System (ADS)

Arrieta-Camacho, Juan Jose

Despite the availability of high fidelity mathematical models, the computation of accurate optimal spacecraft trajectories has never been an easy task. While simplified models of spacecraft motion can provide useful estimates on energy requirements, sizing, and cost; the actual launch window and maneuver scheduling must rely on more accurate representations. We propose an alternative for the computation of optimal transfers that uses an accurate representation of the spacecraft dynamics. Like other methodologies for trajectory optimization, this alternative is able to consider all major disturbances. In contrast, it can handle explicitly equality and inequality constraints throughout the trajectory; it requires neither the derivation of costate equations nor the identification of the constrained arcs. The alternative consist of two steps: (1) discretizing the dynamic model using high-order collocation at Radau points, which displays numerical advantages, and (2) solution to the resulting Nonlinear Programming (NLP) problem using an interior point method, which does not suffer from the performance bottleneck associated with identifying the active set, as required by sequential quadratic programming methods; in this way the methodology exploits the availability of sound numerical methods, and next generation NLP solvers. In practice the methodology is versatile; it can be applied to a variety of aerospace problems like homing, guidance, and aircraft collision avoidance; the methodology is particularly well suited for low-thrust spacecraft trajectory optimization. Examples are presented which consider the optimization of a low-thrust orbit transfer subject to the main disturbances due to Earth's gravity field together with Lunar and Solar attraction. Other example considers the optimization of a multiple asteroid rendezvous problem. In both cases, the ability of our proposed methodology to consider non-standard objective functions and constraints is illustrated. Future research directions are identified, involving the automatic scheduling and optimization of trajectory correction maneuvers. The sensitivity information provided by the methodology is expected to be invaluable in such research pursuit. The collocation scheme and nonlinear programming algorithm presented in this work, complement other existing methodologies by providing reliable and efficient numerical methods able to handle large scale, nonlinear dynamic models.

Network planning under uncertainties

NASA Astrophysics Data System (ADS)

Ho, Kwok Shing; Cheung, Kwok Wai

2008-11-01

One of the main focuses for network planning is on the optimization of network resources required to build a network under certain traffic demand projection. Traditionally, the inputs to this type of network planning problems are treated as deterministic. In reality, the varying traffic requirements and fluctuations in network resources can cause uncertainties in the decision models. The failure to include the uncertainties in the network design process can severely affect the feasibility and economics of the network. Therefore, it is essential to find a solution that can be insensitive to the uncertain conditions during the network planning process. As early as in the 1960's, a network planning problem with varying traffic requirements over time had been studied. Up to now, this kind of network planning problems is still being active researched, especially for the VPN network design. Another kind of network planning problems under uncertainties that has been studied actively in the past decade addresses the fluctuations in network resources. One such hotly pursued research topic is survivable network planning. It considers the design of a network under uncertainties brought by the fluctuations in topology to meet the requirement that the network remains intact up to a certain number of faults occurring anywhere in the network. Recently, the authors proposed a new planning methodology called Generalized Survivable Network that tackles the network design problem under both varying traffic requirements and fluctuations of topology. Although all the above network planning problems handle various kinds of uncertainties, it is hard to find a generic framework under more general uncertainty conditions that allows a more systematic way to solve the problems. With a unified framework, the seemingly diverse models and algorithms can be intimately related and possibly more insights and improvements can be brought out for solving the problem. This motivates us to seek a generic framework for solving the network planning problem under uncertainties. In addition to reviewing the various network planning problems involving uncertainties, we also propose that a unified framework based on robust optimization can be used to solve a rather large segment of network planning problem under uncertainties. Robust optimization is first introduced in the operations research literature and is a framework that incorporates information about the uncertainty sets for the parameters in the optimization model. Even though robust optimization is originated from tackling the uncertainty in the optimization process, it can serve as a comprehensive and suitable framework for tackling generic network planning problems under uncertainties. In this paper, we begin by explaining the main ideas behind the robust optimization approach. Then we demonstrate the capabilities of the proposed framework by giving out some examples of how the robust optimization framework can be applied to the current common network planning problems under uncertain environments. Next, we list some practical considerations for solving the network planning problem under uncertainties with the proposed framework. Finally, we conclude this article with some thoughts on the future directions for applying this framework to solve other network planning problems.

Overcoming Communication Restrictions in Collectives

NASA Technical Reports Server (NTRS)

Tumer, Kagan; Agogino, Adrian K.

2004-01-01

Many large distributed system are characterized by having a large number of components (eg., agents, neurons) whose actions and interactions determine a %orld utility which rates the performance of the overall system. Such collectives are often subject to communication restrictions, making it difficult for components which try to optimize their own private utilities, to take actions that also help optimize the world utility. In this article we address that coordination problem and derive four utility functions which present different compromises between how aligned a component s private utility is with the world utility and how readily that component can determine the actions that optimize its utility. The results show that the utility functions specifically derived to operate under communication restrictions outperform both traditional methods and previous collective-based methods by up to 75%.

A Discriminative Sentence Compression Method as Combinatorial Optimization Problem

NASA Astrophysics Data System (ADS)

Hirao, Tsutomu; Suzuki, Jun; Isozaki, Hideki

In the study of automatic summarization, the main research topic was `important sentence extraction' but nowadays `sentence compression' is a hot research topic. Conventional sentence compression methods usually transform a given sentence into a parse tree or a dependency tree, and modify them to get a shorter sentence. However, this method is sometimes too rigid. In this paper, we regard sentence compression as an combinatorial optimization problem that extracts an optimal subsequence of words. Hori et al. also proposed a similar method, but they used only a small number of features and their weights were tuned by hand. We introduce a large number of features such as part-of-speech bigrams and word position in the sentence. Furthermore, we train the system by discriminative learning. According to our experiments, our method obtained better score than other methods with statistical significance.

Optimal Control of Hybrid Systems in Air Traffic Applications

NASA Astrophysics Data System (ADS)

Kamgarpour, Maryam

Growing concerns over the scalability of air traffic operations, air transportation fuel emissions and prices, as well as the advent of communication and sensing technologies motivate improvements to the air traffic management system. To address such improvements, in this thesis a hybrid dynamical model as an abstraction of the air traffic system is considered. Wind and hazardous weather impacts are included using a stochastic model. This thesis focuses on the design of algorithms for verification and control of hybrid and stochastic dynamical systems and the application of these algorithms to air traffic management problems. In the deterministic setting, a numerically efficient algorithm for optimal control of hybrid systems is proposed based on extensions of classical optimal control techniques. This algorithm is applied to optimize the trajectory of an Airbus 320 aircraft in the presence of wind and storms. In the stochastic setting, the verification problem of reaching a target set while avoiding obstacles (reach-avoid) is formulated as a two-player game to account for external agents' influence on system dynamics. The solution approach is applied to air traffic conflict prediction in the presence of stochastic wind. Due to the uncertainty in forecasts of the hazardous weather, and hence the unsafe regions of airspace for aircraft flight, the reach-avoid framework is extended to account for stochastic target and safe sets. This methodology is used to maximize the probability of the safety of aircraft paths through hazardous weather. Finally, the problem of modeling and optimization of arrival air traffic and runway configuration in dense airspace subject to stochastic weather data is addressed. This problem is formulated as a hybrid optimal control problem and is solved with a hierarchical approach that decouples safety and performance. As illustrated with this problem, the large scale of air traffic operations motivates future work on the efficient implementation of the proposed algorithms.

Adaptive bi-level programming for optimal gene knockouts for targeted overproduction under phenotypic constraints

PubMed Central

2013-01-01

Background Optimization procedures to identify gene knockouts for targeted biochemical overproduction have been widely in use in modern metabolic engineering. Flux balance analysis (FBA) framework has provided conceptual simplifications for genome-scale dynamic analysis at steady states. Based on FBA, many current optimization methods for targeted bio-productions have been developed under the maximum cell growth assumption. The optimization problem to derive gene knockout strategies recently has been formulated as a bi-level programming problem in OptKnock for maximum targeted bio-productions with maximum growth rates. However, it has been shown that knockout mutants in fact reach the steady states with the minimization of metabolic adjustment (MOMA) from the corresponding wild-type strains instead of having maximal growth rates after genetic or metabolic intervention. In this work, we propose a new bi-level computational framework--MOMAKnock--which can derive robust knockout strategies under the MOMA flux distribution approximation. Methods In this new bi-level optimization framework, we aim to maximize the production of targeted chemicals by identifying candidate knockout genes or reactions under phenotypic constraints approximated by the MOMA assumption. Hence, the targeted chemical production is the primary objective of MOMAKnock while the MOMA assumption is formulated as the inner problem of constraining the knockout metabolic flux to be as close as possible to the steady-state phenotypes of wide-type strains. As this new inner problem becomes a quadratic programming problem, a novel adaptive piecewise linearization algorithm is developed in this paper to obtain the exact optimal solution to this new bi-level integer quadratic programming problem for MOMAKnock. Results Our new MOMAKnock model and the adaptive piecewise linearization solution algorithm are tested with a small E. coli core metabolic network and a large-scale iAF1260 E. coli metabolic network. The derived knockout strategies are compared with those from OptKnock. Our preliminary experimental results show that MOMAKnock can provide improved targeted productions with more robust knockout strategies. PMID:23368729

Adaptive bi-level programming for optimal gene knockouts for targeted overproduction under phenotypic constraints.

PubMed

Ren, Shaogang; Zeng, Bo; Qian, Xiaoning

2013-01-01

Optimization procedures to identify gene knockouts for targeted biochemical overproduction have been widely in use in modern metabolic engineering. Flux balance analysis (FBA) framework has provided conceptual simplifications for genome-scale dynamic analysis at steady states. Based on FBA, many current optimization methods for targeted bio-productions have been developed under the maximum cell growth assumption. The optimization problem to derive gene knockout strategies recently has been formulated as a bi-level programming problem in OptKnock for maximum targeted bio-productions with maximum growth rates. However, it has been shown that knockout mutants in fact reach the steady states with the minimization of metabolic adjustment (MOMA) from the corresponding wild-type strains instead of having maximal growth rates after genetic or metabolic intervention. In this work, we propose a new bi-level computational framework--MOMAKnock--which can derive robust knockout strategies under the MOMA flux distribution approximation. In this new bi-level optimization framework, we aim to maximize the production of targeted chemicals by identifying candidate knockout genes or reactions under phenotypic constraints approximated by the MOMA assumption. Hence, the targeted chemical production is the primary objective of MOMAKnock while the MOMA assumption is formulated as the inner problem of constraining the knockout metabolic flux to be as close as possible to the steady-state phenotypes of wide-type strains. As this new inner problem becomes a quadratic programming problem, a novel adaptive piecewise linearization algorithm is developed in this paper to obtain the exact optimal solution to this new bi-level integer quadratic programming problem for MOMAKnock. Our new MOMAKnock model and the adaptive piecewise linearization solution algorithm are tested with a small E. coli core metabolic network and a large-scale iAF1260 E. coli metabolic network. The derived knockout strategies are compared with those from OptKnock. Our preliminary experimental results show that MOMAKnock can provide improved targeted productions with more robust knockout strategies.

Results of an integrated structure-control law design sensitivity analysis

NASA Technical Reports Server (NTRS)

Gilbert, Michael G.

1988-01-01

Next generation air and space vehicle designs are driven by increased performance requirements, demanding a high level of design integration between traditionally separate design disciplines. Interdisciplinary analysis capabilities have been developed, for aeroservoelastic aircraft and large flexible spacecraft control for instance, but the requisite integrated design methods are only beginning to be developed. One integrated design method which has received attention is based on hierarchal problem decompositions, optimization, and design sensitivity analyses. This paper highlights a design sensitivity analysis method for Linear Quadratic Cost, Gaussian (LQG) optimal control laws, which predicts change in the optimal control law due to changes in fixed problem parameters using analytical sensitivity equations. Numerical results of a design sensitivity analysis for a realistic aeroservoelastic aircraft example are presented. In this example, the sensitivity of the optimally controlled aircraft's response to various problem formulation and physical aircraft parameters is determined. These results are used to predict the aircraft's new optimally controlled response if the parameter was to have some other nominal value during the control law design process. The sensitivity results are validated by recomputing the optimal control law for discrete variations in parameters, computing the new actual aircraft response, and comparing with the predicted response. These results show an improvement in sensitivity accuracy for integrated design purposes over methods which do not include changess in the optimal control law. Use of the analytical LQG sensitivity expressions is also shown to be more efficient that finite difference methods for the computation of the equivalent sensitivity information.

Chemical Compound Design Using Nuclear Charge Distributions

DTIC Science & Technology

2012-03-01

Finding optimal solutions to design problems in chemistry is hampered by the combinatorially large search space. We develop a general theoretical ... framework for finding chemical compounds with prescribed properties using nuclear charge distributions. The key is the reformulation of the design

Robust Airfoil Optimization in High Resolution Design Space

NASA Technical Reports Server (NTRS)

Li, Wu; Padula, Sharon L.

2003-01-01

The robust airfoil shape optimization is a direct method for drag reduction over a given range of operating conditions and has three advantages: (1) it prevents severe degradation in the off-design performance by using a smart descent direction in each optimization iteration, (2) it uses a large number of B-spline control points as design variables yet the resulting airfoil shape is fairly smooth, and (3) it allows the user to make a trade-off between the level of optimization and the amount of computing time consumed. The robust optimization method is demonstrated by solving a lift-constrained drag minimization problem for a two-dimensional airfoil in viscous flow with a large number of geometric design variables. Our experience with robust optimization indicates that our strategy produces reasonable airfoil shapes that are similar to the original airfoils, but these new shapes provide drag reduction over the specified range of Mach numbers. We have tested this strategy on a number of advanced airfoil models produced by knowledgeable aerodynamic design team members and found that our strategy produces airfoils better or equal to any designs produced by traditional design methods.

Optimum oil production planning using infeasibility driven evolutionary algorithm.

PubMed

Singh, Hemant Kumar; Ray, Tapabrata; Sarker, Ruhul

2013-01-01

In this paper, we discuss a practical oil production planning optimization problem. For oil wells with insufficient reservoir pressure, gas is usually injected to artificially lift oil, a practice commonly referred to as enhanced oil recovery (EOR). The total gas that can be used for oil extraction is constrained by daily availability limits. The oil extracted from each well is known to be a nonlinear function of the gas injected into the well and varies between wells. The problem is to identify the optimal amount of gas that needs to be injected into each well to maximize the amount of oil extracted subject to the constraint on the total daily gas availability. The problem has long been of practical interest to all major oil exploration companies as it has the potential to derive large financial benefit. In this paper, an infeasibility driven evolutionary algorithm is used to solve a 56 well reservoir problem which demonstrates its efficiency in solving constrained optimization problems. Furthermore, a multi-objective formulation of the problem is posed and solved using a number of algorithms, which eliminates the need for solving the (single objective) problem on a regular basis. Lastly, a modified single objective formulation of the problem is also proposed, which aims to maximize the profit instead of the quantity of oil. It is shown that even with a lesser amount of oil extracted, more economic benefits can be achieved through the modified formulation.

Performance of Extended Local Clustering Organization (LCO) for Large Scale Job-Shop Scheduling Problem (JSP)

NASA Astrophysics Data System (ADS)

Konno, Yohko; Suzuki, Keiji

This paper describes an approach to development of a solution algorithm of a general-purpose for large scale problems using “Local Clustering Organization (LCO)” as a new solution for Job-shop scheduling problem (JSP). Using a performance effective large scale scheduling in the study of usual LCO, a solving JSP keep stability induced better solution is examined. In this study for an improvement of a performance of a solution for JSP, processes to a optimization by LCO is examined, and a scheduling solution-structure is extended to a new solution-structure based on machine-division. A solving method introduced into effective local clustering for the solution-structure is proposed as an extended LCO. An extended LCO has an algorithm which improves scheduling evaluation efficiently by clustering of parallel search which extends over plural machines. A result verified by an application of extended LCO on various scale of problems proved to conduce to minimizing make-span and improving on the stable performance.

Decentralized control of large-scale systems: Fixed modes, sensitivity and parametric robustness. Ph.D. Thesis - Universite Paul Sabatier, 1985

NASA Technical Reports Server (NTRS)

Tarras, A.

1987-01-01

The problem of stabilization/pole placement under structural constraints of large scale linear systems is discussed. The existence of a solution to this problem is expressed in terms of fixed modes. The aim is to provide a bibliographic survey of the available results concerning the fixed modes (characterization, elimination, control structure selection to avoid them, control design in their absence) and to present the author's contribution to this problem which can be summarized by the use of the mode sensitivity concept to detect or to avoid them, the use of vibrational control to stabilize them, and the addition of parametric robustness considerations to design an optimal decentralized robust control.

Optimizing an F-16 Squadron Weekly Pilot Schedule for the Turkish Air Force

DTIC Science & Technology

2010-03-01

disrupted schedules are rescheduled , minimizing the total number of changes with respect to the previous schedule’s objective function. Output...producing rosters for a nursing staff in a large general hospital (Dowsland, 1998) and afterwards Aickelin and Dowsland use an Indirect Genetic...algorithm to improve the solutions of the nurse scheduling problem which is similar to the fighter squadron pilot scheduling problem (Aickelin and

Problems With Deployment of Multi-Domained, Multi-Homed Mobile Networks

NASA Technical Reports Server (NTRS)

Ivancic, William D.

2008-01-01

This document describes numerous problems associated with deployment of multi-homed mobile platforms consisting of multiple networks and traversing large geographical areas. The purpose of this document is to provide insight to real-world deployment issues and provide information to groups that are addressing many issues related to multi-homing, policy-base routing, route optimization and mobile security - particularly those groups within the Internet Engineering Task Force.

Tuning Parameters in Heuristics by Using Design of Experiments Methods

NASA Technical Reports Server (NTRS)

Arin, Arif; Rabadi, Ghaith; Unal, Resit

2010-01-01

With the growing complexity of today's large scale problems, it has become more difficult to find optimal solutions by using exact mathematical methods. The need to find near-optimal solutions in an acceptable time frame requires heuristic approaches. In many cases, however, most heuristics have several parameters that need to be "tuned" before they can reach good results. The problem then turns into "finding best parameter setting" for the heuristics to solve the problems efficiently and timely. One-Factor-At-a-Time (OFAT) approach for parameter tuning neglects the interactions between parameters. Design of Experiments (DOE) tools can be instead employed to tune the parameters more effectively. In this paper, we seek the best parameter setting for a Genetic Algorithm (GA) to solve the single machine total weighted tardiness problem in which n jobs must be scheduled on a single machine without preemption, and the objective is to minimize the total weighted tardiness. Benchmark instances for the problem are available in the literature. To fine tune the GA parameters in the most efficient way, we compare multiple DOE models including 2-level (2k ) full factorial design, orthogonal array design, central composite design, D-optimal design and signal-to-noise (SIN) ratios. In each DOE method, a mathematical model is created using regression analysis, and solved to obtain the best parameter setting. After verification runs using the tuned parameter setting, the preliminary results for optimal solutions of multiple instances were found efficiently.

a Comparison of Simulated Annealing, Genetic Algorithm and Particle Swarm Optimization in Optimal First-Order Design of Indoor Tls Networks

NASA Astrophysics Data System (ADS)

Jia, F.; Lichti, D.

2017-09-01

The optimal network design problem has been well addressed in geodesy and photogrammetry but has not received the same attention for terrestrial laser scanner (TLS) networks. The goal of this research is to develop a complete design system that can automatically provide an optimal plan for high-accuracy, large-volume scanning networks. The aim in this paper is to use three heuristic optimization methods, simulated annealing (SA), genetic algorithm (GA) and particle swarm optimization (PSO), to solve the first-order design (FOD) problem for a small-volume indoor network and make a comparison of their performances. The room is simplified as discretized wall segments and possible viewpoints. Each possible viewpoint is evaluated with a score table representing the wall segments visible from each viewpoint based on scanning geometry constraints. The goal is to find a minimum number of viewpoints that can obtain complete coverage of all wall segments with a minimal sum of incidence angles. The different methods have been implemented and compared in terms of the quality of the solutions, runtime and repeatability. The experiment environment was simulated from a room located on University of Calgary campus where multiple scans are required due to occlusions from interior walls. The results obtained in this research show that PSO and GA provide similar solutions while SA doesn't guarantee an optimal solution within limited iterations. Overall, GA is considered as the best choice for this problem based on its capability of providing an optimal solution and fewer parameters to tune.

A framework for using ant colony optimization to schedule environmental flow management alternatives for rivers, wetlands, and floodplains

NASA Astrophysics Data System (ADS)

Szemis, J. M.; Maier, H. R.; Dandy, G. C.

2012-08-01

Rivers, wetlands, and floodplains are in need of management as they have been altered from natural conditions and are at risk of vanishing because of river development. One method to mitigate these impacts involves the scheduling of environmental flow management alternatives (EFMA); however, this is a complex task as there are generally a large number of ecological assets (e.g., wetlands) that need to be considered, each with species with competing flow requirements. Hence, this problem evolves into an optimization problem to maximize an ecological benefit within constraints imposed by human needs and the physical layout of the system. This paper presents a novel optimization framework which uses ant colony optimization to enable optimal scheduling of EFMAs, given constraints on the environmental water that is available. This optimization algorithm is selected because, unlike other currently popular algorithms, it is able to account for all aspects of the problem. The approach is validated by comparing it to a heuristic approach, and its utility is demonstrated using a case study based on the Murray River in South Australia to investigate (1) the trade-off between plant recruitment (i.e., promoting germination) and maintenance (i.e., maintaining habitat) flow requirements, (2) the trade-off between flora and fauna flow requirements, and (3) a hydrograph inversion case. The results demonstrate the usefulness and flexibility of the proposed framework as it is able to determine EFMA schedules that provide optimal or near-optimal trade-offs between the competing needs of species under a range of operating conditions and valuable insight for managers.

A new Monte Carlo-based treatment plan optimization approach for intensity modulated radiation therapy.

PubMed

Li, Yongbao; Tian, Zhen; Shi, Feng; Song, Ting; Wu, Zhaoxia; Liu, Yaqiang; Jiang, Steve; Jia, Xun

2015-04-07

Intensity-modulated radiation treatment (IMRT) plan optimization needs beamlet dose distributions. Pencil-beam or superposition/convolution type algorithms are typically used because of their high computational speed. However, inaccurate beamlet dose distributions may mislead the optimization process and hinder the resulting plan quality. To solve this problem, the Monte Carlo (MC) simulation method has been used to compute all beamlet doses prior to the optimization step. The conventional approach samples the same number of particles from each beamlet. Yet this is not the optimal use of MC in this problem. In fact, there are beamlets that have very small intensities after solving the plan optimization problem. For those beamlets, it may be possible to use fewer particles in dose calculations to increase efficiency. Based on this idea, we have developed a new MC-based IMRT plan optimization framework that iteratively performs MC dose calculation and plan optimization. At each dose calculation step, the particle numbers for beamlets were adjusted based on the beamlet intensities obtained through solving the plan optimization problem in the last iteration step. We modified a GPU-based MC dose engine to allow simultaneous computations of a large number of beamlet doses. To test the accuracy of our modified dose engine, we compared the dose from a broad beam and the summed beamlet doses in this beam in an inhomogeneous phantom. Agreement within 1% for the maximum difference and 0.55% for the average difference was observed. We then validated the proposed MC-based optimization schemes in one lung IMRT case. It was found that the conventional scheme required 10(6) particles from each beamlet to achieve an optimization result that was 3% difference in fluence map and 1% difference in dose from the ground truth. In contrast, the proposed scheme achieved the same level of accuracy with on average 1.2 × 10(5) particles per beamlet. Correspondingly, the computation time including both MC dose calculations and plan optimizations was reduced by a factor of 4.4, from 494 to 113 s, using only one GPU card.

Advanced Computational Methods for Security Constrained Financial Transmission Rights

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kalsi, Karanjit; Elbert, Stephen T.; Vlachopoulou, Maria

Financial Transmission Rights (FTRs) are financial insurance tools to help power market participants reduce price risks associated with transmission congestion. FTRs are issued based on a process of solving a constrained optimization problem with the objective to maximize the FTR social welfare under power flow security constraints. Security constraints for different FTR categories (monthly, seasonal or annual) are usually coupled and the number of constraints increases exponentially with the number of categories. Commercial software for FTR calculation can only provide limited categories of FTRs due to the inherent computational challenges mentioned above. In this paper, first an innovative mathematical reformulationmore » of the FTR problem is presented which dramatically improves the computational efficiency of optimization problem. After having re-formulated the problem, a novel non-linear dynamic system (NDS) approach is proposed to solve the optimization problem. The new formulation and performance of the NDS solver is benchmarked against widely used linear programming (LP) solvers like CPLEX™ and tested on both standard IEEE test systems and large-scale systems using data from the Western Electricity Coordinating Council (WECC). The performance of the NDS is demonstrated to be comparable and in some cases is shown to outperform the widely used CPLEX algorithms. The proposed formulation and NDS based solver is also easily parallelizable enabling further computational improvement.« less

Artificial Intelligence Based Control Power Optimization on Tailless Aircraft. [ARMD Seedling Fund Phase I

NASA Technical Reports Server (NTRS)

Gern, Frank; Vicroy, Dan D.; Mulani, Sameer B.; Chhabra, Rupanshi; Kapania, Rakesh K.; Schetz, Joseph A.; Brown, Derrell; Princen, Norman H.

2014-01-01

Traditional methods of control allocation optimization have shown difficulties in exploiting the full potential of controlling large arrays of control devices on innovative air vehicles. Artificial neutral networks are inspired by biological nervous systems and neurocomputing has successfully been applied to a variety of complex optimization problems. This project investigates the potential of applying neurocomputing to the control allocation optimization problem of Hybrid Wing Body (HWB) aircraft concepts to minimize control power, hinge moments, and actuator forces, while keeping system weights within acceptable limits. The main objective of this project is to develop a proof-of-concept process suitable to demonstrate the potential of using neurocomputing for optimizing actuation power for aircraft featuring multiple independently actuated control surfaces. A Nastran aeroservoelastic finite element model is used to generate a learning database of hinge moment and actuation power characteristics for an array of flight conditions and control surface deflections. An artificial neural network incorporating a genetic algorithm then uses this training data to perform control allocation optimization for the investigated aircraft configuration. The phase I project showed that optimization results for the sum of required hinge moments are improved by more than 12% over the best Nastran solution by using the neural network optimization process.

Biogeography-based particle swarm optimization with fuzzy elitism and its applications to constrained engineering problems

NASA Astrophysics Data System (ADS)

Guo, Weian; Li, Wuzhao; Zhang, Qun; Wang, Lei; Wu, Qidi; Ren, Hongliang

2014-11-01

In evolutionary algorithms, elites are crucial to maintain good features in solutions. However, too many elites can make the evolutionary process stagnate and cannot enhance the performance. This article employs particle swarm optimization (PSO) and biogeography-based optimization (BBO) to propose a hybrid algorithm termed biogeography-based particle swarm optimization (BPSO) which could make a large number of elites effective in searching optima. In this algorithm, the whole population is split into several subgroups; BBO is employed to search within each subgroup and PSO for the global search. Since not all the population is used in PSO, this structure overcomes the premature convergence in the original PSO. Time complexity analysis shows that the novel algorithm does not increase the time consumption. Fourteen numerical benchmarks and four engineering problems with constraints are used to test the BPSO. To better deal with constraints, a fuzzy strategy for the number of elites is investigated. The simulation results validate the feasibility and effectiveness of the proposed algorithm.

On the optimization of discrete structures with aeroelastic constraints

NASA Technical Reports Server (NTRS)

Mcintosh, S. C., Jr.; Ashley, H.

1978-01-01

The paper deals with the problem of dynamic structural optimization where constraints relating to flutter of a wing (or other dynamic aeroelastic performance) are imposed along with conditions of a more conventional nature such as those relating to stress under load, deflection, minimum dimensions of structural elements, etc. The discussion is limited to a flutter problem for a linear system with a finite number of degrees of freedom and a single constraint involving aeroelastic stability, and the structure motion is assumed to be a simple harmonic time function. Three search schemes are applied to the minimum-weight redesign of a particular wing: the first scheme relies on the method of feasible directions, while the other two are derived from necessary conditions for a local optimum so that they can be referred to as optimality-criteria schemes. The results suggest that a heuristic redesign algorithm involving an optimality criterion may be best suited for treating multiple constraints with large numbers of design variables.

Partial differential equations constrained combinatorial optimization on an adiabatic quantum computer

NASA Astrophysics Data System (ADS)

Chandra, Rishabh

Partial differential equation-constrained combinatorial optimization (PDECCO) problems are a mixture of continuous and discrete optimization problems. PDECCO problems have discrete controls, but since the partial differential equations (PDE) are continuous, the optimization space is continuous as well. Such problems have several applications, such as gas/water network optimization, traffic optimization, micro-chip cooling optimization, etc. Currently, no efficient classical algorithm which guarantees a global minimum for PDECCO problems exists. A new mapping has been developed that transforms PDECCO problem, which only have linear PDEs as constraints, into quadratic unconstrained binary optimization (QUBO) problems that can be solved using an adiabatic quantum optimizer (AQO). The mapping is efficient, it scales polynomially with the size of the PDECCO problem, requires only one PDE solve to form the QUBO problem, and if the QUBO problem is solved correctly and efficiently on an AQO, guarantees a global optimal solution for the original PDECCO problem.

Real time optimal guidance of low-thrust spacecraft: an application of nonlinear model predictive control.

PubMed

Arrieta-Camacho, Juan José; Biegler, Lorenz T

2005-12-01

Real time optimal guidance is considered for a class of low thrust spacecraft. In particular, nonlinear model predictive control (NMPC) is utilized for computing the optimal control actions required to transfer a spacecraft from a low Earth orbit to a mission orbit. The NMPC methodology presented is able to cope with unmodeled disturbances. The dynamics of the transfer are modeled using a set of modified equinoctial elements because they do not exhibit singularities for zero inclination and zero eccentricity. The idea behind NMPC is the repeated solution of optimal control problems; at each time step, a new control action is computed. The optimal control problem is solved using a direct method-fully discretizing the equations of motion. The large scale nonlinear program resulting from the discretization procedure is solved using IPOPT--a primal-dual interior point algorithm. Stability and robustness characteristics of the NMPC algorithm are reviewed. A numerical example is presented that encourages further development of the proposed methodology: the transfer from low-Earth orbit to a molniya orbit.

Resolvent analysis of shear flows using One-Way Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Rigas, Georgios; Schmidt, Oliver; Towne, Aaron; Colonius, Tim

2017-11-01

For three-dimensional flows, questions of stability, receptivity, secondary flows, and coherent structures require the solution of large partial-derivative eigenvalue problems. Reduced-order approximations are thus required for engineering prediction since these problems are often computationally intractable or prohibitively expensive. For spatially slowly evolving flows, such as jets and boundary layers, the One-Way Navier-Stokes (OWNS) equations permit a fast spatial marching procedure that results in a huge reduction in computational cost. Here, an adjoint-based optimization framework is proposed and demonstrated for calculating optimal boundary conditions and optimal volumetric forcing. The corresponding optimal response modes are validated against modes obtained in terms of global resolvent analysis. For laminar base flows, the optimal modes reveal modal and non-modal transition mechanisms. For turbulent base flows, they predict the evolution of coherent structures in a statistical sense. Results from the application of the method to three-dimensional laminar wall-bounded flows and turbulent jets will be presented. This research was supported by the Office of Naval Research (N00014-16-1-2445) and Boeing Company (CT-BA-GTA-1).

The choice of sample size: a mixed Bayesian / frequentist approach.

PubMed

Pezeshk, Hamid; Nematollahi, Nader; Maroufy, Vahed; Gittins, John

2009-04-01

Sample size computations are largely based on frequentist or classical methods. In the Bayesian approach the prior information on the unknown parameters is taken into account. In this work we consider a fully Bayesian approach to the sample size determination problem which was introduced by Grundy et al. and developed by Lindley. This approach treats the problem as a decision problem and employs a utility function to find the optimal sample size of a trial. Furthermore, we assume that a regulatory authority, which is deciding on whether or not to grant a licence to a new treatment, uses a frequentist approach. We then find the optimal sample size for the trial by maximising the expected net benefit, which is the expected benefit of subsequent use of the new treatment minus the cost of the trial.

Optimum testing of multiple hypotheses in quantum detection theory

NASA Technical Reports Server (NTRS)

Yuen, H. P.; Kennedy, R. S.; Lax, M.

1975-01-01

The problem of specifying the optimum quantum detector in multiple hypotheses testing is considered for application to optical communications. The quantum digital detection problem is formulated as a linear programming problem on an infinite-dimensional space. A necessary and sufficient condition is derived by the application of a general duality theorem specifying the optimum detector in terms of a set of linear operator equations and inequalities. Existence of the optimum quantum detector is also established. The optimality of commuting detection operators is discussed in some examples. The structure and performance of the optimal receiver are derived for the quantum detection of narrow-band coherent orthogonal and simplex signals. It is shown that modal photon counting is asymptotically optimum in the limit of a large signaling alphabet and that the capacity goes to infinity in the absence of a bandwidth limitation.

An algorithm for the optimal collection of wet waste.

PubMed

Laureri, Federica; Minciardi, Riccardo; Robba, Michela

2016-02-01

This work refers to the development of an approach for planning wet waste (food waste and other) collection at a metropolitan scale. Some specific modeling features distinguish this specific waste collection problem from the other ones. For instance, there may be significant differences as regards the values of the parameters (such as weight and volume) characterizing the various collection points. As it happens for classical waste collection planning, even in the case of wet waste, one has to deal with difficult combinatorial problems, where the determination of an optimal solution may require a very large computational effort, in the case of problem instances having a noticeable dimensionality. For this reason, in this work, a heuristic procedure for the optimal planning of wet waste is developed and applied to problem instances drawn from a real case study. The performances that can be obtained by applying such a procedure are evaluated by a comparison with those obtainable via a general-purpose mathematical programming software package, as well as those obtained by applying very simple decision rules commonly used in practice. The considered case study consists in an area corresponding to the historical center of the Municipality of Genoa. Copyright © 2015 Elsevier Ltd. All rights reserved.

ReacKnock: Identifying Reaction Deletion Strategies for Microbial Strain Optimization Based on Genome-Scale Metabolic Network

PubMed Central

Xu, Zixiang; Zheng, Ping; Sun, Jibin; Ma, Yanhe

2013-01-01

Gene knockout has been used as a common strategy to improve microbial strains for producing chemicals. Several algorithms are available to predict the target reactions to be deleted. Most of them apply mixed integer bi-level linear programming (MIBLP) based on metabolic networks, and use duality theory to transform bi-level optimization problem of large-scale MIBLP to single-level programming. However, the validity of the transformation was not proved. Solution of MIBLP depends on the structure of inner problem. If the inner problem is continuous, Karush-Kuhn-Tucker (KKT) method can be used to reformulate the MIBLP to a single-level one. We adopt KKT technique in our algorithm ReacKnock to attack the intractable problem of the solution of MIBLP, demonstrated with the genome-scale metabolic network model of E. coli for producing various chemicals such as succinate, ethanol, threonine and etc. Compared to the previous methods, our algorithm is fast, stable and reliable to find the optimal solutions for all the chemical products tested, and able to provide all the alternative deletion strategies which lead to the same industrial objective. PMID:24348984

Knowledge Discovery for Transonic Regional-Jet Wing through Multidisciplinary Design Exploration

NASA Astrophysics Data System (ADS)

Chiba, Kazuhisa; Obayashi, Shigeru; Morino, Hiroyuki

Data mining is an important facet of solving multi-objective optimization problem. Because it is one of the effective manner to discover the design knowledge in the multi-objective optimization problem which obtains large data. In the present study, data mining has been performed for a large-scale and real-world multidisciplinary design optimization (MDO) to provide knowledge regarding the design space. The MDO among aerodynamics, structures, and aeroelasticity of the regional-jet wing was carried out using high-fidelity evaluation models on the adaptive range multi-objective genetic algorithm. As a result, nine non-dominated solutions were generated and used for tradeoff analysis among three objectives. All solutions evaluated during the evolution were analyzed for the tradeoffs and influence of design variables using a self-organizing map to extract key features of the design space. Although the MDO results showed the inverted gull-wings as non-dominated solutions, one of the key features found by data mining was the non-gull wing geometry. When this knowledge was applied to one optimum solution, the resulting design was found to have better performance compared with the original geometry designed in the conventional manner.

State estimation of spatio-temporal phenomena

NASA Astrophysics Data System (ADS)

Yu, Dan

This dissertation addresses the state estimation problem of spatio-temporal phenomena which can be modeled by partial differential equations (PDEs), such as pollutant dispersion in the atmosphere. After discretizing the PDE, the dynamical system has a large number of degrees of freedom (DOF). State estimation using Kalman Filter (KF) is computationally intractable, and hence, a reduced order model (ROM) needs to be constructed first. Moreover, the nonlinear terms, external disturbances or unknown boundary conditions can be modeled as unknown inputs, which leads to an unknown input filtering problem. Furthermore, the performance of KF could be improved by placing sensors at feasible locations. Therefore, the sensor scheduling problem to place multiple mobile sensors is of interest. The first part of the dissertation focuses on model reduction for large scale systems with a large number of inputs/outputs. A commonly used model reduction algorithm, the balanced proper orthogonal decomposition (BPOD) algorithm, is not computationally tractable for large systems with a large number of inputs/outputs. Inspired by the BPOD and randomized algorithms, we propose a randomized proper orthogonal decomposition (RPOD) algorithm and a computationally optimal RPOD (RPOD*) algorithm, which construct an ROM to capture the input-output behaviour of the full order model, while reducing the computational cost of BPOD by orders of magnitude. It is demonstrated that the proposed RPOD* algorithm could construct the ROM in real-time, and the performance of the proposed algorithms on different advection-diffusion equations. Next, we consider the state estimation problem of linear discrete-time systems with unknown inputs which can be treated as a wide-sense stationary process with rational power spectral density, while no other prior information needs to be known. We propose an autoregressive (AR) model based unknown input realization technique which allows us to recover the input statistics from the output data by solving an appropriate least squares problem, then fit an AR model to the recovered input statistics and construct an innovations model of the unknown inputs using the eigensystem realization algorithm. The proposed algorithm outperforms the augmented two-stage Kalman Filter (ASKF) and the unbiased minimum-variance (UMV) algorithm are shown in several examples. Finally, we propose a framework to place multiple mobile sensors to optimize the long-term performance of KF in the estimation of the state of a PDE. The major challenges are that placing multiple sensors is an NP-hard problem, and the optimization problem is non-convex in general. In this dissertation, first, we construct an ROM using RPOD* algorithm, and then reduce the feasible sensor locations into a subset using the ROM. The Information Space Receding Horizon Control (I-RHC) approach and a modified Monte Carlo Tree Search (MCTS) approach are applied to solve the sensor scheduling problem using the subset. Various applications have been provided to demonstrate the performance of the proposed approach.

Optimization of Wireless Power Transfer Systems Enhanced by Passive Elements and Metasurfaces

NASA Astrophysics Data System (ADS)

Lang, Hans-Dieter; Sarris, Costas D.

2017-10-01

This paper presents a rigorous optimization technique for wireless power transfer (WPT) systems enhanced by passive elements, ranging from simple reflectors and intermedi- ate relays all the way to general electromagnetic guiding and focusing structures, such as metasurfaces and metamaterials. At its core is a convex semidefinite relaxation formulation of the otherwise nonconvex optimization problem, of which tightness and optimality can be confirmed by a simple test of its solutions. The resulting method is rigorous, versatile, and general -- it does not rely on any assumptions. As shown in various examples, it is able to efficiently and reliably optimize such WPT systems in order to find their physical limitations on performance, optimal operating parameters and inspect their working principles, even for a large number of active transmitters and passive elements.

Combining gait optimization with passive system to increase the energy efficiency of a humanoid robot walking movement

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pereira, Ana I.; ALGORITMI,University of Minho; Lima, José

There are several approaches to create the Humanoid robot gait planning. This problem presents a large number of unknown parameters that should be found to make the humanoid robot to walk. Optimization in simulation models can be used to find the gait based on several criteria such as energy minimization, acceleration, step length among the others. The energy consumption can also be reduced with elastic elements coupled to each joint. The presented paper addresses an optimization method, the Stretched Simulated Annealing, that runs in an accurate and stable simulation model to find the optimal gait combined with elastic elements. Finalmore » results demonstrate that optimization is a valid gait planning technique.« less

Display analysis with the optimal control model of the human operator. [pilot-vehicle display interface and information processing

NASA Technical Reports Server (NTRS)

Baron, S.; Levison, W. H.

1977-01-01

Application of the optimal control model of the human operator to problems in display analysis is discussed. Those aspects of the model pertaining to the operator-display interface and to operator information processing are reviewed and discussed. The techniques are then applied to the analysis of advanced display/control systems for a Terminal Configured Vehicle. Model results are compared with those obtained in a large, fixed-base simulation.

Multi-objective optimization of GENIE Earth system models.

PubMed

Price, Andrew R; Myerscough, Richard J; Voutchkov, Ivan I; Marsh, Robert; Cox, Simon J

2009-07-13

The tuning of parameters in climate models is essential to provide reliable long-term forecasts of Earth system behaviour. We apply a multi-objective optimization algorithm to the problem of parameter estimation in climate models. This optimization process involves the iterative evaluation of response surface models (RSMs), followed by the execution of multiple Earth system simulations. These computations require an infrastructure that provides high-performance computing for building and searching the RSMs and high-throughput computing for the concurrent evaluation of a large number of models. Grid computing technology is therefore essential to make this algorithm practical for members of the GENIE project.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models.

PubMed

Yuan, Gonglin; Duan, Xiabin; Liu, Wenjie; Wang, Xiaoliang; Cui, Zengru; Sheng, Zhou

2015-01-01

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1) βk ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models

PubMed Central

Yuan, Gonglin; Duan, Xiabin; Liu, Wenjie; Wang, Xiaoliang; Cui, Zengru; Sheng, Zhou

2015-01-01

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1)β k ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations. PMID:26502409

QSPIN: A High Level Java API for Quantum Computing Experimentation

NASA Technical Reports Server (NTRS)

Barth, Tim

2017-01-01

QSPIN is a high level Java language API for experimentation in QC models used in the calculation of Ising spin glass ground states and related quadratic unconstrained binary optimization (QUBO) problems. The Java API is intended to facilitate research in advanced QC algorithms such as hybrid quantum-classical solvers, automatic selection of constraint and optimization parameters, and techniques for the correction and mitigation of model and solution errors. QSPIN includes high level solver objects tailored to the D-Wave quantum annealing architecture that implement hybrid quantum-classical algorithms [Booth et al.] for solving large problems on small quantum devices, elimination of variables via roof duality, and classical computing optimization methods such as GPU accelerated simulated annealing and tabu search for comparison. A test suite of documented NP-complete applications ranging from graph coloring, covering, and partitioning to integer programming and scheduling are provided to demonstrate current capabilities.

The Problem of Size in Robust Design

NASA Technical Reports Server (NTRS)

Koch, Patrick N.; Allen, Janet K.; Mistree, Farrokh; Mavris, Dimitri

1997-01-01

To facilitate the effective solution of multidisciplinary, multiobjective complex design problems, a departure from the traditional parametric design analysis and single objective optimization approaches is necessary in the preliminary stages of design. A necessary tradeoff becomes one of efficiency vs. accuracy as approximate models are sought to allow fast analysis and effective exploration of a preliminary design space. In this paper we apply a general robust design approach for efficient and comprehensive preliminary design to a large complex system: a high speed civil transport (HSCT) aircraft. Specifically, we investigate the HSCT wing configuration design, incorporating life cycle economic uncertainties to identify economically robust solutions. The approach is built on the foundation of statistical experimentation and modeling techniques and robust design principles, and is specialized through incorporation of the compromise Decision Support Problem for multiobjective design. For large problems however, as in the HSCT example, this robust design approach developed for efficient and comprehensive design breaks down with the problem of size - combinatorial explosion in experimentation and model building with number of variables -and both efficiency and accuracy are sacrificed. Our focus in this paper is on identifying and discussing the implications and open issues associated with the problem of size for the preliminary design of large complex systems.

Vibration suppression for large scale adaptive truss structures using direct output feedback control

NASA Technical Reports Server (NTRS)

Lu, Lyan-Ywan; Utku, Senol; Wada, Ben K.

1993-01-01

In this article, the vibration control of adaptive truss structures, where the control actuation is provided by length adjustable active members, is formulated as a direct output feedback control problem. A control method named Model Truncated Output Feedback (MTOF) is presented. The method allows the control feedback gain to be determined in a decoupled and truncated modal space in which only the critical vibration modes are retained. The on-board computation required by MTOF is minimal; thus, the method is favorable for the applications of vibration control of large scale structures. The truncation of the modal space inevitably introduces spillover effect during the control process. In this article, the effect is quantified in terms of active member locations, and it is shown that the optimal placement of active members, which minimizes the spillover effect (and thus, maximizes the control performance) can be sought. The problem of optimally selecting the locations of active members is also treated.

Power oscillation suppression by robust SMES in power system with large wind power penetration

NASA Astrophysics Data System (ADS)

Ngamroo, Issarachai; Cuk Supriyadi, A. N.; Dechanupaprittha, Sanchai; Mitani, Yasunori

2009-01-01

The large penetration of wind farm into interconnected power systems may cause the severe problem of tie-line power oscillations. To suppress power oscillations, the superconducting magnetic energy storage (SMES) which is able to control active and reactive powers simultaneously, can be applied. On the other hand, several generating and loading conditions, variation of system parameters, etc., cause uncertainties in the system. The SMES controller designed without considering system uncertainties may fail to suppress power oscillations. To enhance the robustness of SMES controller against system uncertainties, this paper proposes a robust control design of SMES by taking system uncertainties into account. The inverse additive perturbation is applied to represent the unstructured system uncertainties and included in power system modeling. The configuration of active and reactive power controllers is the first-order lead-lag compensator with single input feedback. To tune the controller parameters, the optimization problem is formulated based on the enhancement of robust stability margin. The particle swarm optimization is used to solve the problem and achieve the controller parameters. Simulation studies in the six-area interconnected power system with wind farms confirm the robustness of the proposed SMES under various operating conditions.

A fast time-difference inverse solver for 3D EIT with application to lung imaging.

PubMed

Javaherian, Ashkan; Soleimani, Manuchehr; Moeller, Knut

2016-08-01

A class of sparse optimization techniques that require solely matrix-vector products, rather than an explicit access to the forward matrix and its transpose, has been paid much attention in the recent decade for dealing with large-scale inverse problems. This study tailors application of the so-called Gradient Projection for Sparse Reconstruction (GPSR) to large-scale time-difference three-dimensional electrical impedance tomography (3D EIT). 3D EIT typically suffers from the need for a large number of voxels to cover the whole domain, so its application to real-time imaging, for example monitoring of lung function, remains scarce since the large number of degrees of freedom of the problem extremely increases storage space and reconstruction time. This study shows the great potential of the GPSR for large-size time-difference 3D EIT. Further studies are needed to improve its accuracy for imaging small-size anomalies.

Multicompare tests of the performance of different metaheuristics in EEG dipole source localization.

PubMed

Escalona-Vargas, Diana Irazú; Lopez-Arevalo, Ivan; Gutiérrez, David

2014-01-01

We study the use of nonparametric multicompare statistical tests on the performance of simulated annealing (SA), genetic algorithm (GA), particle swarm optimization (PSO), and differential evolution (DE), when used for electroencephalographic (EEG) source localization. Such task can be posed as an optimization problem for which the referred metaheuristic methods are well suited. Hence, we evaluate the localization's performance in terms of metaheuristics' operational parameters and for a fixed number of evaluations of the objective function. In this way, we are able to link the efficiency of the metaheuristics with a common measure of computational cost. Our results did not show significant differences in the metaheuristics' performance for the case of single source localization. In case of localizing two correlated sources, we found that PSO (ring and tree topologies) and DE performed the worst, then they should not be considered in large-scale EEG source localization problems. Overall, the multicompare tests allowed to demonstrate the little effect that the selection of a particular metaheuristic and the variations in their operational parameters have in this optimization problem.

A model for managing sources of groundwater pollution

USGS Publications Warehouse

Gorelick, Steven M.

1982-01-01

The waste disposal capacity of a groundwater system can be maximized while maintaining water quality at specified locations by using a groundwater pollutant source management model that is based upon linear programing and numerical simulation. The decision variables of the management model are solute waste disposal rates at various facilities distributed over space. A concentration response matrix is used in the management model to describe transient solute transport and is developed using the U.S. Geological Survey solute transport simulation model. The management model was applied to a complex hypothetical groundwater system. Large-scale management models were formulated as dual linear programing problems to reduce numerical difficulties and computation time. Linear programing problems were solved using a numerically stable, available code. Optimal solutions to problems with successively longer management time horizons indicated that disposal schedules at some sites are relatively independent of the number of disposal periods. Optimal waste disposal schedules exhibited pulsing rather than constant disposal rates. Sensitivity analysis using parametric linear programing showed that a sharp reduction in total waste disposal potential occurs if disposal rates at any site are increased beyond their optimal values.

The role of under-determined approximations in engineering and science application

NASA Technical Reports Server (NTRS)

Carpenter, William C.

1992-01-01

There is currently a great deal of interest in using response surfaces in the optimization of aircraft performance. The objective function and/or constraint equations involved in these optimization problems may come from numerous disciplines such as structures, aerodynamics, environmental engineering, etc. In each of these disciplines, the mathematical complexity of the governing equations usually dictates that numerical results be obtained from large computer programs such as a finite element method program. Thus, when performing optimization studies, response surfaces are a convenient way of transferring information from the various disciplines to the optimization algorithm as opposed to bringing all the sundry computer programs together in a massive computer code. Response surfaces offer another advantage in the optimization of aircraft structures. A characteristic of these types of optimization problems is that evaluation of the objective function and response equations (referred to as a functional evaluation) can be very expensive in a computational sense. Because of the computational expense in obtaining functional evaluations, the present study was undertaken to investigate under-determinined approximations. An under-determined approximation is one in which there are fewer training pairs (pieces of information about a function) than there are undetermined parameters (coefficients or weights) associated with the approximation. Both polynomial approximations and neural net approximations were examined. Three main example problems were investigated: (1) a function of one design variable was considered; (2) a function of two design variables was considered; and (3) a 35 bar truss with 4 design variables was considered.

Three essays on multi-level optimization models and applications

NASA Astrophysics Data System (ADS)

Rahdar, Mohammad

The general form of a multi-level mathematical programming problem is a set of nested optimization problems, in which each level controls a series of decision variables independently. However, the value of decision variables may also impact the objective function of other levels. A two-level model is called a bilevel model and can be considered as a Stackelberg game with a leader and a follower. The leader anticipates the response of the follower and optimizes its objective function, and then the follower reacts to the leader's action. The multi-level decision-making model has many real-world applications such as government decisions, energy policies, market economy, network design, etc. However, there is a lack of capable algorithms to solve medium and large scale these types of problems. The dissertation is devoted to both theoretical research and applications of multi-level mathematical programming models, which consists of three parts, each in a paper format. The first part studies the renewable energy portfolio under two major renewable energy policies. The potential competition for biomass for the growth of the renewable energy portfolio in the United States and other interactions between two policies over the next twenty years are investigated. This problem mainly has two levels of decision makers: the government/policy makers and biofuel producers/electricity generators/farmers. We focus on the lower-level problem to predict the amount of capacity expansions, fuel production, and power generation. In the second part, we address uncertainty over demand and lead time in a multi-stage mathematical programming problem. We propose a two-stage tri-level optimization model in the concept of rolling horizon approach to reducing the dimensionality of the multi-stage problem. In the third part of the dissertation, we introduce a new branch and bound algorithm to solve bilevel linear programming problems. The total time is reduced by solving a smaller relaxation problem in each node and decreasing the number of iterations. Computational experiments show that the proposed algorithm is faster than the existing ones.

Improved teaching-learning-based and JAYA optimization algorithms for solving flexible flow shop scheduling problems

NASA Astrophysics Data System (ADS)

Buddala, Raviteja; Mahapatra, Siba Sankar

2017-11-01

Flexible flow shop (or a hybrid flow shop) scheduling problem is an extension of classical flow shop scheduling problem. In a simple flow shop configuration, a job having `g' operations is performed on `g' operation centres (stages) with each stage having only one machine. If any stage contains more than one machine for providing alternate processing facility, then the problem becomes a flexible flow shop problem (FFSP). FFSP which contains all the complexities involved in a simple flow shop and parallel machine scheduling problems is a well-known NP-hard (Non-deterministic polynomial time) problem. Owing to high computational complexity involved in solving these problems, it is not always possible to obtain an optimal solution in a reasonable computation time. To obtain near-optimal solutions in a reasonable computation time, a large variety of meta-heuristics have been proposed in the past. However, tuning algorithm-specific parameters for solving FFSP is rather tricky and time consuming. To address this limitation, teaching-learning-based optimization (TLBO) and JAYA algorithm are chosen for the study because these are not only recent meta-heuristics but they do not require tuning of algorithm-specific parameters. Although these algorithms seem to be elegant, they lose solution diversity after few iterations and get trapped at the local optima. To alleviate such drawback, a new local search procedure is proposed in this paper to improve the solution quality. Further, mutation strategy (inspired from genetic algorithm) is incorporated in the basic algorithm to maintain solution diversity in the population. Computational experiments have been conducted on standard benchmark problems to calculate makespan and computational time. It is found that the rate of convergence of TLBO is superior to JAYA. From the results, it is found that TLBO and JAYA outperform many algorithms reported in the literature and can be treated as efficient methods for solving the FFSP.

An optimization model for the US Air-Traffic System

NASA Technical Reports Server (NTRS)

Mulvey, J. M.

1986-01-01

A systematic approach for monitoring U.S. air traffic was developed in the context of system-wide planning and control. Towards this end, a network optimization model with nonlinear objectives was chosen as the central element in the planning/control system. The network representation was selected because: (1) it provides a comprehensive structure for depicting essential aspects of the air traffic system, (2) it can be solved efficiently for large scale problems, and (3) the design can be easily communicated to non-technical users through computer graphics. Briefly, the network planning models consider the flow of traffic through a graph as the basic structure. Nodes depict locations and time periods for either individual planes or for aggregated groups of airplanes. Arcs define variables as actual airplanes flying through space or as delays across time periods. As such, a special case of the network can be used to model the so called flow control problem. Due to the large number of interacting variables and the difficulty in subdividing the problem into relatively independent subproblems, an integrated model was designed which will depict the entire high level (above 29000 feet) jet route system for the 48 contiguous states in the U.S. As a first step in demonstrating the concept's feasibility a nonlinear risk/cost model was developed for the Indianapolis Airspace. The nonlinear network program --NLPNETG-- was employed in solving the resulting test cases. This optimization program uses the Truncated-Newton method (quadratic approximation) for determining the search direction at each iteration in the nonlinear algorithm. It was shown that aircraft could be re-routed in an optimal fashion whenever traffic congestion increased beyond an acceptable level, as measured by the nonlinear risk function.

Dynamic remapping of parallel computations with varying resource demands

NASA Technical Reports Server (NTRS)

Nicol, D. M.; Saltz, J. H.

1986-01-01

A large class of computational problems is characterized by frequent synchronization, and computational requirements which change as a function of time. When such a problem must be solved on a message passing multiprocessor machine, the combination of these characteristics lead to system performance which decreases in time. Performance can be improved with periodic redistribution of computational load; however, redistribution can exact a sometimes large delay cost. We study the issue of deciding when to invoke a global load remapping mechanism. Such a decision policy must effectively weigh the costs of remapping against the performance benefits. We treat this problem by constructing two analytic models which exhibit stochastically decreasing performance. One model is quite tractable; we are able to describe the optimal remapping algorithm, and the optimal decision policy governing when to invoke that algorithm. However, computational complexity prohibits the use of the optimal remapping decision policy. We then study the performance of a general remapping policy on both analytic models. This policy attempts to minimize a statistic W(n) which measures the system degradation (including the cost of remapping) per computation step over a period of n steps. We show that as a function of time, the expected value of W(n) has at most one minimum, and that when this minimum exists it defines the optimal fixed-interval remapping policy. Our decision policy appeals to this result by remapping when it estimates that W(n) is minimized. Our performance data suggests that this policy effectively finds the natural frequency of remapping. We also use the analytic models to express the relationship between performance and remapping cost, number of processors, and the computation's stochastic activity.

Fast alternating projection methods for constrained tomographic reconstruction

PubMed Central

Liu, Li; Han, Yongxin

2017-01-01

The alternating projection algorithms are easy to implement and effective for large-scale complex optimization problems, such as constrained reconstruction of X-ray computed tomography (CT). A typical method is to use projection onto convex sets (POCS) for data fidelity, nonnegative constraints combined with total variation (TV) minimization (so called TV-POCS) for sparse-view CT reconstruction. However, this type of method relies on empirically selected parameters for satisfactory reconstruction and is generally slow and lack of convergence analysis. In this work, we use a convex feasibility set approach to address the problems associated with TV-POCS and propose a framework using full sequential alternating projections or POCS (FS-POCS) to find the solution in the intersection of convex constraints of bounded TV function, bounded data fidelity error and non-negativity. The rationale behind FS-POCS is that the mathematically optimal solution of the constrained objective function may not be the physically optimal solution. The breakdown of constrained reconstruction into an intersection of several feasible sets can lead to faster convergence and better quantification of reconstruction parameters in a physical meaningful way than that in an empirical way of trial-and-error. In addition, for large-scale optimization problems, first order methods are usually used. Not only is the condition for convergence of gradient-based methods derived, but also a primal-dual hybrid gradient (PDHG) method is used for fast convergence of bounded TV. The newly proposed FS-POCS is evaluated and compared with TV-POCS and another convex feasibility projection method (CPTV) using both digital phantom and pseudo-real CT data to show its superior performance on reconstruction speed, image quality and quantification. PMID:28253298

Particle Swarm Optimization

NASA Technical Reports Server (NTRS)

Venter, Gerhard; Sobieszczanski-Sobieski Jaroslaw

2002-01-01

The purpose of this paper is to show how the search algorithm known as particle swarm optimization performs. Here, particle swarm optimization is applied to structural design problems, but the method has a much wider range of possible applications. The paper's new contributions are improvements to the particle swarm optimization algorithm and conclusions and recommendations as to the utility of the algorithm, Results of numerical experiments for both continuous and discrete applications are presented in the paper. The results indicate that the particle swarm optimization algorithm does locate the constrained minimum design in continuous applications with very good precision, albeit at a much higher computational cost than that of a typical gradient based optimizer. However, the true potential of particle swarm optimization is primarily in applications with discrete and/or discontinuous functions and variables. Additionally, particle swarm optimization has the potential of efficient computation with very large numbers of concurrently operating processors.

On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scales

NASA Astrophysics Data System (ADS)

Sergeyev, Yaroslav D.; Kvasov, Dmitri E.; Mukhametzhanov, Marat S.

2018-06-01

The necessity to find the global optimum of multiextremal functions arises in many applied problems where finding local solutions is insufficient. One of the desirable properties of global optimization methods is strong homogeneity meaning that a method produces the same sequences of points where the objective function is evaluated independently both of multiplication of the function by a scaling constant and of adding a shifting constant. In this paper, several aspects of global optimization using strongly homogeneous methods are considered. First, it is shown that even if a method possesses this property theoretically, numerically very small and large scaling constants can lead to ill-conditioning of the scaled problem. Second, a new class of global optimization problems where the objective function can have not only finite but also infinite or infinitesimal Lipschitz constants is introduced. Third, the strong homogeneity of several Lipschitz global optimization algorithms is studied in the framework of the Infinity Computing paradigm allowing one to work numerically with a variety of infinities and infinitesimals. Fourth, it is proved that a class of efficient univariate methods enjoys this property for finite, infinite and infinitesimal scaling and shifting constants. Finally, it is shown that in certain cases the usage of numerical infinities and infinitesimals can avoid ill-conditioning produced by scaling. Numerical experiments illustrating theoretical results are described.

Some Issues in Programming Multi-Mini-Processors

DTIC Science & Technology

1975-01-01

Hardware ^nd software are to be combined optimally to perform that specialized task. This in essence is the stategy followed by the BBN group in...large memory is directly addressable. MIXED SOLUTIONS The most promising approach appears to involve mixing several of the previous solutions...mini- or micro-computers. Possibly the problem will be solved by avoiding it. Some new minis are appearing on the market now with large physical

Enhanced nonlinearity interval mapping scheme for high-performance simulation-optimization of watershed-scale BMP placement

NASA Astrophysics Data System (ADS)

Zou, Rui; Riverson, John; Liu, Yong; Murphy, Ryan; Sim, Youn

2015-03-01

Integrated continuous simulation-optimization models can be effective predictors of a process-based responses for cost-benefit optimization of best management practices (BMPs) selection and placement. However, practical application of simulation-optimization model is computationally prohibitive for large-scale systems. This study proposes an enhanced Nonlinearity Interval Mapping Scheme (NIMS) to solve large-scale watershed simulation-optimization problems several orders of magnitude faster than other commonly used algorithms. An efficient interval response coefficient (IRC) derivation method was incorporated into the NIMS framework to overcome a computational bottleneck. The proposed algorithm was evaluated using a case study watershed in the Los Angeles County Flood Control District. Using a continuous simulation watershed/stream-transport model, Loading Simulation Program in C++ (LSPC), three nested in-stream compliance points (CP)—each with multiple Total Maximum Daily Loads (TMDL) targets—were selected to derive optimal treatment levels for each of the 28 subwatersheds, so that the TMDL targets at all the CP were met with the lowest possible BMP implementation cost. Genetic Algorithm (GA) and NIMS were both applied and compared. The results showed that the NIMS took 11 iterations (about 11 min) to complete with the resulting optimal solution having a total cost of 67.2 million, while each of the multiple GA executions took 21-38 days to reach near optimal solutions. The best solution obtained among all the GA executions compared had a minimized cost of 67.7 million—marginally higher, but approximately equal to that of the NIMS solution. The results highlight the utility for decision making in large-scale watershed simulation-optimization formulations.

Mathematical programming formulations for satellite synthesis

NASA Technical Reports Server (NTRS)

Bhasin, Puneet; Reilly, Charles H.

1987-01-01

The problem of satellite synthesis can be described as optimally allotting locations and sometimes frequencies and polarizations, to communication satellites so that interference from unwanted satellite signals does not exceed a specified threshold. In this report, mathematical programming models and optimization methods are used to solve satellite synthesis problems. A nonlinear programming formulation which is solved using Zoutendijk's method and a gradient search method is described. Nine mixed integer programming models are considered. Results of computer runs with these nine models and five geographically compatible scenarios are presented and evaluated. A heuristic solution procedure is also used to solve two of the models studied. Heuristic solutions to three large synthesis problems are presented. The results of our analysis show that the heuristic performs very well, both in terms of solution quality and solution time, on the two models to which it was applied. It is concluded that the heuristic procedure is the best of the methods considered for solving satellite synthesis problems.

Scheduling Non-Preemptible Jobs to Minimize Peak Demand

DOE PAGES

Yaw, Sean; Mumey, Brendan

2017-10-28

Our paper examines an important problem in smart grid energy scheduling; peaks in power demand are proportionally more expensive to generate and provision for. The issue is exacerbated in local microgrids that do not benefit from the aggregate smoothing experienced by large grids. Demand-side scheduling can reduce these peaks by taking advantage of the fact that there is often flexibility in job start times. We then focus attention on the case where the jobs are non-preemptible, meaning once started, they run to completion. The associated optimization problem is called the peak demand minimization problem, and has been previously shown tomore » be NP-hard. These results include an optimal fixed-parameter tractable algorithm, a polynomial-time approximation algorithm, as well as an effective heuristic that can also be used in an online setting of the problem. Simulation results show that these methods can reduce peak demand by up to 50% versus on-demand scheduling for household power jobs.« less

Scheduling Non-Preemptible Jobs to Minimize Peak Demand

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yaw, Sean; Mumey, Brendan

Our paper examines an important problem in smart grid energy scheduling; peaks in power demand are proportionally more expensive to generate and provision for. The issue is exacerbated in local microgrids that do not benefit from the aggregate smoothing experienced by large grids. Demand-side scheduling can reduce these peaks by taking advantage of the fact that there is often flexibility in job start times. We then focus attention on the case where the jobs are non-preemptible, meaning once started, they run to completion. The associated optimization problem is called the peak demand minimization problem, and has been previously shown tomore » be NP-hard. These results include an optimal fixed-parameter tractable algorithm, a polynomial-time approximation algorithm, as well as an effective heuristic that can also be used in an online setting of the problem. Simulation results show that these methods can reduce peak demand by up to 50% versus on-demand scheduling for household power jobs.« less

Development of Quadratic Programming Algorithm Based on Interior Point Method with Estimation Mechanism of Active Constraints

NASA Astrophysics Data System (ADS)

Hashimoto, Hiroyuki; Takaguchi, Yusuke; Nakamura, Shizuka

Instability of calculation process and increase of calculation time caused by increasing size of continuous optimization problem remain the major issues to be solved to apply the technique to practical industrial systems. This paper proposes an enhanced quadratic programming algorithm based on interior point method mainly for improvement of calculation stability. The proposed method has dynamic estimation mechanism of active constraints on variables, which fixes the variables getting closer to the upper/lower limit on them and afterwards releases the fixed ones as needed during the optimization process. It is considered as algorithm-level integration of the solution strategy of active-set method into the interior point method framework. We describe some numerical results on commonly-used bench-mark problems called “CUTEr” to show the effectiveness of the proposed method. Furthermore, the test results on large-sized ELD problem (Economic Load Dispatching problems in electric power supply scheduling) are also described as a practical industrial application.

Optimizing model: insemination, replacement, seasonal production, and cash flow.

PubMed

DeLorenzo, M A; Spreen, T H; Bryan, G R; Beede, D K; Van Arendonk, J A

1992-03-01

Dynamic programming to solve the Markov decision process problem of optimal insemination and replacement decisions was adapted to address large dairy herd management decision problems in the US. Expected net present values of cow states (151,200) were used to determine the optimal policy. States were specified by class of parity (n = 12), production level (n = 15), month of calving (n = 12), month of lactation (n = 16), and days open (n = 7). Methodology optimized decisions based on net present value of an individual cow and all replacements over a 20-yr decision horizon. Length of decision horizon was chosen to ensure that optimal policies were determined for an infinite planning horizon. Optimization took 286 s of central processing unit time. The final probability transition matrix was determined, in part, by the optimal policy. It was estimated iteratively to determine post-optimization steady state herd structure, milk production, replacement, feed inputs and costs, and resulting cash flow on a calendar month and annual basis if optimal policies were implemented. Implementation of the model included seasonal effects on lactation curve shapes, estrus detection rates, pregnancy rates, milk prices, replacement costs, cull prices, and genetic progress. Other inputs included calf values, values of dietary TDN and CP per kilogram, and discount rate. Stochastic elements included conception (and, thus, subsequent freshening), cow milk production level within herd, and survival. Validation of optimized solutions was by separate simulation model, which implemented policies on a simulated herd and also described herd dynamics during transition to optimized structure.

Robust control of systems with real parameter uncertainty and unmodelled dynamics

NASA Technical Reports Server (NTRS)

Chang, Bor-Chin; Fischl, Robert

1991-01-01

During this research period we have made significant progress in the four proposed areas: (1) design of robust controllers via H infinity optimization; (2) design of robust controllers via mixed H2/H infinity optimization; (3) M-delta structure and robust stability analysis for structured uncertainties; and (4) a study on controllability and observability of perturbed plant. It is well known now that the two-Riccati-equation solution to the H infinity control problem can be used to characterize all possible stabilizing optimal or suboptimal H infinity controllers if the optimal H infinity norm or gamma, an upper bound of a suboptimal H infinity norm, is given. In this research, we discovered some useful properties of these H infinity Riccati solutions. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma in the domain of interest. Based on these properties, quadratically convergent algorithms are developed to compute the optimal H infinity norm. We also set up a detailed procedure for applying the H infinity theory to robust control systems design. The desire to design controllers with H infinity robustness but H(exp 2) performance has recently resulted in mixed H(exp 2) and H infinity control problem formulation. The mixed H(exp 2)/H infinity problem have drawn the attention of many investigators. However, solution is only available for special cases of this problem. We formulated a relatively realistic control problem with H(exp 2) performance index and H infinity robustness constraint into a more general mixed H(exp 2)/H infinity problem. No optimal solution yet is available for this more general mixed H(exp 2)/H infinity problem. Although the optimal solution for this mixed H(exp 2)/H infinity control has not yet been found, we proposed a design approach which can be used through proper choice of the available design parameters to influence both robustness and performance. For a large class of linear time-invariant systems with real parametric perturbations, the coefficient vector of the characteristic polynomial is a multilinear function of the real parameter vector. Based on this multilinear mapping relationship together with the recent developments for polytopic polynomials and parameter domain partition technique, we proposed an iterative algorithm for coupling the real structured singular value.

Analytical sizing methods for behind-the-meter battery storage

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Di; Kintner-Meyer, Michael; Yang, Tao

In behind-the-meter application, battery storage system (BSS) is utilized to reduce a commercial or industrial customer’s payment for electricity use, including energy charge and demand charge. The potential value of BSS in payment reduction and the most economic size can be determined by formulating and solving standard mathematical programming problems. In this method, users input system information such as load profiles, energy/demand charge rates, and battery characteristics to construct a standard programming problem that typically involve a large number of constraints and decision variables. Such a large scale programming problem is then solved by optimization solvers to obtain numerical solutions.more » Such a method cannot directly link the obtained optimal battery sizes to input parameters and requires case-by-case analysis. In this paper, we present an objective quantitative analysis of costs and benefits of customer-side energy storage, and thereby identify key factors that affect battery sizing. Based on the analysis, we then develop simple but effective guidelines that can be used to determine the most cost-effective battery size or guide utility rate design for stimulating energy storage development. The proposed analytical sizing methods are innovative, and offer engineering insights on how the optimal battery size varies with system characteristics. We illustrate the proposed methods using practical building load profile and utility rate. The obtained results are compared with the ones using mathematical programming based methods for validation.« less

A LAGRANGIAN GAUSS-NEWTON-KRYLOV SOLVER FOR MASS- AND INTENSITY-PRESERVING DIFFEOMORPHIC IMAGE REGISTRATION.

PubMed

Mang, Andreas; Ruthotto, Lars

2017-01-01

We present an efficient solver for diffeomorphic image registration problems in the framework of Large Deformations Diffeomorphic Metric Mappings (LDDMM). We use an optimal control formulation, in which the velocity field of a hyperbolic PDE needs to be found such that the distance between the final state of the system (the transformed/transported template image) and the observation (the reference image) is minimized. Our solver supports both stationary and non-stationary (i.e., transient or time-dependent) velocity fields. As transformation models, we consider both the transport equation (assuming intensities are preserved during the deformation) and the continuity equation (assuming mass-preservation). We consider the reduced form of the optimal control problem and solve the resulting unconstrained optimization problem using a discretize-then-optimize approach. A key contribution is the elimination of the PDE constraint using a Lagrangian hyperbolic PDE solver. Lagrangian methods rely on the concept of characteristic curves. We approximate these curves using a fourth-order Runge-Kutta method. We also present an efficient algorithm for computing the derivatives of the final state of the system with respect to the velocity field. This allows us to use fast Gauss-Newton based methods. We present quickly converging iterative linear solvers using spectral preconditioners that render the overall optimization efficient and scalable. Our method is embedded into the image registration framework FAIR and, thus, supports the most commonly used similarity measures and regularization functionals. We demonstrate the potential of our new approach using several synthetic and real world test problems with up to 14.7 million degrees of freedom.

Control of large flexible spacecraft by the independent modal-space control method

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Shenar, J.

1984-01-01

The problem of control of a large-order flexible structure in the form of a plate-like lattice by the Independent Modal-Space Control (IMSC) method is presented. The equations of motion are first transformed to the modal space, thus obtaining internal (plant) decoupling of the system. Then, the control laws are designed in the modal space for each mode separately, so that the modal equations of motion are rendered externally (controller) decoupled. This complete decoupling applies both to rigid-body modes and elastic modes. The application of linear optimal control, in conjunction with a quadratic performance index, is first reviewed. A solution for high-order systems is proposed here by the IMSC method, whereby the problem is reduced to a number of modal minimum-fuel problems for the controlled modes.

Global Coverage Measurement Planning Strategies for Mobile Robots Equipped with a Remote Gas Sensor

PubMed Central

Arain, Muhammad Asif; Trincavelli, Marco; Cirillo, Marcello; Schaffernicht, Erik; Lilienthal, Achim J.

2015-01-01

The problem of gas detection is relevant to many real-world applications, such as leak detection in industrial settings and landfill monitoring. In this paper, we address the problem of gas detection in large areas with a mobile robotic platform equipped with a remote gas sensor. We propose an algorithm that leverages a novel method based on convex relaxation for quickly solving sensor placement problems, and for generating an efficient exploration plan for the robot. To demonstrate the applicability of our method to real-world environments, we performed a large number of experimental trials, both on randomly generated maps and on the map of a real environment. Our approach proves to be highly efficient in terms of computational requirements and to provide nearly-optimal solutions. PMID:25803707

Global coverage measurement planning strategies for mobile robots equipped with a remote gas sensor.

PubMed

Arain, Muhammad Asif; Trincavelli, Marco; Cirillo, Marcello; Schaffernicht, Erik; Lilienthal, Achim J

2015-03-20

The problem of gas detection is relevant to many real-world applications, such as leak detection in industrial settings and landfill monitoring. In this paper, we address the problem of gas detection in large areas with a mobile robotic platform equipped with a remote gas sensor. We propose an algorithm that leverages a novel method based on convex relaxation for quickly solving sensor placement problems, and for generating an efficient exploration plan for the robot. To demonstrate the applicability of our method to real-world environments, we performed a large number of experimental trials, both on randomly generated maps and on the map of a real environment. Our approach proves to be highly efficient in terms of computational requirements and to provide nearly-optimal solutions.

Efficient Implementation of an Optimal Interpolator for Large Spatial Data Sets

NASA Technical Reports Server (NTRS)

Memarsadeghi, Nargess; Mount, David M.

2007-01-01

Interpolating scattered data points is a problem of wide ranging interest. A number of approaches for interpolation have been proposed both from theoretical domains such as computational geometry and in applications' fields such as geostatistics. Our motivation arises from geological and mining applications. In many instances data can be costly to compute and are available only at nonuniformly scattered positions. Because of the high cost of collecting measurements, high accuracy is required in the interpolants. One of the most popular interpolation methods in this field is called ordinary kriging. It is popular because it is a best linear unbiased estimator. The price for its statistical optimality is that the estimator is computationally very expensive. This is because the value of each interpolant is given by the solution of a large dense linear system. In practice, kriging problems have been solved approximately by restricting the domain to a small local neighborhood of points that lie near the query point. Determining the proper size for this neighborhood is a solved by ad hoc methods, and it has been shown that this approach leads to undesirable discontinuities in the interpolant. Recently a more principled approach to approximating kriging has been proposed based on a technique called covariance tapering. This process achieves its efficiency by replacing the large dense kriging system with a much sparser linear system. This technique has been applied to a restriction of our problem, called simple kriging, which is not unbiased for general data sets. In this paper we generalize these results by showing how to apply covariance tapering to the more general problem of ordinary kriging. Through experimentation we demonstrate the space and time efficiency and accuracy of approximating ordinary kriging through the use of covariance tapering combined with iterative methods for solving large sparse systems. We demonstrate our approach on large data sizes arising both from synthetic sources and from real applications.

Automated trajectory planning for multiple-flyby interplanetary missions

NASA Astrophysics Data System (ADS)

Englander, Jacob

Many space mission planning problems may be formulated as hybrid optimal control problems (HOCP), i.e. problems that include both real-valued variables and categorical variables. In interplanetary trajectory design problems the categorical variables will typically specify the sequence of planets at which to perform flybys, and the real-valued variables will represent the launch date, ight times between planets, magnitudes and directions of thrust, flyby altitudes, etc. The contribution of this work is a framework for the autonomous optimization of multiple-flyby interplanetary trajectories. The trajectory design problem is converted into a HOCP with two nested loops: an "outer-loop" that finds the sequence of flybys and an "inner-loop" that optimizes the trajectory for each candidate yby sequence. The problem of choosing a sequence of flybys is posed as an integer programming problem and solved using a genetic algorithm (GA). This is an especially difficult problem to solve because GAs normally operate on a fixed-length set of decision variables. Since in interplanetary trajectory design the number of flyby maneuvers is not known a priori, it was necessary to devise a method of parameterizing the problem such that the GA can evolve a variable-length sequence of flybys. A novel "null gene" transcription was developed to meet this need. Then, for each candidate sequence of flybys, a trajectory must be found that visits each of the flyby targets and arrives at the final destination while optimizing some cost metric, such as minimizing ▵v or maximizing the final mass of the spacecraft. Three different classes of trajectory are described in this work, each of which requireda different physical model and optimization method. The choice of a trajectory model and optimization method is especially challenging because of the nature of the hybrid optimal control problem. Because the trajectory optimization problem is generated in real time by the outer-loop, the inner-loop optimization algorithm cannot require any a priori information and must always return a solution. In addition, the upper and lower bounds on each decision variable cannot be chosen a priori by the user because the user has no way to know what problem will be solved. Instead a method of choosing upper and lower bounds via a set of simple rules was developed and used for all three types of trajectory optimization problem. Many optimization algorithms were tested and discarded until suitable algorithms were found for each type of trajectory. The first class of trajectories use chemical propulsion and may only apply a ▵v at the periapse of each flyby. These Multiple Gravity Assist (MGA) trajectories are optimized using a cooperative algorithm of Differential Evolution (DE) and Particle Swarm Optimization (PSO). The second class of trajectories, known as Multiple Gravity Assist with one Deep Space Maneuver (MGA-DSM), also use chemical propulsion but instead of maneuvering at the periapse of each flyby as in the MGA case a maneuver is applied at a free point along each planet-to-planet arc, i.e. there is one maneuver for each pair of flybys. MGA-DSM trajectories are parameterized by more variables than MGA trajectories, and so the cooperative algorithm of DE and PSO that was used to optimize MGA trajectories was found to be less effective when applied to MGA-DSM. Instead, either PSO or DE alone were found to be more effective. The third class of trajectories addressed in this work are those using continuousthrust propulsion. Continuous-thrust trajectory optimization problems are more challenging than impulsive-thrust problems because the control variables are a continuous time series rather than a small set of parameters and because the spacecraft does not follow a conic section trajectory, leading to a large number of nonlinear constraints that must be satisfied to ensure that the spacecraft obeys the equations of motion. Many models and optimization algorithms were applied including direct transcription with nonlinear programming (DTNLP), the inverse-polynomial shapebased method, and feasible region analysis. However the only physical model and optimization method that proved reliable enough were the Sims-Flanagan transcription coupled with a nonlinear programming solver and the monotonic basin hopping (MBH) global search heuristic. The methods developed here are demonstrated to optimize a set of example trajectories, including a recreation of the Cassini mission, a Galileo-like mission, and conceptual continuous-thrust missions to Jupiter, Mercury, and Uranus.

Evolutionary design optimization of traffic signals applied to Quito city.

PubMed

Armas, Rolando; Aguirre, Hernán; Daolio, Fabio; Tanaka, Kiyoshi

2017-01-01

This work applies evolutionary computation and machine learning methods to study the transportation system of Quito from a design optimization perspective. It couples an evolutionary algorithm with a microscopic transport simulator and uses the outcome of the optimization process to deepen our understanding of the problem and gain knowledge about the system. The work focuses on the optimization of a large number of traffic lights deployed on a wide area of the city and studies their impact on travel time, emissions and fuel consumption. An evolutionary algorithm with specialized mutation operators is proposed to search effectively in large decision spaces, evolving small populations for a short number of generations. The effects of the operators combined with a varying mutation schedule are studied, and an analysis of the parameters of the algorithm is also included. In addition, hierarchical clustering is performed on the best solutions found in several runs of the algorithm. An analysis of signal clusters and their geolocation, estimation of fuel consumption, spatial analysis of emissions, and an analysis of signal coordination provide an overall picture of the systemic effects of the optimization process.

Evolutionary design optimization of traffic signals applied to Quito city

PubMed Central

2017-01-01

This work applies evolutionary computation and machine learning methods to study the transportation system of Quito from a design optimization perspective. It couples an evolutionary algorithm with a microscopic transport simulator and uses the outcome of the optimization process to deepen our understanding of the problem and gain knowledge about the system. The work focuses on the optimization of a large number of traffic lights deployed on a wide area of the city and studies their impact on travel time, emissions and fuel consumption. An evolutionary algorithm with specialized mutation operators is proposed to search effectively in large decision spaces, evolving small populations for a short number of generations. The effects of the operators combined with a varying mutation schedule are studied, and an analysis of the parameters of the algorithm is also included. In addition, hierarchical clustering is performed on the best solutions found in several runs of the algorithm. An analysis of signal clusters and their geolocation, estimation of fuel consumption, spatial analysis of emissions, and an analysis of signal coordination provide an overall picture of the systemic effects of the optimization process. PMID:29236733

Simultaneous personnel and vehicle shift scheduling in the waste management sector.

PubMed

Ghiani, Gianpaolo; Guerriero, Emanuela; Manni, Andrea; Manni, Emanuele; Potenza, Agostino

2013-07-01

Urban waste management is becoming an increasingly complex task, absorbing a huge amount of resources, and having a major environmental impact. The design of a waste management system consists in various activities, and one of these is related to the definition of shift schedules for both personnel and vehicles. This activity has a great incidence on the tactical and operational cost for companies. In this paper, we propose an integer programming model to find an optimal solution to the integrated problem. The aim is to determine optimal schedules at minimum cost. Moreover, we design a fast and effective heuristic to face large-size problems. Both approaches are tested on data from a real-world case in Southern Italy and compared to the current practice utilized by the company managing the service, showing that simultaneously solving these problems can lead to significant monetary savings. Copyright © 2013 Elsevier Ltd. All rights reserved.

Applied Distributed Model Predictive Control for Energy Efficient Buildings and Ramp Metering

NASA Astrophysics Data System (ADS)

Koehler, Sarah Muraoka

Industrial large-scale control problems present an interesting algorithmic design challenge. A number of controllers must cooperate in real-time on a network of embedded hardware with limited computing power in order to maximize system efficiency while respecting constraints and despite communication delays. Model predictive control (MPC) can automatically synthesize a centralized controller which optimizes an objective function subject to a system model, constraints, and predictions of disturbance. Unfortunately, the computations required by model predictive controllers for large-scale systems often limit its industrial implementation only to medium-scale slow processes. Distributed model predictive control (DMPC) enters the picture as a way to decentralize a large-scale model predictive control problem. The main idea of DMPC is to split the computations required by the MPC problem amongst distributed processors that can compute in parallel and communicate iteratively to find a solution. Some popularly proposed solutions are distributed optimization algorithms such as dual decomposition and the alternating direction method of multipliers (ADMM). However, these algorithms ignore two practical challenges: substantial communication delays present in control systems and also problem non-convexity. This thesis presents two novel and practically effective DMPC algorithms. The first DMPC algorithm is based on a primal-dual active-set method which achieves fast convergence, making it suitable for large-scale control applications which have a large communication delay across its communication network. In particular, this algorithm is suited for MPC problems with a quadratic cost, linear dynamics, forecasted demand, and box constraints. We measure the performance of this algorithm and show that it significantly outperforms both dual decomposition and ADMM in the presence of communication delay. The second DMPC algorithm is based on an inexact interior point method which is suited for nonlinear optimization problems. The parallel computation of the algorithm exploits iterative linear algebra methods for the main linear algebra computations in the algorithm. We show that the splitting of the algorithm is flexible and can thus be applied to various distributed platform configurations. The two proposed algorithms are applied to two main energy and transportation control problems. The first application is energy efficient building control. Buildings represent 40% of energy consumption in the United States. Thus, it is significant to improve the energy efficiency of buildings. The goal is to minimize energy consumption subject to the physics of the building (e.g. heat transfer laws), the constraints of the actuators as well as the desired operating constraints (thermal comfort of the occupants), and heat load on the system. In this thesis, we describe the control systems of forced air building systems in practice. We discuss the "Trim and Respond" algorithm which is a distributed control algorithm that is used in practice, and show that it performs similarly to a one-step explicit DMPC algorithm. Then, we apply the novel distributed primal-dual active-set method and provide extensive numerical results for the building MPC problem. The second main application is the control of ramp metering signals to optimize traffic flow through a freeway system. This application is particularly important since urban congestion has more than doubled in the past few decades. The ramp metering problem is to maximize freeway throughput subject to freeway dynamics (derived from mass conservation), actuation constraints, freeway capacity constraints, and predicted traffic demand. In this thesis, we develop a hybrid model predictive controller for ramp metering that is guaranteed to be persistently feasible and stable. This contrasts to previous work on MPC for ramp metering where such guarantees are absent. We apply a smoothing method to the hybrid model predictive controller and apply the inexact interior point method to this nonlinear non-convex ramp metering problem.

Dynamic cellular manufacturing system considering machine failure and workload balance

NASA Astrophysics Data System (ADS)

Rabbani, Masoud; Farrokhi-Asl, Hamed; Ravanbakhsh, Mohammad

2018-02-01

Machines are a key element in the production system and their failure causes irreparable effects in terms of cost and time. In this paper, a new multi-objective mathematical model for dynamic cellular manufacturing system (DCMS) is provided with consideration of machine reliability and alternative process routes. In this dynamic model, we attempt to resolve the problem of integrated family (part/machine cell) formation as well as the operators' assignment to the cells. The first objective minimizes the costs associated with the DCMS. The second objective optimizes the labor utilization and, finally, a minimum value of the variance of workload between different cells is obtained by the third objective function. Due to the NP-hard nature of the cellular manufacturing problem, the problem is initially validated by the GAMS software in small-sized problems, and then the model is solved by two well-known meta-heuristic methods including non-dominated sorting genetic algorithm and multi-objective particle swarm optimization in large-scaled problems. Finally, the results of the two algorithms are compared with respect to five different comparison metrics.

Kernel-based least squares policy iteration for reinforcement learning.

PubMed

Xu, Xin; Hu, Dewen; Lu, Xicheng

2007-07-01

In this paper, we present a kernel-based least squares policy iteration (KLSPI) algorithm for reinforcement learning (RL) in large or continuous state spaces, which can be used to realize adaptive feedback control of uncertain dynamic systems. By using KLSPI, near-optimal control policies can be obtained without much a priori knowledge on dynamic models of control plants. In KLSPI, Mercer kernels are used in the policy evaluation of a policy iteration process, where a new kernel-based least squares temporal-difference algorithm called KLSTD-Q is proposed for efficient policy evaluation. To keep the sparsity and improve the generalization ability of KLSTD-Q solutions, a kernel sparsification procedure based on approximate linear dependency (ALD) is performed. Compared to the previous works on approximate RL methods, KLSPI makes two progresses to eliminate the main difficulties of existing results. One is the better convergence and (near) optimality guarantee by using the KLSTD-Q algorithm for policy evaluation with high precision. The other is the automatic feature selection using the ALD-based kernel sparsification. Therefore, the KLSPI algorithm provides a general RL method with generalization performance and convergence guarantee for large-scale Markov decision problems (MDPs). Experimental results on a typical RL task for a stochastic chain problem demonstrate that KLSPI can consistently achieve better learning efficiency and policy quality than the previous least squares policy iteration (LSPI) algorithm. Furthermore, the KLSPI method was also evaluated on two nonlinear feedback control problems, including a ship heading control problem and the swing up control of a double-link underactuated pendulum called acrobot. Simulation results illustrate that the proposed method can optimize controller performance using little a priori information of uncertain dynamic systems. It is also demonstrated that KLSPI can be applied to online learning control by incorporating an initial controller to ensure online performance.

Level-set techniques for facies identification in reservoir modeling

NASA Astrophysics Data System (ADS)

Iglesias, Marco A.; McLaughlin, Dennis

2011-03-01

In this paper we investigate the application of level-set techniques for facies identification in reservoir models. The identification of facies is a geometrical inverse ill-posed problem that we formulate in terms of shape optimization. The goal is to find a region (a geologic facies) that minimizes the misfit between predicted and measured data from an oil-water reservoir. In order to address the shape optimization problem, we present a novel application of the level-set iterative framework developed by Burger in (2002 Interfaces Free Bound. 5 301-29 2004 Inverse Problems 20 259-82) for inverse obstacle problems. The optimization is constrained by (the reservoir model) a nonlinear large-scale system of PDEs that describes the reservoir dynamics. We reformulate this reservoir model in a weak (integral) form whose shape derivative can be formally computed from standard results of shape calculus. At each iteration of the scheme, the current estimate of the shape derivative is utilized to define a velocity in the level-set equation. The proper selection of this velocity ensures that the new shape decreases the cost functional. We present results of facies identification where the velocity is computed with the gradient-based (GB) approach of Burger (2002) and the Levenberg-Marquardt (LM) technique of Burger (2004). While an adjoint formulation allows the straightforward application of the GB approach, the LM technique requires the computation of the large-scale Karush-Kuhn-Tucker system that arises at each iteration of the scheme. We efficiently solve this system by means of the representer method. We present some synthetic experiments to show and compare the capabilities and limitations of the proposed implementations of level-set techniques for the identification of geologic facies.

Acceleration of aircraft-level Traffic Flow Management

NASA Astrophysics Data System (ADS)

Rios, Joseph Lucio

This dissertation describes novel approaches to solving large-scale, high fidelity, aircraft-level Traffic Flow Management scheduling problems. Depending on the methods employed, solving these problems to optimality can take longer than the length of the planning horizon in question. Research in this domain typically focuses on the quality of the modeling used to describe the problem and the benefits achieved from the optimized solution, often treating computational aspects as secondary or tertiary. The work presented here takes the complementary view and considers the computational aspect as the primary concern. To this end, a previously published model for solving this Traffic Flow Management scheduling problem is used as starting point for this study. The model proposed by Bertsimas and Stock-Patterson is a binary integer program taking into account all major resource capacities and the trajectories of each flight to decide which flights should be held in which resource for what amount of time in order to satisfy all capacity requirements. For large instances, the solve time using state-of-the-art solvers is prohibitive for use within a potential decision support tool. With this dissertation, however, it will be shown that solving can be achieved in reasonable time for instances of real-world size. Five other techniques developed and tested for this dissertation will be described in detail. These are heuristic methods that provide good results. Performance is measured in terms of runtime and "optimality gap." We then describe the most successful method presented in this dissertation: Dantzig-Wolfe Decomposition. Results indicate that a parallel implementation of Dantzig-Wolfe Decomposition optimally solves the original problem in much reduced time and with better integrality and smaller optimality gap than any of the heuristic methods or state-of-the-art, commercial solvers. The solution quality improves in every measureable way as the number of subproblems solved in parallel increases. A maximal decomposition provides the best results of any method tested. The convergence qualities of Dantzig-Wolfe Decomposition have been criticized in the past, so we examine what makes the Bertsimas-Stock Patterson model so amenable to use of this method. These mathematical qualities of the model are generalized to provide guidance on other problems that may benefit from massively parallel Dantzig-Wolfe Decomposition. This result, together with the development of the software, and the experimental results indicating the feasibility of real-time, nationwide Traffic Flow Management scheduling represent the major contributions of this dissertation.

Framework to trade optimality for local processing in large-scale wavefront reconstruction problems.

PubMed

Haber, Aleksandar; Verhaegen, Michel

2016-11-15

We show that the minimum variance wavefront estimation problems permit localized approximate solutions, in the sense that the wavefront value at a point (excluding unobservable modes, such as the piston mode) can be approximated by a linear combination of the wavefront slope measurements in the point's neighborhood. This enables us to efficiently compute a wavefront estimate by performing a single sparse matrix-vector multiplication. Moreover, our results open the possibility for the development of wavefront estimators that can be easily implemented in a decentralized/distributed manner, and in which the estimate optimality can be easily traded for computational efficiency. We numerically validate our approach on Hudgin wavefront sensor geometries, and the results can be easily generalized to Fried geometries.

Combined structures-controls optimization of lattice trusses

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1991-01-01

The role that distributed parameter model can play in CSI is demonstrated, in particular in combined structures controls optimization problems of importance in preliminary design. Closed form solutions can be obtained for performance criteria such as rms attitude error, making possible analytical solutions of the optimization problem. This is in contrast to the need for numerical computer solution involving the inversion of large matrices in traditional finite element model (FEM) use. Another advantage of the analytic solution is that it can provide much needed insight into phenomena that can otherwise be obscured or difficult to discern from numerical computer results. As a compromise in level of complexity between a toy lab model and a real space structure, the lattice truss used in the EPS (Earth Pointing Satellite) was chosen. The optimization problem chosen is a generic one: of minimizing the structure mass subject to a specified stability margin and to a specified upper bond on the rms attitude error, using a co-located controller and sensors. Standard FEM treating each bar as a truss element is used, while the continuum model is anisotropic Timoshenko beam model. Performance criteria are derived for each model, except that for the distributed parameter model, explicit closed form solutions was obtained. Numerical results obtained by the two model show complete agreement.

Optimal planning for the sustainable utilization of municipal solid waste.

PubMed

Santibañez-Aguilar, José Ezequiel; Ponce-Ortega, José María; Betzabe González-Campos, J; Serna-González, Medardo; El-Halwagi, Mahmoud M

2013-12-01

The increasing generation of municipal solid waste (MSW) is a major problem particularly for large urban areas with insufficient landfill capacities and inefficient waste management systems. Several options associated to the supply chain for implementing a MSW management system are available, however to determine the optimal solution several technical, economic, environmental and social aspects must be considered. Therefore, this paper proposes a mathematical programming model for the optimal planning of the supply chain associated to the MSW management system to maximize the economic benefit while accounting for technical and environmental issues. The optimization model simultaneously selects the processing technologies and their location, the distribution of wastes from cities as well as the distribution of products to markets. The problem was formulated as a multi-objective mixed-integer linear programing problem to maximize the profit of the supply chain and the amount of recycled wastes, where the results are showed through Pareto curves that tradeoff economic and environmental aspects. The proposed approach is applied to a case study for the west-central part of Mexico to consider the integration of MSW from several cities to yield useful products. The results show that an integrated utilization of MSW can provide economic, environmental and social benefits. Copyright © 2013 Elsevier Ltd. All rights reserved.

Using Ant Colony Optimization for Routing in VLSI Chips

NASA Astrophysics Data System (ADS)

Arora, Tamanna; Moses, Melanie

2009-04-01

Rapid advances in VLSI technology have increased the number of transistors that fit on a single chip to about two billion. A frequent problem in the design of such high performance and high density VLSI layouts is that of routing wires that connect such large numbers of components. Most wire-routing problems are computationally hard. The quality of any routing algorithm is judged by the extent to which it satisfies routing constraints and design objectives. Some of the broader design objectives include minimizing total routed wire length, and minimizing total capacitance induced in the chip, both of which serve to minimize power consumed by the chip. Ant Colony Optimization algorithms (ACO) provide a multi-agent framework for combinatorial optimization by combining memory, stochastic decision and strategies of collective and distributed learning by ant-like agents. This paper applies ACO to the NP-hard problem of finding optimal routes for interconnect routing on VLSI chips. The constraints on interconnect routing are used by ants as heuristics which guide their search process. We found that ACO algorithms were able to successfully incorporate multiple constraints and route interconnects on suite of benchmark chips. On an average, the algorithm routed with total wire length 5.5% less than other established routing algorithms.

Optimization of coupled systems: A critical overview of approaches

NASA Technical Reports Server (NTRS)

Balling, R. J.; Sobieszczanski-Sobieski, J.

1994-01-01

A unified overview is given of problem formulation approaches for the optimization of multidisciplinary coupled systems. The overview includes six fundamental approaches upon which a large number of variations may be made. Consistent approach names and a compact approach notation are given. The approaches are formulated to apply to general nonhierarchic systems. The approaches are compared both from a computational viewpoint and a managerial viewpoint. Opportunities for parallelism of both computation and manpower resources are discussed. Recommendations regarding the need for future research are advanced.

Approximating the Basset force by optimizing the method of van Hinsberg et al.

NASA Astrophysics Data System (ADS)

Casas, G.; Ferrer, A.; Oñate, E.

2018-01-01

In this work we put the method proposed by van Hinsberg et al. [29] to the test, highlighting its accuracy and efficiency in a sequence of benchmarks of increasing complexity. Furthermore, we explore the possibility of systematizing the way in which the method's free parameters are determined by generalizing the optimization problem that was considered originally. Finally, we provide a list of worked-out values, ready for implementation in large-scale particle-laden flow simulations.

Robust penalty method for structural synthesis

NASA Technical Reports Server (NTRS)

Kamat, M. P.

1983-01-01

The Sequential Unconstrained Minimization Technique (SUMT) offers an easy way of solving nonlinearly constrained problems. However, this algorithm frequently suffers from the need to minimize an ill-conditioned penalty function. An ill-conditioned minimization problem can be solved very effectively by posing the problem as one of integrating a system of stiff differential equations utilizing concepts from singular perturbation theory. This paper evaluates the robustness and the reliability of such a singular perturbation based SUMT algorithm on two different problems of structural optimization of widely separated scales. The report concludes that whereas conventional SUMT can be bogged down by frequent ill-conditioning, especially in large scale problems, the singular perturbation SUMT has no such difficulty in converging to very accurate solutions.

High Speed Civil Transport Design Using Collaborative Optimization and Approximate Models

NASA Technical Reports Server (NTRS)

Manning, Valerie Michelle

1999-01-01

The design of supersonic aircraft requires complex analysis in multiple disciplines, posing, a challenge for optimization methods. In this thesis, collaborative optimization, a design architecture developed to solve large-scale multidisciplinary design problems, is applied to the design of supersonic transport concepts. Collaborative optimization takes advantage of natural disciplinary segmentation to facilitate parallel execution of design tasks. Discipline-specific design optimization proceeds while a coordinating mechanism ensures progress toward an optimum and compatibility between disciplinary designs. Two concepts for supersonic aircraft are investigated: a conventional delta-wing design and a natural laminar flow concept that achieves improved performance by exploiting properties of supersonic flow to delay boundary layer transition. The work involves the development of aerodynamics and structural analyses, and integration within a collaborative optimization framework. It represents the most extensive application of the method to date.

Big Data Challenges of High-Dimensional Continuous-Time Mean-Variance Portfolio Selection and a Remedy.

PubMed

Chiu, Mei Choi; Pun, Chi Seng; Wong, Hoi Ying

2017-08-01

Investors interested in the global financial market must analyze financial securities internationally. Making an optimal global investment decision involves processing a huge amount of data for a high-dimensional portfolio. This article investigates the big data challenges of two mean-variance optimal portfolios: continuous-time precommitment and constant-rebalancing strategies. We show that both optimized portfolios implemented with the traditional sample estimates converge to the worst performing portfolio when the portfolio size becomes large. The crux of the problem is the estimation error accumulated from the huge dimension of stock data. We then propose a linear programming optimal (LPO) portfolio framework, which applies a constrained ℓ 1 minimization to the theoretical optimal control to mitigate the risk associated with the dimensionality issue. The resulting portfolio becomes a sparse portfolio that selects stocks with a data-driven procedure and hence offers a stable mean-variance portfolio in practice. When the number of observations becomes large, the LPO portfolio converges to the oracle optimal portfolio, which is free of estimation error, even though the number of stocks grows faster than the number of observations. Our numerical and empirical studies demonstrate the superiority of the proposed approach. © 2017 Society for Risk Analysis.

Including robustness in multi-criteria optimization for intensity-modulated proton therapy

NASA Astrophysics Data System (ADS)

Chen, Wei; Unkelbach, Jan; Trofimov, Alexei; Madden, Thomas; Kooy, Hanne; Bortfeld, Thomas; Craft, David

2012-02-01

We present a method to include robustness in a multi-criteria optimization (MCO) framework for intensity-modulated proton therapy (IMPT). The approach allows one to simultaneously explore the trade-off between different objectives as well as the trade-off between robustness and nominal plan quality. In MCO, a database of plans each emphasizing different treatment planning objectives, is pre-computed to approximate the Pareto surface. An IMPT treatment plan that strikes the best balance between the different objectives can be selected by navigating on the Pareto surface. In our approach, robustness is integrated into MCO by adding robustified objectives and constraints to the MCO problem. Uncertainties (or errors) of the robust problem are modeled by pre-calculated dose-influence matrices for a nominal scenario and a number of pre-defined error scenarios (shifted patient positions, proton beam undershoot and overshoot). Objectives and constraints can be defined for the nominal scenario, thus characterizing nominal plan quality. A robustified objective represents the worst objective function value that can be realized for any of the error scenarios and thus provides a measure of plan robustness. The optimization method is based on a linear projection solver and is capable of handling large problem sizes resulting from a fine dose grid resolution, many scenarios, and a large number of proton pencil beams. A base-of-skull case is used to demonstrate the robust optimization method. It is demonstrated that the robust optimization method reduces the sensitivity of the treatment plan to setup and range errors to a degree that is not achieved by a safety margin approach. A chordoma case is analyzed in more detail to demonstrate the involved trade-offs between target underdose and brainstem sparing as well as robustness and nominal plan quality. The latter illustrates the advantage of MCO in the context of robust planning. For all cases examined, the robust optimization for each Pareto optimal plan takes less than 5 min on a standard computer, making a computationally friendly interface possible to the planner. In conclusion, the uncertainty pertinent to the IMPT procedure can be reduced during treatment planning by optimizing plans that emphasize different treatment objectives, including robustness, and then interactively seeking for a most-preferred one from the solution Pareto surface.

Assessing the weighted multi-objective adaptive surrogate model optimization to derive large-scale reservoir operating rules with sensitivity analysis

NASA Astrophysics Data System (ADS)

Zhang, Jingwen; Wang, Xu; Liu, Pan; Lei, Xiaohui; Li, Zejun; Gong, Wei; Duan, Qingyun; Wang, Hao

2017-01-01

The optimization of large-scale reservoir system is time-consuming due to its intrinsic characteristics of non-commensurable objectives and high dimensionality. One way to solve the problem is to employ an efficient multi-objective optimization algorithm in the derivation of large-scale reservoir operating rules. In this study, the Weighted Multi-Objective Adaptive Surrogate Model Optimization (WMO-ASMO) algorithm is used. It consists of three steps: (1) simplifying the large-scale reservoir operating rules by the aggregation-decomposition model, (2) identifying the most sensitive parameters through multivariate adaptive regression splines (MARS) for dimensional reduction, and (3) reducing computational cost and speeding the searching process by WMO-ASMO, embedded with weighted non-dominated sorting genetic algorithm II (WNSGAII). The intercomparison of non-dominated sorting genetic algorithm (NSGAII), WNSGAII and WMO-ASMO are conducted in the large-scale reservoir system of Xijiang river basin in China. Results indicate that: (1) WNSGAII surpasses NSGAII in the median of annual power generation, increased by 1.03% (from 523.29 to 528.67 billion kW h), and the median of ecological index, optimized by 3.87% (from 1.879 to 1.809) with 500 simulations, because of the weighted crowding distance and (2) WMO-ASMO outperforms NSGAII and WNSGAII in terms of better solutions (annual power generation (530.032 billion kW h) and ecological index (1.675)) with 1000 simulations and computational time reduced by 25% (from 10 h to 8 h) with 500 simulations. Therefore, the proposed method is proved to be more efficient and could provide better Pareto frontier.

Options for Robust Airfoil Optimization under Uncertainty

NASA Technical Reports Server (NTRS)

Padula, Sharon L.; Li, Wu

2002-01-01

A robust optimization method is developed to overcome point-optimization at the sampled design points. This method combines the best features from several preliminary methods proposed by the authors and their colleagues. The robust airfoil shape optimization is a direct method for drag reduction over a given range of operating conditions and has three advantages: (1) it prevents severe degradation in the off-design performance by using a smart descent direction in each optimization iteration, (2) it uses a large number of spline control points as design variables yet the resulting airfoil shape does not need to be smoothed, and (3) it allows the user to make a tradeoff between the level of optimization and the amount of computing time consumed. For illustration purposes, the robust optimization method is used to solve a lift-constrained drag minimization problem for a two-dimensional (2-D) airfoil in Euler flow with 20 geometric design variables.

Optimal swimming of a sheet.

PubMed

Montenegro-Johnson, Thomas D; Lauga, Eric

2014-06-01

Propulsion at microscopic scales is often achieved through propagating traveling waves along hairlike organelles called flagella. Taylor's two-dimensional swimming sheet model is frequently used to provide insight into problems of flagellar propulsion. We derive numerically the large-amplitude wave form of the two-dimensional swimming sheet that yields optimum hydrodynamic efficiency: the ratio of the squared swimming speed to the rate-of-working of the sheet against the fluid. Using the boundary element method, we show that the optimal wave form is a front-back symmetric regularized cusp that is 25% more efficient than the optimal sine wave. This optimal two-dimensional shape is smooth, qualitatively different from the kinked form of Lighthill's optimal three-dimensional flagellum, not predicted by small-amplitude theory, and different from the smooth circular-arc-like shape of active elastic filaments.

Towards quantifying uncertainty in Greenland's contribution to 21st century sea-level rise

NASA Astrophysics Data System (ADS)

Perego, M.; Tezaur, I.; Price, S. F.; Jakeman, J.; Eldred, M.; Salinger, A.; Hoffman, M. J.

2015-12-01

We present recent work towards developing a methodology for quantifying uncertainty in Greenland's 21st century contribution to sea-level rise. While we focus on uncertainties associated with the optimization and calibration of the basal sliding parameter field, the methodology is largely generic and could be applied to other (or multiple) sets of uncertain model parameter fields. The first step in the workflow is the solution of a large-scale, deterministic inverse problem, which minimizes the mismatch between observed and computed surface velocities by optimizing the two-dimensional coefficient field in a linear-friction sliding law. We then expand the deviation in this coefficient field from its estimated "mean" state using a reduced basis of Karhunen-Loeve Expansion (KLE) vectors. A Bayesian calibration is used to determine the optimal coefficient values for this expansion. The prior for the Bayesian calibration can be computed using the Hessian of the deterministic inversion or using an exponential covariance kernel. The posterior distribution is then obtained using Markov Chain Monte Carlo run on an emulator of the forward model. Finally, the uncertainty in the modeled sea-level rise is obtained by performing an ensemble of forward propagation runs. We present and discuss preliminary results obtained using a moderate-resolution model of the Greenland Ice sheet. As demonstrated in previous work, the primary difficulty in applying the complete workflow to realistic, high-resolution problems is that the effective dimension of the parameter space is very large.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gaitsgory, Vladimir, E-mail: vladimir.gaitsgory@mq.edu.au; Rossomakhine, Sergey, E-mail: serguei.rossomakhine@flinders.edu.au

The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem ofmore » optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.« less

Minimization of socioeconomic disruption for displaced populations following disasters.

PubMed

El-Anwar, Omar; El-Rayes, Khaled; Elnashai, Amr

2010-07-01

In the aftermath of catastrophic natural disasters such as hurricanes, tsunamis and earthquakes, emergency management agencies come under intense pressure to provide temporary housing to address the large-scale displacement of the vulnerable population. Temporary housing is essential to enable displaced families to reestablish their normal daily activities until permanent housing solutions can be provided. Temporary housing decisions, however, have often been criticized for their failure to fulfil the socioeconomic needs of the displaced families within acceptable budgets. This paper presents the development of (1) socioeconomic disruption metrics that are capable of quantifying the socioeconomic impacts of temporary housing decisions on displaced populations; and (2) a robust multi-objective optimization model for temporary housing that is capable of simultaneously minimizing socioeconomic disruptions and public expenditures in an effective and efficient manner. A large-scale application example is optimized to illustrate the use of the model and demonstrate its capabilities ingenerating optimal plans for realistic temporary housing problems.

Solving lot-sizing problem with quantity discount and transportation cost

NASA Astrophysics Data System (ADS)

Lee, Amy H. I.; Kang, He-Yau; Lai, Chun-Mei

2013-04-01

Owing to today's increasingly competitive market and ever-changing manufacturing environment, the inventory problem is becoming more complicated to solve. The incorporation of heuristics methods has become a new trend to tackle the complex problem in the past decade. This article considers a lot-sizing problem, and the objective is to minimise total costs, where the costs include ordering, holding, purchase and transportation costs, under the requirement that no inventory shortage is allowed in the system. We first formulate the lot-sizing problem as a mixed integer programming (MIP) model. Next, an efficient genetic algorithm (GA) model is constructed for solving large-scale lot-sizing problems. An illustrative example with two cases in a touch panel manufacturer is used to illustrate the practicality of these models, and a sensitivity analysis is applied to understand the impact of the changes in parameters to the outcomes. The results demonstrate that both the MIP model and the GA model are effective and relatively accurate tools for determining the replenishment for touch panel manufacturing for multi-periods with quantity discount and batch transportation. The contributions of this article are to construct an MIP model to obtain an optimal solution when the problem is not too complicated itself and to present a GA model to find a near-optimal solution efficiently when the problem is complicated.

Design space pruning heuristics and global optimization method for conceptual design of low-thrust asteroid tour missions

NASA Astrophysics Data System (ADS)

Alemany, Kristina

Electric propulsion has recently become a viable technology for spacecraft, enabling shorter flight times, fewer required planetary gravity assists, larger payloads, and/or smaller launch vehicles. With the maturation of this technology, however, comes a new set of challenges in the area of trajectory design. Because low-thrust trajectory optimization has historically required long run-times and significant user-manipulation, mission design has relied on expert-based knowledge for selecting departure and arrival dates, times of flight, and/or target bodies and gravitational swing-bys. These choices are generally based on known configurations that have worked well in previous analyses or simply on trial and error. At the conceptual design level, however, the ability to explore the full extent of the design space is imperative to locating the best solutions in terms of mass and/or flight times. Beginning in 2005, the Global Trajectory Optimization Competition posed a series of difficult mission design problems, all requiring low-thrust propulsion and visiting one or more asteroids. These problems all had large ranges on the continuous variables---launch date, time of flight, and asteroid stay times (when applicable)---as well as being characterized by millions or even billions of possible asteroid sequences. Even with recent advances in low-thrust trajectory optimization, full enumeration of these problems was not possible within the stringent time limits of the competition. This investigation develops a systematic methodology for determining a broad suite of good solutions to the combinatorial, low-thrust, asteroid tour problem. The target application is for conceptual design, where broad exploration of the design space is critical, with the goal being to rapidly identify a reasonable number of promising solutions for future analysis. The proposed methodology has two steps. The first step applies a three-level heuristic sequence developed from the physics of the problem, which allows for efficient pruning of the design space. The second phase applies a global optimization scheme to locate a broad suite of good solutions to the reduced problem. The global optimization scheme developed combines a novel branch-and-bound algorithm with a genetic algorithm and an industry-standard low-thrust trajectory optimization program to solve for the following design variables: asteroid sequence, launch date, times of flight, and asteroid stay times. The methodology is developed based on a small sample problem, which is enumerated and solved so that all possible discretized solutions are known. The methodology is then validated by applying it to a larger intermediate sample problem, which also has a known solution. Next, the methodology is applied to several larger combinatorial asteroid rendezvous problems, using previously identified good solutions as validation benchmarks. These problems include the 2nd and 3rd Global Trajectory Optimization Competition problems. The methodology is shown to be capable of achieving a reduction in the number of asteroid sequences of 6-7 orders of magnitude, in terms of the number of sequences that require low-thrust optimization as compared to the number of sequences in the original problem. More than 70% of the previously known good solutions are identified, along with several new solutions that were not previously reported by any of the competitors. Overall, the methodology developed in this investigation provides an organized search technique for the low-thrust mission design of asteroid rendezvous problems.

Optimal pre-scheduling of problem remappings

NASA Technical Reports Server (NTRS)

Nicol, David M.; Saltz, Joel H.

1987-01-01

A large class of scientific computational problems can be characterized as a sequence of steps where a significant amount of computation occurs each step, but the work performed at each step is not necessarily identical. Two good examples of this type of computation are: (1) regridding methods which change the problem discretization during the course of the computation, and (2) methods for solving sparse triangular systems of linear equations. Recent work has investigated a means of mapping such computations onto parallel processors; the method defines a family of static mappings with differing degrees of importance placed on the conflicting goals of good load balance and low communication/synchronization overhead. The performance tradeoffs are controllable by adjusting the parameters of the mapping method. To achieve good performance it may be necessary to dynamically change these parameters at run-time, but such changes can impose additional costs. If the computation's behavior can be determined prior to its execution, it can be possible to construct an optimal parameter schedule using a low-order-polynomial-time dynamic programming algorithm. Since the latter can be expensive, the performance is studied of the effect of a linear-time scheduling heuristic on one of the model problems, and it is shown to be effective and nearly optimal.

Strategies for global optimization in photonics design.

PubMed

Vukovic, Ana; Sewell, Phillip; Benson, Trevor M

2010-10-01

This paper reports on two important issues that arise in the context of the global optimization of photonic components where large problem spaces must be investigated. The first is the implementation of a fast simulation method and associated matrix solver for assessing particular designs and the second, the strategies that a designer can adopt to control the size of the problem design space to reduce runtimes without compromising the convergence of the global optimization tool. For this study an analytical simulation method based on Mie scattering and a fast matrix solver exploiting the fast multipole method are combined with genetic algorithms (GAs). The impact of the approximations of the simulation method on the accuracy and runtime of individual design assessments and the consequent effects on the GA are also examined. An investigation of optimization strategies for controlling the design space size is conducted on two illustrative examples, namely, 60° and 90° waveguide bends based on photonic microstructures, and their effectiveness is analyzed in terms of a GA's ability to converge to the best solution within an acceptable timeframe. Finally, the paper describes some particular optimized solutions found in the course of this work.

Comparing genomes with rearrangements and segmental duplications.

PubMed

Shao, Mingfu; Moret, Bernard M E

2015-06-15

Large-scale evolutionary events such as genomic rearrange.ments and segmental duplications form an important part of the evolution of genomes and are widely studied from both biological and computational perspectives. A basic computational problem is to infer these events in the evolutionary history for given modern genomes, a task for which many algorithms have been proposed under various constraints. Algorithms that can handle both rearrangements and content-modifying events such as duplications and losses remain few and limited in their applicability. We study the comparison of two genomes under a model including general rearrangements (through double-cut-and-join) and segmental duplications. We formulate the comparison as an optimization problem and describe an exact algorithm to solve it by using an integer linear program. We also devise a sufficient condition and an efficient algorithm to identify optimal substructures, which can simplify the problem while preserving optimality. Using the optimal substructures with the integer linear program (ILP) formulation yields a practical and exact algorithm to solve the problem. We then apply our algorithm to assign in-paralogs and orthologs (a necessary step in handling duplications) and compare its performance with that of the state-of-the-art method MSOAR, using both simulations and real data. On simulated datasets, our method outperforms MSOAR by a significant margin, and on five well-annotated species, MSOAR achieves high accuracy, yet our method performs slightly better on each of the 10 pairwise comparisons. http://lcbb.epfl.ch/softwares/coser. © The Author 2015. Published by Oxford University Press.

Energy minimization on manifolds for docking flexible molecules

PubMed Central

Mirzaei, Hanieh; Zarbafian, Shahrooz; Villar, Elizabeth; Mottarella, Scott; Beglov, Dmitri; Vajda, Sandor; Paschalidis, Ioannis Ch.; Vakili, Pirooz; Kozakov, Dima

2015-01-01

In this paper we extend a recently introduced rigid body minimization algorithm, defined on manifolds, to the problem of minimizing the energy of interacting flexible molecules. The goal is to integrate moving the ligand in six dimensional rotational/translational space with internal rotations around rotatable bonds within the two molecules. We show that adding rotational degrees of freedom to the rigid moves of the ligand results in an overall optimization search space that is a manifold to which our manifold optimization approach can be extended. The effectiveness of the method is shown for three different docking problems of increasing complexity. First we minimize the energy of fragment-size ligands with a single rotatable bond as part of a protein mapping method developed for the identification of binding hot spots. Second, we consider energy minimization for docking a flexible ligand to a rigid protein receptor, an approach frequently used in existing methods. In the third problem we account for flexibility in both the ligand and the receptor. Results show that minimization using the manifold optimization algorithm is substantially more efficient than minimization using a traditional all-atom optimization algorithm while producing solutions of comparable quality. In addition to the specific problems considered, the method is general enough to be used in a large class of applications such as docking multidomain proteins with flexible hinges. The code is available under open source license (at http://cluspro.bu.edu/Code/Code_Rigtree.tar), and with minimal effort can be incorporated into any molecular modeling package. PMID:26478722

Optimization of coronagraph design for segmented aperture telescopes

NASA Astrophysics Data System (ADS)

Jewell, Jeffrey; Ruane, Garreth; Shaklan, Stuart; Mawet, Dimitri; Redding, Dave

2017-09-01

The goal of directly imaging Earth-like planets in the habitable zone of other stars has motivated the design of coronagraphs for use with large segmented aperture space telescopes. In order to achieve an optimal trade-off between planet light throughput and diffracted starlight suppression, we consider coronagraphs comprised of a stage of phase control implemented with deformable mirrors (or other optical elements), pupil plane apodization masks (gray scale or complex valued), and focal plane masks (either amplitude only or complex-valued, including phase only such as the vector vortex coronagraph). The optimization of these optical elements, with the goal of achieving 10 or more orders of magnitude in the suppression of on-axis (starlight) diffracted light, represents a challenging non-convex optimization problem with a nonlinear dependence on control degrees of freedom. We develop a new algorithmic approach to the design optimization problem, which we call the "Auxiliary Field Optimization" (AFO) algorithm. The central idea of the algorithm is to embed the original optimization problem, for either phase or amplitude (apodization) in various planes of the coronagraph, into a problem containing additional degrees of freedom, specifically fictitious "auxiliary" electric fields which serve as targets to inform the variation of our phase or amplitude parameters leading to good feasible designs. We present the algorithm, discuss details of its numerical implementation, and prove convergence to local minima of the objective function (here taken to be the intensity of the on-axis source in a "dark hole" region in the science focal plane). Finally, we present results showing application of the algorithm to both unobscured off-axis and obscured on-axis segmented telescope aperture designs. The application of the AFO algorithm to the coronagraph design problem has produced solutions which are capable of directly imaging planets in the habitable zone, provided end-to-end telescope system stability requirements can be met. Ongoing work includes advances of the AFO algorithm reported here to design in additional robustness to a resolved star, and other phase or amplitude aberrations to be encountered in a real segmented aperture space telescope.

Primal-dual convex optimization in large deformation diffeomorphic metric mapping: LDDMM meets robust regularizers

NASA Astrophysics Data System (ADS)

Hernandez, Monica

2017-12-01

This paper proposes a method for primal-dual convex optimization in variational large deformation diffeomorphic metric mapping problems formulated with robust regularizers and robust image similarity metrics. The method is based on Chambolle and Pock primal-dual algorithm for solving general convex optimization problems. Diagonal preconditioning is used to ensure the convergence of the algorithm to the global minimum. We consider three robust regularizers liable to provide acceptable results in diffeomorphic registration: Huber, V-Huber and total generalized variation. The Huber norm is used in the image similarity term. The primal-dual equations are derived for the stationary and the non-stationary parameterizations of diffeomorphisms. The resulting algorithms have been implemented for running in the GPU using Cuda. For the most memory consuming methods, we have developed a multi-GPU implementation. The GPU implementations allowed us to perform an exhaustive evaluation study in NIREP and LPBA40 databases. The experiments showed that, for all the considered regularizers, the proposed method converges to diffeomorphic solutions while better preserving discontinuities at the boundaries of the objects compared to baseline diffeomorphic registration methods. In most cases, the evaluation showed a competitive performance for the robust regularizers, close to the performance of the baseline diffeomorphic registration methods.

Weighted mining of massive collections of [Formula: see text]-values by convex optimization.

PubMed

Dobriban, Edgar

2018-06-01

Researchers in data-rich disciplines-think of computational genomics and observational cosmology-often wish to mine large bodies of [Formula: see text]-values looking for significant effects, while controlling the false discovery rate or family-wise error rate. Increasingly, researchers also wish to prioritize certain hypotheses, for example, those thought to have larger effect sizes, by upweighting, and to impose constraints on the underlying mining, such as monotonicity along a certain sequence. We introduce Princessp , a principled method for performing weighted multiple testing by constrained convex optimization. Our method elegantly allows one to prioritize certain hypotheses through upweighting and to discount others through downweighting, while constraining the underlying weights involved in the mining process. When the [Formula: see text]-values derive from monotone likelihood ratio families such as the Gaussian means model, the new method allows exact solution of an important optimal weighting problem previously thought to be non-convex and computationally infeasible. Our method scales to massive data set sizes. We illustrate the applications of Princessp on a series of standard genomics data sets and offer comparisons with several previous 'standard' methods. Princessp offers both ease of operation and the ability to scale to extremely large problem sizes. The method is available as open-source software from github.com/dobriban/pvalue_weighting_matlab (accessed 11 October 2017).

Minimizing metastatic risk in radiotherapy fractionation schedules

NASA Astrophysics Data System (ADS)

Badri, Hamidreza; Ramakrishnan, Jagdish; Leder, Kevin

2015-11-01

Metastasis is the process by which cells from a primary tumor disperse and form new tumors at distant anatomical locations. The treatment and prevention of metastatic cancer remains an extremely challenging problem. This work introduces a novel biologically motivated objective function to the radiation optimization community that takes into account metastatic risk instead of the status of the primary tumor. In this work, we consider the problem of developing fractionated irradiation schedules that minimize production of metastatic cancer cells while keeping normal tissue damage below an acceptable level. A dynamic programming framework is utilized to determine the optimal fractionation scheme. We evaluated our approach on a breast cancer case using the heart and the lung as organs-at-risk (OAR). For small tumor α /β values, hypo-fractionated schedules were optimal, which is consistent with standard models. However, for relatively larger α /β values, we found the type of schedule depended on various parameters such as the time when metastatic risk was evaluated, the α /β values of the OARs, and the normal tissue sparing factors. Interestingly, in contrast to standard models, hypo-fractionated and semi-hypo-fractionated schedules (large initial doses with doses tapering off with time) were suggested even with large tumor α/β values. Numerical results indicate the potential for significant reduction in metastatic risk.

Feed Forward Neural Network and Optimal Control Problem with Control and State Constraints

NASA Astrophysics Data System (ADS)

Kmet', Tibor; Kmet'ová, Mária

2009-09-01

A feed forward neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints. The paper extends adaptive critic neural network architecture proposed by [5] to the optimal control problems with control and state constraints. The optimal control problem is transcribed into a nonlinear programming problem which is implemented with adaptive critic neural network. The proposed simulation method is illustrated by the optimal control problem of nitrogen transformation cycle model. Results show that adaptive critic based systematic approach holds promise for obtaining the optimal control with control and state constraints.

Scalability of surrogate-assisted multi-objective optimization of antenna structures exploiting variable-fidelity electromagnetic simulation models

NASA Astrophysics Data System (ADS)

Koziel, Slawomir; Bekasiewicz, Adrian

2016-10-01

Multi-objective optimization of antenna structures is a challenging task owing to the high computational cost of evaluating the design objectives as well as the large number of adjustable parameters. Design speed-up can be achieved by means of surrogate-based optimization techniques. In particular, a combination of variable-fidelity electromagnetic (EM) simulations, design space reduction techniques, response surface approximation models and design refinement methods permits identification of the Pareto-optimal set of designs within a reasonable timeframe. Here, a study concerning the scalability of surrogate-assisted multi-objective antenna design is carried out based on a set of benchmark problems, with the dimensionality of the design space ranging from six to 24 and a CPU cost of the EM antenna model from 10 to 20 min per simulation. Numerical results indicate that the computational overhead of the design process increases more or less quadratically with the number of adjustable geometric parameters of the antenna structure at hand, which is a promising result from the point of view of handling even more complex problems.

TH-EF-BRB-05: 4pi Non-Coplanar IMRT Beam Angle Selection by Convex Optimization with Group Sparsity Penalty

DOE Office of Scientific and Technical Information (OSTI.GOV)

O’Connor, D; Nguyen, D; Voronenko, Y

Purpose: Integrated beam orientation and fluence map optimization is expected to be the foundation of robust automated planning but existing heuristic methods do not promise global optimality. We aim to develop a new method for beam angle selection in 4π non-coplanar IMRT systems based on solving (globally) a single convex optimization problem, and to demonstrate the effectiveness of the method by comparison with a state of the art column generation method for 4π beam angle selection. Methods: The beam angle selection problem is formulated as a large scale convex fluence map optimization problem with an additional group sparsity term thatmore » encourages most candidate beams to be inactive. The optimization problem is solved using an accelerated first-order method, the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). The beam angle selection and fluence map optimization algorithm is used to create non-coplanar 4π treatment plans for several cases (including head and neck, lung, and prostate cases) and the resulting treatment plans are compared with 4π treatment plans created using the column generation algorithm. Results: In our experiments the treatment plans created using the group sparsity method meet or exceed the dosimetric quality of plans created using the column generation algorithm, which was shown superior to clinical plans. Moreover, the group sparsity approach converges in about 3 minutes in these cases, as compared with runtimes of a few hours for the column generation method. Conclusion: This work demonstrates the first non-greedy approach to non-coplanar beam angle selection, based on convex optimization, for 4π IMRT systems. The method given here improves both treatment plan quality and runtime as compared with a state of the art column generation algorithm. When the group sparsity term is set to zero, we obtain an excellent method for fluence map optimization, useful when beam angles have already been selected. NIH R43CA183390, NIH R01CA188300, Varian Medical Systems; Part of this research took place while D. O’Connor was a summer intern at RefleXion Medical.« less

Multidisciplinary optimization of a controlled space structure using 150 design variables

NASA Technical Reports Server (NTRS)

James, Benjamin B.

1992-01-01

A general optimization-based method for the design of large space platforms through integration of the disciplines of structural dynamics and control is presented. The method uses the global sensitivity equations approach and is especially appropriate for preliminary design problems in which the structural and control analyses are tightly coupled. The method is capable of coordinating general purpose structural analysis, multivariable control, and optimization codes, and thus, can be adapted to a variety of controls-structures integrated design projects. The method is used to minimize the total weight of a space platform while maintaining a specified vibration decay rate after slewing maneuvers.

Application of advanced multidisciplinary analysis and optimization methods to vehicle design synthesis

NASA Technical Reports Server (NTRS)

Consoli, Robert David; Sobieszczanski-Sobieski, Jaroslaw

1990-01-01

Advanced multidisciplinary analysis and optimization methods, namely system sensitivity analysis and non-hierarchical system decomposition, are applied to reduce the cost and improve the visibility of an automated vehicle design synthesis process. This process is inherently complex due to the large number of functional disciplines and associated interdisciplinary couplings. Recent developments in system sensitivity analysis as applied to complex non-hierarchic multidisciplinary design optimization problems enable the decomposition of these complex interactions into sub-processes that can be evaluated in parallel. The application of these techniques results in significant cost, accuracy, and visibility benefits for the entire design synthesis process.

Reference View Selection in DIBR-Based Multiview Coding.

PubMed

Maugey, Thomas; Petrazzuoli, Giovanni; Frossard, Pascal; Cagnazzo, Marco; Pesquet-Popescu, Beatrice

2016-04-01

Augmented reality, interactive navigation in 3D scenes, multiview video, and other emerging multimedia applications require large sets of images, hence larger data volumes and increased resources compared with traditional video services. The significant increase in the number of images in multiview systems leads to new challenging problems in data representation and data transmission to provide high quality of experience on resource-constrained environments. In order to reduce the size of the data, different multiview video compression strategies have been proposed recently. Most of them use the concept of reference or key views that are used to estimate other images when there is high correlation in the data set. In such coding schemes, the two following questions become fundamental: 1) how many reference views have to be chosen for keeping a good reconstruction quality under coding cost constraints? And 2) where to place these key views in the multiview data set? As these questions are largely overlooked in the literature, we study the reference view selection problem and propose an algorithm for the optimal selection of reference views in multiview coding systems. Based on a novel metric that measures the similarity between the views, we formulate an optimization problem for the positioning of the reference views, such that both the distortion of the view reconstruction and the coding rate cost are minimized. We solve this new problem with a shortest path algorithm that determines both the optimal number of reference views and their positions in the image set. We experimentally validate our solution in a practical multiview distributed coding system and in the standardized 3D-HEVC multiview coding scheme. We show that considering the 3D scene geometry in the reference view, positioning problem brings significant rate-distortion improvements and outperforms the traditional coding strategy that simply selects key frames based on the distance between cameras.

Multidisciplinary design optimization using genetic algorithms

NASA Technical Reports Server (NTRS)

Unal, Resit

1994-01-01

Multidisciplinary design optimization (MDO) is an important step in the conceptual design and evaluation of launch vehicles since it can have a significant impact on performance and life cycle cost. The objective is to search the system design space to determine values of design variables that optimize the performance characteristic subject to system constraints. Gradient-based optimization routines have been used extensively for aerospace design optimization. However, one limitation of gradient based optimizers is their need for gradient information. Therefore, design problems which include discrete variables can not be studied. Such problems are common in launch vehicle design. For example, the number of engines and material choices must be integer values or assume only a few discrete values. In this study, genetic algorithms are investigated as an approach to MDO problems involving discrete variables and discontinuous domains. Optimization by genetic algorithms (GA) uses a search procedure which is fundamentally different from those gradient based methods. Genetic algorithms seek to find good solutions in an efficient and timely manner rather than finding the best solution. GA are designed to mimic evolutionary selection. A population of candidate designs is evaluated at each iteration, and each individual's probability of reproduction (existence in the next generation) depends on its fitness value (related to the value of the objective function). Progress toward the optimum is achieved by the crossover and mutation operations. GA is attractive since it uses only objective function values in the search process, so gradient calculations are avoided. Hence, GA are able to deal with discrete variables. Studies report success in the use of GA for aircraft design optimization studies, trajectory analysis, space structure design and control systems design. In these studies reliable convergence was achieved, but the number of function evaluations was large compared with efficient gradient methods. Applicaiton of GA is underway for a cost optimization study for a launch-vehicle fuel-tank and structural design of a wing. The strengths and limitations of GA for launch vehicle design optimization is studied.

Cascade Optimization Strategy Maximizes Thrust for High-Speed Civil Transport Propulsion System Concept

NASA Technical Reports Server (NTRS)

1995-01-01

The design of a High-Speed Civil Transport (HSCT) air-breathing propulsion system for multimission, variable-cycle operations was successfully optimized through a soft coupling of the engine performance analyzer NASA Engine Performance Program (NEPP) to a multidisciplinary optimization tool COMETBOARDS that was developed at the NASA Lewis Research Center. The design optimization of this engine was cast as a nonlinear optimization problem, with engine thrust as the merit function and the bypass ratios, r-values of fans, fuel flow, and other factors as important active design variables. Constraints were specified on factors including the maximum speed of the compressors, the positive surge margins for the compressors with specified safety factors, the discharge temperature, the pressure ratios, and the mixer extreme Mach number. Solving the problem by using the most reliable optimization algorithm available in COMETBOARDS would provide feasible optimum results only for a portion of the aircraft flight regime because of the large number of mission points (defined by altitudes, Mach numbers, flow rates, and other factors), diverse constraint types, and overall poor conditioning of the design space. Only the cascade optimization strategy of COMETBOARDS, which was devised especially for difficult multidisciplinary applications, could successfully solve a number of engine design problems for their flight regimes. Furthermore, the cascade strategy converged to the same global optimum solution even when it was initiated from different design points. Multiple optimizers in a specified sequence, pseudorandom damping, and reduction of the design space distortion via a global scaling scheme are some of the key features of the cascade strategy. HSCT engine concept, optimized solution for HSCT engine concept. A COMETBOARDS solution for an HSCT engine (Mach-2.4 mixed-flow turbofan) along with its configuration is shown. The optimum thrust is normalized with respect to NEPP results. COMETBOARDS added value in the design optimization of the HSCT engine.

Reliability Analysis and Reliability-Based Design Optimization of Circular Composite Cylinders Under Axial Compression

NASA Technical Reports Server (NTRS)

Rais-Rohani, Masoud

2001-01-01

This report describes the preliminary results of an investigation on component reliability analysis and reliability-based design optimization of thin-walled circular composite cylinders with average diameter and average length of 15 inches. Structural reliability is based on axial buckling strength of the cylinder. Both Monte Carlo simulation and First Order Reliability Method are considered for reliability analysis with the latter incorporated into the reliability-based structural optimization problem. To improve the efficiency of reliability sensitivity analysis and design optimization solution, the buckling strength of the cylinder is estimated using a second-order response surface model. The sensitivity of the reliability index with respect to the mean and standard deviation of each random variable is calculated and compared. The reliability index is found to be extremely sensitive to the applied load and elastic modulus of the material in the fiber direction. The cylinder diameter was found to have the third highest impact on the reliability index. Also the uncertainty in the applied load, captured by examining different values for its coefficient of variation, is found to have a large influence on cylinder reliability. The optimization problem for minimum weight is solved subject to a design constraint on element reliability index. The methodology, solution procedure and optimization results are included in this report.

Multiresolution strategies for the numerical solution of optimal control problems

NASA Astrophysics Data System (ADS)

Jain, Sachin

There exist many numerical techniques for solving optimal control problems but less work has been done in the field of making these algorithms run faster and more robustly. The main motivation of this work is to solve optimal control problems accurately in a fast and efficient way. Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. The algorithm adapted dynamically to any existing or emerging irregularities in the solution by automatically allocating more grid points to the region where the solution exhibited sharp features and fewer points to the region where the solution was smooth. Thereby, the computational time and memory usage has been reduced significantly, while maintaining an accuracy equivalent to the one obtained using a fine uniform mesh. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a nonlinear programming (NLP) problem that is solved using standard NLP codes. The novelty of the proposed approach hinges on the automatic calculation of a suitable, nonuniform grid over which the NLP problem is solved, which tends to increase numerical efficiency and robustness. Control and/or state constraints are handled with ease, and without any additional computational complexity. The proposed algorithm is based on a simple and intuitive method to balance several conflicting objectives, such as accuracy of the solution, convergence, and speed of the computations. The benefits of the proposed algorithm over uniform grid implementations are demonstrated with the help of several nontrivial examples. Furthermore, two sequential multiresolution trajectory optimization algorithms for solving problems with moving targets and/or dynamically changing environments have been developed. For such problems, high accuracy is desirable only in the immediate future, yet the ultimate mission objectives should be accommodated as well. An intelligent trajectory generation for such situations is thus enabled by introducing the idea of multigrid temporal resolution to solve the associated trajectory optimization problem on a non-uniform grid across time that is adapted to: (i) immediate future, and (ii) potential discontinuities in the state and control variables.

Multi-level systems modeling and optimization for novel aircraft

NASA Astrophysics Data System (ADS)

Subramanian, Shreyas Vathul

This research combines the disciplines of system-of-systems (SoS) modeling, platform-based design, optimization and evolving design spaces to achieve a novel capability for designing solutions to key aeronautical mission challenges. A central innovation in this approach is the confluence of multi-level modeling (from sub-systems to the aircraft system to aeronautical system-of-systems) in a way that coordinates the appropriate problem formulations at each level and enables parametric search in design libraries for solutions that satisfy level-specific objectives. The work here addresses the topic of SoS optimization and discusses problem formulation, solution strategy, the need for new algorithms that address special features of this problem type, and also demonstrates these concepts using two example application problems - a surveillance UAV swarm problem, and the design of noise optimal aircraft and approach procedures. This topic is critical since most new capabilities in aeronautics will be provided not just by a single air vehicle, but by aeronautical Systems of Systems (SoS). At the same time, many new aircraft concepts are pressing the boundaries of cyber-physical complexity through the myriad of dynamic and adaptive sub-systems that are rising up the TRL (Technology Readiness Level) scale. This compositional approach is envisioned to be active at three levels: validated sub-systems are integrated to form conceptual aircraft, which are further connected with others to perform a challenging mission capability at the SoS level. While these multiple levels represent layers of physical abstraction, each discipline is associated with tools of varying fidelity forming strata of 'analysis abstraction'. Further, the design (composition) will be guided by a suitable hierarchical complexity metric formulated for the management of complexity in both the problem (as part of the generative procedure and selection of fidelity level) and the product (i.e., is the mission best achieved via a large collection of interacting simple systems, or a relatively few highly capable, complex air vehicles). The vastly unexplored area of optimization in evolving design spaces will be studied and incorporated into the SoS optimization framework. We envision a framework that resembles a multi-level, mult-fidelity, multi-disciplinary assemblage of optimization problems. The challenge is not simply one of scaling up to a new level (the SoS), but recognizing that the aircraft sub-systems and the integrated vehicle are now intensely cyber-physical, with hardware and software components interacting in complex ways that give rise to new and improved capabilities. The work presented here is a step closer to modeling the information flow that exists in realistic SoS optimization problems between sub-contractors, contractors and the SoS architect.

Shape optimization and CAD

NASA Technical Reports Server (NTRS)

Rasmussen, John

1990-01-01

Structural optimization has attracted the attention since the days of Galileo. Olhoff and Taylor have produced an excellent overview of the classical research within this field. However, the interest in structural optimization has increased greatly during the last decade due to the advent of reliable general numerical analysis methods and the computer power necessary to use them efficiently. This has created the possibility of developing general numerical systems for shape optimization. Several authors, eg., Esping; Braibant & Fleury; Bennet & Botkin; Botkin, Yang, and Bennet; and Stanton have published practical and successful applications of general optimization systems. Ding and Homlein have produced extensive overviews of available systems. Furthermore, a number of commercial optimization systems based on well-established finite element codes have been introduced. Systems like ANSYS, IDEAS, OASIS, and NISAOPT are widely known examples. In parallel to this development, the technology of computer aided design (CAD) has gained a large influence on the design process of mechanical engineering. The CAD technology has already lived through a rapid development driven by the drastically growing capabilities of digital computers. However, the systems of today are still considered as being only the first generation of a long row of computer integrated manufacturing (CIM) systems. These systems to come will offer an integrated environment for design, analysis, and fabrication of products of almost any character. Thus, the CAD system could be regarded as simply a database for geometrical information equipped with a number of tools with the purpose of helping the user in the design process. Among these tools are facilities for structural analysis and optimization as well as present standard CAD features like drawing, modeling, and visualization tools. The state of the art of structural optimization is that a large amount of mathematical and mechanical techniques are available for the solution of single problems. By implementing collections of the available techniques into general software systems, operational environments for structural optimization have been created. The forthcoming years must bring solutions to the problem of integrating such systems into more general design environments. The result of this work should be CAD systems for rational design in which structural optimization is one important design tool among many others.

Using and comparing metaheuristic algorithms for optimizing bidding strategy viewpoint of profit maximization of generators

NASA Astrophysics Data System (ADS)

Mousavi, Seyed Hosein; Nazemi, Ali; Hafezalkotob, Ashkan

2015-03-01

With the formation of the competitive electricity markets in the world, optimization of bidding strategies has become one of the main discussions in studies related to market designing. Market design is challenged by multiple objectives that need to be satisfied. The solution of those multi-objective problems is searched often over the combined strategy space, and thus requires the simultaneous optimization of multiple parameters. The problem is formulated analytically using the Nash equilibrium concept for games composed of large numbers of players having discrete and large strategy spaces. The solution methodology is based on a characterization of Nash equilibrium in terms of minima of a function and relies on a metaheuristic optimization approach to find these minima. This paper presents some metaheuristic algorithms to simulate how generators bid in the spot electricity market viewpoint of their profit maximization according to the other generators' strategies, such as genetic algorithm (GA), simulated annealing (SA) and hybrid simulated annealing genetic algorithm (HSAGA) and compares their results. As both GA and SA are generic search methods, HSAGA is also a generic search method. The model based on the actual data is implemented in a peak hour of Tehran's wholesale spot market in 2012. The results of the simulations show that GA outperforms SA and HSAGA on computing time, number of function evaluation and computing stability, as well as the results of calculated Nash equilibriums by GA are less various and different from each other than the other algorithms.

Object Transportation by Two Mobile Robots with Hand Carts

PubMed Central

Hara, Tatsunori

2014-01-01

This paper proposes a methodology by which two small mobile robots can grasp, lift, and transport large objects using hand carts. The specific problems involve generating robot actions and determining the hand cart positions to achieve the stable loading of objects onto the carts. These problems are solved using nonlinear optimization, and we propose an algorithm for generating robot actions. The proposed method was verified through simulations and experiments using actual devices in a real environment. The proposed method could reduce the number of robots required to transport large objects with 50–60%. In addition, we demonstrated the efficacy of this task in real environments where errors occur in robot sensing and movement. PMID:27433499

Ride comfort control in large flexible aircraft. M.S. Thesis

NASA Technical Reports Server (NTRS)

Warren, M. E.

1971-01-01

The problem of ameliorating the discomfort of passengers on a large air transport subject to flight disturbances is examined. The longitudinal dynamics of the aircraft, including effects of body flexing, are developed in terms of linear, constant coefficient differential equations in state variables. A cost functional, penalizing the rigid body displacements and flexure accelerations over the surface of the aircraft is formulated as a quadratic form. The resulting control problem, to minimize the cost subject to the state equation constraints, is of a class whose solutions are well known. The feedback gains for the optimal controller are calculated digitally, and the resulting autopilot is simulated on an analog computer and its performance evaluated.