Replica analysis for the duality of the portfolio optimization problem

NASA Astrophysics Data System (ADS)

Shinzato, Takashi

2016-11-01

In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we analyzed in a previous study, we herein consider a primal-dual problem in which the investment risk minimization problem with budget and expected return constraints is regarded as the primal problem, and the expected return maximization problem with budget and investment risk constraints is regarded as the dual problem. With respect to these optimal problems, we analyze a quenched disordered system involving both of these optimization problems using the approach developed in statistical mechanical informatics and confirm that both optimal portfolios can possess the primal-dual structure. Finally, the results of numerical simulations are shown to validate the effectiveness of the proposed method.

Replica analysis for the duality of the portfolio optimization problem.

PubMed

Shinzato, Takashi

2016-11-01

In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we analyzed in a previous study, we herein consider a primal-dual problem in which the investment risk minimization problem with budget and expected return constraints is regarded as the primal problem, and the expected return maximization problem with budget and investment risk constraints is regarded as the dual problem. With respect to these optimal problems, we analyze a quenched disordered system involving both of these optimization problems using the approach developed in statistical mechanical informatics and confirm that both optimal portfolios can possess the primal-dual structure. Finally, the results of numerical simulations are shown to validate the effectiveness of the proposed method.

Hybrid Genetic Agorithms and Line Search Method for Industrial Production Planning with Non-Linear Fitness Function

NASA Astrophysics Data System (ADS)

Vasant, Pandian; Barsoum, Nader

2008-10-01

Many engineering, science, information technology and management optimization problems can be considered as non linear programming real world problems where the all or some of the parameters and variables involved are uncertain in nature. These can only be quantified using intelligent computational techniques such as evolutionary computation and fuzzy logic. The main objective of this research paper is to solve non linear fuzzy optimization problem where the technological coefficient in the constraints involved are fuzzy numbers which was represented by logistic membership functions by using hybrid evolutionary optimization approach. To explore the applicability of the present study a numerical example is considered to determine the production planning for the decision variables and profit of the company.

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.

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.

Surrogate assisted multidisciplinary design optimization for an all-electric GEO satellite

NASA Astrophysics Data System (ADS)

Shi, Renhe; Liu, Li; Long, Teng; Liu, Jian; Yuan, Bin

2017-09-01

State-of-the-art all-electric geostationary earth orbit (GEO) satellites use electric thrusters to execute all propulsive duties, which significantly differ from the traditional all-chemical ones in orbit-raising, station-keeping, radiation damage protection, and power budget, etc. Design optimization task of an all-electric GEO satellite is therefore a complex multidisciplinary design optimization (MDO) problem involving unique design considerations. However, solving the all-electric GEO satellite MDO problem faces big challenges in disciplinary modeling techniques and efficient optimization strategy. To address these challenges, we presents a surrogate assisted MDO framework consisting of several modules, i.e., MDO problem definition, multidisciplinary modeling, multidisciplinary analysis (MDA), and surrogate assisted optimizer. Based on the proposed framework, the all-electric GEO satellite MDO problem is formulated to minimize the total mass of the satellite system under a number of practical constraints. Then considerable efforts are spent on multidisciplinary modeling involving geosynchronous transfer, GEO station-keeping, power, thermal control, attitude control, and structure disciplines. Since orbit dynamics models and finite element structural model are computationally expensive, an adaptive response surface surrogate based optimizer is incorporated in the proposed framework to solve the satellite MDO problem with moderate computational cost, where a response surface surrogate is gradually refined to represent the computationally expensive MDA process. After optimization, the total mass of the studied GEO satellite is decreased by 185.3 kg (i.e., 7.3% of the total mass). Finally, the optimal design is further discussed to demonstrate the effectiveness of our proposed framework to cope with the all-electric GEO satellite system design optimization problems. This proposed surrogate assisted MDO framework can also provide valuable references for other all-electric spacecraft system design.

A hybrid nonlinear programming method for design optimization

NASA Technical Reports Server (NTRS)

Rajan, S. D.

1986-01-01

Solutions to engineering design problems formulated as nonlinear programming (NLP) problems usually require the use of more than one optimization technique. Moreover, the interaction between the user (analysis/synthesis) program and the NLP system can lead to interface, scaling, or convergence problems. An NLP solution system is presented that seeks to solve these problems by providing a programming system to ease the user-system interface. A simple set of rules is used to select an optimization technique or to switch from one technique to another in an attempt to detect, diagnose, and solve some potential problems. Numerical examples involving finite element based optimal design of space trusses and rotor bearing systems are used to illustrate the applicability of the proposed methodology.

Near-optimal, asymptotic tracking in control problems involving state-variable inequality constraints

NASA Technical Reports Server (NTRS)

Markopoulos, N.; Calise, A. J.

1993-01-01

The class of all piecewise time-continuous controllers tracking a given hypersurface in the state space of a dynamical system can be split by the present transformation technique into two disjoint classes; while the first of these contains all controllers which track the hypersurface in finite time, the second contains all controllers that track the hypersurface asymptotically. On this basis, a reformulation is presented for optimal control problems involving state-variable inequality constraints. If the state constraint is regarded as 'soft', there may exist controllers which are asymptotic, two-sided, and able to yield the optimal value of the performance index.

Application of fuzzy theories to formulation of multi-objective design problems. [for helicopters

NASA Technical Reports Server (NTRS)

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

1988-01-01

Much of the decision making in real world takes place in an environment in which the goals, the constraints, and the consequences of possible actions are not known precisely. In order to deal with imprecision quantitatively, the tools of fuzzy set theory can by used. This paper demonstrates the effectiveness of fuzzy theories in the formulation and solution of two types of helicopter design problems involving multiple objectives. The first problem deals with the determination of optimal flight parameters to accomplish a specified mission in the presence of three competing objectives. The second problem addresses the optimal design of the main rotor of a helicopter involving eight objective functions. A method of solving these multi-objective problems using nonlinear programming techniques is presented. Results obtained using fuzzy formulation are compared with those obtained using crisp optimization techniques. The outlined procedures are expected to be useful in situations where doubt arises about the exactness of permissible values, degree of credibility, and correctness of statements and judgements.

Decomposition method for zonal resource allocation problems in telecommunication networks

NASA Astrophysics Data System (ADS)

Konnov, I. V.; Kashuba, A. Yu

2016-11-01

We consider problems of optimal resource allocation in telecommunication networks. We first give an optimization formulation for the case where the network manager aims to distribute some homogeneous resource (bandwidth) among users of one region with quadratic charge and fee functions and present simple and efficient solution methods. Next, we consider a more general problem for a provider of a wireless communication network divided into zones (clusters) with common capacity constraints. We obtain a convex quadratic optimization problem involving capacity and balance constraints. By using the dual Lagrangian method with respect to the capacity constraint, we suggest to reduce the initial problem to a single-dimensional optimization problem, but calculation of the cost function value leads to independent solution of zonal problems, which coincide with the above single region problem. Some results of computational experiments confirm the applicability of the new methods.

Fractional Programming for Communication Systems—Part II: Uplink Scheduling via Matching

NASA Astrophysics Data System (ADS)

Shen, Kaiming; Yu, Wei

2018-05-01

This two-part paper develops novel methodologies for using fractional programming (FP) techniques to design and optimize communication systems. Part I of this paper proposes a new quadratic transform for FP and treats its application for continuous optimization problems. In this Part II of the paper, we study discrete problems, such as those involving user scheduling, which are considerably more difficult to solve. Unlike the continuous problems, discrete or mixed discrete-continuous problems normally cannot be recast as convex problems. In contrast to the common heuristic of relaxing the discrete variables, this work reformulates the original problem in an FP form amenable to distributed combinatorial optimization. The paper illustrates this methodology by tackling the important and challenging problem of uplink coordinated multi-cell user scheduling in wireless cellular systems. Uplink scheduling is more challenging than downlink scheduling, because uplink user scheduling decisions significantly affect the interference pattern in nearby cells. Further, the discrete scheduling variable needs to be optimized jointly with continuous variables such as transmit power levels and beamformers. The main idea of the proposed FP approach is to decouple the interaction among the interfering links, thereby permitting a distributed and joint optimization of the discrete and continuous variables with provable convergence. The paper shows that the well-known weighted minimum mean-square-error (WMMSE) algorithm can also be derived from a particular use of FP; but our proposed FP-based method significantly outperforms WMMSE when discrete user scheduling variables are involved, both in term of run-time efficiency and optimizing results.

Optimal control of singularly perturbed nonlinear systems with state-variable inequality constraints

NASA Technical Reports Server (NTRS)

Calise, A. J.; Corban, J. E.

1990-01-01

The established necessary conditions for optimality in nonlinear control problems that involve state-variable inequality constraints are applied to a class of singularly perturbed systems. The distinguishing feature of this class of two-time-scale systems is a transformation of the state-variable inequality constraint, present in the full order problem, to a constraint involving states and controls in the reduced problem. It is shown that, when a state constraint is active in the reduced problem, the boundary layer problem can be of finite time in the stretched time variable. Thus, the usual requirement for asymptotic stability of the boundary layer system is not applicable, and cannot be used to construct approximate boundary layer solutions. Several alternative solution methods are explored and illustrated with simple examples.

Time-domain finite elements in optimal control with application to launch-vehicle guidance. PhD. Thesis

NASA Technical Reports Server (NTRS)

Bless, Robert R.

1991-01-01

A time-domain finite element method is developed for optimal control problems. The theory derived is general enough to handle a large class of problems including optimal control problems that are continuous in the states and controls, problems with discontinuities in the states and/or system equations, problems with control inequality constraints, problems with state inequality constraints, or problems involving any combination of the above. The theory is developed in such a way that no numerical quadrature is necessary regardless of the degree of nonlinearity in the equations. Also, the same shape functions may be employed for every problem because all strong boundary conditions are transformed into natural or weak boundary conditions. In addition, the resulting nonlinear algebraic equations are very sparse. Use of sparse matrix solvers allows for the rapid and accurate solution of very difficult optimization problems. The formulation is applied to launch-vehicle trajectory optimization problems, and results show that real-time optimal guidance is realizable with this method. Finally, a general problem solving environment is created for solving a large class of optimal control problems. The algorithm uses both FORTRAN and a symbolic computation program to solve problems with a minimum of user interaction. The use of symbolic computation eliminates the need for user-written subroutines which greatly reduces the setup time for solving problems.

The Popcorn Box Activity and Reasoning about Optimization

ERIC Educational Resources Information Center

Whiteley, Walter J.; Mamolo, Ami

2012-01-01

A well-known optimization problem is the Popcorn Box investigation, which involves a movie theater snack container. The problem has been tailored for classroom investigations by the Ontario Association for Mathematics Education. The exploration was designed for students in grades 9 through 12. A common strategy proposed for algebra students is to…

Development of a Composite Tailoring Procedure for Airplane Wings

NASA Technical Reports Server (NTRS)

Chattopadhyay, Aditi

2000-01-01

The quest for finding optimum solutions to engineering problems has existed for a long time. In modern times, the development of optimization as a branch of applied mathematics is regarded to have originated in the works of Newton, Bernoulli and Euler. Venkayya has presented a historical perspective on optimization in [1]. The term 'optimization' is defined by Ashley [2] as a procedure "...which attempts to choose the variables in a design process so as formally to achieve the best value of some performance index while not violating any of the associated conditions or constraints". Ashley presented an extensive review of practical applications of optimization in the aeronautical field till about 1980 [2]. It was noted that there existed an enormous amount of published literature in the field of optimization, but its practical applications in industry were very limited. Over the past 15 years, though, optimization has been widely applied to address practical problems in aerospace design [3-5]. The design of high performance aerospace systems is a complex task. It involves the integration of several disciplines such as aerodynamics, structural analysis, dynamics, and aeroelasticity. The problem involves multiple objectives and constraints pertaining to the design criteria associated with each of these disciplines. Many important trade-offs exist between the parameters involved which are used to define the different disciplines. Therefore, the development of multidisciplinary design optimization (MDO) techniques, in which different disciplines and design parameters are coupled into a closed loop numerical procedure, seems appropriate to address such a complex problem. The importance of MDO in successful design of aerospace systems has been long recognized. Recent developments in this field have been surveyed by Sobieszczanski-Sobieski and Haftka [6].

General Methodology for Designing Spacecraft Trajectories

NASA Technical Reports Server (NTRS)

Condon, Gerald; Ocampo, Cesar; Mathur, Ravishankar; Morcos, Fady; Senent, Juan; Williams, Jacob; Davis, Elizabeth C.

2012-01-01

A methodology for designing spacecraft trajectories in any gravitational environment within the solar system has been developed. The methodology facilitates modeling and optimization for problems ranging from that of a single spacecraft orbiting a single celestial body to that of a mission involving multiple spacecraft and multiple propulsion systems operating in gravitational fields of multiple celestial bodies. The methodology consolidates almost all spacecraft trajectory design and optimization problems into a single conceptual framework requiring solution of either a system of nonlinear equations or a parameter-optimization problem with equality and/or inequality constraints.

Application of GA, PSO, and ACO algorithms to path planning of autonomous underwater vehicles

NASA Astrophysics Data System (ADS)

Aghababa, Mohammad Pourmahmood; Amrollahi, Mohammad Hossein; Borjkhani, Mehdi

2012-09-01

In this paper, an underwater vehicle was modeled with six dimensional nonlinear equations of motion, controlled by DC motors in all degrees of freedom. Near-optimal trajectories in an energetic environment for underwater vehicles were computed using a numerical solution of a nonlinear optimal control problem (NOCP). An energy performance index as a cost function, which should be minimized, was defined. The resulting problem was a two-point boundary value problem (TPBVP). A genetic algorithm (GA), particle swarm optimization (PSO), and ant colony optimization (ACO) algorithms were applied to solve the resulting TPBVP. Applying an Euler-Lagrange equation to the NOCP, a conjugate gradient penalty method was also adopted to solve the TPBVP. The problem of energetic environments, involving some energy sources, was discussed. Some near-optimal paths were found using a GA, PSO, and ACO algorithms. Finally, the problem of collision avoidance in an energetic environment was also taken into account.

Udzawa-type iterative method with parareal preconditioner for a parabolic optimal control problem

NASA Astrophysics Data System (ADS)

Lapin, A.; Romanenko, A.

2016-11-01

The article deals with the optimal control problem with the parabolic equation as state problem. There are point-wise constraints on the state and control functions. The objective functional involves the observation given in the domain at each moment. The conditions for convergence Udzawa's type iterative method are given. The parareal method to inverse preconditioner is given. The results of calculations are presented.

Robust optimization modelling with applications to industry and environmental problems

NASA Astrophysics Data System (ADS)

Chaerani, Diah; Dewanto, Stanley P.; Lesmana, Eman

2017-10-01

Robust Optimization (RO) modeling is one of the existing methodology for handling data uncertainty in optimization problem. The main challenge in this RO methodology is how and when we can reformulate the robust counterpart of uncertain problems as a computationally tractable optimization problem or at least approximate the robust counterpart by a tractable problem. Due to its definition the robust counterpart highly depends on how we choose the uncertainty set. As a consequence we can meet this challenge only if this set is chosen in a suitable way. The development on RO grows fast, since 2004, a new approach of RO called Adjustable Robust Optimization (ARO) is introduced to handle uncertain problems when the decision variables must be decided as a ”wait and see” decision variables. Different than the classic Robust Optimization (RO) that models decision variables as ”here and now”. In ARO, the uncertain problems can be considered as a multistage decision problem, thus decision variables involved are now become the wait and see decision variables. In this paper we present the applications of both RO and ARO. We present briefly all results to strengthen the importance of RO and ARO in many real life problems.

Performance Optimizing Multi-Objective Adaptive Control with Time-Varying Model Reference Modification

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Hashemi, Kelley E.; Yucelen, Tansel; Arabi, Ehsan

2017-01-01

This paper presents a new adaptive control approach that involves a performance optimization objective. The problem is cast as a multi-objective optimal control. The control synthesis involves the design of a performance optimizing controller from a subset of control inputs. The effect of the performance optimizing controller is to introduce an uncertainty into the system that can degrade tracking of the reference model. An adaptive controller from the remaining control inputs is designed to reduce the effect of the uncertainty while maintaining a notion of performance optimization in the adaptive control system.

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.

Optimal Control of Thermo--Fluid Phenomena in Variable Domains

NASA Astrophysics Data System (ADS)

Volkov, Oleg; Protas, Bartosz

2008-11-01

This presentation concerns our continued research on adjoint--based optimization of viscous incompressible flows (the Navier--Stokes problem) coupled with heat conduction involving change of phase (the Stefan problem), and occurring in domains with variable boundaries. This problem is motivated by optimization of advanced welding techniques used in automotive manufacturing, where the goal is to determine an optimal heat input, so as to obtain a desired shape of the weld pool surface upon solidification. We argue that computation of sensitivities (gradients) in such free--boundary problems requires the use of the shape--differential calculus as a key ingredient. We also show that, with such tools available, the computational solution of the direct and inverse (optimization) problems can in fact be achieved in a similar manner and in a comparable computational time. Our presentation will address certain mathematical and computational aspects of the method. As an illustration we will consider the two--phase Stefan problem with contact point singularities where our approach allows us to obtain a thermodynamically consistent solution.

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.

Global optimization algorithm for heat exchanger networks

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

Quesada, I.; Grossmann, I.E.

This paper deals with the global optimization of heat exchanger networks with fixed topology. It is shown that if linear area cost functions are assumed, as well as arithmetic mean driving force temperature differences in networks with isothermal mixing, the corresponding nonlinear programming (NLP) optimization problem involves linear constraints and a sum of linear fractional functions in the objective which are nonconvex. A rigorous algorithm is proposed that is based on a convex NLP underestimator that involves linear and nonlinear estimators for fractional and bilinear terms which provide a tight lower bound to the global optimum. This NLP problem ismore » used within a spatial branch and bound method for which branching rules are given. Basic properties of the proposed method are presented, and its application is illustrated with several example problems. The results show that the proposed method only requires few nodes in the branch and bound search.« less

Perspective: Stochastic magnetic devices for cognitive computing

NASA Astrophysics Data System (ADS)

Roy, Kaushik; Sengupta, Abhronil; Shim, Yong

2018-06-01

Stochastic switching of nanomagnets can potentially enable probabilistic cognitive hardware consisting of noisy neural and synaptic components. Furthermore, computational paradigms inspired from the Ising computing model require stochasticity for achieving near-optimality in solutions to various types of combinatorial optimization problems such as the Graph Coloring Problem or the Travelling Salesman Problem. Achieving optimal solutions in such problems are computationally exhaustive and requires natural annealing to arrive at the near-optimal solutions. Stochastic switching of devices also finds use in applications involving Deep Belief Networks and Bayesian Inference. In this article, we provide a multi-disciplinary perspective across the stack of devices, circuits, and algorithms to illustrate how the stochastic switching dynamics of spintronic devices in the presence of thermal noise can provide a direct mapping to the computational units of such probabilistic intelligent systems.

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.

Calibration of neural networks using genetic algorithms, with application to optimal path planning

NASA Technical Reports Server (NTRS)

Smith, Terence R.; Pitney, Gilbert A.; Greenwood, Daniel

1987-01-01

Genetic algorithms (GA) are used to search the synaptic weight space of artificial neural systems (ANS) for weight vectors that optimize some network performance function. GAs do not suffer from some of the architectural constraints involved with other techniques and it is straightforward to incorporate terms into the performance function concerning the metastructure of the ANS. Hence GAs offer a remarkably general approach to calibrating ANS. GAs are applied to the problem of calibrating an ANS that finds optimal paths over a given surface. This problem involves training an ANS on a relatively small set of paths and then examining whether the calibrated ANS is able to find good paths between arbitrary start and end points on the surface.

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

Novel Numerical Methods for Optimal Control Problems Involving Fractional-Order Differential Equations

DTIC Science & Technology

2018-03-14

pricing, Appl. Math . Comp. Vol.305, 174-187 (2017) 5. W. Li, S. Wang, Pricing European options with proportional transaction costs and stochastic...for fractional differential equation. Numer. Math . Theor. Methods Appl. 5, 229–241, 2012. [23] Kilbas A.A. and Marzan, S.A., Cauchy problem for...numerical technique for solving fractional optimal control problems, Comput. Math . Appl., 62, Issue 3, 1055–1067, 2011. [26] Lotfi A., Yousefi SA., Dehghan M

Biokinetic model-based multi-objective optimization of Dunaliella tertiolecta cultivation using elitist non-dominated sorting genetic algorithm with inheritance.

PubMed

Sinha, Snehal K; Kumar, Mithilesh; Guria, Chandan; Kumar, Anup; Banerjee, Chiranjib

2017-10-01

Algal model based multi-objective optimization using elitist non-dominated sorting genetic algorithm with inheritance was carried out for batch cultivation of Dunaliella tertiolecta using NPK-fertilizer. Optimization problems involving two- and three-objective functions were solved simultaneously. The objective functions are: maximization of algae-biomass and lipid productivity with minimization of cultivation time and cost. Time variant light intensity and temperature including NPK-fertilizer, NaCl and NaHCO 3 loadings are the important decision variables. Algal model involving Monod/Andrews adsorption kinetics and Droop model with internal nutrient cell quota was used for optimization studies. Sets of non-dominated (equally good) Pareto optimal solutions were obtained for the problems studied. It was observed that time variant optimal light intensity and temperature trajectories, including optimum NPK fertilizer, NaCl and NaHCO 3 concentration has significant influence to improve biomass and lipid productivity under minimum cultivation time and cost. Proposed optimization studies may be helpful to implement the control strategy in scale-up operation. Copyright © 2017 Elsevier Ltd. All rights reserved.

MULTI-OBJECTIVE OPTIMAL DESIGN OF GROUNDWATER REMEDIATION SYSTEMS: APPLICATION OF THE NICHED PARETO GENETIC ALGORITHM (NPGA). (R826614)

EPA Science Inventory

A multiobjective optimization algorithm is applied to a groundwater quality management problem involving remediation by pump-and-treat (PAT). The multiobjective optimization framework uses the niched Pareto genetic algorithm (NPGA) and is applied to simultaneously minimize the...

Topology-changing shape optimization with the genetic algorithm

NASA Astrophysics Data System (ADS)

Lamberson, Steven E., Jr.

The goal is to take a traditional shape optimization problem statement and modify it slightly to allow for prescribed changes in topology. This modification enables greater flexibility in the choice of parameters for the topology optimization problem, while improving the direct physical relevance of the results. This modification involves changing the optimization problem statement from a nonlinear programming problem into a form of mixed-discrete nonlinear programing problem. The present work demonstrates one possible way of using the Genetic Algorithm (GA) to solve such a problem, including the use of "masking bits" and a new modification to the bit-string affinity (BSA) termination criterion specifically designed for problems with "masking bits." A simple ten-bar truss problem proves the utility of the modified BSA for this type of problem. A more complicated two dimensional bracket problem is solved using both the proposed approach and a more traditional topology optimization approach (Solid Isotropic Microstructure with Penalization or SIMP) to enable comparison. The proposed approach is able to solve problems with both local and global constraints, which is something traditional methods cannot do. The proposed approach has a significantly higher computational burden --- on the order of 100 times larger than SIMP, although the proposed approach is able to offset this with parallel computing.

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...

Optimal timing in biological processes

USGS Publications Warehouse

Williams, B.K.; Nichols, J.D.

1984-01-01

A general approach for obtaining solutions to a class of biological optimization problems is provided. The general problem is one of determining the appropriate time to take some action, when the action can be taken only once during some finite time frame. The approach can also be extended to cover a number of other problems involving animal choice (e.g., mate selection, habitat selection). Returns (assumed to index fitness) are treated as random variables with time-specific distributions, and can be either observable or unobservable at the time action is taken. In the case of unobservable returns, the organism is assumed to base decisions on some ancillary variable that is associated with returns. Optimal policies are derived for both situations and their properties are discussed. Various extensions are also considered, including objective functions based on functions of returns other than the mean, nonmonotonic relationships between the observable variable and returns; possible death of the organism before action is taken; and discounting of future returns. A general feature of the optimal solutions for many of these problems is that an organism should be very selective (i.e., should act only when returns or expected returns are relatively high) at the beginning of the time frame and should become less and less selective as time progresses. An example of the application of optimal timing to a problem involving the timing of bird migration is discussed, and a number of other examples for which the approach is applicable are described.

Generalized Differential Calculus and Applications to Optimization

NASA Astrophysics Data System (ADS)

Rector, Robert Blake Hayden

This thesis contains contributions in three areas: the theory of generalized calculus, numerical algorithms for operations research, and applications of optimization to problems in modern electric power systems. A geometric approach is used to advance the theory and tools used for studying generalized notions of derivatives for nonsmooth functions. These advances specifically pertain to methods for calculating subdifferentials and to expanding our understanding of a certain notion of derivative of set-valued maps, called the coderivative, in infinite dimensions. A strong understanding of the subdifferential is essential for numerical optimization algorithms, which are developed and applied to nonsmooth problems in operations research, including non-convex problems. Finally, an optimization framework is applied to solve a problem in electric power systems involving a smart solar inverter and battery storage system providing energy and ancillary services to the grid.

SeGRAm - A practical and versatile tool for spacecraft trajectory optimization

NASA Technical Reports Server (NTRS)

Rishikof, Brian H.; Mccormick, Bernell R.; Pritchard, Robert E.; Sponaugle, Steven J.

1991-01-01

An implementation of the Sequential Gradient/Restoration Algorithm, SeGRAm, is presented along with selected examples. This spacecraft trajectory optimization and simulation program uses variational calculus to solve problems of spacecraft flying under the influence of one or more gravitational bodies. It produces a series of feasible solutions to problems involving a wide range of vehicles, environments and optimization functions, until an optimal solution is found. The examples included highlight the various capabilities of the program and emphasize in particular its versatility over a wide spectrum of applications from ascent to interplanetary trajectories.

Smell Detection Agent Based Optimization Algorithm

NASA Astrophysics Data System (ADS)

Vinod Chandra, S. S.

2016-09-01

In this paper, a novel nature-inspired optimization algorithm has been employed and the trained behaviour of dogs in detecting smell trails is adapted into computational agents for problem solving. The algorithm involves creation of a surface with smell trails and subsequent iteration of the agents in resolving a path. This algorithm can be applied in different computational constraints that incorporate path-based problems. Implementation of the algorithm can be treated as a shortest path problem for a variety of datasets. The simulated agents have been used to evolve the shortest path between two nodes in a graph. This algorithm is useful to solve NP-hard problems that are related to path discovery. This algorithm is also useful to solve many practical optimization problems. The extensive derivation of the algorithm can be enabled to solve shortest path problems.

Multigrid one shot methods for optimal control problems: Infinite dimensional control

NASA Technical Reports Server (NTRS)

Arian, Eyal; Taasan, Shlomo

1994-01-01

The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times.

Solid-perforated panel layout optimization by topology optimization based on unified transfer matrix.

PubMed

Kim, Yoon Jae; Kim, Yoon Young

2010-10-01

This paper presents a numerical method for the optimization of the sequencing of solid panels, perforated panels and air gaps and their respective thickness for maximizing sound transmission loss and/or absorption. For the optimization, a method based on the topology optimization formulation is proposed. It is difficult to employ only the commonly-used material interpolation technique because the involved layers exhibit fundamentally different acoustic behavior. Thus, an optimization method formulation using a so-called unified transfer matrix is newly proposed. The key idea is to form elements of the transfer matrix such that interpolated elements by the layer design variables can be those of air, perforated and solid panel layers. The problem related to the interpolation is addressed and bench mark-type problems such as sound transmission or absorption maximization problems are solved to check the efficiency of the developed method.

Optimization technique for problems with an inequality constraint

NASA Technical Reports Server (NTRS)

Russell, K. J.

1972-01-01

General technique uses a modified version of an existing technique termed the pattern search technique. New procedure called the parallel move strategy permits pattern search technique to be used with problems involving a constraint.

Multi-Constraint Multi-Variable Optimization of Source-Driven Nuclear Systems

NASA Astrophysics Data System (ADS)

Watkins, Edward Francis

1995-01-01

A novel approach to the search for optimal designs of source-driven nuclear systems is investigated. Such systems include radiation shields, fusion reactor blankets and various neutron spectrum-shaping assemblies. The novel approach involves the replacement of the steepest-descents optimization algorithm incorporated in the code SWAN by a significantly more general and efficient sequential quadratic programming optimization algorithm provided by the code NPSOL. The resulting SWAN/NPSOL code system can be applied to more general, multi-variable, multi-constraint shield optimization problems. The constraints it accounts for may include simple bounds on variables, linear constraints, and smooth nonlinear constraints. It may also be applied to unconstrained, bound-constrained and linearly constrained optimization. The shield optimization capabilities of the SWAN/NPSOL code system is tested and verified in a variety of optimization problems: dose minimization at constant cost, cost minimization at constant dose, and multiple-nonlinear constraint optimization. The replacement of the optimization part of SWAN with NPSOL is found feasible and leads to a very substantial improvement in the complexity of optimization problems which can be efficiently handled.

Stochastic Optimization For Water Resources Allocation

NASA Astrophysics Data System (ADS)

Yamout, G.; Hatfield, K.

2003-12-01

For more than 40 years, water resources allocation problems have been addressed using deterministic mathematical optimization. When data uncertainties exist, these methods could lead to solutions that are sub-optimal or even infeasible. While optimization models have been proposed for water resources decision-making under uncertainty, no attempts have been made to address the uncertainties in water allocation problems in an integrated approach. This paper presents an Integrated Dynamic, Multi-stage, Feedback-controlled, Linear, Stochastic, and Distributed parameter optimization approach to solve a problem of water resources allocation. It attempts to capture (1) the conflict caused by competing objectives, (2) environmental degradation produced by resource consumption, and finally (3) the uncertainty and risk generated by the inherently random nature of state and decision parameters involved in such a problem. A theoretical system is defined throughout its different elements. These elements consisting mainly of water resource components and end-users are described in terms of quantity, quality, and present and future associated risks and uncertainties. Models are identified, modified, and interfaced together to constitute an integrated water allocation optimization framework. This effort is a novel approach to confront the water allocation optimization problem while accounting for uncertainties associated with all its elements; thus resulting in a solution that correctly reflects the physical problem in hand.

Mixed integer simulation optimization for optimal hydraulic fracturing and production of shale gas fields

NASA Astrophysics Data System (ADS)

Li, J. C.; Gong, B.; Wang, H. G.

2016-08-01

Optimal development of shale gas fields involves designing a most productive fracturing network for hydraulic stimulation processes and operating wells appropriately throughout the production time. A hydraulic fracturing network design-determining well placement, number of fracturing stages, and fracture lengths-is defined by specifying a set of integer ordered blocks to drill wells and create fractures in a discrete shale gas reservoir model. The well control variables such as bottom hole pressures or production rates for well operations are real valued. Shale gas development problems, therefore, can be mathematically formulated with mixed-integer optimization models. A shale gas reservoir simulator is used to evaluate the production performance for a hydraulic fracturing and well control plan. To find the optimal fracturing design and well operation is challenging because the problem is a mixed integer optimization problem and entails computationally expensive reservoir simulation. A dynamic simplex interpolation-based alternate subspace (DSIAS) search method is applied for mixed integer optimization problems associated with shale gas development projects. The optimization performance is demonstrated with the example case of the development of the Barnett Shale field. The optimization results of DSIAS are compared with those of a pattern search algorithm.

Efficient Optimization of Low-Thrust Spacecraft Trajectories

NASA Technical Reports Server (NTRS)

Lee, Seungwon; Fink, Wolfgang; Russell, Ryan; Terrile, Richard; Petropoulos, Anastassios; vonAllmen, Paul

2007-01-01

A paper describes a computationally efficient method of optimizing trajectories of spacecraft driven by propulsion systems that generate low thrusts and, hence, must be operated for long times. A common goal in trajectory-optimization problems is to find minimum-time, minimum-fuel, or Pareto-optimal trajectories (here, Pareto-optimality signifies that no other solutions are superior with respect to both flight time and fuel consumption). The present method utilizes genetic and simulated-annealing algorithms to search for globally Pareto-optimal solutions. These algorithms are implemented in parallel form to reduce computation time. These algorithms are coupled with either of two traditional trajectory- design approaches called "direct" and "indirect." In the direct approach, thrust control is discretized in either arc time or arc length, and the resulting discrete thrust vectors are optimized. The indirect approach involves the primer-vector theory (introduced in 1963), in which the thrust control problem is transformed into a co-state control problem and the initial values of the co-state vector are optimized. In application to two example orbit-transfer problems, this method was found to generate solutions comparable to those of other state-of-the-art trajectory-optimization methods while requiring much less computation time.

Nonexpansiveness of a linearized augmented Lagrangian operator for hierarchical convex optimization

NASA Astrophysics Data System (ADS)

Yamagishi, Masao; Yamada, Isao

2017-04-01

Hierarchical convex optimization concerns two-stage optimization problems: the first stage problem is a convex optimization; the second stage problem is the minimization of a convex function over the solution set of the first stage problem. For the hierarchical convex optimization, the hybrid steepest descent method (HSDM) can be applied, where the solution set of the first stage problem must be expressed as the fixed point set of a certain nonexpansive operator. In this paper, we propose a nonexpansive operator that yields a computationally efficient update when it is plugged into the HSDM. The proposed operator is inspired by the update of the linearized augmented Lagrangian method. It is applicable to characterize the solution set of recent sophisticated convex optimization problems found in the context of inverse problems, where the sum of multiple proximable convex functions involving linear operators must be minimized to incorporate preferable properties into the minimizers. For such a problem formulation, there has not yet been reported any nonexpansive operator that yields an update free from the inversions of linear operators in cases where it is utilized in the HSDM. Unlike previously known nonexpansive operators, the proposed operator yields an inversion-free update in such cases. As an application of the proposed operator plugged into the HSDM, we also present, in the context of the so-called superiorization, an algorithmic solution to a convex optimization problem over the generalized convex feasible set where the intersection of the hard constraints is not necessarily simple.

A Projection free method for Generalized Eigenvalue Problem with a nonsmooth Regularizer.

PubMed

Hwang, Seong Jae; Collins, Maxwell D; Ravi, Sathya N; Ithapu, Vamsi K; Adluru, Nagesh; Johnson, Sterling C; Singh, Vikas

2015-12-01

Eigenvalue problems are ubiquitous in computer vision, covering a very broad spectrum of applications ranging from estimation problems in multi-view geometry to image segmentation. Few other linear algebra problems have a more mature set of numerical routines available and many computer vision libraries leverage such tools extensively. However, the ability to call the underlying solver only as a "black box" can often become restrictive. Many 'human in the loop' settings in vision frequently exploit supervision from an expert, to the extent that the user can be considered a subroutine in the overall system. In other cases, there is additional domain knowledge, side or even partial information that one may want to incorporate within the formulation. In general, regularizing a (generalized) eigenvalue problem with such side information remains difficult. Motivated by these needs, this paper presents an optimization scheme to solve generalized eigenvalue problems (GEP) involving a (nonsmooth) regularizer. We start from an alternative formulation of GEP where the feasibility set of the model involves the Stiefel manifold. The core of this paper presents an end to end stochastic optimization scheme for the resultant problem. We show how this general algorithm enables improved statistical analysis of brain imaging data where the regularizer is derived from other 'views' of the disease pathology, involving clinical measurements and other image-derived representations.

Optimal Control Inventory Stochastic With Production Deteriorating

NASA Astrophysics Data System (ADS)

Affandi, Pardi

2018-01-01

In this paper, we are using optimal control approach to determine the optimal rate in production. Most of the inventory production models deal with a single item. First build the mathematical models inventory stochastic, in this model we also assume that the items are in the same store. The mathematical model of the problem inventory can be deterministic and stochastic models. In this research will be discussed how to model the stochastic as well as how to solve the inventory model using optimal control techniques. The main tool in the study problems for the necessary optimality conditions in the form of the Pontryagin maximum principle involves the Hamilton function. So we can have the optimal production rate in a production inventory system where items are subject deterioration.

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.

Control of functional differential equations with function space boundary conditions

NASA Technical Reports Server (NTRS)

Banks, H. T.

1972-01-01

Problems involving functional differential equations with terminal conditions in function space are considered. Their application to mechanical and electrical systems is discussed. Investigations of controllability, existence of optimal controls, and necessary and sufficient conditions for optimality are reported.

Fleet Assignment Using Collective Intelligence

NASA Technical Reports Server (NTRS)

Antoine, Nicolas E.; Bieniawski, Stefan R.; Kroo, Ilan M.; Wolpert, David H.

2004-01-01

Product distribution theory is a new collective intelligence-based framework for analyzing and controlling distributed systems. Its usefulness in distributed stochastic optimization is illustrated here through an airline fleet assignment problem. This problem involves the allocation of aircraft to a set of flights legs in order to meet passenger demand, while satisfying a variety of linear and non-linear constraints. Over the course of the day, the routing of each aircraft is determined in order to minimize the number of required flights for a given fleet. The associated flow continuity and aircraft count constraints have led researchers to focus on obtaining quasi-optimal solutions, especially at larger scales. In this paper, the authors propose the application of this new stochastic optimization algorithm to a non-linear objective cold start fleet assignment problem. Results show that the optimizer can successfully solve such highly-constrained problems (130 variables, 184 constraints).

Numerical Leak Detection in a Pipeline Network of Complex Structure with Unsteady Flow

NASA Astrophysics Data System (ADS)

Aida-zade, K. R.; Ashrafova, E. R.

2017-12-01

An inverse problem for a pipeline network of complex loopback structure is solved numerically. The problem is to determine the locations and amounts of leaks from unsteady flow characteristics measured at some pipeline points. The features of the problem include impulse functions involved in a system of hyperbolic differential equations, the absence of classical initial conditions, and boundary conditions specified as nonseparated relations between the states at the endpoints of adjacent pipeline segments. The problem is reduced to a parametric optimal control problem without initial conditions, but with nonseparated boundary conditions. The latter problem is solved by applying first-order optimization methods. Results of numerical experiments are presented.

Comparison of polynomial approximations and artificial neural nets for response surfaces in engineering optimization

NASA Technical Reports Server (NTRS)

Carpenter, William C.

1991-01-01

Engineering optimization problems involve minimizing some function subject to constraints. In areas such as aircraft optimization, the constraint equations may be from numerous disciplines such as transfer of information between these disciplines and the optimization algorithm. They are also suited to problems which may require numerous re-optimizations such as in multi-objective function optimization or to problems where the design space contains numerous local minima, thus requiring repeated optimizations from different initial designs. Their use has been limited, however, by the fact that development of response surfaces randomly selected or preselected points in the design space. Thus, they have been thought to be inefficient compared to algorithms to the optimum solution. A development has taken place in the last several years which may effect the desirability of using response surfaces. It may be possible that artificial neural nets are more efficient in developing response surfaces than polynomial approximations which have been used in the past. This development is the concern of the work.

Multiple crack detection in 3D using a stable XFEM and global optimization

NASA Astrophysics Data System (ADS)

Agathos, Konstantinos; Chatzi, Eleni; Bordas, Stéphane P. A.

2018-02-01

A numerical scheme is proposed for the detection of multiple cracks in three dimensional (3D) structures. The scheme is based on a variant of the extended finite element method (XFEM) and a hybrid optimizer solution. The proposed XFEM variant is particularly well-suited for the simulation of 3D fracture problems, and as such serves as an efficient solution to the so-called forward problem. A set of heuristic optimization algorithms are recombined into a multiscale optimization scheme. The introduced approach proves effective in tackling the complex inverse problem involved, where identification of multiple flaws is sought on the basis of sparse measurements collected near the structural boundary. The potential of the scheme is demonstrated through a set of numerical case studies of varying complexity.

The individual time trial as an optimal control problem

PubMed Central

de Jong, Jenny; Fokkink, Robbert; Olsder, Geert Jan; Schwab, AL

2017-01-01

In a cycling time trial, the rider needs to distribute his power output optimally to minimize the time between start and finish. Mathematically, this is an optimal control problem. Even for a straight and flat course, its solution is non-trivial and involves a singular control, which corresponds to a power that is slightly above the aerobic level. The rider must start at full anaerobic power to reach an optimal speed and maintain that speed for the rest of the course. If the course is flat but not straight, then the speed at which the rider can round the bends becomes crucial. PMID:29388631

Performance Optimizing Adaptive Control with Time-Varying Reference Model Modification

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Hashemi, Kelley E.

2017-01-01

This paper presents a new adaptive control approach that involves a performance optimization objective. The control synthesis involves the design of a performance optimizing adaptive controller from a subset of control inputs. The resulting effect of the performance optimizing adaptive controller is to modify the initial reference model into a time-varying reference model which satisfies the performance optimization requirement obtained from an optimal control problem. The time-varying reference model modification is accomplished by the real-time solutions of the time-varying Riccati and Sylvester equations coupled with the least-squares parameter estimation of the sensitivities of the performance metric. The effectiveness of the proposed method is demonstrated by an application of maneuver load alleviation control for a flexible aircraft.

An approach to optimal semi-active control of vibration energy harvesting based on MEMS

NASA Astrophysics Data System (ADS)

Rojas, Rafael A.; Carcaterra, Antonio

2018-07-01

In this paper the energy harvesting problem involving typical MEMS technology is reduced to an optimal control problem, where the objective function is the absorption of the maximum amount of energy in a given time interval from a vibrating environment. The interest here is to identify a physical upper bound for this energy storage. The mathematical tool is a new optimal control called Krotov's method, that has not yet been applied to engineering problems, except in quantum dynamics. This approach leads to identify new maximum bounds to the energy harvesting performance. Novel MEMS-based device control configurations for vibration energy harvesting are proposed with particular emphasis to piezoelectric, electromagnetic and capacitive circuits.

An optimized treatment for algorithmic differentiation of an important glaciological fixed-point problem

DOE PAGES

Goldberg, Daniel N.; Narayanan, Sri Hari Krishna; Hascoet, Laurent; ...

2016-05-20

We apply an optimized method to the adjoint generation of a time-evolving land ice model through algorithmic differentiation (AD). The optimization involves a special treatment of the fixed-point iteration required to solve the nonlinear stress balance, which differs from a straightforward application of AD software, and leads to smaller memory requirements and in some cases shorter computation times of the adjoint. The optimization is done via implementation of the algorithm of Christianson (1994) for reverse accumulation of fixed-point problems, with the AD tool OpenAD. For test problems, the optimized adjoint is shown to have far lower memory requirements, potentially enablingmore » larger problem sizes on memory-limited machines. In the case of the land ice model, implementation of the algorithm allows further optimization by having the adjoint model solve a sequence of linear systems with identical (as opposed to varying) matrices, greatly improving performance. Finally, the methods introduced here will be of value to other efforts applying AD tools to ice models, particularly ones which solve a hybrid shallow ice/shallow shelf approximation to the Stokes equations.« less

Optimum Design of High-Speed Prop-Rotors

NASA Technical Reports Server (NTRS)

Chattopadhyay, Aditi; McCarthy, Thomas Robert

1993-01-01

An integrated multidisciplinary optimization procedure is developed for application to rotary wing aircraft design. The necessary disciplines such as dynamics, aerodynamics, aeroelasticity, and structures are coupled within a closed-loop optimization process. The procedure developed is applied to address two different problems. The first problem considers the optimization of a helicopter rotor blade and the second problem addresses the optimum design of a high-speed tilting proprotor. In the helicopter blade problem, the objective is to reduce the critical vibratory shear forces and moments at the blade root, without degrading rotor aerodynamic performance and aeroelastic stability. In the case of the high-speed proprotor, the goal is to maximize the propulsive efficiency in high-speed cruise without deteriorating the aeroelastic stability in cruise and the aerodynamic performance in hover. The problems studied involve multiple design objectives; therefore, the optimization problems are formulated using multiobjective design procedures. A comprehensive helicopter analysis code is used for the rotary wing aerodynamic, dynamic and aeroelastic stability analyses and an algorithm developed specifically for these purposes is used for the structural analysis. A nonlinear programming technique coupled with an approximate analysis procedure is used to perform the optimization. The optimum blade designs obtained in each case are compared to corresponding reference designs.

Optimization in Radiation Therapy: Applications in Brachytherapy and Intensity Modulated Radiation Therapy

NASA Astrophysics Data System (ADS)

McGeachy, Philip David

Over 50% of cancer patients require radiation therapy (RT). RT is an optimization problem requiring maximization of the radiation damage to the tumor while minimizing the harm to the healthy tissues. This dissertation focuses on two main RT optimization problems: 1) brachytherapy and 2) intensity modulated radiation therapy (IMRT). The brachytherapy research involved solving a non-convex optimization problem by creating an open-source genetic algorithm optimizer to determine the optimal radioactive seed distribution for a given set of patient volumes and constraints, both dosimetric- and implant-based. The optimizer was tested for a set of 45 prostate brachytherapy patients. While all solutions met the clinical standards, they also benchmarked favorably with those generated by a standard commercial solver. Compared to its compatriot, the salient features of the generated solutions were: slightly reduced prostate coverage, lower dose to the urethra and rectum, and a smaller number of needles required for an implant. Historically, IMRT requires modulation of fluence while keeping the photon beam energy fixed. The IMRT-related investigation in this thesis aimed at broadening the solution space by varying photon energy. The problem therefore involved simultaneous optimization of photon beamlet energy and fluence, denoted by XMRT. Formulating the problem as convex, linear programming was applied to obtain solutions for optimal energy-dependent fluences, while achieving all clinical objectives and constraints imposed. Dosimetric advantages of XMRT over single-energy IMRT in the improved sparing of organs at risk (OARs) was demonstrated in simplified phantom studies. The XMRT algorithm was improved to include clinical dose-volume constraints and clinical studies for prostate and head and neck cancer patients were investigated. Compared to IMRT, XMRT provided improved dosimetric benefit in the prostate case, particularly within intermediate- to low-dose regions (≤ 40 Gy) for OARs. For head and neck cases, XMRT solutions showed no significant disadvantage or advantage over IMRT. The deliverability concerns for the fluence maps generated from XMRT were addressed by incorporating smoothing constraints during the optimization and through successful generation of treatment machine files. Further research is needed to explore the full potential of the XMRT approach to RT.

Tunneling and speedup in quantum optimization for permutation-symmetric problems

DOE PAGES

Muthukrishnan, Siddharth; Albash, Tameem; Lidar, Daniel A.

2016-07-21

Tunneling is often claimed to be the key mechanism underlying possible speedups in quantum optimization via quantum annealing (QA), especially for problems featuring a cost function with tall and thin barriers. We present and analyze several counterexamples from the class of perturbed Hamming weight optimization problems with qubit permutation symmetry. We first show that, for these problems, the adiabatic dynamics that make tunneling possible should be understood not in terms of the cost function but rather the semiclassical potential arising from the spin-coherent path-integral formalism. We then provide an example where the shape of the barrier in the final costmore » function is short and wide, which might suggest no quantum advantage for QA, yet where tunneling renders QA superior to simulated annealing in the adiabatic regime. However, the adiabatic dynamics turn out not be optimal. Instead, an evolution involving a sequence of diabatic transitions through many avoided-level crossings, involving no tunneling, is optimal and outperforms adiabatic QA. We show that this phenomenon of speedup by diabatic transitions is not unique to this example, and we provide an example where it provides an exponential speedup over adiabatic QA. In yet another twist, we show that a classical algorithm, spin-vector dynamics, is at least as efficient as diabatic QA. Lastly, in a different example with a convex cost function, the diabatic transitions result in a speedup relative to both adiabatic QA with tunneling and classical spin-vector dynamics.« less

Tunneling and speedup in quantum optimization for permutation-symmetric problems

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

Muthukrishnan, Siddharth; Albash, Tameem; Lidar, Daniel A.

Tunneling is often claimed to be the key mechanism underlying possible speedups in quantum optimization via quantum annealing (QA), especially for problems featuring a cost function with tall and thin barriers. We present and analyze several counterexamples from the class of perturbed Hamming weight optimization problems with qubit permutation symmetry. We first show that, for these problems, the adiabatic dynamics that make tunneling possible should be understood not in terms of the cost function but rather the semiclassical potential arising from the spin-coherent path-integral formalism. We then provide an example where the shape of the barrier in the final costmore » function is short and wide, which might suggest no quantum advantage for QA, yet where tunneling renders QA superior to simulated annealing in the adiabatic regime. However, the adiabatic dynamics turn out not be optimal. Instead, an evolution involving a sequence of diabatic transitions through many avoided-level crossings, involving no tunneling, is optimal and outperforms adiabatic QA. We show that this phenomenon of speedup by diabatic transitions is not unique to this example, and we provide an example where it provides an exponential speedup over adiabatic QA. In yet another twist, we show that a classical algorithm, spin-vector dynamics, is at least as efficient as diabatic QA. Lastly, in a different example with a convex cost function, the diabatic transitions result in a speedup relative to both adiabatic QA with tunneling and classical spin-vector dynamics.« less

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.

Use of a Computer Language in Teaching Dynamic Programming. Final Report.

ERIC Educational Resources Information Center

Trimble, C. J.; And Others

Most optimization problems of any degree of complexity must be solved using a computer. In the teaching of dynamic programing courses, it is often desirable to use a computer in problem solution. The solution process involves conceptual formulation and computational Solution. Generalized computer codes for dynamic programing problem solution…

Differential geometric methods in system theory.

NASA Technical Reports Server (NTRS)

Brockett, R. W.

1971-01-01

Discussion of certain problems in system theory which have been or might be solved using some basic concepts from differential geometry. The problems considered involve differential equations, controllability, optimal control, qualitative behavior, stochastic processes, and bilinear systems. The main goal is to extend the essentials of linear theory to some nonlinear classes of problems.

Discrete Optimization Model for Vehicle Routing Problem with Scheduling Side Cosntraints

NASA Astrophysics Data System (ADS)

Juliandri, Dedy; Mawengkang, Herman; Bu'ulolo, F.

2018-01-01

Vehicle Routing Problem (VRP) is an important element of many logistic systems which involve routing and scheduling of vehicles from a depot to a set of customers node. This is a hard combinatorial optimization problem with the objective to find an optimal set of routes used by a fleet of vehicles to serve the demands a set of customers It is required that these vehicles return to the depot after serving customers’ demand. The problem incorporates time windows, fleet and driver scheduling, pick-up and delivery in the planning horizon. The goal is to determine the scheduling of fleet and driver and routing policies of the vehicles. The objective is to minimize the overall costs of all routes over the planning horizon. We model the problem as a linear mixed integer program. We develop a combination of heuristics and exact method for solving the model.

Solving deterministic non-linear programming problem using Hopfield artificial neural network and genetic programming techniques

NASA Astrophysics Data System (ADS)

Vasant, P.; Ganesan, T.; Elamvazuthi, I.

2012-11-01

A fairly reasonable result was obtained for non-linear engineering problems using the optimization techniques such as neural network, genetic algorithms, and fuzzy logic independently in the past. Increasingly, hybrid techniques are being used to solve the non-linear problems to obtain better output. This paper discusses the use of neuro-genetic hybrid technique to optimize the geological structure mapping which is known as seismic survey. It involves the minimization of objective function subject to the requirement of geophysical and operational constraints. In this work, the optimization was initially performed using genetic programming, and followed by hybrid neuro-genetic programming approaches. Comparative studies and analysis were then carried out on the optimized results. The results indicate that the hybrid neuro-genetic hybrid technique produced better results compared to the stand-alone genetic programming method.

Method for using global optimization to the estimation of surface-consistent residual statics

DOEpatents

Reister, David B.; Barhen, Jacob; Oblow, Edward M.

2001-01-01

An efficient method for generating residual statics corrections to compensate for surface-consistent static time shifts in stacked seismic traces. The method includes a step of framing the residual static corrections as a global optimization problem in a parameter space. The method also includes decoupling the global optimization problem involving all seismic traces into several one-dimensional problems. The method further utilizes a Stochastic Pijavskij Tunneling search to eliminate regions in the parameter space where a global minimum is unlikely to exist so that the global minimum may be quickly discovered. The method finds the residual statics corrections by maximizing the total stack power. The stack power is a measure of seismic energy transferred from energy sources to receivers.

Continued research on selected parameters to minimize community annoyance from airplane noise

NASA Technical Reports Server (NTRS)

Frair, L.

1981-01-01

Results from continued research on selected parameters to minimize community annoyance from airport noise are reported. First, a review of the initial work on this problem is presented. Then the research focus is expanded by considering multiobjective optimization approaches for this problem. A multiobjective optimization algorithm review from the open literature is presented. This is followed by the multiobjective mathematical formulation for the problem of interest. A discussion of the appropriate solution algorithm for the multiobjective formulation is conducted. Alternate formulations and associated solution algorithms are discussed and evaluated for this airport noise problem. Selected solution algorithms that have been implemented are then used to produce computational results for example airports. These computations involved finding the optimal operating scenario for a moderate size airport and a series of sensitivity analyses for a smaller example airport.

Guidance and flight control law development for hypersonic vehicles

NASA Technical Reports Server (NTRS)

Calise, A. J.; Markopoulos, N.

1993-01-01

During the third reporting period our efforts were focused on a reformulation of the optimal control problem involving active state-variable inequality constraints. In the reformulated problem the optimization is carried out not with respect to all controllers, but only with respect to asymptotic controllers leading to the state constraint boundary. Intimately connected with the traditional formulation is the fact that when the reduced solution for such problems lies on a state constraint boundary, the corresponding boundary layer transitions are of finite time in the stretched time scale. Thus, it has been impossible so far to apply the classical asymptotic boundary layer theory to such problems. Moreover, the traditional formulation leads to optimal controllers that are one-sided, that is, they break down when a disturbance throws the system on the prohibited side of the state constraint boundary.

Optimal control of first order distributed systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Johnson, T. L.

1972-01-01

The problem of characterizing optimal controls for a class of distributed-parameter systems is considered. The system dynamics are characterized mathematically by a finite number of coupled partial differential equations involving first-order time and space derivatives of the state variables, which are constrained at the boundary by a finite number of algebraic relations. Multiple control inputs, extending over the entire spatial region occupied by the system ("distributed controls') are to be designed so that the response of the system is optimal. A major example involving boundary control of an unstable low-density plasma is developed from physical laws.

Towards sub-optimal stochastic control of partially observable stochastic systems

NASA Technical Reports Server (NTRS)

Ruzicka, G. J.

1980-01-01

A class of multidimensional stochastic control problems with noisy data and bounded controls encountered in aerospace design is examined. The emphasis is on suboptimal design, the optimality being taken in quadratic mean sense. To that effect the problem is viewed as a stochastic version of the Lurie problem known from nonlinear control theory. The main result is a separation theorem (involving a nonlinear Kalman-like filter) suitable for Lurie-type approximations. The theorem allows for discontinuous characteristics. As a byproduct the existence of strong solutions to a class of non-Lipschitzian stochastic differential equations in dimensions is proven.

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Development Optimization and Uncertainty Analysis Methods for Oil and Gas Reservoirs

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

Ettehadtavakkol, Amin, E-mail: amin.ettehadtavakkol@ttu.edu; Jablonowski, Christopher; Lake, Larry

Uncertainty complicates the development optimization of oil and gas exploration and production projects, but methods have been devised to analyze uncertainty and its impact on optimal decision-making. This paper compares two methods for development optimization and uncertainty analysis: Monte Carlo (MC) simulation and stochastic programming. Two example problems for a gas field development and an oilfield development are solved and discussed to elaborate the advantages and disadvantages of each method. Development optimization involves decisions regarding the configuration of initial capital investment and subsequent operational decisions. Uncertainty analysis involves the quantification of the impact of uncertain parameters on the optimum designmore » concept. The gas field development problem is designed to highlight the differences in the implementation of the two methods and to show that both methods yield the exact same optimum design. The results show that both MC optimization and stochastic programming provide unique benefits, and that the choice of method depends on the goal of the analysis. While the MC method generates more useful information, along with the optimum design configuration, the stochastic programming method is more computationally efficient in determining the optimal solution. Reservoirs comprise multiple compartments and layers with multiphase flow of oil, water, and gas. We present a workflow for development optimization under uncertainty for these reservoirs, and solve an example on the design optimization of a multicompartment, multilayer oilfield development.« less

Medical Problem-Solving: A Critique of the Literature.

ERIC Educational Resources Information Center

McGuire, Christine H.

1985-01-01

Prescriptive, decision-analysis of medical problem-solving has been based on decision theory that involves calculation and manipulation of complex probability and utility values to arrive at optimal decisions that will maximize patient benefits. The studies offer a methodology for improving clinical judgment. (Author/MLW)

AITSO: A Tool for Spatial Optimization Based on Artificial Immune Systems

PubMed Central

Zhao, Xiang; Liu, Yaolin; Liu, Dianfeng; Ma, Xiaoya

2015-01-01

A great challenge facing geocomputation and spatial analysis is spatial optimization, given that it involves various high-dimensional, nonlinear, and complicated relationships. Many efforts have been made with regard to this specific issue, and the strong ability of artificial immune system algorithms has been proven in previous studies. However, user-friendly professional software is still unavailable, which is a great impediment to the popularity of artificial immune systems. This paper describes a free, universal tool, named AITSO, which is capable of solving various optimization problems. It provides a series of standard application programming interfaces (APIs) which can (1) assist researchers in the development of their own problem-specific application plugins to solve practical problems and (2) allow the implementation of some advanced immune operators into the platform to improve the performance of an algorithm. As an integrated, flexible, and convenient tool, AITSO contributes to knowledge sharing and practical problem solving. It is therefore believed that it will advance the development and popularity of spatial optimization in geocomputation and spatial analysis. PMID:25678911

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.

Harmony search algorithm: application to the redundancy optimization problem

NASA Astrophysics Data System (ADS)

Nahas, Nabil; Thien-My, Dao

2010-09-01

The redundancy optimization problem is a well known NP-hard problem which involves the selection of elements and redundancy levels to maximize system performance, given different system-level constraints. This article presents an efficient algorithm based on the harmony search algorithm (HSA) to solve this optimization problem. The HSA is a new nature-inspired algorithm which mimics the improvization process of music players. Two kinds of problems are considered in testing the proposed algorithm, with the first limited to the binary series-parallel system, where the problem consists of a selection of elements and redundancy levels used to maximize the system reliability given various system-level constraints; the second problem for its part concerns the multi-state series-parallel systems with performance levels ranging from perfect operation to complete failure, and in which identical redundant elements are included in order to achieve a desirable level of availability. Numerical results for test problems from previous research are reported and compared. The results of HSA showed that this algorithm could provide very good solutions when compared to those obtained through other approaches.

Multiobjective optimization in structural design with uncertain parameters and stochastic processes

NASA Technical Reports Server (NTRS)

Rao, S. S.

1984-01-01

The application of multiobjective optimization techniques to structural design problems involving uncertain parameters and random processes is studied. The design of a cantilever beam with a tip mass subjected to a stochastic base excitation is considered for illustration. Several of the problem parameters are assumed to be random variables and the structural mass, fatigue damage, and negative of natural frequency of vibration are considered for minimization. The solution of this three-criteria design problem is found by using global criterion, utility function, game theory, goal programming, goal attainment, bounded objective function, and lexicographic methods. It is observed that the game theory approach is superior in finding a better optimum solution, assuming the proper balance of the various objective functions. The procedures used in the present investigation are expected to be useful in the design of general dynamic systems involving uncertain parameters, stochastic process, and multiple objectives.

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.

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.

Transient responses' optimization by means of set-based multi-objective evolution

NASA Astrophysics Data System (ADS)

Avigad, Gideon; Eisenstadt, Erella; Goldvard, Alex; Salomon, Shaul

2012-04-01

In this article, a novel solution to multi-objective problems involving the optimization of transient responses is suggested. It is claimed that the common approach of treating such problems by introducing auxiliary objectives overlooks tradeoffs that should be presented to the decision makers. This means that, if at some time during the responses, one of the responses is optimal, it should not be overlooked. An evolutionary multi-objective algorithm is suggested in order to search for these optimal solutions. For this purpose, state-wise domination is utilized with a new crowding measure for ordered sets being suggested. The approach is tested on both artificial as well as on real life problems in order to explain the methodology and demonstrate its applicability and importance. The results indicate that, from an engineering point of view, the approach possesses several advantages over existing approaches. Moreover, the applications highlight the importance of set-based evolution.

Optical Sensor/Actuator Locations for Active Structural Acoustic Control

NASA Technical Reports Server (NTRS)

Padula, Sharon L.; Palumbo, Daniel L.; Kincaid, Rex K.

1998-01-01

Researchers at NASA Langley Research Center have extensive experience using active structural acoustic control (ASAC) for aircraft interior noise reduction. One aspect of ASAC involves the selection of optimum locations for microphone sensors and force actuators. This paper explains the importance of sensor/actuator selection, reviews optimization techniques, and summarizes experimental and numerical results. Three combinatorial optimization problems are described. Two involve the determination of the number and position of piezoelectric actuators, and the other involves the determination of the number and location of the sensors. For each case, a solution method is suggested, and typical results are examined. The first case, a simplified problem with simulated data, is used to illustrate the method. The second and third cases are more representative of the potential of the method and use measured data. The three case studies and laboratory test results establish the usefulness of the numerical methods.

Planning and Scheduling for Fleets of Earth Observing Satellites

NASA Technical Reports Server (NTRS)

Frank, Jeremy; Jonsson, Ari; Morris, Robert; Smith, David E.; Norvig, Peter (Technical Monitor)

2001-01-01

We address the problem of scheduling observations for a collection of earth observing satellites. This scheduling task is a difficult optimization problem, potentially involving many satellites, hundreds of requests, constraints on when and how to service each request, and resources such as instruments, recording devices, transmitters, and ground stations. High-fidelity models are required to ensure the validity of schedules; at the same time, the size and complexity of the problem makes it unlikely that systematic optimization search methods will be able to solve them in a reasonable time. This paper presents a constraint-based approach to solving the Earth Observing Satellites (EOS) scheduling problem, and proposes a stochastic heuristic search method for solving it.

A preliminary study to metaheuristic approach in multilayer radiation shielding optimization

NASA Astrophysics Data System (ADS)

Arif Sazali, Muhammad; Rashid, Nahrul Khair Alang Md; Hamzah, Khaidzir

2018-01-01

Metaheuristics are high-level algorithmic concepts that can be used to develop heuristic optimization algorithms. One of their applications is to find optimal or near optimal solutions to combinatorial optimization problems (COPs) such as scheduling, vehicle routing, and timetabling. Combinatorial optimization deals with finding optimal combinations or permutations in a given set of problem components when exhaustive search is not feasible. A radiation shield made of several layers of different materials can be regarded as a COP. The time taken to optimize the shield may be too high when several parameters are involved such as the number of materials, the thickness of layers, and the arrangement of materials. Metaheuristics can be applied to reduce the optimization time, trading guaranteed optimal solutions for near-optimal solutions in comparably short amount of time. The application of metaheuristics for radiation shield optimization is lacking. In this paper, we present a review on the suitability of using metaheuristics in multilayer shielding design, specifically the genetic algorithm and ant colony optimization algorithm (ACO). We would also like to propose an optimization model based on the ACO method.

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.

Fleet Assignment Using Collective Intelligence

NASA Technical Reports Server (NTRS)

Antoine, Nicolas E.; Bieniawski, Stefan R.; Kroo, Ilan M.; Wolpert, David H.

2004-01-01

Airline fleet assignment involves the allocation of aircraft to a set of flights legs in order to meet passenger demand, while satisfying a variety of constraints. Over the course of the day, the routing of each aircraft is determined in order to minimize the number of required flights for a given fleet. The associated flow continuity and aircraft count constraints have led researchers to focus on obtaining quasi-optimal solutions, especially at larger scales. In this paper, the authors propose the application of an agent-based integer optimization algorithm to a "cold start" fleet assignment problem. Results show that the optimizer can successfully solve such highly- constrained problems (129 variables, 184 constraints).

A deterministic global optimization using smooth diagonal auxiliary functions

NASA Astrophysics Data System (ADS)

Sergeyev, Yaroslav D.; Kvasov, Dmitri E.

2015-04-01

In many practical decision-making problems it happens that functions involved in optimization process are black-box with unknown analytical representations and hard to evaluate. In this paper, a global optimization problem is considered where both the goal function f (x) and its gradient f‧ (x) are black-box functions. It is supposed that f‧ (x) satisfies the Lipschitz condition over the search hyperinterval with an unknown Lipschitz constant K. A new deterministic 'Divide-the-Best' algorithm based on efficient diagonal partitions and smooth auxiliary functions is proposed in its basic version, its convergence conditions are studied and numerical experiments executed on eight hundred test functions are presented.

Control system estimation and design for aerospace vehicles with time delay

NASA Technical Reports Server (NTRS)

Allgaier, G. R.; Williams, T. L.

1972-01-01

The problems of estimation and control of discrete, linear, time-varying systems are considered. Previous solutions to these problems involved either approximate techniques, open-loop control solutions, or results which required excessive computation. The estimation problem is solved by two different methods, both of which yield the identical algorithm for determining the optimal filter. The partitioned results achieve a substantial reduction in computation time and storage requirements over the expanded solution, however. The results reduce to the Kalman filter when no delays are present in the system. The control problem is also solved by two different methods, both of which yield identical algorithms for determining the optimal control gains. The stochastic control is shown to be identical to the deterministic control, thus extending the separation principle to time delay systems. The results obtained reduce to the familiar optimal control solution when no time delays are present in the system.

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.

A Nonlinear Programming Perspective on Sensitivity Calculations for Systems Governed by State Equations

NASA Technical Reports Server (NTRS)

Lewis, Robert Michael

1997-01-01

This paper discusses the calculation of sensitivities. or derivatives, for optimization problems involving systems governed by differential equations and other state relations. The subject is examined from the point of view of nonlinear programming, beginning with the analytical structure of the first and second derivatives associated with such problems and the relation of these derivatives to implicit differentiation and equality constrained optimization. We also outline an error analysis of the analytical formulae and compare the results with similar results for finite-difference estimates of derivatives. We then attend to an investigation of the nature of the adjoint method and the adjoint equations and their relation to directions of steepest descent. We illustrate the points discussed with an optimization problem in which the variables are the coefficients in a differential operator.

A predictive machine learning approach for microstructure optimization and materials design

NASA Astrophysics Data System (ADS)

Liu, Ruoqian; Kumar, Abhishek; Chen, Zhengzhang; Agrawal, Ankit; Sundararaghavan, Veera; Choudhary, Alok

2015-06-01

This paper addresses an important materials engineering question: How can one identify the complete space (or as much of it as possible) of microstructures that are theoretically predicted to yield the desired combination of properties demanded by a selected application? We present a problem involving design of magnetoelastic Fe-Ga alloy microstructure for enhanced elastic, plastic and magnetostrictive properties. While theoretical models for computing properties given the microstructure are known for this alloy, inversion of these relationships to obtain microstructures that lead to desired properties is challenging, primarily due to the high dimensionality of microstructure space, multi-objective design requirement and non-uniqueness of solutions. These challenges render traditional search-based optimization methods incompetent in terms of both searching efficiency and result optimality. In this paper, a route to address these challenges using a machine learning methodology is proposed. A systematic framework consisting of random data generation, feature selection and classification algorithms is developed. Experiments with five design problems that involve identification of microstructures that satisfy both linear and nonlinear property constraints show that our framework outperforms traditional optimization methods with the average running time reduced by as much as 80% and with optimality that would not be achieved otherwise.

Preconditioned Alternating Projection Algorithms for Maximum a Posteriori ECT Reconstruction

PubMed Central

Krol, Andrzej; Li, Si; Shen, Lixin; Xu, Yuesheng

2012-01-01

We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constrain involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the preconditioned alternating projection algorithm. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality. PMID:23271835

Preconditioned alternating projection algorithms for maximum a posteriori ECT reconstruction

NASA Astrophysics Data System (ADS)

Krol, Andrzej; Li, Si; Shen, Lixin; Xu, Yuesheng

2012-11-01

We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show that it satisfies a system of fixed-point equations defined in terms of two proximity operators raised from the convex functions that define the TV-norm and the constraint involved in the problem. The characterization (of the solution) via the proximity operators that define two projection operators naturally leads to an alternating projection algorithm for finding the solution. For efficient numerical computation, we introduce to the alternating projection algorithm a preconditioning matrix (the EM-preconditioner) for the dense system matrix involved in the optimization problem. We prove theoretically convergence of the PAPA. In numerical experiments, performance of our algorithms, with an appropriately selected preconditioning matrix, is compared with performance of the conventional MAP expectation-maximization (MAP-EM) algorithm with TV regularizer (EM-TV) and that of the recently developed nested EM-TV algorithm for ECT reconstruction. Based on the numerical experiments performed in this work, we observe that the alternating projection algorithm with the EM-preconditioner outperforms significantly the EM-TV in all aspects including the convergence speed, the noise in the reconstructed images and the image quality. It also outperforms the nested EM-TV in the convergence speed while providing comparable image quality.

Optimization of an auto-thermal ammonia synthesis reactor using cyclic coordinate method

NASA Astrophysics Data System (ADS)

A-N Nguyen, T.; Nguyen, T.-A.; Vu, T.-D.; Nguyen, K.-T.; K-T Dao, T.; P-H Huynh, K.

2017-06-01

The ammonia synthesis system is an important chemical process used in the manufacture of fertilizers, chemicals, explosives, fibers, plastics, refrigeration. In the literature, many works approaching the modeling, simulation and optimization of an auto-thermal ammonia synthesis reactor can be found. However, they just focus on the optimization of the reactor length while keeping the others parameters constant. In this study, the other parameters are also considered in the optimization problem such as the temperature of feed gas enters the catalyst zone, the initial nitrogen proportion. The optimal problem requires the maximization of an objective function which is multivariable function and subject to a number of equality constraints involving the solution of coupled differential equations and also inequality constraint. The cyclic coordinate search was applied to solve the multivariable-optimization problem. In each coordinate, the golden section method was applied to find the maximum value. The inequality constraints were treated using penalty method. The coupled differential equations system was solved using Runge-Kutta 4th order method. The results obtained from this study are also compared to the results from the literature.

Prediction-Correction Algorithms for Time-Varying Constrained Optimization

DOE PAGES

Simonetto, Andrea; Dall'Anese, Emiliano

2017-07-26

This article develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve prediction-correction steps to provably track the trajectory of the optimal solutions of time-varying convex problems. The merits of existing prediction-correction methods have been shown for unconstrained problems and for setups where computing the inverse of the Hessian of the cost function is computationally affordable. This paper addresses the limitations of existing methods by tackling constrained problems and by designing first-order prediction steps that rely on the Hessian of the cost function (and do notmore » require the computation of its inverse). In addition, the proposed methods are shown to improve the convergence speed of existing prediction-correction methods when applied to unconstrained problems. Numerical simulations corroborate the analytical results and showcase performance and benefits of the proposed algorithms. A realistic application of the proposed method to real-time control of energy resources is presented.« less

Comparison of penalty functions on a penalty approach to mixed-integer optimization

NASA Astrophysics Data System (ADS)

Francisco, Rogério B.; Costa, M. Fernanda P.; Rocha, Ana Maria A. C.; Fernandes, Edite M. G. P.

2016-06-01

In this paper, we present a comparative study involving several penalty functions that can be used in a penalty approach for globally solving bound mixed-integer nonlinear programming (bMIMLP) problems. The penalty approach relies on a continuous reformulation of the bMINLP problem by adding a particular penalty term to the objective function. A penalty function based on the `erf' function is proposed. The continuous nonlinear optimization problems are sequentially solved by the population-based firefly algorithm. Preliminary numerical experiments are carried out in order to analyze the quality of the produced solutions, when compared with other penalty functions available in the literature.

Combined genetic algorithm and multiple linear regression (GA-MLR) optimizer: Application to multi-exponential fluorescence decay surface.

PubMed

Fisz, Jacek J

2006-12-07

The optimization approach based on the genetic algorithm (GA) combined with multiple linear regression (MLR) method, is discussed. The GA-MLR optimizer is designed for the nonlinear least-squares problems in which the model functions are linear combinations of nonlinear functions. GA optimizes the nonlinear parameters, and the linear parameters are calculated from MLR. GA-MLR is an intuitive optimization approach and it exploits all advantages of the genetic algorithm technique. This optimization method results from an appropriate combination of two well-known optimization methods. The MLR method is embedded in the GA optimizer and linear and nonlinear model parameters are optimized in parallel. The MLR method is the only one strictly mathematical "tool" involved in GA-MLR. The GA-MLR approach simplifies and accelerates considerably the optimization process because the linear parameters are not the fitted ones. Its properties are exemplified by the analysis of the kinetic biexponential fluorescence decay surface corresponding to a two-excited-state interconversion process. A short discussion of the variable projection (VP) algorithm, designed for the same class of the optimization problems, is presented. VP is a very advanced mathematical formalism that involves the methods of nonlinear functionals, algebra of linear projectors, and the formalism of Fréchet derivatives and pseudo-inverses. Additional explanatory comments are added on the application of recently introduced the GA-NR optimizer to simultaneous recovery of linear and weakly nonlinear parameters occurring in the same optimization problem together with nonlinear parameters. The GA-NR optimizer combines the GA method with the NR method, in which the minimum-value condition for the quadratic approximation to chi(2), obtained from the Taylor series expansion of chi(2), is recovered by means of the Newton-Raphson algorithm. The application of the GA-NR optimizer to model functions which are multi-linear combinations of nonlinear functions, is indicated. The VP algorithm does not distinguish the weakly nonlinear parameters from the nonlinear ones and it does not apply to the model functions which are multi-linear combinations of nonlinear functions.

A computational algorithm for spacecraft control and momentum management

NASA Technical Reports Server (NTRS)

Dzielski, John; Bergmann, Edward; Paradiso, Joseph

1990-01-01

Developments in the area of nonlinear control theory have shown how coordinate changes in the state and input spaces of a dynamical system can be used to transform certain nonlinear differential equations into equivalent linear equations. These techniques are applied to the control of a spacecraft equipped with momentum exchange devices. An optimal control problem is formulated that incorporates a nonlinear spacecraft model. An algorithm is developed for solving the optimization problem using feedback linearization to transform to an equivalent problem involving a linear dynamical constraint and a functional approximation technique to solve for the linear dynamics in terms of the control. The original problem is transformed into an unconstrained nonlinear quadratic program that yields an approximate solution to the original problem. Two examples are presented to illustrate the results.

Quadratic Optimization in the Problems of Active Control of Sound

NASA Technical Reports Server (NTRS)

Loncaric, J.; Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).

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

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

Guidance and control strategies for aerospace vehicles

NASA Technical Reports Server (NTRS)

Naidu, Desineni S.; Hibey, Joseph L.

1988-01-01

The optimal control problem arising in coplanar, orbital transfer employing aeroassist technology is addressed. The maneuver involves the transfer from high Earth orbit to low Earth orbit. A performance index is chosen the minimize the fuel consumpltion for the transfer. Simulations are carried out for establishing a corridor of entry conditions which are suitable for flying the spacecraft through the atmosphere. A highlight of the paper is the application of an efficient multiple shooting method for taming the notorious nonlinear, two-point, boundary value problem resulting from optimization procedure.

Necessary optimality conditions for infinite dimensional state constrained control problems

NASA Astrophysics Data System (ADS)

Frankowska, H.; Marchini, E. M.; Mazzola, M.

2018-06-01

This paper is concerned with first order necessary optimality conditions for state constrained control problems in separable Banach spaces. Assuming inward pointing conditions on the constraint, we give a simple proof of Pontryagin maximum principle, relying on infinite dimensional neighboring feasible trajectories theorems proved in [20]. Further, we provide sufficient conditions guaranteeing normality of the maximum principle. We work in the abstract semigroup setting, but nevertheless we apply our results to several concrete models involving controlled PDEs. Pointwise state constraints (as positivity of the solutions) are allowed.

Algorithm Optimally Allocates Actuation of a Spacecraft

NASA Technical Reports Server (NTRS)

Motaghedi, Shi

2007-01-01

A report presents an algorithm that solves the following problem: Allocate the force and/or torque to be exerted by each thruster and reaction-wheel assembly on a spacecraft for best performance, defined as minimizing the error between (1) the total force and torque commanded by the spacecraft control system and (2) the total of forces and torques actually exerted by all the thrusters and reaction wheels. The algorithm incorporates the matrix vector relationship between (1) the total applied force and torque and (2) the individual actuator force and torque values. It takes account of such constraints as lower and upper limits on the force or torque that can be applied by a given actuator. The algorithm divides the aforementioned problem into two optimization problems that it solves sequentially. These problems are of a type, known in the art as semi-definite programming problems, that involve linear matrix inequalities. The algorithm incorporates, as sub-algorithms, prior algorithms that solve such optimization problems very efficiently. The algorithm affords the additional advantage that the solution requires the minimum rate of consumption of fuel for the given best performance.

Computationally efficient stochastic optimization using multiple realizations

NASA Astrophysics Data System (ADS)

Bayer, P.; Bürger, C. M.; Finkel, M.

2008-02-01

The presented study is concerned with computationally efficient methods for solving stochastic optimization problems involving multiple equally probable realizations of uncertain parameters. A new and straightforward technique is introduced that is based on dynamically ordering the stack of realizations during the search procedure. The rationale is that a small number of critical realizations govern the output of a reliability-based objective function. By utilizing a problem, which is typical to designing a water supply well field, several variants of this "stack ordering" approach are tested. The results are statistically assessed, in terms of optimality and nominal reliability. This study demonstrates that the simple ordering of a given number of 500 realizations while applying an evolutionary search algorithm can save about half of the model runs without compromising the optimization procedure. More advanced variants of stack ordering can, if properly configured, save up to more than 97% of the computational effort that would be required if the entire number of realizations were considered. The findings herein are promising for similar problems of water management and reliability-based design in general, and particularly for non-convex problems that require heuristic search techniques.

Pseudo-time methods for constrained optimization problems governed by PDE

NASA Technical Reports Server (NTRS)

Taasan, Shlomo

1995-01-01

In this paper we present a novel method for solving optimization problems governed by partial differential equations. Existing methods are gradient information in marching toward the minimum, where the constrained PDE is solved once (sometimes only approximately) per each optimization step. Such methods can be viewed as a marching techniques on the intersection of the state and costate hypersurfaces while improving the residuals of the design equations per each iteration. In contrast, the method presented here march on the design hypersurface and at each iteration improve the residuals of the state and costate equations. The new method is usually much less expensive per iteration step since, in most problems of practical interest, the design equation involves much less unknowns that that of either the state or costate equations. Convergence is shown using energy estimates for the evolution equations governing the iterative process. Numerical tests show that the new method allows the solution of the optimization problem in a cost of solving the analysis problems just a few times, independent of the number of design parameters. The method can be applied using single grid iterations as well as with multigrid solvers.

Trajectory optimization for the National Aerospace Plane

NASA Technical Reports Server (NTRS)

Lu, Ping

1993-01-01

The objective of this second phase research is to investigate the optimal ascent trajectory for the National Aerospace Plane (NASP) from runway take-off to orbital insertion and address the unique problems associated with the hypersonic flight trajectory optimization. The trajectory optimization problem for an aerospace plane is a highly challenging problem because of the complexity involved. Previous work has been successful in obtaining sub-optimal trajectories by using energy-state approximation and time-scale decomposition techniques. But it is known that the energy-state approximation is not valid in certain portions of the trajectory. This research aims at employing full dynamics of the aerospace plane and emphasizing direct trajectory optimization methods. The major accomplishments of this research include the first-time development of an inverse dynamics approach in trajectory optimization which enables us to generate optimal trajectories for the aerospace plane efficiently and reliably, and general analytical solutions to constrained hypersonic trajectories that has wide application in trajectory optimization as well as in guidance and flight dynamics. Optimal trajectories in abort landing and ascent augmented with rocket propulsion and thrust vectoring control were also investigated. Motivated by this study, a new global trajectory optimization tool using continuous simulated annealing and a nonlinear predictive feedback guidance law have been under investigation and some promising results have been obtained, which may well lead to more significant development and application in the near future.

Comparison of multiobjective evolutionary algorithms: empirical results.

PubMed

Zitzler, E; Deb, K; Thiele, L

2000-01-01

In this paper, we provide a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions. Each test function involves a particular feature that is known to cause difficulty in the evolutionary optimization process, mainly in converging to the Pareto-optimal front (e.g., multimodality and deception). By investigating these different problem features separately, it is possible to predict the kind of problems to which a certain technique is or is not well suited. However, in contrast to what was suspected beforehand, the experimental results indicate a hierarchy of the algorithms under consideration. Furthermore, the emerging effects are evidence that the suggested test functions provide sufficient complexity to compare multiobjective optimizers. Finally, elitism is shown to be an important factor for improving evolutionary multiobjective search.

Multiobjective genetic algorithm conjunctive use optimization for production, cost, and energy with dynamic return flow

NASA Astrophysics Data System (ADS)

Peralta, Richard C.; Forghani, Ali; Fayad, Hala

2014-04-01

Many real water resources optimization problems involve conflicting objectives for which the main goal is to find a set of optimal solutions on, or near to the Pareto front. E-constraint and weighting multiobjective optimization techniques have shortcomings, especially as the number of objectives increases. Multiobjective Genetic Algorithms (MGA) have been previously proposed to overcome these difficulties. Here, an MGA derives a set of optimal solutions for multiobjective multiuser conjunctive use of reservoir, stream, and (un)confined groundwater resources. The proposed methodology is applied to a hydraulically and economically nonlinear system in which all significant flows, including stream-aquifer-reservoir-diversion-return flow interactions, are simulated and optimized simultaneously for multiple periods. Neural networks represent constrained state variables. The addressed objectives that can be optimized simultaneously in the coupled simulation-optimization model are: (1) maximizing water provided from sources, (2) maximizing hydropower production, and (3) minimizing operation costs of transporting water from sources to destinations. Results show the efficiency of multiobjective genetic algorithms for generating Pareto optimal sets for complex nonlinear multiobjective optimization problems.

Multidimensional spectral load balancing

DOEpatents

Hendrickson, Bruce A.; Leland, Robert W.

1996-12-24

A method of and apparatus for graph partitioning involving the use of a plurality of eigenvectors of the Laplacian matrix of the graph of the problem for which load balancing is desired. The invention is particularly useful for optimizing parallel computer processing of a problem and for minimizing total pathway lengths of integrated circuits in the design stage.

The Rigid Orthogonal Procrustes Rotation Problem

ERIC Educational Resources Information Center

ten Berge, Jos M. F.

2006-01-01

The problem of rotating a matrix orthogonally to a best least squares fit with another matrix of the same order has a closed-form solution based on a singular value decomposition. The optimal rotation matrix is not necessarily rigid, but may also involve a reflection. In some applications, only rigid rotations are permitted. Gower (1976) has…

Absorbable energy monitoring scheme: new design protocol to test vehicle structural crashworthiness.

PubMed

Ofochebe, Sunday M; Enibe, Samuel O; Ozoegwu, Chigbogu G

2016-05-01

In vehicle crashworthiness design optimization detailed system evaluation capable of producing reliable results are basically achieved through high-order numerical computational (HNC) models such as the dynamic finite element model, mesh-free model etc. However the application of these models especially during optimization studies is basically challenged by their inherent high demand on computational resources, conditional stability of the solution process, and lack of knowledge of viable parameter range for detailed optimization studies. The absorbable energy monitoring scheme (AEMS) presented in this paper suggests a new design protocol that attempts to overcome such problems in evaluation of vehicle structure for crashworthiness. The implementation of the AEMS involves studying crash performance of vehicle components at various absorbable energy ratios based on a 2DOF lumped-mass-spring (LMS) vehicle impact model. This allows for prompt prediction of useful parameter values in a given design problem. The application of the classical one-dimensional LMS model in vehicle crash analysis is further improved in the present work by developing a critical load matching criterion which allows for quantitative interpretation of the results of the abstract model in a typical vehicle crash design. The adequacy of the proposed AEMS for preliminary vehicle crashworthiness design is demonstrated in this paper, however its extension to full-scale design-optimization problem involving full vehicle model that shows greater structural detail requires more theoretical development.

Optimal design of groundwater remediation system using a probabilistic multi-objective fast harmony search algorithm under uncertainty

NASA Astrophysics Data System (ADS)

Luo, Qiankun; Wu, Jianfeng; Yang, Yun; Qian, Jiazhong; Wu, Jichun

2014-11-01

This study develops a new probabilistic multi-objective fast harmony search algorithm (PMOFHS) for optimal design of groundwater remediation systems under uncertainty associated with the hydraulic conductivity (K) of aquifers. The PMOFHS integrates the previously developed deterministic multi-objective optimization method, namely multi-objective fast harmony search algorithm (MOFHS) with a probabilistic sorting technique to search for Pareto-optimal solutions to multi-objective optimization problems in a noisy hydrogeological environment arising from insufficient K data. The PMOFHS is then coupled with the commonly used flow and transport codes, MODFLOW and MT3DMS, to identify the optimal design of groundwater remediation systems for a two-dimensional hypothetical test problem and a three-dimensional Indiana field application involving two objectives: (i) minimization of the total remediation cost through the engineering planning horizon, and (ii) minimization of the mass remaining in the aquifer at the end of the operational period, whereby the pump-and-treat (PAT) technology is used to clean up contaminated groundwater. Also, Monte Carlo (MC) analysis is employed to evaluate the effectiveness of the proposed methodology. Comprehensive analysis indicates that the proposed PMOFHS can find Pareto-optimal solutions with low variability and high reliability and is a potentially effective tool for optimizing multi-objective groundwater remediation problems under uncertainty.

New theoretical framework for designing nonionic surfactant mixtures that exhibit a desired adsorption kinetics behavior.

PubMed

Moorkanikkara, Srinivas Nageswaran; Blankschtein, Daniel

2010-12-21

How does one design a surfactant mixture using a set of available surfactants such that it exhibits a desired adsorption kinetics behavior? The traditional approach used to address this design problem involves conducting trial-and-error experiments with specific surfactant mixtures. This approach is typically time-consuming and resource-intensive and becomes increasingly challenging when the number of surfactants that can be mixed increases. In this article, we propose a new theoretical framework to identify a surfactant mixture that most closely meets a desired adsorption kinetics behavior. Specifically, the new theoretical framework involves (a) formulating the surfactant mixture design problem as an optimization problem using an adsorption kinetics model and (b) solving the optimization problem using a commercial optimization package. The proposed framework aims to identify the surfactant mixture that most closely satisfies the desired adsorption kinetics behavior subject to the predictive capabilities of the chosen adsorption kinetics model. Experiments can then be conducted at the identified surfactant mixture condition to validate the predictions. We demonstrate the reliability and effectiveness of the proposed theoretical framework through a realistic case study by identifying a nonionic surfactant mixture consisting of up to four alkyl poly(ethylene oxide) surfactants (C(10)E(4), C(12)E(5), C(12)E(6), and C(10)E(8)) such that it most closely exhibits a desired dynamic surface tension (DST) profile. Specifically, we use the Mulqueen-Stebe-Blankschtein (MSB) adsorption kinetics model (Mulqueen, M.; Stebe, K. J.; Blankschtein, D. Langmuir 2001, 17, 5196-5207) to formulate the optimization problem as well as the SNOPT commercial optimization solver to identify a surfactant mixture consisting of these four surfactants that most closely exhibits the desired DST profile. Finally, we compare the experimental DST profile measured at the surfactant mixture condition identified by the new theoretical framework with the desired DST profile and find good agreement between the two profiles.

Markerless human motion tracking using hierarchical multi-swarm cooperative particle swarm optimization.

PubMed

Saini, Sanjay; Zakaria, Nordin; Rambli, Dayang Rohaya Awang; Sulaiman, Suziah

2015-01-01

The high-dimensional search space involved in markerless full-body articulated human motion tracking from multiple-views video sequences has led to a number of solutions based on metaheuristics, the most recent form of which is Particle Swarm Optimization (PSO). However, the classical PSO suffers from premature convergence and it is trapped easily into local optima, significantly affecting the tracking accuracy. To overcome these drawbacks, we have developed a method for the problem based on Hierarchical Multi-Swarm Cooperative Particle Swarm Optimization (H-MCPSO). The tracking problem is formulated as a non-linear 34-dimensional function optimization problem where the fitness function quantifies the difference between the observed image and a projection of the model configuration. Both the silhouette and edge likelihoods are used in the fitness function. Experiments using Brown and HumanEva-II dataset demonstrated that H-MCPSO performance is better than two leading alternative approaches-Annealed Particle Filter (APF) and Hierarchical Particle Swarm Optimization (HPSO). Further, the proposed tracking method is capable of automatic initialization and self-recovery from temporary tracking failures. Comprehensive experimental results are presented to support the claims.

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.

Mixed H(2)/H(sub infinity): Control with output feedback compensators using parameter optimization

NASA Technical Reports Server (NTRS)

Schoemig, Ewald; Ly, Uy-Loi

1992-01-01

Among the many possible norm-based optimization methods, the concept of H-infinity optimal control has gained enormous attention in the past few years. Here the H-infinity framework, based on the Small Gain Theorem and the Youla Parameterization, effectively treats system uncertainties in the control law synthesis. A design approach involving a mixed H(sub 2)/H-infinity norm strives to combine the advantages of both methods. This advantage motivates researchers toward finding solutions to the mixed H(sub 2)/H-infinity control problem. The approach developed in this research is based on a finite time cost functional that depicts an H-infinity bound control problem in a H(sub 2)-optimization setting. The goal is to define a time-domain cost function that optimizes the H(sub 2)-norm of a system with an H-infinity-constraint function.

Mixed H2/H(infinity)-Control with an output-feedback compensator using parameter optimization

NASA Technical Reports Server (NTRS)

Schoemig, Ewald; Ly, Uy-Loi

1992-01-01

Among the many possible norm-based optimization methods, the concept of H-infinity optimal control has gained enormous attention in the past few years. Here the H-infinity framework, based on the Small Gain Theorem and the Youla Parameterization, effectively treats system uncertainties in the control law synthesis. A design approach involving a mixed H(sub 2)/H-infinity norm strives to combine the advantages of both methods. This advantage motivates researchers toward finding solutions to the mixed H(sub 2)/H-infinity control problem. The approach developed in this research is based on a finite time cost functional that depicts an H-infinity bound control problem in a H(sub 2)-optimization setting. The goal is to define a time-domain cost function that optimizes the H(sub 2)-norm of a system with an H-infinity-constraint function.

Optimum Tolerance Design Using Component-Amount and Mixture-Amount Experiments

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

Piepel, Gregory F.; Ozler, Cenk; Sehirlioglu, Ali Kemal

2013-08-01

One type of tolerance design problem involves optimizing component and assembly tolerances to minimize the total cost (sum of manufacturing cost and quality loss). Previous literature recommended using traditional response surface (RS) designs and models to solve this type of tolerance design problem. In this article, component-amount (CA) and mixture-amount (MA) approaches are proposed as more appropriate for solving this type of tolerance design problem. The advantages of the CA and MA approaches over the RS approach are discussed. Reasons for choosing between the CA and MA approaches are also discussed. The CA and MA approaches (experimental design, response modeling,more » and optimization) are illustrated using real examples.« less

A predictive machine learning approach for microstructure optimization and materials design

DOE PAGES

Liu, Ruoqian; Kumar, Abhishek; Chen, Zhengzhang; ...

2015-06-23

This paper addresses an important materials engineering question: How can one identify the complete space (or as much of it as possible) of microstructures that are theoretically predicted to yield the desired combination of properties demanded by a selected application? We present a problem involving design of magnetoelastic Fe-Ga alloy microstructure for enhanced elastic, plastic and magnetostrictive properties. While theoretical models for computing properties given the microstructure are known for this alloy, inversion of these relationships to obtain microstructures that lead to desired properties is challenging, primarily due to the high dimensionality of microstructure space, multi-objective design requirement and non-uniquenessmore » of solutions. These challenges render traditional search-based optimization methods incompetent in terms of both searching efficiency and result optimality. In this paper, a route to address these challenges using a machine learning methodology is proposed. A systematic framework consisting of random data generation, feature selection and classification algorithms is developed. In conclusion, experiments with five design problems that involve identification of microstructures that satisfy both linear and nonlinear property constraints show that our framework outperforms traditional optimization methods with the average running time reduced by as much as 80% and with optimality that would not be achieved otherwise.« less

One shot methods for optimal control of distributed parameter systems 1: Finite dimensional control

NASA Technical Reports Server (NTRS)

Taasan, Shlomo

1991-01-01

The efficient numerical treatment of optimal control problems governed by elliptic partial differential equations (PDEs) and systems of elliptic PDEs, where the control is finite dimensional is discussed. Distributed control as well as boundary control cases are discussed. The main characteristic of the new methods is that they are designed to solve the full optimization problem directly, rather than accelerating a descent method by an efficient multigrid solver for the equations involved. The methods use the adjoint state in order to achieve efficient smoother and a robust coarsening strategy. The main idea is the treatment of the control variables on appropriate scales, i.e., control variables that correspond to smooth functions are solved for on coarse grids depending on the smoothness of these functions. Solution of the control problems is achieved with the cost of solving the constraint equations about two to three times (by a multigrid solver). Numerical examples demonstrate the effectiveness of the method proposed in distributed control case, pointwise control and boundary control problems.

Multiple Choice Knapsack Problem: example of planning choice in transportation.

PubMed

Zhong, Tao; Young, Rhonda

2010-05-01

Transportation programming, a process of selecting projects for funding given budget and other constraints, is becoming more complex as a result of new federal laws, local planning regulations, and increased public involvement. This article describes the use of an integer programming tool, Multiple Choice Knapsack Problem (MCKP), to provide optimal solutions to transportation programming problems in cases where alternative versions of projects are under consideration. In this paper, optimization methods for use in the transportation programming process are compared and then the process of building and solving the optimization problems is discussed. The concepts about the use of MCKP are presented and a real-world transportation programming example at various budget levels is provided. This article illustrates how the use of MCKP addresses the modern complexities and provides timely solutions in transportation programming practice. While the article uses transportation programming as a case study, MCKP can be useful in other fields where a similar decision among a subset of the alternatives is required. Copyright 2009 Elsevier Ltd. All rights reserved.

Exponential approximations in optimal design

NASA Technical Reports Server (NTRS)

Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.

1990-01-01

One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.

Control of functional differential equations with function space boundary conditions.

NASA Technical Reports Server (NTRS)

Banks, H. T.

1972-01-01

The results of various authors dealing with problems involving functional differential equations with terminal conditions in function space are reviewed. The review includes not only very recent results, but also some little known results of Soviet mathematicians prior to 1970. Particular attention is given to results concerning controllability, existence of optimal controls, and necessary and sufficient conditions for optimality.

A Model for Engaging Students in a Research Experience Involving Variational Techniques, Mathematica, and Descent Methods.

ERIC Educational Resources Information Center

Mahavier, W. Ted

2002-01-01

Describes a two-semester numerical methods course that serves as a research experience for undergraduate students without requiring external funding or the modification of current curriculum. Uses an engineering problem to introduce students to constrained optimization via a variation of the traditional isoperimetric problem of finding the curve…

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.

Towards Robust Designs Via Multiple-Objective Optimization Methods

NASA Technical Reports Server (NTRS)

Man Mohan, Rai

2006-01-01

Fabricating and operating complex systems involves dealing with uncertainty in the relevant variables. In the case of aircraft, flow conditions are subject to change during operation. Efficiency and engine noise may be different from the expected values because of manufacturing tolerances and normal wear and tear. Engine components may have a shorter life than expected because of manufacturing tolerances. In spite of the important effect of operating- and manufacturing-uncertainty on the performance and expected life of the component or system, traditional aerodynamic shape optimization has focused on obtaining the best design given a set of deterministic flow conditions. Clearly it is important to both maintain near-optimal performance levels at off-design operating conditions, and, ensure that performance does not degrade appreciably when the component shape differs from the optimal shape due to manufacturing tolerances and normal wear and tear. These requirements naturally lead to the idea of robust optimal design wherein the concept of robustness to various perturbations is built into the design optimization procedure. The basic ideas involved in robust optimal design will be included in this lecture. The imposition of the additional requirement of robustness results in a multiple-objective optimization problem requiring appropriate solution procedures. Typically the costs associated with multiple-objective optimization are substantial. Therefore efficient multiple-objective optimization procedures are crucial to the rapid deployment of the principles of robust design in industry. Hence the companion set of lecture notes (Single- and Multiple-Objective Optimization with Differential Evolution and Neural Networks ) deals with methodology for solving multiple-objective Optimization problems efficiently, reliably and with little user intervention. Applications of the methodologies presented in the companion lecture to robust design will be included here. The evolutionary method (DE) is first used to solve a relatively difficult problem in extended surface heat transfer wherein optimal fin geometries are obtained for different safe operating base temperatures. The objective of maximizing the safe operating base temperature range is in direct conflict with the objective of maximizing fin heat transfer. This problem is a good example of achieving robustness in the context of changing operating conditions. The evolutionary method is then used to design a turbine airfoil; the two objectives being reduced sensitivity of the pressure distribution to small changes in the airfoil shape and the maximization of the trailing edge wedge angle with the consequent increase in airfoil thickness and strength. This is a relevant example of achieving robustness to manufacturing tolerances and wear and tear in the presence of other objectives.

Optimization of structures undergoing harmonic or stochastic excitation. Ph.D. Thesis; [atmospheric turbulence and white noise

NASA Technical Reports Server (NTRS)

Johnson, E. H.

1975-01-01

The optimal design was investigated of simple structures subjected to dynamic loads, with constraints on the structures' responses. Optimal designs were examined for one dimensional structures excited by harmonically oscillating loads, similar structures excited by white noise, and a wing in the presence of continuous atmospheric turbulence. The first has constraints on the maximum allowable stress while the last two place bounds on the probability of failure of the structure. Approximations were made to replace the time parameter with a frequency parameter. For the first problem, this involved the steady state response, and in the remaining cases, power spectral techniques were employed to find the root mean square values of the responses. Optimal solutions were found by using computer algorithms which combined finite elements methods with optimization techniques based on mathematical programming. It was found that the inertial loads for these dynamic problems result in optimal structures that are radically different from those obtained for structures loaded statically by forces of comparable magnitude.

Decentralized Bayesian search using approximate dynamic programming methods.

PubMed

Zhao, Yijia; Patek, Stephen D; Beling, Peter A

2008-08-01

We consider decentralized Bayesian search problems that involve a team of multiple autonomous agents searching for targets on a network of search points operating under the following constraints: 1) interagent communication is limited; 2) the agents do not have the opportunity to agree in advance on how to resolve equivalent but incompatible strategies; and 3) each agent lacks the ability to control or predict with certainty the actions of the other agents. We formulate the multiagent search-path-planning problem as a decentralized optimal control problem and introduce approximate dynamic heuristics that can be implemented in a decentralized fashion. After establishing some analytical properties of the heuristics, we present computational results for a search problem involving two agents on a 5 x 5 grid.

QUADRO: A SUPERVISED DIMENSION REDUCTION METHOD VIA RAYLEIGH QUOTIENT OPTIMIZATION.

PubMed

Fan, Jianqing; Ke, Zheng Tracy; Liu, Han; Xia, Lucy

We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method-named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization)-for analyzing high-dimensional data. Unlike in the linear setting where Rayleigh quotient optimization coincides with classification, these two problems are very different under nonlinear settings. In this paper, we clarify this difference and show that Rayleigh quotient optimization may be of independent scientific interests. One major challenge of Rayleigh quotient optimization is that the variance of quadratic statistics involves all fourth cross-moments of predictors, which are infeasible to compute for high-dimensional applications and may accumulate too many stochastic errors. This issue is resolved by considering a family of elliptical models. Moreover, for heavy-tail distributions, robust estimates of mean vectors and covariance matrices are employed to guarantee uniform convergence in estimating non-polynomially many parameters, even though only the fourth moments are assumed. Methodologically, QUADRO is based on elliptical models which allow us to formulate the Rayleigh quotient maximization as a convex optimization problem. Computationally, we propose an efficient linearized augmented Lagrangian method to solve the constrained optimization problem. Theoretically, we provide explicit rates of convergence in terms of Rayleigh quotient under both Gaussian and general elliptical models. Thorough numerical results on both synthetic and real datasets are also provided to back up our theoretical results.

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.

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

Smith, Brennan T; Jager, Yetta; March, Patrick

Reservoir releases are typically operated to maximize the efficiency of hydropower production and the value of hydropower produced. In practice, ecological considerations are limited to those required by law. We first describe reservoir optimization methods that include mandated constraints on environmental and other water uses. Next, we describe research to formulate and solve reservoir optimization problems involving both energy and environmental water needs as objectives. Evaluating ecological objectives is a challenge in these problems for several reasons. First, it is difficult to predict how biological populations will respond to flow release patterns. This problem can be circumvented by using ecologicalmore » models. Second, most optimization methods require complex ecological responses to flow to be quantified by a single metric, preferably a currency that can also represent hydropower benefits. Ecological valuation of instream flows can make optimization methods that require a single currency for the effects of flow on energy and river ecology possible. Third, holistic reservoir optimization problems are unlikely to be structured such that simple solution methods can be used, necessitating the use of flexible numerical methods. One strong advantage of optimal control is the ability to plan for the effects of climate change. We present ideas for developing holistic methods to the point where they can be used for real-time operation of reservoirs. We suggest that developing ecologically sound optimization tools should be a priority for hydropower in light of the increasing value placed on sustaining both the ecological and energy benefits of riverine ecosystems long into the future.« less

The design of aircraft using the decision support problem technique

NASA Technical Reports Server (NTRS)

Mistree, Farrokh; Marinopoulos, Stergios; Jackson, David M.; Shupe, Jon A.

1988-01-01

The Decision Support Problem Technique for unified design, manufacturing and maintenance is being developed at the Systems Design Laboratory at the University of Houston. This involves the development of a domain-independent method (and the associated software) that can be used to process domain-dependent information and thereby provide support for human judgment. In a computer assisted environment, this support is provided in the form of optimal solutions to Decision Support Problems.

Cost effective campaigning in social networks

NASA Astrophysics Data System (ADS)

Kotnis, Bhushan; Kuri, Joy

2016-05-01

Campaigners are increasingly using online social networking platforms for promoting products, ideas and information. A popular method of promoting a product or even an idea is incentivizing individuals to evangelize the idea vigorously by providing them with referral rewards in the form of discounts, cash backs, or social recognition. Due to budget constraints on scarce resources such as money and manpower, it may not be possible to provide incentives for the entire population, and hence incentives need to be allocated judiciously to appropriate individuals for ensuring the highest possible outreach size. We aim to do the same by formulating and solving an optimization problem using percolation theory. In particular, we compute the set of individuals that are provided incentives for minimizing the expected cost while ensuring a given outreach size. We also solve the problem of computing the set of individuals to be incentivized for maximizing the outreach size for given cost budget. The optimization problem turns out to be non trivial; it involves quantities that need to be computed by numerically solving a fixed point equation. Our primary contribution is, that for a fairly general cost structure, we show that the optimization problems can be solved by solving a simple linear program. We believe that our approach of using percolation theory to formulate an optimization problem is the first of its kind.

Hodograph analysis in aircraft trajectory optimization

NASA Technical Reports Server (NTRS)

Cliff, Eugene M.; Seywald, Hans; Bless, Robert R.

1993-01-01

An account is given of key geometrical concepts involved in the use of a hodograph as an optimal control theory resource which furnishes a framework for geometrical interpretation of the minimum principle. Attention is given to the effects of different convexity properties on the hodograph, which bear on the existence of solutions and such types of controls as chattering controls, 'bang-bang' control, and/or singular control. Illustrative aircraft trajectory optimization problems are examined in view of this use of the hodograph.

Exploiting Quantum Resonance to Solve Combinatorial Problems

NASA Technical Reports Server (NTRS)

Zak, Michail; Fijany, Amir

2006-01-01

Quantum resonance would be exploited in a proposed quantum-computing approach to the solution of combinatorial optimization problems. In quantum computing in general, one takes advantage of the fact that an algorithm cannot be decoupled from the physical effects available to implement it. Prior approaches to quantum computing have involved exploitation of only a subset of known quantum physical effects, notably including parallelism and entanglement, but not including resonance. In the proposed approach, one would utilize the combinatorial properties of tensor-product decomposability of unitary evolution of many-particle quantum systems for physically simulating solutions to NP-complete problems (a class of problems that are intractable with respect to classical methods of computation). In this approach, reinforcement and selection of a desired solution would be executed by means of quantum resonance. Classes of NP-complete problems that are important in practice and could be solved by the proposed approach include planning, scheduling, search, and optimal design.

Distributed query plan generation using multiobjective genetic algorithm.

PubMed

Panicker, Shina; Kumar, T V Vijay

2014-01-01

A distributed query processing strategy, which is a key performance determinant in accessing distributed databases, aims to minimize the total query processing cost. One way to achieve this is by generating efficient distributed query plans that involve fewer sites for processing a query. In the case of distributed relational databases, the number of possible query plans increases exponentially with respect to the number of relations accessed by the query and the number of sites where these relations reside. Consequently, computing optimal distributed query plans becomes a complex problem. This distributed query plan generation (DQPG) problem has already been addressed using single objective genetic algorithm, where the objective is to minimize the total query processing cost comprising the local processing cost (LPC) and the site-to-site communication cost (CC). In this paper, this DQPG problem is formulated and solved as a biobjective optimization problem with the two objectives being minimize total LPC and minimize total CC. These objectives are simultaneously optimized using a multiobjective genetic algorithm NSGA-II. Experimental comparison of the proposed NSGA-II based DQPG algorithm with the single objective genetic algorithm shows that the former performs comparatively better and converges quickly towards optimal solutions for an observed crossover and mutation probability.

Distributed Query Plan Generation Using Multiobjective Genetic Algorithm

PubMed Central

Panicker, Shina; Vijay Kumar, T. V.

2014-01-01

A distributed query processing strategy, which is a key performance determinant in accessing distributed databases, aims to minimize the total query processing cost. One way to achieve this is by generating efficient distributed query plans that involve fewer sites for processing a query. In the case of distributed relational databases, the number of possible query plans increases exponentially with respect to the number of relations accessed by the query and the number of sites where these relations reside. Consequently, computing optimal distributed query plans becomes a complex problem. This distributed query plan generation (DQPG) problem has already been addressed using single objective genetic algorithm, where the objective is to minimize the total query processing cost comprising the local processing cost (LPC) and the site-to-site communication cost (CC). In this paper, this DQPG problem is formulated and solved as a biobjective optimization problem with the two objectives being minimize total LPC and minimize total CC. These objectives are simultaneously optimized using a multiobjective genetic algorithm NSGA-II. Experimental comparison of the proposed NSGA-II based DQPG algorithm with the single objective genetic algorithm shows that the former performs comparatively better and converges quickly towards optimal solutions for an observed crossover and mutation probability. PMID:24963513

A Multi-Objective Optimization Technique to Model the Pareto Front of Organic Dielectric Polymers

NASA Astrophysics Data System (ADS)

Gubernatis, J. E.; Mannodi-Kanakkithodi, A.; Ramprasad, R.; Pilania, G.; Lookman, T.

Multi-objective optimization is an area of decision making that is concerned with mathematical optimization problems involving more than one objective simultaneously. Here we describe two new Monte Carlo methods for this type of optimization in the context of their application to the problem of designing polymers with more desirable dielectric and optical properties. We present results of applying these Monte Carlo methods to a two-objective problem (maximizing the total static band dielectric constant and energy gap) and a three objective problem (maximizing the ionic and electronic contributions to the static band dielectric constant and energy gap) of a 6-block organic polymer. Our objective functions were constructed from high throughput DFT calculations of 4-block polymers, following the method of Sharma et al., Nature Communications 5, 4845 (2014) and Mannodi-Kanakkithodi et al., Scientific Reports, submitted. Our high throughput and Monte Carlo methods of analysis extend to general N-block organic polymers. This work was supported in part by the LDRD DR program of the Los Alamos National Laboratory and in part by a Multidisciplinary University Research Initiative (MURI) Grant from the Office of Naval Research.

Calculating complete and exact Pareto front for multiobjective optimization: a new deterministic approach for discrete problems.

PubMed

Hu, Xiao-Bing; Wang, Ming; Di Paolo, Ezequiel

2013-06-01

Searching the Pareto front for multiobjective optimization problems usually involves the use of a population-based search algorithm or of a deterministic method with a set of different single aggregate objective functions. The results are, in fact, only approximations of the real Pareto front. In this paper, we propose a new deterministic approach capable of fully determining the real Pareto front for those discrete problems for which it is possible to construct optimization algorithms to find the k best solutions to each of the single-objective problems. To this end, two theoretical conditions are given to guarantee the finding of the actual Pareto front rather than its approximation. Then, a general methodology for designing a deterministic search procedure is proposed. A case study is conducted, where by following the general methodology, a ripple-spreading algorithm is designed to calculate the complete exact Pareto front for multiobjective route optimization. When compared with traditional Pareto front search methods, the obvious advantage of the proposed approach is its unique capability of finding the complete Pareto front. This is illustrated by the simulation results in terms of both solution quality and computational efficiency.

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.

AHPCRC - Army High Performance Computing Research Center

DTIC Science & Technology

2010-01-01

shielding fabrics. Contact with a projectile induces electromagnetic forces on the fabric that can cause the projectile to rotate , making it less...other AHPCRC projects in need of optimization techniques. A major focus of this research addresses solving partial differential equation ( PDE ...plat- forms. One such problem is the determination of optimal wing shapes and motions. Work in progress involves coupling the PDE -solver AERO-F and

Aspects of the Mother-Nanny Relationship: Some Concepts from Psychoanalytic Research to Understand Problem Areas Which Can Interfere with the Optimal Care for Children.

ERIC Educational Resources Information Center

Magagna, Jeanne

Elaborating on two main styles of multiple caretaking, this paper discusses those aspects of the mother-nanny relationship which influence the optimal care of the child. A caretaking style based in denial involves obliterating, denying, and distracting the child from his painful emotional experiences, fostering "the stiff upper lip," and…

Least Squares Computations in Science and Engineering

DTIC Science & Technology

1994-02-01

iterative least squares deblurring procedure. Because of the ill-posed characteristics of the deconvolution problem, in the presence of noise , direct...optimization methods. Generally, the problems are accompanied by constraints, such as bound constraints, and the observations are corrupted by noise . The...engineering. This effort has involved interaction with researchers in closed-loop active noise (vibration) control at Phillips Air Force Laboratory

Adaptive Multi-Agent Systems for Constrained Optimization

NASA Technical Reports Server (NTRS)

Macready, William; Bieniawski, Stefan; Wolpert, David H.

2004-01-01

Product Distribution (PD) theory is a new framework for analyzing and controlling distributed systems. Here we demonstrate its use for distributed stochastic optimization. First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (probability distribution of) the joint state of the agents. When the game in question is a team game with constraints, that equilibrium optimizes the expected value of the team game utility, subject to those constraints. The updating of the Lagrange parameters in the Lagrangian can be viewed as a form of automated annealing, that focuses the MAS more and more on the optimal pure strategy. This provides a simple way to map the solution of any constrained optimization problem onto the equilibrium of a Multi-Agent System (MAS). We present computer experiments involving both the Queen s problem and K-SAT validating the predictions of PD theory and its use for off-the-shelf distributed adaptive optimization.

Application of modern control theory to scheduling and path-stretching maneuvers of aircraft in the near terminal area

NASA Technical Reports Server (NTRS)

Athans, M.

1974-01-01

A design concept of the dynamic control of aircraft in the near terminal area is discussed. An arbitrary set of nominal air routes, with possible multiple merging points, all leading to a single runway, is considered. The system allows for the automated determination of acceleration/deceleration of aircraft along the nominal air routes, as well as for the automated determination of path-stretching delay maneuvers. In addition to normal operating conditions, the system accommodates: (1) variable commanded separations over the outer marker to allow for takeoffs and between successive landings and (2) emergency conditions under which aircraft in distress have priority. The system design is based on a combination of three distinct optimal control problems involving a standard linear-quadratic problem, a parameter optimization problem, and a minimum-time rendezvous problem.

Optimal trajectories for aeroassisted orbital transfer

NASA Technical Reports Server (NTRS)

Miele, A.; Venkataraman, P.

1983-01-01

Consideration is given to classical and minimax problems involved in aeroassisted transfer from high earth orbit (HEO) to low earth orbit (LEO). The transfer is restricted to coplanar operation, with trajectory control effected by means of lift modulation. The performance of the maneuver is indexed to the energy expenditure or, alternatively, the time integral of the heating rate. Firist-order optimality conditions are defined for the classical approach, as are a sequential gradient-restoration algorithm and a combined gradient-restoration algorithm. Minimization techniques are presented for the aeroassisted transfer energy consumption and time-delay integral of the heating rate, as well as minimization of the pressure. It is shown that the eigenvalues of the Jacobian matrix of the differential system is both stiff and unstable, implying that the sequential gradient restoration algorithm in its present version is unsuitable. A new method, involving a multipoint approach to the two-poing boundary value problem, is recommended.

Optimal quantum cloning based on the maximin principle by using a priori information

NASA Astrophysics Data System (ADS)

Kang, Peng; Dai, Hong-Yi; Wei, Jia-Hua; Zhang, Ming

2016-10-01

We propose an optimal 1 →2 quantum cloning method based on the maximin principle by making full use of a priori information of amplitude and phase about the general cloned qubit input set, which is a simply connected region enclosed by a "longitude-latitude grid" on the Bloch sphere. Theoretically, the fidelity of the optimal quantum cloning machine derived from this method is the largest in terms of the maximin principle compared with that of any other machine. The problem solving is an optimization process that involves six unknown complex variables, six vectors in an uncertain-dimensional complex vector space, and four equality constraints. Moreover, by restricting the structure of the quantum cloning machine, the optimization problem is simplified as a three-real-parameter suboptimization problem with only one equality constraint. We obtain the explicit formula for a suboptimal quantum cloning machine. Additionally, the fidelity of our suboptimal quantum cloning machine is higher than or at least equal to that of universal quantum cloning machines and phase-covariant quantum cloning machines. It is also underlined that the suboptimal cloning machine outperforms the "belt quantum cloning machine" for some cases.

Optimal Fault-Tolerant Control for Discrete-Time Nonlinear Strict-Feedback Systems Based on Adaptive Critic Design.

PubMed

Wang, Zhanshan; Liu, Lei; Wu, Yanming; Zhang, Huaguang

2018-06-01

This paper investigates the problem of optimal fault-tolerant control (FTC) for a class of unknown nonlinear discrete-time systems with actuator fault in the framework of adaptive critic design (ACD). A pivotal highlight is the adaptive auxiliary signal of the actuator fault, which is designed to offset the effect of the fault. The considered systems are in strict-feedback forms and involve unknown nonlinear functions, which will result in the causal problem. To solve this problem, the original nonlinear systems are transformed into a novel system by employing the diffeomorphism theory. Besides, the action neural networks (ANNs) are utilized to approximate a predefined unknown function in the backstepping design procedure. Combined the strategic utility function and the ACD technique, a reinforcement learning algorithm is proposed to set up an optimal FTC, in which the critic neural networks (CNNs) provide an approximate structure of the cost function. In this case, it not only guarantees the stability of the systems, but also achieves the optimal control performance as well. In the end, two simulation examples are used to show the effectiveness of the proposed optimal FTC strategy.

Multimodel methods for optimal control of aeroacoustics.

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

Chen, Guoquan; Collis, Samuel Scott

2005-01-01

A new multidomain/multiphysics computational framework for optimal control of aeroacoustic noise has been developed based on a near-field compressible Navier-Stokes solver coupled with a far-field linearized Euler solver both based on a discontinuous Galerkin formulation. In this approach, the coupling of near- and far-field domains is achieved by weakly enforcing continuity of normal fluxes across a coupling surface that encloses all nonlinearities and noise sources. For optimal control, gradient information is obtained by the solution of an appropriate adjoint problem that involves the propagation of adjoint information from the far-field to the near-field. This computational framework has been successfully appliedmore » to study optimal boundary-control of blade-vortex interaction, which is a significant noise source for helicopters on approach to landing. In the model-problem presented here, the noise propagated toward the ground is reduced by 12dB.« less

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.

Theory and implementation of H-matrix based iterative and direct solvers for Helmholtz and elastodynamic oscillatory kernels

NASA Astrophysics Data System (ADS)

Chaillat, Stéphanie; Desiderio, Luca; Ciarlet, Patrick

2017-12-01

In this work, we study the accuracy and efficiency of hierarchical matrix (H-matrix) based fast methods for solving dense linear systems arising from the discretization of the 3D elastodynamic Green's tensors. It is well known in the literature that standard H-matrix based methods, although very efficient tools for asymptotically smooth kernels, are not optimal for oscillatory kernels. H2-matrix and directional approaches have been proposed to overcome this problem. However the implementation of such methods is much more involved than the standard H-matrix representation. The central questions we address are twofold. (i) What is the frequency-range in which the H-matrix format is an efficient representation for 3D elastodynamic problems? (ii) What can be expected of such an approach to model problems in mechanical engineering? We show that even though the method is not optimal (in the sense that more involved representations can lead to faster algorithms) an efficient solver can be easily developed. The capabilities of the method are illustrated on numerical examples using the Boundary Element Method.

An explicit solution to the exoatmospheric powered flight guidance and trajectory optimization problem for rocket propelled vehicles

NASA Technical Reports Server (NTRS)

Jaggers, R. F.

1977-01-01

A derivation of an explicit solution to the two point boundary-value problem of exoatmospheric guidance and trajectory optimization is presented. Fixed initial conditions and continuous burn, multistage thrusting are assumed. Any number of end conditions from one to six (throttling is required in the case of six) can be satisfied in an explicit and practically optimal manner. The explicit equations converge for off nominal conditions such as engine failure, abort, target switch, etc. The self starting, predictor/corrector solution involves no Newton-Rhapson iterations, numerical integration, or first guess values, and converges rapidly if physically possible. A form of this algorithm has been chosen for onboard guidance, as well as real time and preflight ground targeting and trajectory shaping for the NASA Space Shuttle Program.

Learning automata-based solutions to the nonlinear fractional knapsack problem with applications to optimal resource allocation.

PubMed

Granmo, Ole-Christoffer; Oommen, B John; Myrer, Svein Arild; Olsen, Morten Goodwin

2007-02-01

This paper considers the nonlinear fractional knapsack problem and demonstrates how its solution can be effectively applied to two resource allocation problems dealing with the World Wide Web. The novel solution involves a "team" of deterministic learning automata (LA). The first real-life problem relates to resource allocation in web monitoring so as to "optimize" information discovery when the polling capacity is constrained. The disadvantages of the currently reported solutions are explained in this paper. The second problem concerns allocating limited sampling resources in a "real-time" manner with the purpose of estimating multiple binomial proportions. This is the scenario encountered when the user has to evaluate multiple web sites by accessing a limited number of web pages, and the proportions of interest are the fraction of each web site that is successfully validated by an HTML validator. Using the general LA paradigm to tackle both of the real-life problems, the proposed scheme improves a current solution in an online manner through a series of informed guesses that move toward the optimal solution. At the heart of the scheme, a team of deterministic LA performs a controlled random walk on a discretized solution space. Comprehensive experimental results demonstrate that the discretization resolution determines the precision of the scheme, and that for a given precision, the current solution (to both problems) is consistently improved until a nearly optimal solution is found--even for switching environments. Thus, the scheme, while being novel to the entire field of LA, also efficiently handles a class of resource allocation problems previously not addressed in the literature.

Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming

NASA Technical Reports Server (NTRS)

Shi, Yun. Y.; Nelson, R. L.; Young, D. H.

1990-01-01

The fuel optimal control problem arising in the non-planar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) with orbital plane change. The basic strategy here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the aeroassisted HEO to LEO transfer consists of three phases. In the first phase, the orbital transfer begins with a deorbit impulse at HEO which injects the vehicle into an elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and bank angle modulations to perform the desired orbital plane change and to satisfy heating constraints. Because of the energy loss during the turn, an impulse is required to initiate the third phase to boost the vehicle back to the desired LEO orbital altitude. The third impulse is then used to circularize the orbit at LEO. The problem is solved by a direct optimization technique which uses piecewise polynomial representation for the state and control variables and collocation to satisfy the differential equations. This technique converts the optimal control problem into a nonlinear programming problem which is solved numerically. Solutions were obtained for cases with and without heat constraints and for cases of different orbital inclination changes. The method appears to be more powerful and robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

Closed-form recursive formula for an optimal tracker with terminal constraints

NASA Technical Reports Server (NTRS)

Juang, J. N.; Turner, J. D.; Chun, H. M.

1986-01-01

Feedback control laws are derived for a class of optimal finite time tracking problems with terminal constraints. Analytical solutions are obtained for the feedback gain and the closed-loop response trajectory. Such formulations are expressed in recursive forms so that a real-time computer implementation becomes feasible. An example involving the feedback slewing of a flexible spacecraft is given to illustrate the validity and usefulness of the formulations.

Optimal discrete-time LQR problems for parabolic systems with unbounded input: Approximation and convergence

NASA Technical Reports Server (NTRS)

Rosen, I. G.

1988-01-01

An abstract approximation and convergence theory for the closed-loop solution of discrete-time linear-quadratic regulator problems for parabolic systems with unbounded input is developed. Under relatively mild stabilizability and detectability assumptions, functional analytic, operator techniques are used to demonstrate the norm convergence of Galerkin-based approximations to the optimal feedback control gains. The application of the general theory to a class of abstract boundary control systems is considered. Two examples, one involving the Neumann boundary control of a one-dimensional heat equation, and the other, the vibration control of a cantilevered viscoelastic beam via shear input at the free end, are discussed.

QUADRO: A SUPERVISED DIMENSION REDUCTION METHOD VIA RAYLEIGH QUOTIENT OPTIMIZATION

PubMed Central

Fan, Jianqing; Ke, Zheng Tracy; Liu, Han; Xia, Lucy

2016-01-01

We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method—named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization)—for analyzing high-dimensional data. Unlike in the linear setting where Rayleigh quotient optimization coincides with classification, these two problems are very different under nonlinear settings. In this paper, we clarify this difference and show that Rayleigh quotient optimization may be of independent scientific interests. One major challenge of Rayleigh quotient optimization is that the variance of quadratic statistics involves all fourth cross-moments of predictors, which are infeasible to compute for high-dimensional applications and may accumulate too many stochastic errors. This issue is resolved by considering a family of elliptical models. Moreover, for heavy-tail distributions, robust estimates of mean vectors and covariance matrices are employed to guarantee uniform convergence in estimating non-polynomially many parameters, even though only the fourth moments are assumed. Methodologically, QUADRO is based on elliptical models which allow us to formulate the Rayleigh quotient maximization as a convex optimization problem. Computationally, we propose an efficient linearized augmented Lagrangian method to solve the constrained optimization problem. Theoretically, we provide explicit rates of convergence in terms of Rayleigh quotient under both Gaussian and general elliptical models. Thorough numerical results on both synthetic and real datasets are also provided to back up our theoretical results. PMID:26778864

Stochastic Adaptive Estimation and Control.

DTIC Science & Technology

1994-10-26

Marcus, "Language Stability and Stabilizability of Discrete Event Dynamical Systems ," SIAM Journal on Control and Optimization, 31, September 1993...in the hierarchical control of flexible manufacturing systems ; in this problem, the model involves a hybrid process in continuous time whose state is...of the average cost control problem for discrete- time Markov processes. Our exposition covers from finite to Borel state and action spaces and

Self-calibration of robot-sensor system

NASA Technical Reports Server (NTRS)

Yeh, Pen-Shu

1990-01-01

The process of finding the coordinate transformation between a robot and an external sensor system has been addressed. This calibration is equivalent to solving a nonlinear optimization problem for the parameters that characterize the transformation. A two-step procedure is herein proposed for solving the problem. The first step involves finding a nominal solution that is a good approximation of the final solution. A varational problem is then generated to replace the original problem in the next step. With the assumption that the variational parameters are small compared to unity, the problem that can be more readily solved with relatively small computation effort.

An Optimization of Manufacturing Systems using a Feedback Control Scheduling Model

NASA Astrophysics Data System (ADS)

Ikome, John M.; Kanakana, Grace M.

2018-03-01

In complex production system that involves multiple process, unplanned disruption often turn to make the entire production system vulnerable to a number of problems which leads to customer’s dissatisfaction. However, this problem has been an ongoing problem that requires a research and methods to streamline the entire process or develop a model that will address it, in contrast to this, we have developed a feedback scheduling model that can minimize some of this problem and after a number of experiment, it shows that some of this problems can be eliminated if the correct remedial actions are implemented on time.

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.

Multiswarm comprehensive learning particle swarm optimization for solving multiobjective optimization problems.

PubMed

Yu, Xiang; Zhang, Xueqing

2017-01-01

Comprehensive learning particle swarm optimization (CLPSO) is a powerful state-of-the-art single-objective metaheuristic. Extending from CLPSO, this paper proposes multiswarm CLPSO (MSCLPSO) for multiobjective optimization. MSCLPSO involves multiple swarms, with each swarm associated with a separate original objective. Each particle's personal best position is determined just according to the corresponding single objective. Elitists are stored externally. MSCLPSO differs from existing multiobjective particle swarm optimizers in three aspects. First, each swarm focuses on optimizing the associated objective using CLPSO, without learning from the elitists or any other swarm. Second, mutation is applied to the elitists and the mutation strategy appropriately exploits the personal best positions and elitists. Third, a modified differential evolution (DE) strategy is applied to some extreme and least crowded elitists. The DE strategy updates an elitist based on the differences of the elitists. The personal best positions carry useful information about the Pareto set, and the mutation and DE strategies help MSCLPSO discover the true Pareto front. Experiments conducted on various benchmark problems demonstrate that MSCLPSO can find nondominated solutions distributed reasonably over the true Pareto front in a single run.

Application of Multi-Objective Human Learning Optimization Method to Solve AC/DC Multi-Objective Optimal Power Flow Problem

NASA Astrophysics Data System (ADS)

Cao, Jia; Yan, Zheng; He, Guangyu

2016-06-01

This paper introduces an efficient algorithm, multi-objective human learning optimization method (MOHLO), to solve AC/DC multi-objective optimal power flow problem (MOPF). Firstly, the model of AC/DC MOPF including wind farms is constructed, where includes three objective functions, operating cost, power loss, and pollutant emission. Combining the non-dominated sorting technique and the crowding distance index, the MOHLO method can be derived, which involves individual learning operator, social learning operator, random exploration learning operator and adaptive strategies. Both the proposed MOHLO method and non-dominated sorting genetic algorithm II (NSGAII) are tested on an improved IEEE 30-bus AC/DC hybrid system. Simulation results show that MOHLO method has excellent search efficiency and the powerful ability of searching optimal. Above all, MOHLO method can obtain more complete pareto front than that by NSGAII method. However, how to choose the optimal solution from pareto front depends mainly on the decision makers who stand from the economic point of view or from the energy saving and emission reduction point of view.

A stochastic discrete optimization model for designing container terminal facilities

NASA Astrophysics Data System (ADS)

Zukhruf, Febri; Frazila, Russ Bona; Burhani, Jzolanda Tsavalista

2017-11-01

As uncertainty essentially affect the total transportation cost, it remains important in the container terminal that incorporates several modes and transshipments process. This paper then presents a stochastic discrete optimization model for designing the container terminal, which involves the decision of facilities improvement action. The container terminal operation model is constructed by accounting the variation of demand and facilities performance. In addition, for illustrating the conflicting issue that practically raises in the terminal operation, the model also takes into account the possible increment delay of facilities due to the increasing number of equipment, especially the container truck. Those variations expectantly reflect the uncertainty issue in the container terminal operation. A Monte Carlo simulation is invoked to propagate the variations by following the observed distribution. The problem is constructed within the framework of the combinatorial optimization problem for investigating the optimal decision of facilities improvement. A new variant of glow-worm swarm optimization (GSO) is thus proposed for solving the optimization, which is rarely explored in the transportation field. The model applicability is tested by considering the actual characteristics of the container terminal.

A PDE Sensitivity Equation Method for Optimal Aerodynamic Design

NASA Technical Reports Server (NTRS)

Borggaard, Jeff; Burns, John

1996-01-01

The use of gradient based optimization algorithms in inverse design is well established as a practical approach to aerodynamic design. A typical procedure uses a simulation scheme to evaluate the objective function (from the approximate states) and its gradient, then passes this information to an optimization algorithm. Once the simulation scheme (CFD flow solver) has been selected and used to provide approximate function evaluations, there are several possible approaches to the problem of computing gradients. One popular method is to differentiate the simulation scheme and compute design sensitivities that are then used to obtain gradients. Although this black-box approach has many advantages in shape optimization problems, one must compute mesh sensitivities in order to compute the design sensitivity. In this paper, we present an alternative approach using the PDE sensitivity equation to develop algorithms for computing gradients. This approach has the advantage that mesh sensitivities need not be computed. Moreover, when it is possible to use the CFD scheme for both the forward problem and the sensitivity equation, then there are computational advantages. An apparent disadvantage of this approach is that it does not always produce consistent derivatives. However, for a proper combination of discretization schemes, one can show asymptotic consistency under mesh refinement, which is often sufficient to guarantee convergence of the optimal design algorithm. In particular, we show that when asymptotically consistent schemes are combined with a trust-region optimization algorithm, the resulting optimal design method converges. We denote this approach as the sensitivity equation method. The sensitivity equation method is presented, convergence results are given and the approach is illustrated on two optimal design problems involving shocks.

Problems of millipound thrust measurement. The "Hansen Suspension"

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

Carta, David G.

Considered in detail are problems which led to the need and use of the 'Hansen Suspension'. Also discussed are problems which are likely to be encountered in any low level thrust measuring system. The methods of calibration and the accuracies involved are given careful attention. With all parameters optimized and calibration techniques perfected, the system was found capable of a resolution of 10 {mu} lbs. A comparison of thrust measurements made by the 'Hansen Suspension' with measurements of a less sophisticated device leads to some surprising results.

Self-Adaptive Stepsize Search Applied to Optimal Structural Design

NASA Astrophysics Data System (ADS)

Nolle, L.; Bland, J. A.

Structural engineering often involves the design of space frames that are required to resist predefined external forces without exhibiting plastic deformation. The weight of the structure and hence the weight of its constituent members has to be as low as possible for economical reasons without violating any of the load constraints. Design spaces are usually vast and the computational costs for analyzing a single design are usually high. Therefore, not every possible design can be evaluated for real-world problems. In this work, a standard structural design problem, the 25-bar problem, has been solved using self-adaptive stepsize search (SASS), a relatively new search heuristic. This algorithm has only one control parameter and therefore overcomes the drawback of modern search heuristics, i.e. the need to first find a set of optimum control parameter settings for the problem at hand. In this work, SASS outperforms simulated-annealing, genetic algorithms, tabu search and ant colony optimization.

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.

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

Vehicle routing problem with time windows using natural inspired algorithms

NASA Astrophysics Data System (ADS)

Pratiwi, A. B.; Pratama, A.; Sa’diyah, I.; Suprajitno, H.

2018-03-01

Process of distribution of goods needs a strategy to make the total cost spent for operational activities minimized. But there are several constrains have to be satisfied which are the capacity of the vehicles and the service time of the customers. This Vehicle Routing Problem with Time Windows (VRPTW) gives complex constrains problem. This paper proposes natural inspired algorithms for dealing with constrains of VRPTW which involves Bat Algorithm and Cat Swarm Optimization. Bat Algorithm is being hybrid with Simulated Annealing, the worst solution of Bat Algorithm is replaced by the solution from Simulated Annealing. Algorithm which is based on behavior of cats, Cat Swarm Optimization, is improved using Crow Search Algorithm to make simplier and faster convergence. From the computational result, these algorithms give good performances in finding the minimized total distance. Higher number of population causes better computational performance. The improved Cat Swarm Optimization with Crow Search gives better performance than the hybridization of Bat Algorithm and Simulated Annealing in dealing with big data.

Multirate sampled-data yaw-damper and modal suppression system design

NASA Technical Reports Server (NTRS)

Berg, Martin C.; Mason, Gregory S.

1990-01-01

A multirate control law synthesized algorithm based on an infinite-time quadratic cost function, was developed along with a method for analyzing the robustness of multirate systems. A generalized multirate sampled-data control law structure (GMCLS) was introduced. A new infinite-time-based parameter optimization multirate sampled-data control law synthesis method and solution algorithm were developed. A singular-value-based method for determining gain and phase margins for multirate systems was also developed. The finite-time-based parameter optimization multirate sampled-data control law synthesis algorithm originally intended to be applied to the aircraft problem was instead demonstrated by application to a simpler problem involving the control of the tip position of a two-link robot arm. The GMCLS, the infinite-time-based parameter optimization multirate control law synthesis method and solution algorithm, and the singular-value based method for determining gain and phase margins were all demonstrated by application to the aircraft control problem originally proposed for this project.

Optimal Culling and Biocontrol in a Predator-Prey Model.

PubMed

Numfor, Eric; Hilker, Frank M; Lenhart, Suzanne

2017-01-01

Invasive species cause enormous problems in ecosystems around the world. Motivated by introduced feral cats that prey on bird populations and threaten to drive them extinct on remote oceanic islands, we formulate and analyze optimal control problems. Their novelty is that they involve both scalar and time-dependent controls. They represent different forms of control, namely the initial release of infected predators on the one hand and culling as well as trapping, infecting, and returning predators on the other hand. Combinations of different control methods have been proposed to complement their respective strengths in reducing predator numbers and thus protecting endangered prey. Here, we formulate and analyze an eco-epidemiological model, provide analytical results on the optimal control problem, and use a forward-backward sweep method for numerical simulations. By taking into account different ecological scenarios, initial conditions, and control durations, our model allows to gain insight how the different methods interact and in which cases they could be effective.

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.

Performance evaluation of different types of particle representation procedures of Particle Swarm Optimization in Job-shop Scheduling Problems

NASA Astrophysics Data System (ADS)

Izah Anuar, Nurul; Saptari, Adi

2016-02-01

This paper addresses the types of particle representation (encoding) procedures in a population-based stochastic optimization technique in solving scheduling problems known in the job-shop manufacturing environment. It intends to evaluate and compare the performance of different particle representation procedures in Particle Swarm Optimization (PSO) in the case of solving Job-shop Scheduling Problems (JSP). Particle representation procedures refer to the mapping between the particle position in PSO and the scheduling solution in JSP. It is an important step to be carried out so that each particle in PSO can represent a schedule in JSP. Three procedures such as Operation and Particle Position Sequence (OPPS), random keys representation and random-key encoding scheme are used in this study. These procedures have been tested on FT06 and FT10 benchmark problems available in the OR-Library, where the objective function is to minimize the makespan by the use of MATLAB software. Based on the experimental results, it is discovered that OPPS gives the best performance in solving both benchmark problems. The contribution of this paper is the fact that it demonstrates to the practitioners involved in complex scheduling problems that different particle representation procedures can have significant effects on the performance of PSO in solving JSP.

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.

Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Reich, Simeon; Rosen, I. G.

1988-01-01

An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.

Robust Maneuvering Envelope Estimation Based on Reachability Analysis in an Optimal Control Formulation

NASA Technical Reports Server (NTRS)

Lombaerts, Thomas; Schuet, Stefan R.; Wheeler, Kevin; Acosta, Diana; Kaneshige, John

2013-01-01

This paper discusses an algorithm for estimating the safe maneuvering envelope of damaged aircraft. The algorithm performs a robust reachability analysis through an optimal control formulation while making use of time scale separation and taking into account uncertainties in the aerodynamic derivatives. Starting with an optimal control formulation, the optimization problem can be rewritten as a Hamilton- Jacobi-Bellman equation. This equation can be solved by level set methods. This approach has been applied on an aircraft example involving structural airframe damage. Monte Carlo validation tests have confirmed that this approach is successful in estimating the safe maneuvering envelope for damaged aircraft.

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

Simonetto, Andrea; Dall'Anese, Emiliano

This article develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve prediction-correction steps to provably track the trajectory of the optimal solutions of time-varying convex problems. The merits of existing prediction-correction methods have been shown for unconstrained problems and for setups where computing the inverse of the Hessian of the cost function is computationally affordable. This paper addresses the limitations of existing methods by tackling constrained problems and by designing first-order prediction steps that rely on the Hessian of the cost function (and do notmore » require the computation of its inverse). In addition, the proposed methods are shown to improve the convergence speed of existing prediction-correction methods when applied to unconstrained problems. Numerical simulations corroborate the analytical results and showcase performance and benefits of the proposed algorithms. A realistic application of the proposed method to real-time control of energy resources is presented.« less

Experimental quantum annealing: case study involving the graph isomorphism problem.

PubMed

Zick, Kenneth M; Shehab, Omar; French, Matthew

2015-06-08

Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical pre- and post-processing; at this early stage, little is known about how to partition and optimize the processing. This article presents an experimental case study of quantum annealing and some of the factors involved in real-world solvers, using a 504-qubit D-Wave Two machine and the graph isomorphism problem. To illustrate the role of classical pre-processing, a compact Hamiltonian is presented that enables a reduced Ising model for each problem instance. On random N-vertex graphs, the median number of variables is reduced from N(2) to fewer than N log2 N and solvable graph sizes increase from N = 5 to N = 13. Additionally, error correction via classical post-processing majority voting is evaluated. While the solution times are not competitive with classical approaches to graph isomorphism, the enhanced solver ultimately classified correctly every problem that was mapped to the processor and demonstrated clear advantages over the baseline approach. The results shed some light on the nature of real-world quantum annealing and the associated hybrid classical-quantum solvers.

Experimental quantum annealing: case study involving the graph isomorphism problem

PubMed Central

Zick, Kenneth M.; Shehab, Omar; French, Matthew

2015-01-01

Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical pre- and post-processing; at this early stage, little is known about how to partition and optimize the processing. This article presents an experimental case study of quantum annealing and some of the factors involved in real-world solvers, using a 504-qubit D-Wave Two machine and the graph isomorphism problem. To illustrate the role of classical pre-processing, a compact Hamiltonian is presented that enables a reduced Ising model for each problem instance. On random N-vertex graphs, the median number of variables is reduced from N2 to fewer than N log2 N and solvable graph sizes increase from N = 5 to N = 13. Additionally, error correction via classical post-processing majority voting is evaluated. While the solution times are not competitive with classical approaches to graph isomorphism, the enhanced solver ultimately classified correctly every problem that was mapped to the processor and demonstrated clear advantages over the baseline approach. The results shed some light on the nature of real-world quantum annealing and the associated hybrid classical-quantum solvers. PMID:26053973

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.

Software Performs Complex Design Analysis

NASA Technical Reports Server (NTRS)

2008-01-01

Designers use computational fluid dynamics (CFD) to gain greater understanding of the fluid flow phenomena involved in components being designed. They also use finite element analysis (FEA) as a tool to help gain greater understanding of the structural response of components to loads, stresses and strains, and the prediction of failure modes. Automated CFD and FEA engineering design has centered on shape optimization, which has been hindered by two major problems: 1) inadequate shape parameterization algorithms, and 2) inadequate algorithms for CFD and FEA grid modification. Working with software engineers at Stennis Space Center, a NASA commercial partner, Optimal Solutions Software LLC, was able to utilize its revolutionary, one-of-a-kind arbitrary shape deformation (ASD) capability-a major advancement in solving these two aforementioned problems-to optimize the shapes of complex pipe components that transport highly sensitive fluids. The ASD technology solves the problem of inadequate shape parameterization algorithms by allowing the CFD designers to freely create their own shape parameters, therefore eliminating the restriction of only being able to use the computer-aided design (CAD) parameters. The problem of inadequate algorithms for CFD grid modification is solved by the fact that the new software performs a smooth volumetric deformation. This eliminates the extremely costly process of having to remesh the grid for every shape change desired. The program can perform a design change in a markedly reduced amount of time, a process that would traditionally involve the designer returning to the CAD model to reshape and then remesh the shapes, something that has been known to take hours, days-even weeks or months-depending upon the size of the model.

Simulating variable source problems via post processing of individual particle tallies

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

Bleuel, D.L.; Donahue, R.J.; Ludewigt, B.A.

2000-10-20

Monte Carlo is an extremely powerful method of simulating complex, three dimensional environments without excessive problem simplification. However, it is often time consuming to simulate models in which the source can be highly varied. Similarly difficult are optimization studies involving sources in which many input parameters are variable, such as particle energy, angle, and spatial distribution. Such studies are often approached using brute force methods or intelligent guesswork. One field in which these problems are often encountered is accelerator-driven Boron Neutron Capture Therapy (BNCT) for the treatment of cancers. Solving the reverse problem of determining the best neutron source formore » optimal BNCT treatment can be accomplished by separating the time-consuming particle-tracking process of a full Monte Carlo simulation from the calculation of the source weighting factors which is typically performed at the beginning of a Monte Carlo simulation. By post-processing these weighting factors on a recorded file of individual particle tally information, the effect of changing source variables can be realized in a matter of seconds, instead of requiring hours or days for additional complete simulations. By intelligent source biasing, any number of different source distributions can be calculated quickly from a single Monte Carlo simulation. The source description can be treated as variable and the effect of changing multiple interdependent source variables on the problem's solution can be determined. Though the focus of this study is on BNCT applications, this procedure may be applicable to any problem that involves a variable source.« less

Surgery scheduling optimization considering real life constraints and comprehensive operation cost of operating room.

PubMed

Xiang, Wei; Li, Chong

2015-01-01

Operating Room (OR) is the core sector in hospital expenditure, the operation management of which involves a complete three-stage surgery flow, multiple resources, prioritization of the various surgeries, and several real-life OR constraints. As such reasonable surgery scheduling is crucial to OR management. To optimize OR management and reduce operation cost, a short-term surgery scheduling problem is proposed and defined based on the survey of the OR operation in a typical hospital in China. The comprehensive operation cost is clearly defined considering both under-utilization and overutilization. A nested Ant Colony Optimization (nested-ACO) incorporated with several real-life OR constraints is proposed to solve such a combinatorial optimization problem. The 10-day manual surgery schedules from a hospital in China are compared with the optimized schedules solved by the nested-ACO. Comparison results show the advantage using the nested-ACO in several measurements: OR-related time, nurse-related time, variation in resources' working time, and the end time. The nested-ACO considering real-life operation constraints such as the difference between first and following case, surgeries priority, and fixed nurses in pre/post-operative stage is proposed to solve the surgery scheduling optimization problem. The results clearly show the benefit of using the nested-ACO in enhancing the OR management efficiency and minimizing the comprehensive overall operation cost.

Enhanced Multiobjective Optimization Technique for Comprehensive Aerospace Design. Part A

NASA Technical Reports Server (NTRS)

Chattopadhyay, Aditi; Rajadas, John N.

1997-01-01

A multidisciplinary design optimization procedure which couples formal multiobjectives based techniques and complex analysis procedures (such as computational fluid dynamics (CFD) codes) developed. The procedure has been demonstrated on a specific high speed flow application involving aerodynamics and acoustics (sonic boom minimization). In order to account for multiple design objectives arising from complex performance requirements, multiobjective formulation techniques are used to formulate the optimization problem. Techniques to enhance the existing Kreisselmeier-Steinhauser (K-S) function multiobjective formulation approach have been developed. The K-S function procedure used in the proposed work transforms a constrained multiple objective functions problem into an unconstrained problem which then is solved using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. Weight factors are introduced during the transformation process to each objective function. This enhanced procedure will provide the designer the capability to emphasize specific design objectives during the optimization process. The demonstration of the procedure utilizes a computational Fluid dynamics (CFD) code which solves the three-dimensional parabolized Navier-Stokes (PNS) equations for the flow field along with an appropriate sonic boom evaluation procedure thus introducing both aerodynamic performance as well as sonic boom as the design objectives to be optimized simultaneously. Sensitivity analysis is performed using a discrete differentiation approach. An approximation technique has been used within the optimizer to improve the overall computational efficiency of the procedure in order to make it suitable for design applications in an industrial setting.

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.

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.

Integrating NOE and RDC using sum-of-squares relaxation for protein structure determination.

PubMed

Khoo, Y; Singer, A; Cowburn, D

2017-07-01

We revisit the problem of protein structure determination from geometrical restraints from NMR, using convex optimization. It is well-known that the NP-hard distance geometry problem of determining atomic positions from pairwise distance restraints can be relaxed into a convex semidefinite program (SDP). However, often the NOE distance restraints are too imprecise and sparse for accurate structure determination. Residual dipolar coupling (RDC) measurements provide additional geometric information on the angles between atom-pair directions and axes of the principal-axis-frame. The optimization problem involving RDC is highly non-convex and requires a good initialization even within the simulated annealing framework. In this paper, we model the protein backbone as an articulated structure composed of rigid units. Determining the rotation of each rigid unit gives the full protein structure. We propose solving the non-convex optimization problems using the sum-of-squares (SOS) hierarchy, a hierarchy of convex relaxations with increasing complexity and approximation power. Unlike classical global optimization approaches, SOS optimization returns a certificate of optimality if the global optimum is found. Based on the SOS method, we proposed two algorithms-RDC-SOS and RDC-NOE-SOS, that have polynomial time complexity in the number of amino-acid residues and run efficiently on a standard desktop. In many instances, the proposed methods exactly recover the solution to the original non-convex optimization problem. To the best of our knowledge this is the first time SOS relaxation is introduced to solve non-convex optimization problems in structural biology. We further introduce a statistical tool, the Cramér-Rao bound (CRB), to provide an information theoretic bound on the highest resolution one can hope to achieve when determining protein structure from noisy measurements using any unbiased estimator. Our simulation results show that when the RDC measurements are corrupted by Gaussian noise of realistic variance, both SOS based algorithms attain the CRB. We successfully apply our method in a divide-and-conquer fashion to determine the structure of ubiquitin from experimental NOE and RDC measurements obtained in two alignment media, achieving more accurate and faster reconstructions compared to the current state of the art.

Students’ difficulties in probabilistic problem-solving

NASA Astrophysics Data System (ADS)

Arum, D. P.; Kusmayadi, T. A.; Pramudya, I.

2018-03-01

There are many errors can be identified when students solving mathematics problems, particularly in solving the probabilistic problem. This present study aims to investigate students’ difficulties in solving the probabilistic problem. It focuses on analyzing and describing students errors during solving the problem. This research used the qualitative method with case study strategy. The subjects in this research involve ten students of 9th grade that were selected by purposive sampling. Data in this research involve students’ probabilistic problem-solving result and recorded interview regarding students’ difficulties in solving the problem. Those data were analyzed descriptively using Miles and Huberman steps. The results show that students have difficulties in solving the probabilistic problem and can be divided into three categories. First difficulties relate to students’ difficulties in understanding the probabilistic problem. Second, students’ difficulties in choosing and using appropriate strategies for solving the problem. Third, students’ difficulties with the computational process in solving the problem. Based on the result seems that students still have difficulties in solving the probabilistic problem. It means that students have not able to use their knowledge and ability for responding probabilistic problem yet. Therefore, it is important for mathematics teachers to plan probabilistic learning which could optimize students probabilistic thinking ability.

On optimal dividends: From reflection to refraction

NASA Astrophysics Data System (ADS)

Gerber, Hans U.; Shiu, Elias S. W.

2006-02-01

The problem goes back to a paper that Bruno de Finetti presented to the International Congress of Actuaries in New York (1957). In a stock company that is involved in risky business, what is the optimal dividend strategy, that is, what is the strategy that maximizes the expectation of the discounted dividends (until possible ruin) to the shareholders? Jeanblanc-Picque and Shiryaev [Russian Math. Surveys 20 (1995) 257-277] and Asmussen and Taksar [Insurance: Math. Econom. 20 (1997) 1-15] solved the problem by modeling the income process of the company by a Wiener process and imposing the condition of a bounded dividend rate. Here, we present some down-to-earth calculations in this context.

Optimal experimental design for placement of boreholes

NASA Astrophysics Data System (ADS)

Padalkina, Kateryna; Bücker, H. Martin; Seidler, Ralf; Rath, Volker; Marquart, Gabriele; Niederau, Jan; Herty, Michael

2014-05-01

Drilling for deep resources is an expensive endeavor. Among the many problems finding the optimal drilling location for boreholes is one of the challenging questions. We contribute to this discussion by using a simulation based assessment of possible future borehole locations. We study the problem of finding a new borehole location in a given geothermal reservoir in terms of a numerical optimization problem. In a geothermal reservoir the temporal and spatial distribution of temperature and hydraulic pressure may be simulated using the coupled differential equations for heat transport and mass and momentum conservation for Darcy flow. Within this model the permeability and thermal conductivity are dependent on the geological layers present in the subsurface model of the reservoir. In general, those values involve some uncertainty making it difficult to predict actual heat source in the ground. Within optimal experimental the question is which location and to which depth to drill the borehole in order to estimate conductivity and permeability with minimal uncertainty. We introduce a measure for computing the uncertainty based on simulations of the coupled differential equations. The measure is based on the Fisher information matrix of temperature data obtained through the simulations. We assume that the temperature data is available within the full borehole. A minimization of the measure representing the uncertainty in the unknown permeability and conductivity parameters is performed to determine the optimal borehole location. We present the theoretical framework as well as numerical results for several 2d subsurface models including up to six geological layers. Also, the effect of unknown layers on the introduced measure is studied. Finally, to obtain a more realistic estimate of optimal borehole locations, we couple the optimization to a cost model for deep drilling problems.

Multivariable optimization of an auto-thermal ammonia synthesis reactor using genetic algorithm

NASA Astrophysics Data System (ADS)

Anh-Nga, Nguyen T.; Tuan-Anh, Nguyen; Tien-Dung, Vu; Kim-Trung, Nguyen

2017-09-01

The ammonia synthesis system is an important chemical process used in the manufacture of fertilizers, chemicals, explosives, fibers, plastics, refrigeration. In the literature, many works approaching the modeling, simulation and optimization of an auto-thermal ammonia synthesis reactor can be found. However, they just focus on the optimization of the reactor length while keeping the others parameters constant. In this study, the other parameters are also considered in the optimization problem such as the temperature of feed gas enters the catalyst zone. The optimal problem requires the maximization of a multivariable objective function which subjects to a number of equality constraints involving the solution of coupled differential equations and also inequality constraints. The solution of an optimization problem can be found through, among others, deterministic or stochastic approaches. The stochastic methods, such as evolutionary algorithm (EA), which is based on natural phenomenon, can overcome the drawbacks such as the requirement of the derivatives of the objective function and/or constraints, or being not efficient in non-differentiable or discontinuous problems. Genetic algorithm (GA) which is a class of EA, exceptionally simple, robust at numerical optimization and is more likely to find a true global optimum. In this study, the genetic algorithm is employed to find the optimum profit of the process. The inequality constraints were treated using penalty method. The coupled differential equations system was solved using Runge-Kutta 4th order method. The results showed that the presented numerical method could be applied to model the ammonia synthesis reactor. The optimum economic profit obtained from this study are also compared to the results from the literature. It suggests that the process should be operated at higher temperature of feed gas in catalyst zone and the reactor length is slightly longer.

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

Weighted interior penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows

NASA Astrophysics Data System (ADS)

Di Pietro, Daniele A.; Marche, Fabien

2018-02-01

In this paper, we further investigate the use of a fully discontinuous Finite Element discrete formulation for the study of shallow water free surface flows in the fully nonlinear and weakly dispersive flow regime. We consider a decoupling strategy in which we approximate the solutions of the classical shallow water equations supplemented with a source term globally accounting for the non-hydrostatic effects. This source term can be computed through the resolution of elliptic second-order linear sub-problems, which only involve second order partial derivatives in space. We then introduce an associated Symmetric Weighted Internal Penalty discrete bilinear form, allowing to deal with the discontinuous nature of the elliptic problem's coefficients in a stable and consistent way. Similar discrete formulations are also introduced for several recent optimized fully nonlinear and weakly dispersive models. These formulations are validated again several benchmarks involving h-convergence, p-convergence and comparisons with experimental data, showing optimal convergence properties.

The feasibility of manual parameter tuning for deformable breast MR image registration from a multi-objective optimization perspective.

PubMed

Pirpinia, Kleopatra; Bosman, Peter A N; Loo, Claudette E; Winter-Warnars, Gonneke; Janssen, Natasja N Y; Scholten, Astrid N; Sonke, Jan-Jakob; van Herk, Marcel; Alderliesten, Tanja

2017-06-23

Deformable image registration is typically formulated as an optimization problem involving a linearly weighted combination of terms that correspond to objectives of interest (e.g. similarity, deformation magnitude). The weights, along with multiple other parameters, need to be manually tuned for each application, a task currently addressed mainly via trial-and-error approaches. Such approaches can only be successful if there is a sensible interplay between parameters, objectives, and desired registration outcome. This, however, is not well established. To study this interplay, we use multi-objective optimization, where multiple solutions exist that represent the optimal trade-offs between the objectives, forming a so-called Pareto front. Here, we focus on weight tuning. To study the space a user has to navigate during manual weight tuning, we randomly sample multiple linear combinations. To understand how these combinations relate to desirability of registration outcome, we associate with each outcome a mean target registration error (TRE) based on expert-defined anatomical landmarks. Further, we employ a multi-objective evolutionary algorithm that optimizes the weight combinations, yielding a Pareto front of solutions, which can be directly navigated by the user. To study how the complexity of manual weight tuning changes depending on the registration problem, we consider an easy problem, prone-to-prone breast MR image registration, and a hard problem, prone-to-supine breast MR image registration. Lastly, we investigate how guidance information as an additional objective influences the prone-to-supine registration outcome. Results show that the interplay between weights, objectives, and registration outcome makes manual weight tuning feasible for the prone-to-prone problem, but very challenging for the harder prone-to-supine problem. Here, patient-specific, multi-objective weight optimization is needed, obtaining a mean TRE of 13.6 mm without guidance information reduced to 7.3 mm with guidance information, but also providing a Pareto front that exhibits an intuitively sensible interplay between weights, objectives, and registration outcome, allowing outcome selection.

The feasibility of manual parameter tuning for deformable breast MR image registration from a multi-objective optimization perspective

NASA Astrophysics Data System (ADS)

Pirpinia, Kleopatra; Bosman, Peter A. N.; E Loo, Claudette; Winter-Warnars, Gonneke; Y Janssen, Natasja N.; Scholten, Astrid N.; Sonke, Jan-Jakob; van Herk, Marcel; Alderliesten, Tanja

2017-07-01

Deformable image registration is typically formulated as an optimization problem involving a linearly weighted combination of terms that correspond to objectives of interest (e.g. similarity, deformation magnitude). The weights, along with multiple other parameters, need to be manually tuned for each application, a task currently addressed mainly via trial-and-error approaches. Such approaches can only be successful if there is a sensible interplay between parameters, objectives, and desired registration outcome. This, however, is not well established. To study this interplay, we use multi-objective optimization, where multiple solutions exist that represent the optimal trade-offs between the objectives, forming a so-called Pareto front. Here, we focus on weight tuning. To study the space a user has to navigate during manual weight tuning, we randomly sample multiple linear combinations. To understand how these combinations relate to desirability of registration outcome, we associate with each outcome a mean target registration error (TRE) based on expert-defined anatomical landmarks. Further, we employ a multi-objective evolutionary algorithm that optimizes the weight combinations, yielding a Pareto front of solutions, which can be directly navigated by the user. To study how the complexity of manual weight tuning changes depending on the registration problem, we consider an easy problem, prone-to-prone breast MR image registration, and a hard problem, prone-to-supine breast MR image registration. Lastly, we investigate how guidance information as an additional objective influences the prone-to-supine registration outcome. Results show that the interplay between weights, objectives, and registration outcome makes manual weight tuning feasible for the prone-to-prone problem, but very challenging for the harder prone-to-supine problem. Here, patient-specific, multi-objective weight optimization is needed, obtaining a mean TRE of 13.6 mm without guidance information reduced to 7.3 mm with guidance information, but also providing a Pareto front that exhibits an intuitively sensible interplay between weights, objectives, and registration outcome, allowing outcome selection.

Minimizing transient influence in WHPA delineation: An optimization approach for optimal pumping rate schemes

NASA Astrophysics Data System (ADS)

Rodriguez-Pretelin, A.; Nowak, W.

2017-12-01

For most groundwater protection management programs, Wellhead Protection Areas (WHPAs) have served as primarily protection measure. In their delineation, the influence of time-varying groundwater flow conditions is often underestimated because steady-state assumptions are commonly made. However, it has been demonstrated that temporary variations lead to significant changes in the required size and shape of WHPAs. Apart from natural transient groundwater drivers (e.g., changes in the regional angle of flow direction and seasonal natural groundwater recharge), anthropogenic causes such as transient pumping rates are of the most influential factors that require larger WHPAs. We hypothesize that WHPA programs that integrate adaptive and optimized pumping-injection management schemes can counter transient effects and thus reduce the additional areal demand in well protection under transient conditions. The main goal of this study is to present a novel management framework that optimizes pumping schemes dynamically, in order to minimize the impact triggered by transient conditions in WHPA delineation. For optimizing pumping schemes, we consider three objectives: 1) to minimize the risk of pumping water from outside a given WHPA, 2) to maximize the groundwater supply and 3) to minimize the involved operating costs. We solve transient groundwater flow through an available transient groundwater and Lagrangian particle tracking model. The optimization problem is formulated as a dynamic programming problem. Two different optimization approaches are explored: I) the first approach aims for single-objective optimization under objective (1) only. The second approach performs multiobjective optimization under all three objectives where compromise pumping rates are selected from the current Pareto front. Finally, we look for WHPA outlines that are as small as possible, yet allow the optimization problem to find the most suitable solutions.

Upper Limits for Power Yield in Thermal, Chemical, and Electrochemical Systems

NASA Astrophysics Data System (ADS)

Sieniutycz, Stanislaw

2010-03-01

We consider modeling and power optimization of energy converters, such as thermal, solar and chemical engines and fuel cells. Thermodynamic principles lead to expressions for converter's efficiency and generated power. Efficiency equations serve to solve the problems of upgrading or downgrading a resource. Power yield is a cumulative effect in a system consisting of a resource, engines, and an infinite bath. While optimization of steady state systems requires using the differential calculus and Lagrange multipliers, dynamic optimization involves variational calculus and dynamic programming. The primary result of static optimization is the upper limit of power, whereas that of dynamic optimization is a finite-rate counterpart of classical reversible work (exergy). The latter quantity depends on the end state coordinates and a dissipation index, h, which is the Hamiltonian of the problem of minimum entropy production. In reacting systems, an active part of chemical affinity constitutes a major component of the overall efficiency. The theory is also applied to fuel cells regarded as electrochemical flow engines. Enhanced bounds on power yield follow, which are stronger than those predicted by the reversible work potential.

An improved parent-centric mutation with normalized neighborhoods for inducing niching behavior in differential evolution.

PubMed

Biswas, Subhodip; Kundu, Souvik; Das, Swagatam

2014-10-01

In real life, we often need to find multiple optimally sustainable solutions of an optimization problem. Evolutionary multimodal optimization algorithms can be very helpful in such cases. They detect and maintain multiple optimal solutions during the run by incorporating specialized niching operations in their actual framework. Differential evolution (DE) is a powerful evolutionary algorithm (EA) well-known for its ability and efficiency as a single peak global optimizer for continuous spaces. This article suggests a niching scheme integrated with DE for achieving a stable and efficient niching behavior by combining the newly proposed parent-centric mutation operator with synchronous crowding replacement rule. The proposed approach is designed by considering the difficulties associated with the problem dependent niching parameters (like niche radius) and does not make use of such control parameter. The mutation operator helps to maintain the population diversity at an optimum level by using well-defined local neighborhoods. Based on a comparative study involving 13 well-known state-of-the-art niching EAs tested on an extensive collection of benchmarks, we observe a consistent statistical superiority enjoyed by our proposed niching algorithm.

Layout optimization using the homogenization method

NASA Technical Reports Server (NTRS)

Suzuki, Katsuyuki; Kikuchi, Noboru

1993-01-01

A generalized layout problem involving sizing, shape, and topology optimization is solved by using the homogenization method for three-dimensional linearly elastic shell structures in order to seek a possibility of establishment of an integrated design system of automotive car bodies, as an extension of the previous work by Bendsoe and Kikuchi. A formulation of a three-dimensional homogenized shell, a solution algorithm, and several examples of computing the optimum layout are presented in this first part of the two articles.

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.

Reactive power planning under high penetration of wind energy using Benders decomposition

DOE PAGES

Xu, Yan; Wei, Yanli; Fang, Xin; ...

2015-11-05

This study addresses the optimal allocation of reactive power volt-ampere reactive (VAR) sources under the paradigm of high penetration of wind energy. Reactive power planning (RPP) in this particular condition involves a high level of uncertainty because of wind power characteristic. To properly model wind generation uncertainty, a multi-scenario framework optimal power flow that considers the voltage stability constraint under the worst wind scenario and transmission N 1 contingency is developed. The objective of RPP in this study is to minimise the total cost including the VAR investment cost and the expected generation cost. Therefore RPP under this condition ismore » modelled as a two-stage stochastic programming problem to optimise the VAR location and size in one stage, then to minimise the fuel cost in the other stage, and eventually, to find the global optimal RPP results iteratively. Benders decomposition is used to solve this model with an upper level problem (master problem) for VAR allocation optimisation and a lower problem (sub-problem) for generation cost minimisation. Impact of the potential reactive power support from doubly-fed induction generator (DFIG) is also analysed. Lastly, case studies on the IEEE 14-bus and 118-bus systems are provided to verify the proposed method.« less

Seismic waveform inversion best practices: regional, global and exploration test cases

NASA Astrophysics Data System (ADS)

Modrak, Ryan; Tromp, Jeroen

2016-09-01

Reaching the global minimum of a waveform misfit function requires careful choices about the nonlinear optimization, preconditioning and regularization methods underlying an inversion. Because waveform inversion problems are susceptible to erratic convergence associated with strong nonlinearity, one or two test cases are not enough to reliably inform such decisions. We identify best practices, instead, using four seismic near-surface problems, one regional problem and two global problems. To make meaningful quantitative comparisons between methods, we carry out hundreds of inversions, varying one aspect of the implementation at a time. Comparing nonlinear optimization algorithms, we find that limited-memory BFGS provides computational savings over nonlinear conjugate gradient methods in a wide range of test cases. Comparing preconditioners, we show that a new diagonal scaling derived from the adjoint of the forward operator provides better performance than two conventional preconditioning schemes. Comparing regularization strategies, we find that projection, convolution, Tikhonov regularization and total variation regularization are effective in different contexts. Besides questions of one strategy or another, reliability and efficiency in waveform inversion depend on close numerical attention and care. Implementation details involving the line search and restart conditions have a strong effect on computational cost, regardless of the chosen nonlinear optimization algorithm.

New Approaches to HSCT Multidisciplinary Design and Optimization

NASA Technical Reports Server (NTRS)

Schrage, D. P.; Craig, J. I.; Fulton, R. E.; Mistree, F.

1996-01-01

The successful development of a capable and economically viable high speed civil transport (HSCT) is perhaps one of the most challenging tasks in aeronautics for the next two decades. At its heart it is fundamentally the design of a complex engineered system that has significant societal, environmental and political impacts. As such it presents a formidable challenge to all areas of aeronautics, and it is therefore a particularly appropriate subject for research in multidisciplinary design and optimization (MDO). In fact, it is starkly clear that without the availability of powerful and versatile multidisciplinary design, analysis and optimization methods, the design, construction and operation of im HSCT simply cannot be achieved. The present research project is focused on the development and evaluation of MDO methods that, while broader and more general in scope, are particularly appropriate to the HSCT design problem. The research aims to not only develop the basic methods but also to apply them to relevant examples from the NASA HSCT R&D effort. The research involves a three year effort aimed first at the HSCT MDO problem description, next the development of the problem, and finally a solution to a significant portion of the problem.

Algorithms for Heterogeneous, Multiple Depot, Multiple Unmanned Vehicle Path Planning Problems

DOE PAGES

Sundar, Kaarthik; Rathinam, Sivakumar

2016-12-26

Unmanned vehicles, both aerial and ground, are being used in several monitoring applications to collect data from a set of targets. This article addresses a problem where a group of heterogeneous aerial or ground vehicles with different motion constraints located at distinct depots visit a set of targets. The vehicles also may be equipped with different sensors, and therefore, a target may not be visited by any vehicle. The objective is to find an optimal path for each vehicle starting and ending at its respective depot such that each target is visited at least once by some vehicle, the vehicle–targetmore » constraints are satisfied, and the sum of the length of the paths for all the vehicles is minimized. Two variants of this problem are formulated (one for ground vehicles and another for aerial vehicles) as mixed-integer linear programs and a branchand- cut algorithm is developed to compute an optimal solution to each of the variants. Computational results show that optimal solutions for problems involving 100 targets and 5 vehicles can be obtained within 300 seconds on average, further corroborating the effectiveness of the proposed approach.« less

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.

Reliability-based optimization of maintenance scheduling of mechanical components under fatigue

PubMed Central

Beaurepaire, P.; Valdebenito, M.A.; Schuëller, G.I.; Jensen, H.A.

2012-01-01

This study presents the optimization of the maintenance scheduling of mechanical components under fatigue loading. The cracks of damaged structures may be detected during non-destructive inspection and subsequently repaired. Fatigue crack initiation and growth show inherent variability, and as well the outcome of inspection activities. The problem is addressed under the framework of reliability based optimization. The initiation and propagation of fatigue cracks are efficiently modeled using cohesive zone elements. The applicability of the method is demonstrated by a numerical example, which involves a plate with two holes subject to alternating stress. PMID:23564979

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.

Optimization of magnet end-winding geometry

NASA Astrophysics Data System (ADS)

Reusch, Michael F.; Weissenburger, Donald W.; Nearing, James C.

1994-03-01

A simple, almost entirely analytic, method for the optimization of stress-reduced magnet-end winding paths for ribbon-like superconducting cable is presented. This technique is based on characterization of these paths as developable surfaces, i.e., surfaces whose intrinsic geometry is flat. The method is applicable to winding mandrels of arbitrary geometry. Computational searches for optimal winding paths are easily implemented via the technique. Its application to the end configuration of cylindrical Superconducting Super Collider (SSC)-type magnets is discussed. The method may be useful for other engineering problems involving the placement of thin sheets of material.

Optimal working zone division for safe track maintenance in The Netherlands.

PubMed

den Hertog, D; van Zante-de Fokkert, J I; Sjamaar, S A; Beusmans, R

2005-09-01

After a sequence of serious accidents, the safety of rail track workers became an urgent and political problem in The Netherlands. It turned out that the rail track workers had one of the most dangerous jobs. The board of the Dutch Railways decided that the Dutch railway infrastructure had to be divided into so-called working zones. Moreover, to carry out maintenance activities, that particular working zone of the railway system had to be taken out of service. An essential problem was how to divide the Dutch railway infrastructure into working zones such that all parties involved are satisfied. Since many parties with conflicting interests were involved, this problem was extremely difficult. In this paper we show the division rules we developed, and which had been implemented in The Netherlands.

Optimal scheduling of micro grids based on single objective programming

NASA Astrophysics Data System (ADS)

Chen, Yue

2018-04-01

Faced with the growing demand for electricity and the shortage of fossil fuels, how to optimally optimize the micro-grid has become an important research topic to maximize the economic, technological and environmental benefits of the micro-grid. This paper considers the role of the battery and the micro-grid and power grid to allow the exchange of power not exceeding 150kW preconditions, the main study of the economy to load for the goal is to minimize the electricity cost (abandonment of wind), to establish an optimization model, and to solve the problem by genetic algorithm. The optimal scheduling scheme is obtained and the utilization of renewable energy and the impact of the battery involved in regulation are analyzed.

Constrained Multiobjective Biogeography Optimization Algorithm

PubMed Central

Mo, Hongwei; Xu, Zhidan; Xu, Lifang; Wu, Zhou; Ma, Haiping

2014-01-01

Multiobjective optimization involves minimizing or maximizing multiple objective functions subject to a set of constraints. In this study, a novel constrained multiobjective biogeography optimization algorithm (CMBOA) is proposed. It is the first biogeography optimization algorithm for constrained multiobjective optimization. In CMBOA, a disturbance migration operator is designed to generate diverse feasible individuals in order to promote the diversity of individuals on Pareto front. Infeasible individuals nearby feasible region are evolved to feasibility by recombining with their nearest nondominated feasible individuals. The convergence of CMBOA is proved by using probability theory. The performance of CMBOA is evaluated on a set of 6 benchmark problems and experimental results show that the CMBOA performs better than or similar to the classical NSGA-II and IS-MOEA. PMID:25006591

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.

Cascaded Optimization for a Persistent Data Ferrying Unmanned Aircraft

NASA Astrophysics Data System (ADS)

Carfang, Anthony

This dissertation develops and assesses a cascaded method for designing optimal periodic trajectories and link schedules for an unmanned aircraft to ferry data between stationary ground nodes. This results in a fast solution method without the need to artificially constrain system dynamics. Focusing on a fundamental ferrying problem that involves one source and one destination, but includes complex vehicle and Radio-Frequency (RF) dynamics, a cascaded structure to the system dynamics is uncovered. This structure is exploited by reformulating the nonlinear optimization problem into one that reduces the independent control to the vehicle's motion, while the link scheduling control is folded into the objective function and implemented as an optimal policy that depends on candidate motion control. This formulation is proven to maintain optimality while reducing computation time in comparison to traditional ferry optimization methods. The discrete link scheduling problem takes the form of a combinatorial optimization problem that is known to be NP-Hard. A derived necessary condition for optimality guides the development of several heuristic algorithms, specifically the Most-Data-First Algorithm and the Knapsack Adaptation. These heuristics are extended to larger ferrying scenarios, and assessed analytically and through Monte Carlo simulation, showing better throughput performance in the same order of magnitude of computation time in comparison to other common link scheduling policies. The cascaded optimization method is implemented with a novel embedded software system on a small, unmanned aircraft to validate the simulation results with field experiments. To address the sensitivity of results on trajectory tracking performance, a system that combines motion and link control with waypoint-based navigation is developed and assessed through field experiments. The data ferrying algorithms are further extended by incorporating a Gaussian process to opportunistically learn the RF environment. By continuously improving RF models, the cascaded planner can continually improve the ferrying system's overall performance.

Optimization of shallow arches against instability using sensitivity derivatives

NASA Technical Reports Server (NTRS)

Kamat, Manohar P.

1987-01-01

The author discusses the problem of optimization of shallow frame structures which involve a coupling of axial and bending responses. A shallow arch of a given shape and of given weight is optimized such that its limit point load is maximized. The cross-sectional area, A(x) and the moment of inertia, I(x) of the arch obey the relationship I(x) = rho A(x) sup n, n = 1,2,3 and rho is a specified constant. Analysis of the arch for its limit point calculation involves a geometric nonlinear analysis which is performed using a corotational formulation. The optimization is carried out using a second-order projected Lagrangian algorithm and the sensitivity derivatives of the critical load parameter with respect to the areas of the finite elements of the arch are calculated using implicit differentation. Results are presented for an arch of a specified rise to span ratio under two different loadings and the limitations of the approach for the intermediate rise arches are addressed.

GMOtrack: generator of cost-effective GMO testing strategies.

PubMed

Novak, Petra Krau; Gruden, Kristina; Morisset, Dany; Lavrac, Nada; Stebih, Dejan; Rotter, Ana; Zel, Jana

2009-01-01

Commercialization of numerous genetically modified organisms (GMOs) has already been approved worldwide, and several additional GMOs are in the approval process. Many countries have adopted legislation to deal with GMO-related issues such as food safety, environmental concerns, and consumers' right of choice, making GMO traceability a necessity. The growing extent of GMO testing makes it important to study optimal GMO detection and identification strategies. This paper formally defines the problem of routine laboratory-level GMO tracking as a cost optimization problem, thus proposing a shift from "the same strategy for all samples" to "sample-centered GMO testing strategies." An algorithm (GMOtrack) for finding optimal two-phase (screening-identification) testing strategies is proposed. The advantages of cost optimization with increasing GMO presence on the market are demonstrated, showing that optimization approaches to analytic GMO traceability can result in major cost reductions. The optimal testing strategies are laboratory-dependent, as the costs depend on prior probabilities of local GMO presence, which are exemplified on food and feed samples. The proposed GMOtrack approach, publicly available under the terms of the General Public License, can be extended to other domains where complex testing is involved, such as safety and quality assurance in the food supply chain.

A Multiobjective Interval Programming Model for Wind-Hydrothermal Power System Dispatching Using 2-Step Optimization Algorithm

PubMed Central

Jihong, Qu

2014-01-01

Wind-hydrothermal power system dispatching has received intensive attention in recent years because it can help develop various reasonable plans to schedule the power generation efficiency. But future data such as wind power output and power load would not be accurately predicted and the nonlinear nature involved in the complex multiobjective scheduling model; therefore, to achieve accurate solution to such complex problem is a very difficult task. This paper presents an interval programming model with 2-step optimization algorithm to solve multiobjective dispatching. Initially, we represented the future data into interval numbers and simplified the object function to a linear programming problem to search the feasible and preliminary solutions to construct the Pareto set. Then the simulated annealing method was used to search the optimal solution of initial model. Thorough experimental results suggest that the proposed method performed reasonably well in terms of both operating efficiency and precision. PMID:24895663

A multiobjective interval programming model for wind-hydrothermal power system dispatching using 2-step optimization algorithm.

PubMed

Ren, Kun; Jihong, Qu

2014-01-01

Wind-hydrothermal power system dispatching has received intensive attention in recent years because it can help develop various reasonable plans to schedule the power generation efficiency. But future data such as wind power output and power load would not be accurately predicted and the nonlinear nature involved in the complex multiobjective scheduling model; therefore, to achieve accurate solution to such complex problem is a very difficult task. This paper presents an interval programming model with 2-step optimization algorithm to solve multiobjective dispatching. Initially, we represented the future data into interval numbers and simplified the object function to a linear programming problem to search the feasible and preliminary solutions to construct the Pareto set. Then the simulated annealing method was used to search the optimal solution of initial model. Thorough experimental results suggest that the proposed method performed reasonably well in terms of both operating efficiency and precision.

Scheduling Policies for an Antiterrorist Surveillance System

DTIC Science & Technology

2008-06-27

times; for example, see Reiman and Wein [17] and Olsen [15]. For real-time scheduling problems involving impatient customers, see Gaver et al. [2...heavy traffic with throughput time constraints: Asymptotically optimal dynamic controls. Queueing Systems 39, 23–54. 30 [17] Reiman , M. I. and Wein

Traumatic Brain Injury Inpatient Rehabilitation

ERIC Educational Resources Information Center

Im, Brian; Schrer, Marcia J.; Gaeta, Raphael; Elias, Eileen

2010-01-01

Traumatic brain injuries (TBI) can cause multiple medical and functional problems. As the brain is involved in regulating nearly every bodily function, a TBI can affect any part of the body and aspect of cognitive, behavioral, and physical functioning. However, TBI affects each individual differently. Optimal management requires understanding the…

Learning Incoherent Sparse and Low-Rank Patterns from Multiple Tasks

PubMed Central

Chen, Jianhui; Liu, Ji; Ye, Jieping

2013-01-01

We consider the problem of learning incoherent sparse and low-rank patterns from multiple tasks. Our approach is based on a linear multi-task learning formulation, in which the sparse and low-rank patterns are induced by a cardinality regularization term and a low-rank constraint, respectively. This formulation is non-convex; we convert it into its convex surrogate, which can be routinely solved via semidefinite programming for small-size problems. We propose to employ the general projected gradient scheme to efficiently solve such a convex surrogate; however, in the optimization formulation, the objective function is non-differentiable and the feasible domain is non-trivial. We present the procedures for computing the projected gradient and ensuring the global convergence of the projected gradient scheme. The computation of projected gradient involves a constrained optimization problem; we show that the optimal solution to such a problem can be obtained via solving an unconstrained optimization subproblem and an Euclidean projection subproblem. We also present two projected gradient algorithms and analyze their rates of convergence in details. In addition, we illustrate the use of the presented projected gradient algorithms for the proposed multi-task learning formulation using the least squares loss. Experimental results on a collection of real-world data sets demonstrate the effectiveness of the proposed multi-task learning formulation and the efficiency of the proposed projected gradient algorithms. PMID:24077658

Learning Incoherent Sparse and Low-Rank Patterns from Multiple Tasks.

PubMed

Chen, Jianhui; Liu, Ji; Ye, Jieping

2012-02-01

We consider the problem of learning incoherent sparse and low-rank patterns from multiple tasks. Our approach is based on a linear multi-task learning formulation, in which the sparse and low-rank patterns are induced by a cardinality regularization term and a low-rank constraint, respectively. This formulation is non-convex; we convert it into its convex surrogate, which can be routinely solved via semidefinite programming for small-size problems. We propose to employ the general projected gradient scheme to efficiently solve such a convex surrogate; however, in the optimization formulation, the objective function is non-differentiable and the feasible domain is non-trivial. We present the procedures for computing the projected gradient and ensuring the global convergence of the projected gradient scheme. The computation of projected gradient involves a constrained optimization problem; we show that the optimal solution to such a problem can be obtained via solving an unconstrained optimization subproblem and an Euclidean projection subproblem. We also present two projected gradient algorithms and analyze their rates of convergence in details. In addition, we illustrate the use of the presented projected gradient algorithms for the proposed multi-task learning formulation using the least squares loss. Experimental results on a collection of real-world data sets demonstrate the effectiveness of the proposed multi-task learning formulation and the efficiency of the proposed projected gradient algorithms.

An Explicit Linear Filtering Solution for the Optimization of Guidance Systems with Statistical Inputs

NASA Technical Reports Server (NTRS)

Stewart, Elwood C.

1961-01-01

The determination of optimum filtering characteristics for guidance system design is generally a tedious process which cannot usually be carried out in general terms. In this report a simple explicit solution is given which is applicable to many different types of problems. It is shown to be applicable to problems which involve optimization of constant-coefficient guidance systems and time-varying homing type systems for several stationary and nonstationary inputs. The solution is also applicable to off-design performance, that is, the evaluation of system performance for inputs for which the system was not specifically optimized. The solution is given in generalized form in terms of the minimum theoretical error, the optimum transfer functions, and the optimum transient response. The effects of input signal, contaminating noise, and limitations on the response are included. From the results given, it is possible in an interception problem, for example, to rapidly assess the effects on minimum theoretical error of such factors as target noise and missile acceleration. It is also possible to answer important questions regarding the effect of type of target maneuver on optimum performance.

A single-loop optimization method for reliability analysis with second order uncertainty

NASA Astrophysics Data System (ADS)

Xie, Shaojun; Pan, Baisong; Du, Xiaoping

2015-08-01

Reliability analysis may involve random variables and interval variables. In addition, some of the random variables may have interval distribution parameters owing to limited information. This kind of uncertainty is called second order uncertainty. This article develops an efficient reliability method for problems involving the three aforementioned types of uncertain input variables. The analysis produces the maximum and minimum reliability and is computationally demanding because two loops are needed: a reliability analysis loop with respect to random variables and an interval analysis loop for extreme responses with respect to interval variables. The first order reliability method and nonlinear optimization are used for the two loops, respectively. For computational efficiency, the two loops are combined into a single loop by treating the Karush-Kuhn-Tucker (KKT) optimal conditions of the interval analysis as constraints. Three examples are presented to demonstrate the proposed method.

Automatic yield-line analysis of slabs using discontinuity layout optimization

PubMed Central

Gilbert, Matthew; He, Linwei; Smith, Colin C.; Le, Canh V.

2014-01-01

The yield-line method of analysis is a long established and extremely effective means of estimating the maximum load sustainable by a slab or plate. However, although numerous attempts to automate the process of directly identifying the critical pattern of yield-lines have been made over the past few decades, to date none has proved capable of reliably analysing slabs of arbitrary geometry. Here, it is demonstrated that the discontinuity layout optimization (DLO) procedure can successfully be applied to such problems. The procedure involves discretization of the problem using nodes inter-connected by potential yield-line discontinuities, with the critical layout of these then identified using linear programming. The procedure is applied to various benchmark problems, demonstrating that highly accurate solutions can be obtained, and showing that DLO provides a truly systematic means of directly and reliably automatically identifying yield-line patterns. Finally, since the critical yield-line patterns for many problems are found to be quite complex in form, a means of automatically simplifying these is presented. PMID:25104905

New Approaches to HSCT Multidisciplinary Design and Optimization

NASA Technical Reports Server (NTRS)

Schrage, Daniel P.; Craig, James I.; Fulton, Robert E.; Mistree, Farrokh

1999-01-01

New approaches to MDO have been developed and demonstrated during this project on a particularly challenging aeronautics problem- HSCT Aeroelastic Wing Design. To tackle this problem required the integration of resources and collaboration from three Georgia Tech laboratories: ASDL, SDL, and PPRL, along with close coordination and participation from industry. Its success can also be contributed to the close interaction and involvement of fellows from the NASA Multidisciplinary Analysis and Optimization (MAO) program, which was going on in parallel, and provided additional resources to work the very complex, multidisciplinary problem, along with the methods being developed. The development of the Integrated Design Engineering Simulator (IDES) and its initial demonstration is a necessary first step in transitioning the methods and tools developed to larger industrial sized problems of interest. It also provides a framework for the implementation and demonstration of the methodology. Attachment: Appendix A - List of publications. Appendix B - Year 1 report. Appendix C - Year 2 report. Appendix D - Year 3 report. Appendix E - accompanying CDROM.

The traveling salesman problem: a hierarchical model.

PubMed

Graham, S M; Joshi, A; Pizlo, Z

2000-10-01

Our review of prior literature on spatial information processing in perception, attention, and memory indicates that these cognitive functions involve similar mechanisms based on a hierarchical architecture. The present study extends the application of hierarchical models to the area of problem solving. First, we report results of an experiment in which human subjects were tested on a Euclidean traveling salesman problem (TSP) with 6 to 30 cities. The subject's solutions were either optimal or near-optimal in length and were produced in a time that was, on average, a linear function of the number of cities. Next, the performance of the subjects is compared with that of five representative artificial intelligence and operations research algorithms, that produce approximate solutions for Euclidean problems. None of these algorithms was found to be an adequate psychological model. Finally, we present a new algorithm for solving the TSP, which is based on a hierarchical pyramid architecture. The performance of this new algorithm is quite similar to the performance of the subjects.

Aerodynamic Design Using Neural Networks

NASA Technical Reports Server (NTRS)

Rai, Man Mohan; Madavan, Nateri K.

2003-01-01

The design of aerodynamic components of aircraft, such as wings or engines, involves a process of obtaining the most optimal component shape that can deliver the desired level of component performance, subject to various constraints, e.g., total weight or cost, that the component must satisfy. Aerodynamic design can thus be formulated as an optimization problem that involves the minimization of an objective function subject to constraints. A new aerodynamic design optimization procedure based on neural networks and response surface methodology (RSM) incorporates the advantages of both traditional RSM and neural networks. The procedure uses a strategy, denoted parameter-based partitioning of the design space, to construct a sequence of response surfaces based on both neural networks and polynomial fits to traverse the design space in search of the optimal solution. Some desirable characteristics of the new design optimization procedure include the ability to handle a variety of design objectives, easily impose constraints, and incorporate design guidelines and rules of thumb. It provides an infrastructure for variable fidelity analysis and reduces the cost of computation by using less-expensive, lower fidelity simulations in the early stages of the design evolution. The initial or starting design can be far from optimal. The procedure is easy and economical to use in large-dimensional design space and can be used to perform design tradeoff studies rapidly. Designs involving multiple disciplines can also be optimized. Some practical applications of the design procedure that have demonstrated some of its capabilities include the inverse design of an optimal turbine airfoil starting from a generic shape and the redesign of transonic turbines to improve their unsteady aerodynamic characteristics.

Creating IRT-Based Parallel Test Forms Using the Genetic Algorithm Method

ERIC Educational Resources Information Center

Sun, Koun-Tem; Chen, Yu-Jen; Tsai, Shu-Yen; Cheng, Chien-Fen

2008-01-01

In educational measurement, the construction of parallel test forms is often a combinatorial optimization problem that involves the time-consuming selection of items to construct tests having approximately the same test information functions (TIFs) and constraints. This article proposes a novel method, genetic algorithm (GA), to construct parallel…

A simple language to script and simulate breeding schemes: the breeding scheme language

USDA-ARS?s Scientific Manuscript database

It is difficult for plant breeders to determine an optimal breeding strategy given that the problem involves many factors, such as target trait genetic architecture and breeding resource availability. There are many possible breeding schemes for each breeding program. Although simulation study may b...

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.

Finite element solution of optimal control problems with inequality constraints

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Hodges, Dewey H.

1990-01-01

A finite-element method based on a weak Hamiltonian form of the necessary conditions is summarized for optimal control problems. Very crude shape functions (so simple that element numerical quadrature is not necessary) can be used to develop an efficient procedure for obtaining candidate solutions (i.e., those which satisfy all the necessary conditions) even for highly nonlinear problems. An extension of the formulation allowing for discontinuities in the states and derivatives of the states is given. A theory that includes control inequality constraints is fully developed. An advanced launch vehicle (ALV) model is presented. The model involves staging and control constraints, thus demonstrating the full power of the weak formulation to date. Numerical results are presented along with total elapsed computer time required to obtain the results. The speed and accuracy in obtaining the results make this method a strong candidate for a real-time guidance algorithm.

Research on Optimization of Pooling System and Its Application in Drug Supply Chain Based on Big Data Analysis

PubMed Central

2017-01-01

Reform of drug procurement is being extensively implemented and expanded in China, especially in today's big data environment. However, the pattern of supply mode innovation lags behind procurement improvement. Problems in financial strain and supply break frequently occur, which affect the stability of drug supply. Drug Pooling System is proposed and applied in a few pilot cities to resolve these problems. From the perspective of supply chain, this study analyzes the process of setting important parameters and sets out the tasks of involved parties in a pooling system according to the issues identified in the pilot run. The approach is based on big data analysis and simulation using system dynamic theory and modeling of Vensim software to optimize system performance. This study proposes a theoretical framework to resolve problems and attempts to provide a valuable reference for future application of pooling systems. PMID:28293258

Parana Basin Structure from Multi-Objective Inversion of Surface Wave and Receiver Function by Competent Genetic Algorithm

NASA Astrophysics Data System (ADS)

An, M.; Assumpcao, M.

2003-12-01

The joint inversion of receiver function and surface wave is an effective way to diminish the influences of the strong tradeoff among parameters and the different sensitivity to the model parameters in their respective inversions, but the inversion problem becomes more complex. Multi-objective problems can be much more complicated than single-objective inversion in the model selection and optimization. If objectives are involved and conflicting, models can be ordered only partially. In this case, Pareto-optimal preference should be used to select solutions. On the other hand, the inversion to get only a few optimal solutions can not deal properly with the strong tradeoff between parameters, the uncertainties in the observation, the geophysical complexities and even the incompetency of the inversion technique. The effective way is to retrieve the geophysical information statistically from many acceptable solutions, which requires more competent global algorithms. Competent genetic algorithms recently proposed are far superior to the conventional genetic algorithm and can solve hard problems quickly, reliably and accurately. In this work we used one of competent genetic algorithms, Bayesian Optimization Algorithm as the main inverse procedure. This algorithm uses Bayesian networks to draw out inherited information and can use Pareto-optimal preference in the inversion. With this algorithm, the lithospheric structure of Paran"› basin is inverted to fit both the observations of inter-station surface wave dispersion and receiver function.

Dynamic optimization of open-loop input signals for ramp-up current profiles in tokamak plasmas

NASA Astrophysics Data System (ADS)

Ren, Zhigang; Xu, Chao; Lin, Qun; Loxton, Ryan; Teo, Kok Lay

2016-03-01

Establishing a good current spatial profile in tokamak fusion reactors is crucial to effective steady-state operation. The evolution of the current spatial profile is related to the evolution of the poloidal magnetic flux, which can be modeled in the normalized cylindrical coordinates using a parabolic partial differential equation (PDE) called the magnetic diffusion equation. In this paper, we consider the dynamic optimization problem of attaining the best possible current spatial profile during the ramp-up phase of the tokamak. We first use the Galerkin method to obtain a finite-dimensional ordinary differential equation (ODE) model based on the original magnetic diffusion PDE. Then, we combine the control parameterization method with a novel time-scaling transformation to obtain an approximate optimal parameter selection problem, which can be solved using gradient-based optimization techniques such as sequential quadratic programming (SQP). This control parameterization approach involves approximating the tokamak input signals by piecewise-linear functions whose slopes and break-points are decision variables to be optimized. We show that the gradient of the objective function with respect to the decision variables can be computed by solving an auxiliary dynamic system governing the state sensitivity matrix. Finally, we conclude the paper with simulation results for an example problem based on experimental data from the DIII-D tokamak in San Diego, California.

Graph cuts via l1 norm minimization.

PubMed

Bhusnurmath, Arvind; Taylor, Camillo J

2008-10-01

Graph cuts have become an increasingly important tool for solving a number of energy minimization problems in computer vision and other fields. In this paper, the graph cut problem is reformulated as an unconstrained l1 norm minimization that can be solved effectively using interior point methods. This reformulation exposes connections between the graph cuts and other related continuous optimization problems. Eventually the problem is reduced to solving a sequence of sparse linear systems involving the Laplacian of the underlying graph. The proposed procedure exploits the structure of these linear systems in a manner that is easily amenable to parallel implementations. Experimental results obtained by applying the procedure to graphs derived from image processing problems are provided.

Calibration of Lévy Processes with American Options

NASA Astrophysics Data System (ADS)

Achdou, Yves

We study options on financial assets whose discounted prices are exponential of Lévy processes. The price of an American vanilla option as a function of the maturity and the strike satisfies a linear complementarity problem involving a non-local partial integro-differential operator. It leads to a variational inequality in a suitable weighted Sobolev space. Calibrating the Lévy process may be done by solving an inverse least square problem where the state variable satisfies the previously mentioned variational inequality. We first assume that the volatility is positive: after carefully studying the direct problem, we propose necessary optimality conditions for the least square inverse problem. We also consider the direct problem when the volatility is zero.

Aerodynamics of an airfoil with a jet issuing from its surface

NASA Technical Reports Server (NTRS)

Tavella, D. A.; Karamcheti, K.

1982-01-01

A simple, two dimensional, incompressible and inviscid model for the problem posed by a two dimensional wing with a jet issuing from its lower surface is considered and a parametric analysis is carried out to observe how the aerodynamic characteristics depend on the different parameters. The mathematical problem constitutes a boundary value problem where the position of part of the boundary is not known a priori. A nonlinear optimization approach was used to solve the problem, and the analysis reveals interesting characteristics that may help to better understand the physics involved in more complex situations in connection with high lift systems.

REVIEWS OF TOPICAL PROBLEMS: Global phase-stable radiointerferometric systems

NASA Astrophysics Data System (ADS)

Dravskikh, A. F.; Korol'kov, Dimitrii V.; Pariĭskiĭ, Yu N.; Stotskiĭ, A. A.; Finkel'steĭn, A. M.; Fridman, P. A.

1981-12-01

We discuss from a unitary standpoint the possibility of building a phase-stable interferometric system with very long baselines that operate around the clock with real-time data processing. The various problems involved in the realization of this idea are discussed: the methods of suppression of instrumental and tropospheric phase fluctuations, the methods for constructing two-dimensional images and determining the coordinates of radio sources with high angular resolution, and the problem of the optimal structure of the interferometric system. We review in detail the scientific problems from the various branches of natural science (astrophysics, cosmology, geophysics, geodynamics, astrometry, etc.) whose solution requires superhigh angular resolution.

An optimal control method for fluid structure interaction systems via adjoint boundary pressure

NASA Astrophysics Data System (ADS)

Chirco, L.; Da Vià, R.; Manservisi, S.

2017-11-01

In recent year, in spite of the computational complexity, Fluid-structure interaction (FSI) problems have been widely studied due to their applicability in science and engineering. Fluid-structure interaction systems consist of one or more solid structures that deform by interacting with a surrounding fluid flow. FSI simulations evaluate the tensional state of the mechanical component and take into account the effects of the solid deformations on the motion of the interior fluids. The inverse FSI problem can be described as the achievement of a certain objective by changing some design parameters such as forces, boundary conditions and geometrical domain shapes. In this paper we would like to study the inverse FSI problem by using an optimal control approach. In particular we propose a pressure boundary optimal control method based on Lagrangian multipliers and adjoint variables. The objective is the minimization of a solid domain displacement matching functional obtained by finding the optimal pressure on the inlet boundary. The optimality system is derived from the first order necessary conditions by taking the Fréchet derivatives of the Lagrangian with respect to all the variables involved. The optimal solution is then obtained through a standard steepest descent algorithm applied to the optimality system. The approach presented in this work is general and could be used to assess other objective functionals and controls. In order to support the proposed approach we perform a few numerical tests where the fluid pressure on the domain inlet controls the displacement that occurs in a well defined region of the solid domain.

Problems Experienced by Ovarian Cancer Survivors During Treatment.

PubMed

Keim-Malpass, Jessica; Mihalko, Shannon L; Russell, Greg; Case, Doug; Miller, Brigitte; Avis, Nancy E

To identify problems at different treatment points (early treatment, mid-treatment, early posttreatment, and late posttreatment) among women with ovarian cancer. Longitudinal and cross-sectional study design. An academic and community clinical cancer center in the Southeastern United States. Sixty-eight women with Stage I to IV ovarian cancer. Variables assessed included reported problems (physical, psychosocial, pain, marital, medical interaction), social support, optimism, and responses to open-ended questions. Analysis involved mixed models for longitudinal repeated measures and unpaired t tests and content analysis to describe responses to open-ended questions. Physical and psychosocial problems were greatest during early treatment and decreased throughout the treatment trajectory. Women with greater levels of social support and optimism at baseline had fewer problems over time. Women who did not have trouble paying for basics had fewer problems related to pain and psychological problems. Problems across all domains must be addressed throughout the treatment trajectory, even after chemotherapy has ended. Nurses are well positioned to refer women appropriately to social workers and clinical navigators across all domains of care and should consider systematic assessment of patient-reported problems as a routine form of practice. Copyright © 2017 AWHONN, the Association of Women's Health, Obstetric and Neonatal Nurses. Published by Elsevier Inc. All rights reserved.

Topology optimization under stochastic stiffness

NASA Astrophysics Data System (ADS)

Asadpoure, Alireza

Topology optimization is a systematic computational tool for optimizing the layout of materials within a domain for engineering design problems. It allows variation of structural boundaries and connectivities. This freedom in the design space often enables discovery of new, high performance designs. However, solutions obtained by performing the optimization in a deterministic setting may be impractical or suboptimal when considering real-world engineering conditions with inherent variabilities including (for example) variabilities in fabrication processes and operating conditions. The aim of this work is to provide a computational methodology for topology optimization in the presence of uncertainties associated with structural stiffness, such as uncertain material properties and/or structural geometry. Existing methods for topology optimization under deterministic conditions are first reviewed. Modifications are then proposed to improve the numerical performance of the so-called Heaviside Projection Method (HPM) in continuum domains. Next, two approaches, perturbation and Polynomial Chaos Expansion (PCE), are proposed to account for uncertainties in the optimization procedure. These approaches are intrusive, allowing tight and efficient coupling of the uncertainty quantification with the optimization sensitivity analysis. The work herein develops a robust topology optimization framework aimed at reducing the sensitivity of optimized solutions to uncertainties. The perturbation-based approach combines deterministic topology optimization with a perturbation method for the quantification of uncertainties. The use of perturbation transforms the problem of topology optimization under uncertainty to an augmented deterministic topology optimization problem. The PCE approach combines the spectral stochastic approach for the representation and propagation of uncertainties with an existing deterministic topology optimization technique. The resulting compact representations for the response quantities allow for efficient and accurate calculation of sensitivities of response statistics with respect to the design variables. The proposed methods are shown to be successful at generating robust optimal topologies. Examples from topology optimization in continuum and discrete domains (truss structures) under uncertainty are presented. It is also shown that proposed methods lead to significant computational savings when compared to Monte Carlo-based optimization which involve multiple formations and inversions of the global stiffness matrix and that results obtained from the proposed method are in excellent agreement with those obtained from a Monte Carlo-based optimization algorithm.

Autonomous optimal trajectory design employing convex optimization for powered descent on an asteroid

NASA Astrophysics Data System (ADS)

Pinson, Robin Marie

Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant (fuel) optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from ground control. The goal is to autonomously design the optimal powered descent trajectory onboard the spacecraft immediately prior to the descent burn for use during the burn. Compared to a planetary powered landing problem, the challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies, and low thrust vehicles. The nonlinear gravity fields cannot be represented by a constant gravity model nor a Newtonian model. The trajectory design algorithm needs to be robust and efficient to guarantee a designed trajectory and complete the calculations in a reasonable time frame. This research investigates the following questions: Can convex optimization be used to design the minimum propellant powered descent trajectory for a soft landing on an asteroid? Is this method robust and reliable to allow autonomy onboard the spacecraft without interaction from ground control? This research designed a convex optimization based method that rapidly generates the propellant optimal asteroid powered descent trajectory. The solution to the convex optimization problem is the thrust magnitude and direction, which designs and determines the trajectory. The propellant optimal problem was formulated as a second order cone program, a subset of convex optimization, through relaxation techniques by including a slack variable, change of variables, and incorporation of the successive solution method. Convex optimization solvers, especially second order cone programs, are robust, reliable, and are guaranteed to find the global minimum provided one exists. In addition, an outer optimization loop using Brent's method determines the optimal flight time corresponding to the minimum propellant usage over all flight times. Inclusion of additional trajectory constraints, solely vertical motion near the landing site and glide slope, were evaluated. Through a theoretical proof involving the Minimum Principle from Optimal Control Theory and the Karush-Kuhn-Tucker conditions it was shown that the relaxed problem is identical to the original problem at the minimum point. Therefore, the optimal solution of the relaxed problem is an optimal solution of the original problem, referred to as lossless convexification. A key finding is that this holds for all levels of gravity model fidelity. The designed thrust magnitude profiles were the bang-bang predicted by Optimal Control Theory. The first high fidelity gravity model employed was the 2x2 spherical harmonics model assuming a perfect triaxial ellipsoid and placement of the coordinate frame at the asteroid's center of mass and aligned with the semi-major axes. The spherical harmonics model is not valid inside the Brillouin sphere and this becomes relevant for irregularly shaped asteroids. Then, a higher fidelity model was implemented combining the 4x4 spherical harmonics gravity model with the interior spherical Bessel gravity model. All gravitational terms in the equations of motion are evaluated with the position vector from the previous iteration, creating the successive solution method. Methodology success was shown by applying the algorithm to three triaxial ellipsoidal asteroids with four different rotation speeds using the 2x2 gravity model. Finally, the algorithm was tested using the irregularly shaped asteroid, Castalia.

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.

Deterministic Design Optimization of Structures in OpenMDAO Framework

NASA Technical Reports Server (NTRS)

Coroneos, Rula M.; Pai, Shantaram S.

2012-01-01

Nonlinear programming algorithms play an important role in structural design optimization. Several such algorithms have been implemented in OpenMDAO framework developed at NASA Glenn Research Center (GRC). OpenMDAO is an open source engineering analysis framework, written in Python, for analyzing and solving Multi-Disciplinary Analysis and Optimization (MDAO) problems. It provides a number of solvers and optimizers, referred to as components and drivers, which users can leverage to build new tools and processes quickly and efficiently. Users may download, use, modify, and distribute the OpenMDAO software at no cost. This paper summarizes the process involved in analyzing and optimizing structural components by utilizing the framework s structural solvers and several gradient based optimizers along with a multi-objective genetic algorithm. For comparison purposes, the same structural components were analyzed and optimized using CometBoards, a NASA GRC developed code. The reliability and efficiency of the OpenMDAO framework was compared and reported in this report.

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.

Stochastic Set-Based Particle Swarm Optimization Based on Local Exploration for Solving the Carpool Service Problem.

PubMed

Chou, Sheng-Kai; Jiau, Ming-Kai; Huang, Shih-Chia

2016-08-01

The growing ubiquity of vehicles has led to increased concerns about environmental issues. These concerns can be mitigated by implementing an effective carpool service. In an intelligent carpool system, an automated service process assists carpool participants in determining routes and matches. It is a discrete optimization problem that involves a system-wide condition as well as participants' expectations. In this paper, we solve the carpool service problem (CSP) to provide satisfactory ride matches. To this end, we developed a particle swarm carpool algorithm based on stochastic set-based particle swarm optimization (PSO). Our method introduces stochastic coding to augment traditional particles, and uses three terminologies to represent a particle: 1) particle position; 2) particle view; and 3) particle velocity. In this way, the set-based PSO (S-PSO) can be realized by local exploration. In the simulation and experiments, two kind of discrete PSOs-S-PSO and binary PSO (BPSO)-and a genetic algorithm (GA) are compared and examined using tested benchmarks that simulate a real-world metropolis. We observed that the S-PSO outperformed the BPSO and the GA thoroughly. Moreover, our method yielded the best result in a statistical test and successfully obtained numerical results for meeting the optimization objectives of the CSP.

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.

Uncluttered Single-Image Visualization of Vascular Structures using GPU and Integer Programming

PubMed Central

Won, Joong-Ho; Jeon, Yongkweon; Rosenberg, Jarrett; Yoon, Sungroh; Rubin, Geoffrey D.; Napel, Sandy

2013-01-01

Direct projection of three-dimensional branching structures, such as networks of cables, blood vessels, or neurons onto a 2D image creates the illusion of intersecting structural parts and creates challenges for understanding and communication. We present a method for visualizing such structures, and demonstrate its utility in visualizing the abdominal aorta and its branches, whose tomographic images might be obtained by computed tomography or magnetic resonance angiography, in a single two-dimensional stylistic image, without overlaps among branches. The visualization method, termed uncluttered single-image visualization (USIV), involves optimization of geometry. This paper proposes a novel optimization technique that utilizes an interesting connection of the optimization problem regarding USIV to the protein structure prediction problem. Adopting the integer linear programming-based formulation for the protein structure prediction problem, we tested the proposed technique using 30 visualizations produced from five patient scans with representative anatomical variants in the abdominal aortic vessel tree. The novel technique can exploit commodity-level parallelism, enabling use of general-purpose graphics processing unit (GPGPU) technology that yields a significant speedup. Comparison of the results with the other optimization technique previously reported elsewhere suggests that, in most aspects, the quality of the visualization is comparable to that of the previous one, with a significant gain in the computation time of the algorithm. PMID:22291148

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.

Scenario generation for stochastic optimization problems via the sparse grid method

DOE PAGES

Chen, Michael; Mehrotra, Sanjay; Papp, David

2015-04-19

We study the use of sparse grids in the scenario generation (or discretization) problem in stochastic programming problems where the uncertainty is modeled using a continuous multivariate distribution. We show that, under a regularity assumption on the random function involved, the sequence of optimal objective function values of the sparse grid approximations converges to the true optimal objective function values as the number of scenarios increases. The rate of convergence is also established. We treat separately the special case when the underlying distribution is an affine transform of a product of univariate distributions, and show how the sparse grid methodmore » can be adapted to the distribution by the use of quadrature formulas tailored to the distribution. We numerically compare the performance of the sparse grid method using different quadrature rules with classic quasi-Monte Carlo (QMC) methods, optimal rank-one lattice rules, and Monte Carlo (MC) scenario generation, using a series of utility maximization problems with up to 160 random variables. The results show that the sparse grid method is very efficient, especially if the integrand is sufficiently smooth. In such problems the sparse grid scenario generation method is found to need several orders of magnitude fewer scenarios than MC and QMC scenario generation to achieve the same accuracy. As a result, it is indicated that the method scales well with the dimension of the distribution--especially when the underlying distribution is an affine transform of a product of univariate distributions, in which case the method appears scalable to thousands of random variables.« less

Determination of Nerve Fiber Diameter Distribution From Compound Action Potential: A Continuous Approach.

PubMed

Un, M Kerem; Kaghazchi, Hamed

2018-01-01

When a signal is initiated in the nerve, it is transmitted along each nerve fiber via an action potential (called single fiber action potential (SFAP)) which travels with a velocity that is related with the diameter of the fiber. The additive superposition of SFAPs constitutes the compound action potential (CAP) of the nerve. The fiber diameter distribution (FDD) in the nerve can be computed from the CAP data by solving an inverse problem. This is usually achieved by dividing the fibers into a finite number of diameter groups and solve a corresponding linear system to optimize FDD. However, number of fibers in a nerve can be measured sometimes in thousands and it is possible to assume a continuous distribution for the fiber diameters which leads to a gradient optimization problem. In this paper, we have evaluated this continuous approach to the solution of the inverse problem. We have utilized an analytical function for SFAP and an assumed a polynomial form for FDD. The inverse problem involves the optimization of polynomial coefficients to obtain the best estimate for the FDD. We have observed that an eighth order polynomial for FDD can capture both unimodal and bimodal fiber distributions present in vivo, even in case of noisy CAP data. The assumed FDD distribution regularizes the ill-conditioned inverse problem and produces good results.

Overview of field gamma spectrometries based on Si-photomultiplier

NASA Astrophysics Data System (ADS)

Denisov, Viktor; Korotaev, Valery; Titov, Aleksandr; Blokhina, Anastasia; Kleshchenok, Maksim

2017-05-01

Design of optical-electronic devices and systems involves the selection of such technical patterns that under given initial requirements and conditions are optimal according to certain criteria. The original characteristic of the OES for any purpose, defining its most important feature ability is a threshold detection. Based on this property, will be achieved the required functional quality of the device or system. Therefore, the original criteria and optimization methods have to subordinate to the idea of a better detectability. Generally reduces to the problem of optimal selection of the expected (predetermined) signals in the predetermined observation conditions. Thus the main purpose of optimization of the system when calculating its detectability is the choice of circuits and components that provide the most effective selection of a target.

Particle swarm optimization and its application in MEG source localization using single time sliced data

NASA Astrophysics Data System (ADS)

Lin, Juan; Liu, Chenglian; Guo, Yongning

2014-10-01

The estimation of neural active sources from the magnetoencephalography (MEG) data is a very critical issue for both clinical neurology and brain functions research. A widely accepted source-modeling technique for MEG involves calculating a set of equivalent current dipoles (ECDs). Depth in the brain is one of difficulties in MEG source localization. Particle swarm optimization(PSO) is widely used to solve various optimization problems. In this paper we discuss its ability and robustness to find the global optimum in different depths of the brain when using single equivalent current dipole (sECD) model and single time sliced data. The results show that PSO is an effective global optimization to MEG source localization when given one dipole in different depths.

On the robust optimization to the uncertain vaccination strategy problem

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

Chaerani, D., E-mail: d.chaerani@unpad.ac.id; Anggriani, N., E-mail: d.chaerani@unpad.ac.id; Firdaniza, E-mail: d.chaerani@unpad.ac.id

2014-02-21

In order to prevent an epidemic of infectious diseases, the vaccination coverage needs to be minimized and also the basic reproduction number needs to be maintained below 1. This means that as we get the vaccination coverage as minimum as possible, thus we need to prevent the epidemic to a small number of people who already get infected. In this paper, we discuss the case of vaccination strategy in term of minimizing vaccination coverage, when the basic reproduction number is assumed as an uncertain parameter that lies between 0 and 1. We refer to the linear optimization model for vaccinationmore » strategy that propose by Becker and Starrzak (see [2]). Assuming that there is parameter uncertainty involved, we can see Tanner et al (see [9]) who propose the optimal solution of the problem using stochastic programming. In this paper we discuss an alternative way of optimizing the uncertain vaccination strategy using Robust Optimization (see [3]). In this approach we assume that the parameter uncertainty lies within an ellipsoidal uncertainty set such that we can claim that the obtained result will be achieved in a polynomial time algorithm (as it is guaranteed by the RO methodology). The robust counterpart model is presented.« less

An optimization program based on the method of feasible directions: Theory and users guide

NASA Technical Reports Server (NTRS)

Belegundu, Ashok D.; Berke, Laszlo; Patnaik, Surya N.

1994-01-01

The theory and user instructions for an optimization code based on the method of feasible directions are presented. The code was written for wide distribution and ease of attachment to other simulation software. Although the theory of the method of feasible direction was developed in the 1960's, many considerations are involved in its actual implementation as a computer code. Included in the code are a number of features to improve robustness in optimization. The search direction is obtained by solving a quadratic program using an interior method based on Karmarkar's algorithm. The theory is discussed focusing on the important and often overlooked role played by the various parameters guiding the iterations within the program. Also discussed is a robust approach for handling infeasible starting points. The code was validated by solving a variety of structural optimization test problems that have known solutions obtained by other optimization codes. It has been observed that this code is robust: it has solved a variety of problems from different starting points. However, the code is inefficient in that it takes considerable CPU time as compared with certain other available codes. Further work is required to improve its efficiency while retaining its robustness.

Reconstructing Networks from Profit Sequences in Evolutionary Games via a Multiobjective Optimization Approach with Lasso Initialization

PubMed Central

Wu, Kai; Liu, Jing; Wang, Shuai

2016-01-01

Evolutionary games (EG) model a common type of interactions in various complex, networked, natural and social systems. Given such a system with only profit sequences being available, reconstructing the interacting structure of EG networks is fundamental to understand and control its collective dynamics. Existing approaches used to handle this problem, such as the lasso, a convex optimization method, need a user-defined constant to control the tradeoff between the natural sparsity of networks and measurement error (the difference between observed data and simulated data). However, a shortcoming of these approaches is that it is not easy to determine these key parameters which can maximize the performance. In contrast to these approaches, we first model the EG network reconstruction problem as a multiobjective optimization problem (MOP), and then develop a framework which involves multiobjective evolutionary algorithm (MOEA), followed by solution selection based on knee regions, termed as MOEANet, to solve this MOP. We also design an effective initialization operator based on the lasso for MOEA. We apply the proposed method to reconstruct various types of synthetic and real-world networks, and the results show that our approach is effective to avoid the above parameter selecting problem and can reconstruct EG networks with high accuracy. PMID:27886244

Reconstructing Networks from Profit Sequences in Evolutionary Games via a Multiobjective Optimization Approach with Lasso Initialization

NASA Astrophysics Data System (ADS)

Wu, Kai; Liu, Jing; Wang, Shuai

2016-11-01

Evolutionary games (EG) model a common type of interactions in various complex, networked, natural and social systems. Given such a system with only profit sequences being available, reconstructing the interacting structure of EG networks is fundamental to understand and control its collective dynamics. Existing approaches used to handle this problem, such as the lasso, a convex optimization method, need a user-defined constant to control the tradeoff between the natural sparsity of networks and measurement error (the difference between observed data and simulated data). However, a shortcoming of these approaches is that it is not easy to determine these key parameters which can maximize the performance. In contrast to these approaches, we first model the EG network reconstruction problem as a multiobjective optimization problem (MOP), and then develop a framework which involves multiobjective evolutionary algorithm (MOEA), followed by solution selection based on knee regions, termed as MOEANet, to solve this MOP. We also design an effective initialization operator based on the lasso for MOEA. We apply the proposed method to reconstruct various types of synthetic and real-world networks, and the results show that our approach is effective to avoid the above parameter selecting problem and can reconstruct EG networks with high accuracy.

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.

Aeroelastic optimization methodology for viscous and turbulent flows

NASA Astrophysics Data System (ADS)

Barcelos Junior, Manuel Nascimento Dias

2007-12-01

In recent years, the development of faster computers and parallel processing allowed the application of high-fidelity analysis methods to the aeroelastic design of aircraft. However, these methods are restricted to the final design verification, mainly due to the computational cost involved in iterative design processes. Therefore, this work is concerned with the creation of a robust and efficient aeroelastic optimization methodology for inviscid, viscous and turbulent flows by using high-fidelity analysis and sensitivity analysis techniques. Most of the research in aeroelastic optimization, for practical reasons, treat the aeroelastic system as a quasi-static inviscid problem. In this work, as a first step toward the creation of a more complete aeroelastic optimization methodology for realistic problems, an analytical sensitivity computation technique was developed and tested for quasi-static aeroelastic viscous and turbulent flow configurations. Viscous and turbulent effects are included by using an averaged discretization of the Navier-Stokes equations, coupled with an eddy viscosity turbulence model. For quasi-static aeroelastic problems, the traditional staggered solution strategy has unsatisfactory performance when applied to cases where there is a strong fluid-structure coupling. Consequently, this work also proposes a solution methodology for aeroelastic and sensitivity analyses of quasi-static problems, which is based on the fixed point of an iterative nonlinear block Gauss-Seidel scheme. The methodology can also be interpreted as the solution of the Schur complement of the aeroelastic and sensitivity analyses linearized systems of equations. The methodologies developed in this work are tested and verified by using realistic aeroelastic systems.

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…

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.

System design and improvement of an emergency department using Simulation-Based Multi-Objective Optimization

NASA Astrophysics Data System (ADS)

Goienetxea Uriarte, A.; Ruiz Zúñiga, E.; Urenda Moris, M.; Ng, A. H. C.

2015-05-01

Discrete Event Simulation (DES) is nowadays widely used to support decision makers in system analysis and improvement. However, the use of simulation for improving stochastic logistic processes is not common among healthcare providers. The process of improving healthcare systems involves the necessity to deal with trade-off optimal solutions that take into consideration a multiple number of variables and objectives. Complementing DES with Multi-Objective Optimization (SMO) creates a superior base for finding these solutions and in consequence, facilitates the decision-making process. This paper presents how SMO has been applied for system improvement analysis in a Swedish Emergency Department (ED). A significant number of input variables, constraints and objectives were considered when defining the optimization problem. As a result of the project, the decision makers were provided with a range of optimal solutions which reduces considerably the length of stay and waiting times for the ED patients. SMO has proved to be an appropriate technique to support healthcare system design and improvement processes. A key factor for the success of this project has been the involvement and engagement of the stakeholders during the whole process.

Minimax confidence intervals in geomagnetism

NASA Technical Reports Server (NTRS)

Stark, Philip B.

1992-01-01

The present paper uses theory of Donoho (1989) to find lower bounds on the lengths of optimally short fixed-length confidence intervals (minimax confidence intervals) for Gauss coefficients of the field of degree 1-12 using the heat flow constraint. The bounds on optimal minimax intervals are about 40 percent shorter than Backus' intervals: no procedure for producing fixed-length confidence intervals, linear or nonlinear, can give intervals shorter than about 60 percent the length of Backus' in this problem. While both methods rigorously account for the fact that core field models are infinite-dimensional, the application of the techniques to the geomagnetic problem involves approximations and counterfactual assumptions about the data errors, and so these results are likely to be extremely optimistic estimates of the actual uncertainty in Gauss coefficients.

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.

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.

Optimization of MLS receivers for multipath environments

NASA Technical Reports Server (NTRS)

Mcalpine, G. A.; Highfill, J. H., III

1976-01-01

The design of a microwave landing system (MLS) aircraft receiver, capable of optimal performance in multipath environments found in air terminal areas, is reported. Special attention was given to the angle tracking problem of the receiver and includes tracking system design considerations, study and application of locally optimum estimation involving multipath adaptive reception and then envelope processing, and microcomputer system design. Results show processing is competitive in this application with i-f signal processing performance-wise and is much more simple and cheaper. A summary of the signal model is given.

Simulated annealing in orbital flight planning

NASA Technical Reports Server (NTRS)

Soller, Jeffrey

1990-01-01

Simulated annealing is used to solve a minimum fuel trajectory problem in the space station environment. The environment is unique because the space station will define the first true multivehicle environment in space. The optimization yields surfaces which are potentially complex, with multiple local minima. Because of the likelihood of these local minima, descent techniques are unable to offer robust solutions. Other deterministic optimization techniques were explored without success. The simulated annealing optimization is capable of identifying a minimum-fuel, two-burn trajectory subject to four constraints. Furthermore, the computational efforts involved in the optimization are such that missions could be planned on board the space station. Potential applications could include the on-site planning of rendezvous with a target craft of the emergency rescue of an astronaut. Future research will include multiwaypoint maneuvers, using a knowledge base to guide the optimization.

Targeted Pressure Management During CO 2 Sequestration: Optimization of Well Placement and Brine Extraction

DOE PAGES

Cihan, Abdullah; Birkholzer, Jens; Bianchi, Marco

2014-12-31

Large-scale pressure increases resulting from carbon dioxide (CO 2) injection in the subsurface can potentially impact caprock integrity, induce reactivation of critically stressed faults, and drive CO 2 or brine through conductive features into shallow groundwater. Pressure management involving the extraction of native fluids from storage formations can be used to minimize pressure increases while maximizing CO2 storage. However, brine extraction requires pumping, transportation, possibly treatment, and disposal of substantial volumes of extracted brackish or saline water, all of which can be technically challenging and expensive. This paper describes a constrained differential evolution (CDE) algorithm for optimal well placement andmore » injection/ extraction control with the goal of minimizing brine extraction while achieving predefined pressure contraints. The CDE methodology was tested for a simple optimization problem whose solution can be partially obtained with a gradient-based optimization methodology. The CDE successfully estimated the true global optimum for both extraction well location and extraction rate, needed for the test problem. A more complex example application of the developed strategy was also presented for a hypothetical CO 2 storage scenario in a heterogeneous reservoir consisting of a critically stressed fault nearby an injection zone. Through the CDE optimization algorithm coupled to a numerical vertically-averaged reservoir model, we successfully estimated optimal rates and locations for CO 2 injection and brine extraction wells while simultaneously satisfying multiple pressure buildup constraints to avoid fault activation and caprock fracturing. The study shows that the CDE methodology is a very promising tool to solve also other optimization problems related to GCS, such as reducing ‘Area of Review’, monitoring design, reducing risk of leakage and increasing storage capacity and trapping.« less

On the use of PGD for optimal control applied to automated fibre placement

NASA Astrophysics Data System (ADS)

Bur, N.; Joyot, P.

2017-10-01

Automated Fibre Placement (AFP) is an incipient manufacturing process for composite structures. Despite its concep-tual simplicity it involves many complexities related to the necessity of melting the thermoplastic at the interface tape-substrate, ensuring the consolidation that needs the diffusion of molecules and control the residual stresses installation responsible of the residual deformations of the formed parts. The optimisation of the process and the determination of the process window cannot be achieved in a traditional way since it requires a plethora of trials/errors or numerical simulations, because there are many parameters involved in the characterisation of the material and the process. Using reduced order modelling such as the so called Proper Generalised Decomposition method, allows the construction of multi-parametric solution taking into account many parameters. This leads to virtual charts that can be explored on-line in real time in order to perform process optimisation or on-line simulation-based control. Thus, for a given set of parameters, determining the power leading to an optimal temperature becomes easy. However, instead of controlling the power knowing the temperature field by particularizing an abacus, we propose here an approach based on optimal control: we solve by PGD a dual problem from heat equation and optimality criteria. To circumvent numerical issue due to ill-conditioned system, we propose an algorithm based on Uzawa's method. That way, we are able to solve the dual problem, setting the desired state as an extra-coordinate in the PGD framework. In a single computation, we get both the temperature field and the required heat flux to reach a parametric optimal temperature on a given zone.

A BDDC Algorithm with Deluxe Scaling for Three-Dimensional H (curl) Problems

DOE PAGES

Dohrmann, Clark R.; Widlund, Olof B.

2015-04-28

In our paper, we present and analyze a BDDC algorithm for a class of elliptic problems in the three-dimensional H(curl) space. Compared with existing results, our condition number estimate requires fewer assumptions and also involves two fewer powers of log(H/h), making it consistent with optimal estimates for other elliptic problems. Here, H/his the maximum of Hi/hi over all subdomains, where Hi and hi are the diameter and the smallest element diameter for the subdomain Ωi. The analysis makes use of two recent developments. The first is our new approach to averaging across the subdomain interfaces, while the second is amore » new technical tool that allows arguments involving trace classes to be avoided. Furthermore, numerical examples are presented to confirm the theory and demonstrate the importance of the new averaging approach in certain cases.« less

Quantum speedup in solving the maximal-clique problem

NASA Astrophysics Data System (ADS)

Chang, Weng-Long; Yu, Qi; Li, Zhaokai; Chen, Jiahui; Peng, Xinhua; Feng, Mang

2018-03-01

The maximal-clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electrical engineering, computational chemistry, and bioinformatics to social networks. Here we develop a quantum algorithm to solve the maximal-clique problem for any graph G with n vertices with quadratic speedup over its classical counterparts, where the time and spatial complexities are reduced to, respectively, O (√{2n}) and O (n2) . With respect to oracle-related quantum algorithms for the NP-complete problems, we identify our algorithm as optimal. To justify the feasibility of the proposed quantum algorithm, we successfully solve a typical clique problem for a graph G with two vertices and one edge by carrying out a nuclear magnetic resonance experiment involving four qubits.

A Stochastic Inversion Method for Potential Field Data: Ant Colony Optimization

NASA Astrophysics Data System (ADS)

Liu, Shuang; Hu, Xiangyun; Liu, Tianyou

2014-07-01

Simulating natural ants' foraging behavior, the ant colony optimization (ACO) algorithm performs excellently in combinational optimization problems, for example the traveling salesman problem and the quadratic assignment problem. However, the ACO is seldom used to inverted for gravitational and magnetic data. On the basis of the continuous and multi-dimensional objective function for potential field data optimization inversion, we present the node partition strategy ACO (NP-ACO) algorithm for inversion of model variables of fixed shape and recovery of physical property distributions of complicated shape models. We divide the continuous variables into discrete nodes and ants directionally tour the nodes by use of transition probabilities. We update the pheromone trails by use of Gaussian mapping between the objective function value and the quantity of pheromone. It can analyze the search results in real time and promote the rate of convergence and precision of inversion. Traditional mapping, including the ant-cycle system, weaken the differences between ant individuals and lead to premature convergence. We tested our method by use of synthetic data and real data from scenarios involving gravity and magnetic anomalies. The inverted model variables and recovered physical property distributions were in good agreement with the true values. The ACO algorithm for binary representation imaging and full imaging can recover sharper physical property distributions than traditional linear inversion methods. The ACO has good optimization capability and some excellent characteristics, for example robustness, parallel implementation, and portability, compared with other stochastic metaheuristics.

Multi-Objective Approach for Energy-Aware Workflow Scheduling in Cloud Computing Environments

PubMed Central

Kadima, Hubert; Granado, Bertrand

2013-01-01

We address the problem of scheduling workflow applications on heterogeneous computing systems like cloud computing infrastructures. In general, the cloud workflow scheduling is a complex optimization problem which requires considering different criteria so as to meet a large number of QoS (Quality of Service) requirements. Traditional research in workflow scheduling mainly focuses on the optimization constrained by time or cost without paying attention to energy consumption. The main contribution of this study is to propose a new approach for multi-objective workflow scheduling in clouds, and present the hybrid PSO algorithm to optimize the scheduling performance. Our method is based on the Dynamic Voltage and Frequency Scaling (DVFS) technique to minimize energy consumption. This technique allows processors to operate in different voltage supply levels by sacrificing clock frequencies. This multiple voltage involves a compromise between the quality of schedules and energy. Simulation results on synthetic and real-world scientific applications highlight the robust performance of the proposed approach. PMID:24319361

Multi-objective approach for energy-aware workflow scheduling in cloud computing environments.

PubMed

Yassa, Sonia; Chelouah, Rachid; Kadima, Hubert; Granado, Bertrand

2013-01-01

We address the problem of scheduling workflow applications on heterogeneous computing systems like cloud computing infrastructures. In general, the cloud workflow scheduling is a complex optimization problem which requires considering different criteria so as to meet a large number of QoS (Quality of Service) requirements. Traditional research in workflow scheduling mainly focuses on the optimization constrained by time or cost without paying attention to energy consumption. The main contribution of this study is to propose a new approach for multi-objective workflow scheduling in clouds, and present the hybrid PSO algorithm to optimize the scheduling performance. Our method is based on the Dynamic Voltage and Frequency Scaling (DVFS) technique to minimize energy consumption. This technique allows processors to operate in different voltage supply levels by sacrificing clock frequencies. This multiple voltage involves a compromise between the quality of schedules and energy. Simulation results on synthetic and real-world scientific applications highlight the robust performance of the proposed approach.

Optimization of custom cementless stem using finite element analysis and elastic modulus distribution for reducing stress-shielding effect.

PubMed

Saravana Kumar, Gurunathan; George, Subin Philip

2017-02-01

This work proposes a methodology involving stiffness optimization for subject-specific cementless hip implant design based on finite element analysis for reducing stress-shielding effect. To assess the change in the stress-strain state of the femur and the resulting stress-shielding effect due to insertion of the implant, a finite element analysis of the resected femur with implant assembly is carried out for a clinically relevant loading condition. Selecting the von Mises stress as the criterion for discriminating regions for elastic modulus difference, a stiffness minimization method was employed by varying the elastic modulus distribution in custom implant stem. The stiffness minimization problem is formulated as material distribution problem without explicitly penalizing partial volume elements. This formulation enables designs that could be fabricated using additive manufacturing to make porous implant with varying levels of porosity. Stress-shielding effect, measured as difference between the von Mises stress in the intact and implanted femur, decreased as the elastic modulus distribution is optimized.

Development of a multiple-parameter nonlinear perturbation procedure for transonic turbomachinery flows: Preliminary application to design/optimization problems

NASA Technical Reports Server (NTRS)

Stahara, S. S.; Elliott, J. P.; Spreiter, J. R.

1983-01-01

An investigation was conducted to continue the development of perturbation procedures and associated computational codes for rapidly determining approximations to nonlinear flow solutions, with the purpose of establishing a method for minimizing computational requirements associated with parametric design studies of transonic flows in turbomachines. The results reported here concern the extension of the previously developed successful method for single parameter perturbations to simultaneous multiple-parameter perturbations, and the preliminary application of the multiple-parameter procedure in combination with an optimization method to blade design/optimization problem. In order to provide as severe a test as possible of the method, attention is focused in particular on transonic flows which are highly supercritical. Flows past both isolated blades and compressor cascades, involving simultaneous changes in both flow and geometric parameters, are considered. Comparisons with the corresponding exact nonlinear solutions display remarkable accuracy and range of validity, in direct correspondence with previous results for single-parameter perturbations.

A Review on Medical Image Registration as an Optimization Problem

PubMed Central

Song, Guoli; Han, Jianda; Zhao, Yiwen; Wang, Zheng; Du, Huibin

2017-01-01

Objective: In the course of clinical treatment, several medical media are required by a phy-sician in order to provide accurate and complete information about a patient. Medical image registra-tion techniques can provide a richer diagnosis and treatment information to doctors and to provide a comprehensive reference source for the researchers involved in image registration as an optimization problem. Methods: The essence of image registration is associating two or more different images spatial asso-ciation, and getting the translation of their spatial relationship. For medical image registration, its pro-cess is not absolute. Its core purpose is finding the conversion relationship between different images. Result: The major step of image registration includes the change of geometrical dimensions, and change of the image of the combination, image similarity measure, iterative optimization and interpo-lation process. Conclusion: The contribution of this review is sort of related image registration research methods, can provide a brief reference for researchers about image registration. PMID:28845149

Adjoint-Based Methodology for Time-Dependent Optimization

NASA Technical Reports Server (NTRS)

Yamaleev, N. K.; Diskin, B.; Nielsen, E. J.

2008-01-01

This paper presents a discrete adjoint method for a broad class of time-dependent optimization problems. The time-dependent adjoint equations are derived in terms of the discrete residual of an arbitrary finite volume scheme which approximates unsteady conservation law equations. Although only the 2-D unsteady Euler equations are considered in the present analysis, this time-dependent adjoint method is applicable to the 3-D unsteady Reynolds-averaged Navier-Stokes equations with minor modifications. The discrete adjoint operators involving the derivatives of the discrete residual and the cost functional with respect to the flow variables are computed using a complex-variable approach, which provides discrete consistency and drastically reduces the implementation and debugging cycle. The implementation of the time-dependent adjoint method is validated by comparing the sensitivity derivative with that obtained by forward mode differentiation. Our numerical results show that O(10) optimization iterations of the steepest descent method are needed to reduce the objective functional by 3-6 orders of magnitude for test problems considered.

Resolving the multiple sequence alignment problem using biogeography-based optimization with multiple populations.

PubMed

Zemali, El-Amine; Boukra, Abdelmadjid

2015-08-01

The multiple sequence alignment (MSA) is one of the most challenging problems in bioinformatics, it involves discovering similarity between a set of protein or DNA sequences. This paper introduces a new method for the MSA problem called biogeography-based optimization with multiple populations (BBOMP). It is based on a recent metaheuristic inspired from the mathematics of biogeography named biogeography-based optimization (BBO). To improve the exploration ability of BBO, we have introduced a new concept allowing better exploration of the search space. It consists of manipulating multiple populations having each one its own parameters. These parameters are used to build up progressive alignments allowing more diversity. At each iteration, the best found solution is injected in each population. Moreover, to improve solution quality, six operators are defined. These operators are selected with a dynamic probability which changes according to the operators efficiency. In order to test proposed approach performance, we have considered a set of datasets from Balibase 2.0 and compared it with many recent algorithms such as GAPAM, MSA-GA, QEAMSA and RBT-GA. The results show that the proposed approach achieves better average score than the previously cited methods.

An improved 3D MoF method based on analytical partial derivatives

NASA Astrophysics Data System (ADS)

Chen, Xiang; Zhang, Xiong

2016-12-01

MoF (Moment of Fluid) method is one of the most accurate approaches among various surface reconstruction algorithms. As other second order methods, MoF method needs to solve an implicit optimization problem to obtain the optimal approximate surface. Therefore, the partial derivatives of the objective function have to be involved during the iteration for efficiency and accuracy. However, to the best of our knowledge, the derivatives are currently estimated numerically by finite difference approximation because it is very difficult to obtain the analytical derivatives of the object function for an implicit optimization problem. Employing numerical derivatives in an iteration not only increase the computational cost, but also deteriorate the convergence rate and robustness of the iteration due to their numerical error. In this paper, the analytical first order partial derivatives of the objective function are deduced for 3D problems. The analytical derivatives can be calculated accurately, so they are incorporated into the MoF method to improve its accuracy, efficiency and robustness. Numerical studies show that by using the analytical derivatives the iterations are converged in all mixed cells with the efficiency improvement of 3 to 4 times.

Modified allocation capacitated planning model in blood supply chain management

NASA Astrophysics Data System (ADS)

Mansur, A.; Vanany, I.; Arvitrida, N. I.

2018-04-01

Blood supply chain management (BSCM) is a complex process management that involves many cooperating stakeholders. BSCM involves four echelon processes, which are blood collection or procurement, production, inventory, and distribution. This research develops an optimization model of blood distribution planning. The efficiency of decentralization and centralization policies in a blood distribution chain are compared, by optimizing the amount of blood delivered from a blood center to a blood bank. This model is developed based on allocation problem of capacitated planning model. At the first stage, the capacity and the cost of transportation are considered to create an initial capacitated planning model. Then, the inventory holding and shortage costs are added to the model. These additional parameters of inventory costs lead the model to be more realistic and accurate.

Fully probabilistic control design in an adaptive critic framework.

PubMed

Herzallah, Randa; Kárný, Miroslav

2011-12-01

Optimal stochastic controller pushes the closed-loop behavior as close as possible to the desired one. The fully probabilistic design (FPD) uses probabilistic description of the desired closed loop and minimizes Kullback-Leibler divergence of the closed-loop description to the desired one. Practical exploitation of the fully probabilistic design control theory continues to be hindered by the computational complexities involved in numerically solving the associated stochastic dynamic programming problem; in particular, very hard multivariate integration and an approximate interpolation of the involved multivariate functions. This paper proposes a new fully probabilistic control algorithm that uses the adaptive critic methods to circumvent the need for explicitly evaluating the optimal value function, thereby dramatically reducing computational requirements. This is a main contribution of this paper. Copyright © 2011 Elsevier Ltd. All rights reserved.

Swimming of a sphere in a viscous incompressible fluid with inertia

NASA Astrophysics Data System (ADS)

Felderhof, B. U.; Jones, R. B.

2017-08-01

The swimming of a sphere immersed in a viscous incompressible fluid with inertia is studied for surface modulations of small amplitude on the basis of the Navier-Stokes equations. The mean swimming velocity and the mean rate of dissipation are expressed as quadratic forms in term of the surface displacements. With a choice of a basis set of modes the quadratic forms correspond to two Hermitian matrices. Optimization of the mean swimming velocity for given rate of dissipation requires the solution of a generalized eigenvalue problem involving the two matrices. It is found for surface modulations of low multipole order that the optimal swimming efficiency depends in intricate fashion on a dimensionless scale number involving the radius of the sphere, the period of the cycle, and the kinematic viscosity of the fluid.

Computing global minimizers to a constrained B-spline image registration problem from optimal l1 perturbations to block match data

PubMed Central

Castillo, Edward; Castillo, Richard; Fuentes, David; Guerrero, Thomas

2014-01-01

Purpose: Block matching is a well-known strategy for estimating corresponding voxel locations between a pair of images according to an image similarity metric. Though robust to issues such as image noise and large magnitude voxel displacements, the estimated point matches are not guaranteed to be spatially accurate. However, the underlying optimization problem solved by the block matching procedure is similar in structure to the class of optimization problem associated with B-spline based registration methods. By exploiting this relationship, the authors derive a numerical method for computing a global minimizer to a constrained B-spline registration problem that incorporates the robustness of block matching with the global smoothness properties inherent to B-spline parameterization. Methods: The method reformulates the traditional B-spline registration problem as a basis pursuit problem describing the minimal l1-perturbation to block match pairs required to produce a B-spline fitting error within a given tolerance. The sparsity pattern of the optimal perturbation then defines a voxel point cloud subset on which the B-spline fit is a global minimizer to a constrained variant of the B-spline registration problem. As opposed to traditional B-spline algorithms, the optimization step involving the actual image data is addressed by block matching. Results: The performance of the method is measured in terms of spatial accuracy using ten inhale/exhale thoracic CT image pairs (available for download at www.dir-lab.com) obtained from the COPDgene dataset and corresponding sets of expert-determined landmark point pairs. The results of the validation procedure demonstrate that the method can achieve a high spatial accuracy on a significantly complex image set. Conclusions: The proposed methodology is demonstrated to achieve a high spatial accuracy and is generalizable in that in can employ any displacement field parameterization described as a least squares fit to block match generated estimates. Thus, the framework allows for a wide range of image similarity block match metric and physical modeling combinations. PMID:24694135

Blind Deconvolution for Distributed Parameter Systems with Unbounded Input and Output and Determining Blood Alcohol Concentration from Transdermal Biosensor Data.

PubMed

Rosen, I G; Luczak, Susan E; Weiss, Jordan

2014-03-15

We develop a blind deconvolution scheme for input-output systems described by distributed parameter systems with boundary input and output. An abstract functional analytic theory based on results for the linear quadratic control of infinite dimensional systems with unbounded input and output operators is presented. The blind deconvolution problem is then reformulated as a series of constrained linear and nonlinear optimization problems involving infinite dimensional dynamical systems. A finite dimensional approximation and convergence theory is developed. The theory is applied to the problem of estimating blood or breath alcohol concentration (respectively, BAC or BrAC) from biosensor-measured transdermal alcohol concentration (TAC) in the field. A distributed parameter model with boundary input and output is proposed for the transdermal transport of ethanol from the blood through the skin to the sensor. The problem of estimating BAC or BrAC from the TAC data is formulated as a blind deconvolution problem. A scheme to identify distinct drinking episodes in TAC data based on a Hodrick Prescott filter is discussed. Numerical results involving actual patient data are presented.

Sustainable aggregate production planning in the chemical process industry - A benchmark problem and dataset.

PubMed

Brandenburg, Marcus; Hahn, Gerd J

2018-06-01

Process industries typically involve complex manufacturing operations and thus require adequate decision support for aggregate production planning (APP). The need for powerful and efficient approaches to solve complex APP problems persists. Problem-specific solution approaches are advantageous compared to standardized approaches that are designed to provide basic decision support for a broad range of planning problems but inadequate to optimize under consideration of specific settings. This in turn calls for methods to compare different approaches regarding their computational performance and solution quality. In this paper, we present a benchmarking problem for APP in the chemical process industry. The presented problem focuses on (i) sustainable operations planning involving multiple alternative production modes/routings with specific production-related carbon emission and the social dimension of varying operating rates and (ii) integrated campaign planning with production mix/volume on the operational level. The mutual trade-offs between economic, environmental and social factors can be considered as externalized factors (production-related carbon emission and overtime working hours) as well as internalized ones (resulting costs). We provide data for all problem parameters in addition to a detailed verbal problem statement. We refer to Hahn and Brandenburg [1] for a first numerical analysis based on and for future research perspectives arising from this benchmarking problem.

Adaptive building skin structures

NASA Astrophysics Data System (ADS)

Del Grosso, A. E.; Basso, P.

2010-12-01

The concept of adaptive and morphing structures has gained considerable attention in the recent years in many fields of engineering. In civil engineering very few practical applications are reported to date however. Non-conventional structural concepts like deployable, inflatable and morphing structures may indeed provide innovative solutions to some of the problems that the construction industry is being called to face. To give some examples, searches for low-energy consumption or even energy-harvesting green buildings are amongst such problems. This paper first presents a review of the above problems and technologies, which shows how the solution to these problems requires a multidisciplinary approach, involving the integration of architectural and engineering disciplines. The discussion continues with the presentation of a possible application of two adaptive and dynamically morphing structures which are proposed for the realization of an acoustic envelope. The core of the two applications is the use of a novel optimization process which leads the search for optimal solutions by means of an evolutionary technique while the compatibility of the resulting configurations of the adaptive envelope is ensured by the virtual force density method.

Schizotypy and Performance on an Insight Problem-Solving Task: The Contribution of Persecutory Ideation.

PubMed

Cosgrave, Jan; Haines, Ross; Golodetz, Stuart; Claridge, Gordon; Wulff, Katharina; van Heugten-van der Kloet, Dalena

2018-01-01

Insight problem solving is thought to underpin creative thought as it incorporates both divergent (generating multiple ideas and solutions) and convergent (arriving at the optimal solution) thinking approaches. The current literature on schizotypy and creativity is mixed and requires clarification. An alternate approach was employed by designing an exploratory web-based study using only correlates of schizotypal traits (paranoia, dissociation, cognitive failures, fantasy proneness, and unusual sleep experiences) and examining which (if any) predicted optimal performance on an insight problem-solving task. One hundred and twenty-one participants were recruited online from the general population and completed the number reduction task. The discovery of the hidden rule (HR) was used as a measure of insight. Multivariate logistic regression analyses highlighted persecutory ideation to best predict the discovery of the HR (OR = 1.05; 95% CI 1.01-1.10, p = 0.017), with a one-point increase in persecutory ideas corresponding to the participant being 5% more likely to discover the HR. This result suggests that persecutory ideation, above other schizotypy correlates, may be involved in insight problem solving.

Bi-objective optimization of a multiple-target active debris removal mission

NASA Astrophysics Data System (ADS)

Bérend, Nicolas; Olive, Xavier

2016-05-01

The increasing number of space debris in Low-Earth Orbit (LEO) raises the question of future Active Debris Removal (ADR) operations. Typical ADR scenarios rely on an Orbital Transfer Vehicle (OTV) using one of the two following disposal strategies: the first one consists in attaching a deorbiting kit, such as a solid rocket booster, to the debris after rendezvous; with the second one, the OTV captures the debris and moves it to a low-perigee disposal orbit. For multiple-target ADR scenarios, the design of such a mission is very complex, as it involves two optimization levels: one for the space debris sequence, and a second one for the "elementary" orbit transfer strategy from a released debris to the next one in the sequence. This problem can be seen as a Time-Dependant Traveling Salesman Problem (TDTSP) with two objective functions to minimize: the total mission duration and the total propellant consumption. In order to efficiently solve this problem, ONERA has designed, under CNES contract, TOPAS (Tool for Optimal Planning of ADR Sequence), a tool that implements a Branch & Bound method developed in previous work together with a dedicated algorithm for optimizing the "elementary" orbit transfer. A single run of this tool yields an estimation of the Pareto front of the problem, which exhibits the trade-off between mission duration and propellant consumption. We first detail our solution to cope with the combinatorial explosion of complex ADR scenarios with 10 debris. The key point of this approach is to define the orbit transfer strategy through a small set of parameters, allowing an acceptable compromise between the quality of the optimum solution and the calculation cost. Then we present optimization results obtained for various 10 debris removal scenarios involving a 15-ton OTV, using either the deorbiting kit or the disposal orbit strategy. We show that the advantage of one strategy upon the other depends on the propellant margin, the maximum duration allowed for the mission and the orbit inclination domain. For high inclination orbits near 98 deg, the disposal orbit strategy is more appropriate for short duration missions, while the deorbiting kit strategy ensures a better propellant margin. Conversely, for lower inclination orbits near 65 deg, the deorbiting kit strategy appears to be the only possible with a 10 debris set. We eventually explain the consistency of these results with regards to astrodynamics.

A neural network strategy for end-point optimization of batch processes.

PubMed

Krothapally, M; Palanki, S

1999-01-01

The traditional way of operating batch processes has been to utilize an open-loop "golden recipe". However, there can be substantial batch to batch variation in process conditions and this open-loop strategy can lead to non-optimal operation. In this paper, a new approach is presented for end-point optimization of batch processes by utilizing neural networks. This strategy involves the training of two neural networks; one to predict switching times and the other to predict the input profile in the singular region. This approach alleviates the computational problems associated with the classical Pontryagin's approach and the nonlinear programming approach. The efficacy of this scheme is illustrated via simulation of a fed-batch fermentation.

Using ant colony optimization on the quadratic assignment problem to achieve low energy cost in geo-distributed data centers

NASA Astrophysics Data System (ADS)

Osei, Richard

There are many problems associated with operating a data center. Some of these problems include data security, system performance, increasing infrastructure complexity, increasing storage utilization, keeping up with data growth, and increasing energy costs. Energy cost differs by location, and at most locations fluctuates over time. The rising cost of energy makes it harder for data centers to function properly and provide a good quality of service. With reduced energy cost, data centers will have longer lasting servers/equipment, higher availability of resources, better quality of service, a greener environment, and reduced service and software costs for consumers. Some of the ways that data centers have tried to using to reduce energy costs include dynamically switching on and off servers based on the number of users and some predefined conditions, the use of environmental monitoring sensors, and the use of dynamic voltage and frequency scaling (DVFS), which enables processors to run at different combinations of frequencies with voltages to reduce energy cost. This thesis presents another method by which energy cost at data centers could be reduced. This method involves the use of Ant Colony Optimization (ACO) on a Quadratic Assignment Problem (QAP) in assigning user request to servers in geo-distributed data centers. In this paper, an effort to reduce data center energy cost involves the use of front portals, which handle users' requests, were used as ants to find cost effective ways to assign users requests to a server in heterogeneous geo-distributed data centers. The simulation results indicate that the ACO for Optimal Server Activation and Task Placement algorithm reduces energy cost on a small and large number of users' requests in a geo-distributed data center and its performance increases as the input data grows. In a simulation with 3 geo-distributed data centers, and user's resource request ranging from 25,000 to 25,000,000, the ACO algorithm was able to reduce energy cost on an average of $.70 per second. The ACO for Optimal Server Activation and Task Placement algorithm has proven to work as an alternative or improvement in reducing energy cost in geo-distributed data centers.

Dual-mode nested search method for categorical uncertain multi-objective optimization

NASA Astrophysics Data System (ADS)

Tang, Long; Wang, Hu

2016-10-01

Categorical multi-objective optimization is an important issue involved in many matching design problems. Non-numerical variables and their uncertainty are the major challenges of such optimizations. Therefore, this article proposes a dual-mode nested search (DMNS) method. In the outer layer, kriging metamodels are established using standard regular simplex mapping (SRSM) from categorical candidates to numerical values. Assisted by the metamodels, a k-cluster-based intelligent sampling strategy is developed to search Pareto frontier points. The inner layer uses an interval number method to model the uncertainty of categorical candidates. To improve the efficiency, a multi-feature convergent optimization via most-promising-area stochastic search (MFCOMPASS) is proposed to determine the bounds of objectives. Finally, typical numerical examples are employed to demonstrate the effectiveness of the proposed DMNS method.

Optimal control on hybrid ode systems with application to a tick disease model.

PubMed

Ding, Wandi

2007-10-01

We are considering an optimal control problem for a type of hybrid system involving ordinary differential equations and a discrete time feature. One state variable has dynamics in only one season of the year and has a jump condition to obtain the initial condition for that corresponding season in the next year. The other state variable has continuous dynamics. Given a general objective functional, existence, necessary conditions and uniqueness for an optimal control are established. We apply our approach to a tick-transmitted disease model with age structure in which the tick dynamics changes seasonally while hosts have continuous dynamics. The goal is to maximize disease-free ticks and minimize infected ticks through an optimal control strategy of treatment with acaricide. Numerical examples are given to illustrate the results.

An experimental sample of the field gamma-spectrometer based on solid state Si-photomultiplier

NASA Astrophysics Data System (ADS)

Denisov, Viktor; Korotaev, Valery; Titov, Aleksandr; Blokhina, Anastasia; Kleshchenok, Maksim

2017-05-01

Design of optical-electronic devices and systems involves the selection of such technical patterns that under given initial requirements and conditions are optimal according to certain criteria. The original characteristic of the OES for any purpose, defining its most important feature ability is a threshold detection. Based on this property, will be achieved the required functional quality of the device or system. Therefore, the original criteria and optimization methods have to subordinate to the idea of a better detectability. Generally reduces to the problem of optimal selection of the expected (predetermined) signals in the predetermined observation conditions. Thus the main purpose of optimization of the system when calculating its detectability is the choice of circuits and components that provide the most effective selection of a target.

Is there more to communications technology than just information transfer

NASA Astrophysics Data System (ADS)

Kaltschmidt, H.

1980-02-01

In the present paper, communications is discussed in terms of information transfer among people, among automata, and among people and automata. Communications is treated as a cybernetics problem involving information sources and sinks. The principal signals and components of a communications system are examined, along with frequency- and time-multiplexing, optimal detection, correlators, etc.

IFSM fractal image compression with entropy and sparsity constraints: A sequential quadratic programming approach

NASA Astrophysics Data System (ADS)

Kunze, Herb; La Torre, Davide; Lin, Jianyi

2017-01-01

We consider the inverse problem associated with IFSM: Given a target function f , find an IFSM, such that its fixed point f ¯ is sufficiently close to f in the Lp distance. Forte and Vrscay [1] showed how to reduce this problem to a quadratic optimization model. In this paper, we extend the collage-based method developed by Kunze, La Torre and Vrscay ([2][3][4]), by proposing the minimization of the 1-norm instead of the 0-norm. In fact, optimization problems involving the 0-norm are combinatorial in nature, and hence in general NP-hard. To overcome these difficulties, we introduce the 1-norm and propose a Sequential Quadratic Programming algorithm to solve the corresponding inverse problem. As in Kunze, La Torre and Vrscay [3] in our formulation, the minimization of collage error is treated as a multi-criteria problem that includes three different and conflicting criteria i.e., collage error, entropy and sparsity. This multi-criteria program is solved by means of a scalarization technique which reduces the model to a single-criterion program by combining all objective functions with different trade-off weights. The results of some numerical computations are presented.

A Two-Stage Stochastic Mixed-Integer Programming Approach to the Smart House Scheduling Problem

NASA Astrophysics Data System (ADS)

Ozoe, Shunsuke; Tanaka, Yoichi; Fukushima, Masao

A “Smart House” is a highly energy-optimized house equipped with photovoltaic systems (PV systems), electric battery systems, fuel cell cogeneration systems (FC systems), electric vehicles (EVs) and so on. Smart houses are attracting much attention recently thanks to their enhanced ability to save energy by making full use of renewable energy and by achieving power grid stability despite an increased power draw for installed PV systems. Yet running a smart house's power system, with its multiple power sources and power storages, is no simple task. In this paper, we consider the problem of power scheduling for a smart house with a PV system, an FC system and an EV. We formulate the problem as a mixed integer programming problem, and then extend it to a stochastic programming problem involving recourse costs to cope with uncertain electricity demand, heat demand and PV power generation. Using our method, we seek to achieve the optimal power schedule running at the minimum expected operation cost. We present some results of numerical experiments with data on real-life demands and PV power generation to show the effectiveness of our method.

Closed-loop optimization of chromatography column sizing strategies in biopharmaceutical manufacture.

PubMed

Allmendinger, Richard; Simaria, Ana S; Turner, Richard; Farid, Suzanne S

2014-10-01

This paper considers a real-world optimization problem involving the identification of cost-effective equipment sizing strategies for the sequence of chromatography steps employed to purify biopharmaceuticals. Tackling this problem requires solving a combinatorial optimization problem subject to multiple constraints, uncertain parameters, and time-consuming fitness evaluations. An industrially-relevant case study is used to illustrate that evolutionary algorithms can identify chromatography sizing strategies with significant improvements in performance criteria related to process cost, time and product waste over the base case. The results demonstrate also that evolutionary algorithms perform best when infeasible solutions are repaired intelligently, the population size is set appropriately, and elitism is combined with a low number of Monte Carlo trials (needed to account for uncertainty). Adopting this setup turns out to be more important for scenarios where less time is available for the purification process. Finally, a data-visualization tool is employed to illustrate how user preferences can be accounted for when it comes to selecting a sizing strategy to be implemented in a real industrial setting. This work demonstrates that closed-loop evolutionary optimization, when tuned properly and combined with a detailed manufacturing cost model, acts as a powerful decisional tool for the identification of cost-effective purification strategies. © 2013 The Authors. Journal of Chemical Technology & Biotechnology published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry.

Closed-loop optimization of chromatography column sizing strategies in biopharmaceutical manufacture

PubMed Central

Allmendinger, Richard; Simaria, Ana S; Turner, Richard; Farid, Suzanne S

2014-01-01

BACKGROUND This paper considers a real-world optimization problem involving the identification of cost-effective equipment sizing strategies for the sequence of chromatography steps employed to purify biopharmaceuticals. Tackling this problem requires solving a combinatorial optimization problem subject to multiple constraints, uncertain parameters, and time-consuming fitness evaluations. RESULTS An industrially-relevant case study is used to illustrate that evolutionary algorithms can identify chromatography sizing strategies with significant improvements in performance criteria related to process cost, time and product waste over the base case. The results demonstrate also that evolutionary algorithms perform best when infeasible solutions are repaired intelligently, the population size is set appropriately, and elitism is combined with a low number of Monte Carlo trials (needed to account for uncertainty). Adopting this setup turns out to be more important for scenarios where less time is available for the purification process. Finally, a data-visualization tool is employed to illustrate how user preferences can be accounted for when it comes to selecting a sizing strategy to be implemented in a real industrial setting. CONCLUSION This work demonstrates that closed-loop evolutionary optimization, when tuned properly and combined with a detailed manufacturing cost model, acts as a powerful decisional tool for the identification of cost-effective purification strategies. © 2013 The Authors. Journal of Chemical Technology & Biotechnology published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry. PMID:25506115

The pre-image problem in kernel methods.

PubMed

Kwok, James Tin-yau; Tsang, Ivor Wai-hung

2004-11-01

In this paper, we address the problem of finding the pre-image of a feature vector in the feature space induced by a kernel. This is of central importance in some kernel applications, such as on using kernel principal component analysis (PCA) for image denoising. Unlike the traditional method which relies on nonlinear optimization, our proposed method directly finds the location of the pre-image based on distance constraints in the feature space. It is noniterative, involves only linear algebra and does not suffer from numerical instability or local minimum problems. Evaluations on performing kernel PCA and kernel clustering on the USPS data set show much improved performance.

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.

Scope of Gradient and Genetic Algorithms in Multivariable Function Optimization

NASA Technical Reports Server (NTRS)

Shaykhian, Gholam Ali; Sen, S. K.

2007-01-01

Global optimization of a multivariable function - constrained by bounds specified on each variable and also unconstrained - is an important problem with several real world applications. Deterministic methods such as the gradient algorithms as well as the randomized methods such as the genetic algorithms may be employed to solve these problems. In fact, there are optimization problems where a genetic algorithm/an evolutionary approach is preferable at least from the quality (accuracy) of the results point of view. From cost (complexity) point of view, both gradient and genetic approaches are usually polynomial-time; there are no serious differences in this regard, i.e., the computational complexity point of view. However, for certain types of problems, such as those with unacceptably erroneous numerical partial derivatives and those with physically amplified analytical partial derivatives whose numerical evaluation involves undesirable errors and/or is messy, a genetic (stochastic) approach should be a better choice. We have presented here the pros and cons of both the approaches so that the concerned reader/user can decide which approach is most suited for the problem at hand. Also for the function which is known in a tabular form, instead of an analytical form, as is often the case in an experimental environment, we attempt to provide an insight into the approaches focusing our attention toward accuracy. Such an insight will help one to decide which method, out of several available methods, should be employed to obtain the best (least error) output. *

Optimisation multi-objectif des systemes energetiques

NASA Astrophysics Data System (ADS)

Dipama, Jean

The increasing demand of energy and the environmental concerns related to greenhouse gas emissions lead to more and more private or public utilities to turn to nuclear energy as an alternative for the future. Nuclear power plants are then called to experience large expansion in the coming years. Improved technologies will then be put in place to support the development of these plants. This thesis considers the optimization of the thermodynamic cycle of the secondary loop of Gentilly-2 nuclear power plant in terms of output power and thermal efficiency. In this thesis, investigations are carried out to determine the optimal operating conditions of steam power cycles by the judicious use of the combination of steam extraction at the different stages of the turbines. Whether it is the case of superheating or regeneration, we are confronted in all cases to an optimization problem involving two conflicting objectives, as increasing the efficiency imply the decrease of mechanical work and vice versa. Solving this kind of problem does not lead to unique solution, but to a set of solutions that are tradeoffs between the conflicting objectives. To search all of these solutions, called Pareto optimal solutions, the use of an appropriate optimization algorithm is required. Before starting the optimization of the secondary loop, we developed a thermodynamic model of the secondary loop which includes models for the main thermal components (e.g., turbine, moisture separator-superheater, condenser, feedwater heater and deaerator). This model is used to calculate the thermodynamic state of the steam and water at the different points of the installation. The thermodynamic model has been developed with Matlab and validated by comparing its predictions with the operating data provided by the engineers of the power plant. The optimizer developed in VBA (Visual Basic for Applications) uses an optimization algorithm based on the principle of genetic algorithms, a stochastic optimization method which is very robust and widely used to solve problems usually difficult to handle by traditional methods. Genetic algorithms (GAs) have been used in previous research and proved to be efficient in optimizing heat exchangers networks (HEN) (Dipama et al., 2008). So, HEN have been synthesized to recover the maximum heat in an industrial process. The optimization problem formulated in the context of this work consists of a single objective, namely the maximization of energy recovery. The optimization algorithm developed in this thesis extends the ability of GAs by taking into account several objectives simultaneously. This algorithm provides an innovation in the method of finding optimal solutions, by using a technique which consist of partitioning the solutions space in the form of parallel grids called "watching corridors". These corridors permit to specify areas (the observation corridors) in which the most promising feasible solutions are found and used to guide the search towards optimal solutions. A measure of the progress of the search is incorporated into the optimization algorithm to make it self-adaptive through the use of appropriate genetic operators at each stage of optimization process. The proposed method allows a fast convergence and ensure a diversity of solutions. Moreover, this method gives the algorithm the ability to overcome difficulties associated with optimizing problems with complex Pareto front landscapes (e.g., discontinuity, disjunction, etc.). The multi-objective optimization algorithm has been first validated using numerical test problems found in the literature as well as energy systems optimization problems. Finally, the proposed optimization algorithm has been applied for the optimization of the secondary loop of Gentilly-2 nuclear power plant, and a set of solutions have been found which permit to make the power plant operate in optimal conditions. (Abstract shortened by UMI.)

An optimizing start-up strategy for a bio-methanator.

PubMed

Sbarciog, Mihaela; Loccufier, Mia; Vande Wouwer, Alain

2012-05-01

This paper presents an optimizing start-up strategy for a bio-methanator. The goal of the control strategy is to maximize the outflow rate of methane in anaerobic digestion processes, which can be described by a two-population model. The methodology relies on a thorough analysis of the system dynamics and involves the solution of two optimization problems: steady-state optimization for determining the optimal operating point and transient optimization. The latter is a classical optimal control problem, which can be solved using the maximum principle of Pontryagin. The proposed control law is of the bang-bang type. The process is driven from an initial state to a small neighborhood of the optimal steady state by switching the manipulated variable (dilution rate) from the minimum to the maximum value at a certain time instant. Then the dilution rate is set to the optimal value and the system settles down in the optimal steady state. This control law ensures the convergence of the system to the optimal steady state and substantially increases its stability region. The region of attraction of the steady state corresponding to maximum production of methane is considerably enlarged. In some cases, which are related to the possibility of selecting the minimum dilution rate below a certain level, the stability region of the optimal steady state equals the interior of the state space. Aside its efficiency, which is evaluated not only in terms of biogas production but also from the perspective of treatment of the organic load, the strategy is also characterized by simplicity, being thus appropriate for implementation in real-life systems. Another important advantage is its generality: this technique may be applied to any anaerobic digestion process, for which the acidogenesis and methanogenesis are, respectively, characterized by Monod and Haldane kinetics.

Sensitivity Analysis of Genetic Algorithm Parameters for Optimal Groundwater Monitoring Network Design

NASA Astrophysics Data System (ADS)

Abdeh-Kolahchi, A.; Satish, M.; Datta, B.

2004-05-01

A state art groundwater monitoring network design is introduced. The method combines groundwater flow and transport results with optimization Genetic Algorithm (GA) to identify optimal monitoring well locations. Optimization theory uses different techniques to find a set of parameter values that minimize or maximize objective functions. The suggested groundwater optimal monitoring network design is based on the objective of maximizing the probability of tracking a transient contamination plume by determining sequential monitoring locations. The MODFLOW and MT3DMS models included as separate modules within the Groundwater Modeling System (GMS) are used to develop three dimensional groundwater flow and contamination transport simulation. The groundwater flow and contamination simulation results are introduced as input to the optimization model, using Genetic Algorithm (GA) to identify the groundwater optimal monitoring network design, based on several candidate monitoring locations. The groundwater monitoring network design model is used Genetic Algorithms with binary variables representing potential monitoring location. As the number of decision variables and constraints increase, the non-linearity of the objective function also increases which make difficulty to obtain optimal solutions. The genetic algorithm is an evolutionary global optimization technique, which is capable of finding the optimal solution for many complex problems. In this study, the GA approach capable of finding the global optimal solution to a groundwater monitoring network design problem involving 18.4X 1018 feasible solutions will be discussed. However, to ensure the efficiency of the solution process and global optimality of the solution obtained using GA, it is necessary that appropriate GA parameter values be specified. The sensitivity analysis of genetic algorithms parameters such as random number, crossover probability, mutation probability, and elitism are discussed for solution of monitoring network design.

Ethnic variation in localized prostate cancer: a pilot study of preferences, optimism, and quality of life among black and white veterans.

PubMed

Knight, Sara J; Siston, Amy K; Chmiel, Joan S; Slimack, Nicholas; Elstein, Arthur S; Chapman, Gretchen B; Nadler, Robert B; Bennett, Charles L

2004-06-01

Ethnic variations that may influence the preferences and outcomes associated with prostate cancer treatment are not well delineated. Our objective was to evaluate prospectively preferences, optimism, involvement in care, and quality of life (QOL) in black and white veterans newly diagnosed with localized prostate cancer. A total of 95 men who identified themselves as black/African-American or white who had newly diagnosed, localized prostate cancer completed a "time trade-off" task to assess utilities for current health and mild, moderate, and severe functional impairment; importance rankings for attributes associated with prostate cancer (eg, urinary function); and baseline and follow-up measures of optimism, involvement in care, and QOL. Interviews were scheduled before treatment, and at 3 and 12 months after treatment. At baseline, both blacks and whites ranked pain, bowel, and bladder function as their most important concerns. Optimism, involvement in care, and QOL were similar. Utilities for mild impairment were lower for blacks than whites, but were similar for moderate and severe problems. Decline in QOL at 3 and 12 months compared to baseline occurred for both groups. However, even with adjustment for marital status, education level, and treatment, blacks had less increase in nausea and vomiting and more increase in difficulty with sexual interest and weight gain compared with whites. Black and white veterans entered localized prostate cancer treatment with similar priorities, optimism, and involvement in care. Quality-of-life declines were common to both groups during the first year after diagnosis, but ethnic variation occurred with respect to nausea and vomiting, sexual interest, and weight gain.

Calibrating the Spatiotemporal Root Density Distribution for Macroscopic Water Uptake Models Using Tikhonov Regularization

NASA Astrophysics Data System (ADS)

Li, N.; Yue, X. Y.

2018-03-01

Macroscopic root water uptake models proportional to a root density distribution function (RDDF) are most commonly used to model water uptake by plants. As the water uptake is difficult and labor intensive to measure, these models are often calibrated by inverse modeling. Most previous inversion studies assume RDDF to be constant with depth and time or dependent on only depth for simplification. However, under field conditions, this function varies with type of soil and root growth and thus changes with both depth and time. This study proposes an inverse method to calibrate both spatially and temporally varying RDDF in unsaturated water flow modeling. To overcome the difficulty imposed by the ill-posedness, the calibration is formulated as an optimization problem in the framework of the Tikhonov regularization theory, adding additional constraint to the objective function. Then the formulated nonlinear optimization problem is numerically solved with an efficient algorithm on the basis of the finite element method. The advantage of our method is that the inverse problem is translated into a Tikhonov regularization functional minimization problem and then solved based on the variational construction, which circumvents the computational complexity in calculating the sensitivity matrix involved in many derivative-based parameter estimation approaches (e.g., Levenberg-Marquardt optimization). Moreover, the proposed method features optimization of RDDF without any prior form, which is applicable to a more general root water uptake model. Numerical examples are performed to illustrate the applicability and effectiveness of the proposed method. Finally, discussions on the stability and extension of this method are presented.

Recourse-based facility-location problems in hybrid uncertain environment.

PubMed

Wang, Shuming; Watada, Junzo; Pedrycz, Witold

2010-08-01

The objective of this paper is to study facility-location problems in the presence of a hybrid uncertain environment involving both randomness and fuzziness. A two-stage fuzzy-random facility-location model with recourse (FR-FLMR) is developed in which both the demands and costs are assumed to be fuzzy-random variables. The bounds of the optimal objective value of the two-stage FR-FLMR are derived. As, in general, the fuzzy-random parameters of the FR-FLMR can be regarded as continuous fuzzy-random variables with an infinite number of realizations, the computation of the recourse requires solving infinite second-stage programming problems. Owing to this requirement, the recourse function cannot be determined analytically, and, hence, the model cannot benefit from the use of techniques of classical mathematical programming. In order to solve the location problems of this nature, we first develop a technique of fuzzy-random simulation to compute the recourse function. The convergence of such simulation scenarios is discussed. In the sequel, we propose a hybrid mutation-based binary ant-colony optimization (MBACO) approach to the two-stage FR-FLMR, which comprises the fuzzy-random simulation and the simplex algorithm. A numerical experiment illustrates the application of the hybrid MBACO algorithm. The comparison shows that the hybrid MBACO finds better solutions than the one using other discrete metaheuristic algorithms, such as binary particle-swarm optimization, genetic algorithm, and tabu search.

Cohesive phase-field fracture and a PDE constrained optimization approach to fracture inverse problems

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

Tupek, Michael R.

2016-06-30

In recent years there has been a proliferation of modeling techniques for forward predictions of crack propagation in brittle materials, including: phase-field/gradient damage models, peridynamics, cohesive-zone models, and G/XFEM enrichment techniques. However, progress on the corresponding inverse problems has been relatively lacking. Taking advantage of key features of existing modeling approaches, we propose a parabolic regularization of Barenblatt cohesive models which borrows extensively from previous phase-field and gradient damage formulations. An efficient explicit time integration strategy for this type of nonlocal fracture model is then proposed and justified. In addition, we present a C++ computational framework for computing in- putmore » parameter sensitivities efficiently for explicit dynamic problems using the adjoint method. This capability allows for solving inverse problems involving crack propagation to answer interesting engineering questions such as: 1) what is the optimal design topology and material placement for a heterogeneous structure to maximize fracture resistance, 2) what loads must have been applied to a structure for it to have failed in an observed way, 3) what are the existing cracks in a structure given various experimental observations, etc. In this work, we focus on the first of these engineering questions and demonstrate a capability to automatically and efficiently compute optimal designs intended to minimize crack propagation in structures.« less

Three examples of applied remote sensing of vegetation

NASA Technical Reports Server (NTRS)

Rouse, J. W., Jr.; Benton, A. R., Jr.; Toler, R. W.; Haas, R. H.

1975-01-01

Cause studies in which remote sensing techniques were adapted to assist in the solution of particular problem situations in Texas involving vegetation are described. In each case, the final sensing technique developed for operational use by the concerned organizations employed photographic sensors which were optimized through studies of the spectral reflectance characteristics of the vegetation species and background conditions unique to the problem being considered. The three examples described are: (1) Assisting Aquatic Plant Monitoring and Control; (2) Improving Vegetation Utilization in Urban Planning; and (3) Enforcing the Quarantine of Diseased Crops.

Maximum principle for a stochastic delayed system involving terminal state constraints.

PubMed

Wen, Jiaqiang; Shi, Yufeng

2017-01-01

We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set. We firstly introduce an equivalent backward delayed system depicted as a time-delayed backward stochastic differential equation. Then a stochastic maximum principle is obtained by virtue of Ekeland's variational principle. Finally, applications to a state constrained stochastic delayed linear-quadratic control model and a production-consumption choice problem are studied to illustrate the main obtained result.

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

Remote Sensing of Precipitation from Airborne and Spaceborne Radar. Chapter 13

NASA Technical Reports Server (NTRS)

Munchak, S. Joseph

2017-01-01

Weather radar measurements from airborne or satellite platforms can be an effective remote sensing tool for examining the three-dimensional structures of clouds and precipitation. This chapter describes some fundamental properties of radar measurements and their dependence on the particle size distribution (PSD) and radar frequency. The inverse problem of solving for the vertical profile of PSD from a profile of measured reflectivity is stated as an optimal estimation problem for single- and multi-frequency measurements. Phenomena that can change the measured reflectivity Z(sub m) from its intrinsic value Z(sub e), namely attenuation, non-uniform beam filling, and multiple scattering, are described and mitigation of these effects in the context of the optimal estimation framework is discussed. Finally, some techniques involving the use of passive microwave measurements to further constrain the retrieval of the PSD are presented.

Optimal use of human and machine resources for Space Station assembly operations

NASA Technical Reports Server (NTRS)

Parrish, Joseph C.

1988-01-01

This paper investigates the issues involved in determining the best mix of human and machine resources for assembly of the Space Station. It presents the current Station assembly sequence, along with descriptions of the available assembly resources. A number of methodologies for optimizing the human/machine tradeoff problem have been developed, but the Space Station assembly offers some unique issues that have not yet been addressed. These include a strong constraint on available EVA time for early flights and a phased deployment of assembly resources over time. A methodology for incorporating the previously developed decision methods to the special case of the Space Station is presented. This methodology emphasizes an application of multiple qualitative and quantitative techniques, including simulation and decision analysis, for producing an objective, robust solution to the tradeoff problem.

A fast direct solver for boundary value problems on locally perturbed geometries

NASA Astrophysics Data System (ADS)

Zhang, Yabin; Gillman, Adrianna

2018-03-01

Many applications including optimal design and adaptive discretization techniques involve solving several boundary value problems on geometries that are local perturbations of an original geometry. This manuscript presents a fast direct solver for boundary value problems that are recast as boundary integral equations. The idea is to write the discretized boundary integral equation on a new geometry as a low rank update to the discretized problem on the original geometry. Using the Sherman-Morrison formula, the inverse can be expressed in terms of the inverse of the original system applied to the low rank factors and the right hand side. Numerical results illustrate for problems where perturbation is localized the fast direct solver is three times faster than building a new solver from scratch.

Performance of Grey Wolf Optimizer on large scale problems

NASA Astrophysics Data System (ADS)

Gupta, Shubham; Deep, Kusum

2017-01-01

For solving nonlinear continuous problems of optimization numerous nature inspired optimization techniques are being proposed in literature which can be implemented to solve real life problems wherein the conventional techniques cannot be applied. Grey Wolf Optimizer is one of such technique which is gaining popularity since the last two years. The objective of this paper is to investigate the performance of Grey Wolf Optimization Algorithm on large scale optimization problems. The Algorithm is implemented on 5 common scalable problems appearing in literature namely Sphere, Rosenbrock, Rastrigin, Ackley and Griewank Functions. The dimensions of these problems are varied from 50 to 1000. The results indicate that Grey Wolf Optimizer is a powerful nature inspired Optimization Algorithm for large scale problems, except Rosenbrock which is a unimodal function.

Stochastic optimization of GeantV code by use of genetic algorithms

DOE PAGES

Amadio, G.; Apostolakis, J.; Bandieramonte, M.; ...

2017-10-01

GeantV is a complex system based on the interaction of different modules needed for detector simulation, which include transport of particles in fields, physics models simulating their interactions with matter and a geometrical modeler library for describing the detector and locating the particles and computing the path length to the current volume boundary. The GeantV project is recasting the classical simulation approach to get maximum benefit from SIMD/MIMD computational architectures and highly massive parallel systems. This involves finding the appropriate balance between several aspects influencing computational performance (floating-point performance, usage of off-chip memory bandwidth, specification of cache hierarchy, etc.) andmore » handling a large number of program parameters that have to be optimized to achieve the best simulation throughput. This optimization task can be treated as a black-box optimization problem, which requires searching the optimum set of parameters using only point-wise function evaluations. Here, the goal of this study is to provide a mechanism for optimizing complex systems (high energy physics particle transport simulations) with the help of genetic algorithms and evolution strategies as tuning procedures for massive parallel simulations. One of the described approaches is based on introducing a specific multivariate analysis operator that could be used in case of resource expensive or time consuming evaluations of fitness functions, in order to speed-up the convergence of the black-box optimization problem.« less

Stochastic optimization of GeantV code by use of genetic algorithms

NASA Astrophysics Data System (ADS)

Amadio, G.; Apostolakis, J.; Bandieramonte, M.; Behera, S. P.; Brun, R.; Canal, P.; Carminati, F.; Cosmo, G.; Duhem, L.; Elvira, D.; Folger, G.; Gheata, A.; Gheata, M.; Goulas, I.; Hariri, F.; Jun, S. Y.; Konstantinov, D.; Kumawat, H.; Ivantchenko, V.; Lima, G.; Nikitina, T.; Novak, M.; Pokorski, W.; Ribon, A.; Seghal, R.; Shadura, O.; Vallecorsa, S.; Wenzel, S.

2017-10-01

GeantV is a complex system based on the interaction of different modules needed for detector simulation, which include transport of particles in fields, physics models simulating their interactions with matter and a geometrical modeler library for describing the detector and locating the particles and computing the path length to the current volume boundary. The GeantV project is recasting the classical simulation approach to get maximum benefit from SIMD/MIMD computational architectures and highly massive parallel systems. This involves finding the appropriate balance between several aspects influencing computational performance (floating-point performance, usage of off-chip memory bandwidth, specification of cache hierarchy, etc.) and handling a large number of program parameters that have to be optimized to achieve the best simulation throughput. This optimization task can be treated as a black-box optimization problem, which requires searching the optimum set of parameters using only point-wise function evaluations. The goal of this study is to provide a mechanism for optimizing complex systems (high energy physics particle transport simulations) with the help of genetic algorithms and evolution strategies as tuning procedures for massive parallel simulations. One of the described approaches is based on introducing a specific multivariate analysis operator that could be used in case of resource expensive or time consuming evaluations of fitness functions, in order to speed-up the convergence of the black-box optimization problem.

Stochastic optimization of GeantV code by use of genetic algorithms

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

Amadio, G.; Apostolakis, J.; Bandieramonte, M.

GeantV is a complex system based on the interaction of different modules needed for detector simulation, which include transport of particles in fields, physics models simulating their interactions with matter and a geometrical modeler library for describing the detector and locating the particles and computing the path length to the current volume boundary. The GeantV project is recasting the classical simulation approach to get maximum benefit from SIMD/MIMD computational architectures and highly massive parallel systems. This involves finding the appropriate balance between several aspects influencing computational performance (floating-point performance, usage of off-chip memory bandwidth, specification of cache hierarchy, etc.) andmore » handling a large number of program parameters that have to be optimized to achieve the best simulation throughput. This optimization task can be treated as a black-box optimization problem, which requires searching the optimum set of parameters using only point-wise function evaluations. Here, the goal of this study is to provide a mechanism for optimizing complex systems (high energy physics particle transport simulations) with the help of genetic algorithms and evolution strategies as tuning procedures for massive parallel simulations. One of the described approaches is based on introducing a specific multivariate analysis operator that could be used in case of resource expensive or time consuming evaluations of fitness functions, in order to speed-up the convergence of the black-box optimization problem.« less

A numerical study of different projection-based model reduction techniques applied to computational homogenisation

NASA Astrophysics Data System (ADS)

Soldner, Dominic; Brands, Benjamin; Zabihyan, Reza; Steinmann, Paul; Mergheim, Julia

2017-10-01

Computing the macroscopic material response of a continuum body commonly involves the formulation of a phenomenological constitutive model. However, the response is mainly influenced by the heterogeneous microstructure. Computational homogenisation can be used to determine the constitutive behaviour on the macro-scale by solving a boundary value problem at the micro-scale for every so-called macroscopic material point within a nested solution scheme. Hence, this procedure requires the repeated solution of similar microscopic boundary value problems. To reduce the computational cost, model order reduction techniques can be applied. An important aspect thereby is the robustness of the obtained reduced model. Within this study reduced-order modelling (ROM) for the geometrically nonlinear case using hyperelastic materials is applied for the boundary value problem on the micro-scale. This involves the Proper Orthogonal Decomposition (POD) for the primary unknown and hyper-reduction methods for the arising nonlinearity. Therein three methods for hyper-reduction, differing in how the nonlinearity is approximated and the subsequent projection, are compared in terms of accuracy and robustness. Introducing interpolation or Gappy-POD based approximations may not preserve the symmetry of the system tangent, rendering the widely used Galerkin projection sub-optimal. Hence, a different projection related to a Gauss-Newton scheme (Gauss-Newton with Approximated Tensors- GNAT) is favoured to obtain an optimal projection and a robust reduced model.

AQMAN; linear and quadratic programming matrix generator using two-dimensional ground-water flow simulation for aquifer management modeling

USGS Publications Warehouse

Lefkoff, L.J.; Gorelick, S.M.

1987-01-01

A FORTRAN-77 computer program code that helps solve a variety of aquifer management problems involving the control of groundwater hydraulics. It is intended for use with any standard mathematical programming package that uses Mathematical Programming System input format. The computer program creates the input files to be used by the optimization program. These files contain all the hydrologic information and management objectives needed to solve the management problem. Used in conjunction with a mathematical programming code, the computer program identifies the pumping or recharge strategy that achieves a user 's management objective while maintaining groundwater hydraulic conditions within desired limits. The objective may be linear or quadratic, and may involve the minimization of pumping and recharge rates or of variable pumping costs. The problem may contain constraints on groundwater heads, gradients, and velocities for a complex, transient hydrologic system. Linear superposition of solutions to the transient, two-dimensional groundwater flow equation is used by the computer program in conjunction with the response matrix optimization method. A unit stress is applied at each decision well and transient responses at all control locations are computed using a modified version of the U.S. Geological Survey two dimensional aquifer simulation model. The program also computes discounted cost coefficients for the objective function and accounts for transient aquifer conditions. (Author 's abstract)

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.

Solving a four-destination traveling salesman problem using Escherichia coli cells as biocomputers.

PubMed

Esau, Michael; Rozema, Mark; Zhang, Tuo Huang; Zeng, Dawson; Chiu, Stephanie; Kwan, Rachel; Moorhouse, Cadence; Murray, Cameron; Tseng, Nien-Tsu; Ridgway, Doug; Sauvageau, Dominic; Ellison, Michael

2014-12-19

The Traveling Salesman Problem involves finding the shortest possible route visiting all destinations on a map only once before returning to the point of origin. The present study demonstrates a strategy for solving Traveling Salesman Problems using modified E. coli cells as processors for massively parallel computing. Sequential, combinatorial DNA assembly was used to generate routes, in the form of plasmids made up of marker genes, each representing a path between destinations, and short connecting linkers, each representing a given destination. Upon growth of the population of modified E. coli, phenotypic selection was used to eliminate invalid routes, and statistical analysis was performed to successfully identify the optimal solution. The strategy was successfully employed to solve a four-destination test problem.

An Efficient Method Coupling Kernel Principal Component Analysis with Adjoint-Based Optimal Control and Its Goal-Oriented Extensions

NASA Astrophysics Data System (ADS)

Thimmisetty, C.; Talbot, C.; Tong, C. H.; Chen, X.

2016-12-01

The representativeness of available data poses a significant fundamental challenge to the quantification of uncertainty in geophysical systems. Furthermore, the successful application of machine learning methods to geophysical problems involving data assimilation is inherently constrained by the extent to which obtainable data represent the problem considered. We show how the adjoint method, coupled with optimization based on methods of machine learning, can facilitate the minimization of an objective function defined on a space of significantly reduced dimension. By considering uncertain parameters as constituting a stochastic process, the Karhunen-Loeve expansion and its nonlinear extensions furnish an optimal basis with respect to which optimization using L-BFGS can be carried out. In particular, we demonstrate that kernel PCA can be coupled with adjoint-based optimal control methods to successfully determine the distribution of material parameter values for problems in the context of channelized deformable media governed by the equations of linear elasticity. Since certain subsets of the original data are characterized by different features, the convergence rate of the method in part depends on, and may be limited by, the observations used to furnish the kernel principal component basis. By determining appropriate weights for realizations of the stochastic random field, then, one may accelerate the convergence of the method. To this end, we present a formulation of Weighted PCA combined with a gradient-based means using automatic differentiation to iteratively re-weight observations concurrent with the determination of an optimal reduced set control variables in the feature space. We demonstrate how improvements in the accuracy and computational efficiency of the weighted linear method can be achieved over existing unweighted kernel methods, and discuss nonlinear extensions of the algorithm.

Application of an Evolution Strategy in Planetary Ephemeris Optimization

NASA Astrophysics Data System (ADS)

Mai, E.

2016-12-01

Classical planetary ephemeris construction comprises three major steps, which are performed iteratively: simultaneous numerical integration of coupled equations of motion of a multi-body system (propagator step), reduction of thousands of observations (reduction step), and optimization of various selected model parameters (adjustment step). This traditional approach is challenged by ongoing refinements in force modeling, e.g. inclusion of much more significant minor bodies, an ever-growing number of planetary observations, e.g. vast amount of spacecraft tracking data, etc. To master the high computational burden and in order to circumvent the need for inversion of huge normal equation matrices, we propose an alternative ephemeris construction method. The main idea is to solve the overall optimization problem by a straightforward direct evaluation of the whole set of mathematical formulas involved, rather than to solve it as an inverse problem with all its tacit mathematical assumptions and numerical difficulties. We replace the usual gradient search by a stochastic search, namely an evolution strategy, the latter of which is also perfect for the exploitation of parallel computing capabilities. Furthermore, this new approach enables multi-criteria optimization and time-varying optima. This issue will become important in future once ephemeris construction is just one part of even larger optimization problems, e.g. the combined and consistent determination of the physical state (orbit, size, shape, rotation, gravity,…) of celestial bodies (planets, satellites, asteroids, or comets), and if one seeks near real-time solutions. Here we outline the general idea and discuss first results. As an example, we present a simultaneous optimization of high-correlated asteroidal ring model parameters (total mass and heliocentric radius), based on simulations.

Applications of wavelet-based compression to multidimensional Earth science data

NASA Technical Reports Server (NTRS)

Bradley, Jonathan N.; Brislawn, Christopher M.

1993-01-01

A data compression algorithm involving vector quantization (VQ) and the discrete wavelet transform (DWT) is applied to two different types of multidimensional digital earth-science data. The algorithms (WVQ) is optimized for each particular application through an optimization procedure that assigns VQ parameters to the wavelet transform subbands subject to constraints on compression ratio and encoding complexity. Preliminary results of compressing global ocean model data generated on a Thinking Machines CM-200 supercomputer are presented. The WVQ scheme is used in both a predictive and nonpredictive mode. Parameters generated by the optimization algorithm are reported, as are signal-to-noise (SNR) measurements of actual quantized data. The problem of extrapolating hydrodynamic variables across the continental landmasses in order to compute the DWT on a rectangular grid is discussed. Results are also presented for compressing Landsat TM 7-band data using the WVQ scheme. The formulation of the optimization problem is presented along with SNR measurements of actual quantized data. Postprocessing applications are considered in which the seven spectral bands are clustered into 256 clusters using a k-means algorithm and analyzed using the Los Alamos multispectral data analysis program, SPECTRUM, both before and after being compressed using the WVQ program.

Software for Optimizing Plans Involving Interdependent Goals

NASA Technical Reports Server (NTRS)

Estlin, Tara; Gaines, Daniel; Rabideau, Gregg

2005-01-01

A computer program enables construction and optimization of plans for activities that are directed toward achievement of goals that are interdependent. Goal interdependence is defined as the achievement of one or more goals affecting the desirability or priority of achieving one or more other goals. This program is overlaid on the Automated Scheduling and Planning Environment (ASPEN) software system, aspects of which have been described in a number of prior NASA Tech Briefs articles. Unlike other known or related planning programs, this program considers interdependences among goals that can change between problems and provides a language for easily specifying such dependences. Specifications of the interdependences can be formulated dynamically and provided to the associated planning software as part of the goal input. Then an optimization algorithm provided by this program enables the planning software to reason about the interdependences and incorporate them into an overall objective function that it uses to rate the quality of a plan under construction and to direct its optimization search. In tests on a series of problems of planning geological experiments by a team of instrumented robotic vehicles (rovers) on new terrain, this program was found to enhance plan quality.

Convex relaxations for gas expansion planning

DOE PAGES

Borraz-Sanchez, Conrado; Bent, Russell Whitford; Backhaus, Scott N.; ...

2016-01-01

Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Here, given the non-convex nature of gas transmission constraints, global optimality and infeasibility guarantees can only be offered by global optimisation approaches. Unfortunately, state-of-the-art global optimisation solvers are unable to scale up to real-world size instances. In this study, we present a convex mixed-integer second-order cone relaxation for the gas expansion planning problem under steady-state conditions. The underlying model offers tight lower bounds with high computational efficiency. In addition, the optimal solution of the relaxation can often be used to derive high-quality solutionsmore » to the original problem, leading to provably tight optimality gaps and, in some cases, global optimal solutions. The convex relaxation is based on a few key ideas, including the introduction of flux direction variables, exact McCormick relaxations, on/off constraints, and integer cuts. Numerical experiments are conducted on the traditional Belgian gas network, as well as other real larger networks. The results demonstrate both the accuracy and computational speed of the relaxation and its ability to produce high-quality solution« less

On the role of constant-stress surfaces in the problem of minimizing elastic stress concentration

NASA Technical Reports Server (NTRS)

Wheeler, L.

1976-01-01

Cases involving antiplane shear deformation, axisymmetric torsion, and plane strain theory, with surfaces of constant stress magnitude optimal in terms of minimizing stress, are investigated. Results for the plane theory refer to exterior doubly connected domains. Stresses generated by torsion of an elastic solid lying within a radially convex region of revolution with plane ends, body force absent, and lateral surface traction-free, are examined. The unknown portion of the boundary of such domains may involve a hole, fillet, or notch.

A sequential solution for anisotropic total variation image denoising with interval constraints

NASA Astrophysics Data System (ADS)

Xu, Jingyan; Noo, Frédéric

2017-09-01

We show that two problems involving the anisotropic total variation (TV) and interval constraints on the unknown variables admit, under some conditions, a simple sequential solution. Problem 1 is a constrained TV penalized image denoising problem; problem 2 is a constrained fused lasso signal approximator. The sequential solution entails finding first the solution to the unconstrained problem, and then applying a thresholding to satisfy the constraints. If the interval constraints are uniform, this sequential solution solves problem 1. If the interval constraints furthermore contain zero, the sequential solution solves problem 2. Here uniform interval constraints refer to all unknowns being constrained to the same interval. A typical example of application is image denoising in x-ray CT, where the image intensities are non-negative as they physically represent linear attenuation coefficient in the patient body. Our results are simple yet seem unknown; we establish them using the Karush-Kuhn-Tucker conditions for constrained convex optimization.

Estimating 3D positions and velocities of projectiles from monocular views.

PubMed

Ribnick, Evan; Atev, Stefan; Papanikolopoulos, Nikolaos P

2009-05-01

In this paper, we consider the problem of localizing a projectile in 3D based on its apparent motion in a stationary monocular view. A thorough theoretical analysis is developed, from which we establish the minimum conditions for the existence of a unique solution. The theoretical results obtained have important implications for applications involving projectile motion. A robust, nonlinear optimization-based formulation is proposed, and the use of a local optimization method is justified by detailed examination of the local convexity structure of the cost function. The potential of this approach is validated by experimental results.

Genetic learning in rule-based and neural systems

NASA Technical Reports Server (NTRS)

Smith, Robert E.

1993-01-01

The design of neural networks and fuzzy systems can involve complex, nonlinear, and ill-conditioned optimization problems. Often, traditional optimization schemes are inadequate or inapplicable for such tasks. Genetic Algorithms (GA's) are a class of optimization procedures whose mechanics are based on those of natural genetics. Mathematical arguments show how GAs bring substantial computational leverage to search problems, without requiring the mathematical characteristics often necessary for traditional optimization schemes (e.g., modality, continuity, availability of derivative information, etc.). GA's have proven effective in a variety of search tasks that arise in neural networks and fuzzy systems. This presentation begins by introducing the mechanism and theoretical underpinnings of GA's. GA's are then related to a class of rule-based machine learning systems called learning classifier systems (LCS's). An LCS implements a low-level production-system that uses a GA as its primary rule discovery mechanism. This presentation illustrates how, despite its rule-based framework, an LCS can be thought of as a competitive neural network. Neural network simulator code for an LCS is presented. In this context, the GA is doing more than optimizing and objective function. It is searching for an ecology of hidden nodes with limited connectivity. The GA attempts to evolve this ecology such that effective neural network performance results. The GA is particularly well adapted to this task, given its naturally-inspired basis. The LCS/neural network analogy extends itself to other, more traditional neural networks. Conclusions to the presentation discuss the implications of using GA's in ecological search problems that arise in neural and fuzzy systems.

A method for optimizing multi-objective reservoir operation upon human and riverine ecosystem demands

NASA Astrophysics Data System (ADS)

Ai, Xueshan; Dong, Zuo; Mo, Mingzhu

2017-04-01

The optimal reservoir operation is in generally a multi-objective problem. In real life, most of the reservoir operation optimization problems involve conflicting objectives, for which there is no single optimal solution which can simultaneously gain an optimal result of all the purposes, but rather a set of well distributed non-inferior solutions or Pareto frontier exists. On the other hand, most of the reservoirs operation rules is to gain greater social and economic benefits at the expense of ecological environment, resulting to the destruction of riverine ecology and reduction of aquatic biodiversity. To overcome these drawbacks, this study developed a multi-objective model for the reservoir operating with the conflicting functions of hydroelectric energy generation, irrigation and ecological protection. To solve the model with the objectives of maximize energy production, maximize the water demand satisfaction rate of irrigation and ecology, we proposed a multi-objective optimization method of variable penalty coefficient (VPC), which was based on integrate dynamic programming (DP) with discrete differential dynamic programming (DDDP), to generate a well distributed non-inferior along the Pareto front by changing the penalties coefficient of different objectives. This method was applied to an existing China reservoir named Donggu, through a course of a year, which is a multi-annual storage reservoir with multiple purposes. The case study results showed a good relationship between any two of the objectives and a good Pareto optimal solutions, which provide a reference for the reservoir decision makers.

COPS: Large-scale nonlinearly constrained optimization problems

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

Bondarenko, A.S.; Bortz, D.M.; More, J.J.

2000-02-10

The authors have started the development of COPS, a collection of large-scale nonlinearly Constrained Optimization Problems. The primary purpose of this collection is to provide difficult test cases for optimization software. Problems in the current version of the collection come from fluid dynamics, population dynamics, optimal design, and optimal control. For each problem they provide a short description of the problem, notes on the formulation of the problem, and results of computational experiments with general optimization solvers. They currently have results for DONLP2, LANCELOT, MINOS, SNOPT, and LOQO.

Optimizing Home-School Collaboration: Strategies for School Psychologists and Latino Parent Involvement for Positive Mental Health Outcomes

ERIC Educational Resources Information Center

Olvera, Pedro; Olvera, Veronica I.

2012-01-01

Public schools across the United States are experiencing an increase in Cultural and Linguistically Diverse (CLD) students, particularly those of Latino descent. Latino children are at a high-risk for mental health problems (i.e., depression, anxiety, risk of suicide, etc.) and face greater risk factors when compared to many of their ethnic…

Methods of Establishing Occupational Skill Structure of Admissions in the System of Vocational Education

ERIC Educational Resources Information Center

Kosorukov, Oleg A.; Makarov, Alexander N.; Bagisbayev, Karmak B.

2016-01-01

The purpose of the study is to determine the business need for vocational training. This article gives a detailed analysis of the problem aimed at finding optimal occupational skill structure of training, which involves all kinds of positive effects in various areas of public life--from the economy up to the spiritual sphere of human life.…

A free interactive matching program

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

J.-F. Ostiguy

1999-04-16

For physicists and engineers involved in the design and analysis of beamlines (transfer lines or insertions) the lattice function matching problem is central and can be time-consuming because it involves constrained nonlinear optimization. For such problems convergence can be difficult to obtain in general without expert human intervention. Over the years, powerful codes have been developed to assist beamline designers. The canonical example is MAD (Methodical Accelerator Design) developed at CERN by Christophe Iselin. MAD, through a specialized command language, allows one to solve a wide variety of problems, including matching problems. Although in principle, the MAD command interpreter canmore » be run interactively, in practice the solution of a matching problem involves a sequence of independent trial runs. Unfortunately, but perhaps not surprisingly, there still exists relatively few tools exploiting the resources offered by modern environments to assist lattice designer with this routine and repetitive task. In this paper, we describe a fully interactive lattice matching program, written in C++ and assembled using freely available software components. An important feature of the code is that the evolution of the lattice functions during the nonlinear iterative process can be graphically monitored in real time; the user can dynamically interrupt the iterations at will to introduce new variables, freeze existing ones into their current state and/or modify constraints. The program runs under both UNIX and Windows NT.« less

Structural design of high-performance capacitive accelerometers using parametric optimization with uncertainties

NASA Astrophysics Data System (ADS)

Teves, André da Costa; Lima, Cícero Ribeiro de; Passaro, Angelo; Silva, Emílio Carlos Nelli

2017-03-01

Electrostatic or capacitive accelerometers are among the highest volume microelectromechanical systems (MEMS) products nowadays. The design of such devices is a complex task, since they depend on many performance requirements, which are often conflicting. Therefore, optimization techniques are often used in the design stage of these MEMS devices. Because of problems with reliability, the technology of MEMS is not yet well established. Thus, in this work, size optimization is combined with the reliability-based design optimization (RBDO) method to improve the performance of accelerometers. To account for uncertainties in the dimensions and material properties of these devices, the first order reliability method is applied to calculate the probabilities involved in the RBDO formulation. Practical examples of bulk-type capacitive accelerometer designs are presented and discussed to evaluate the potential of the implemented RBDO solver.

Model predictive and reallocation problem for CubeSat fault recovery and attitude control

NASA Astrophysics Data System (ADS)

Franchi, Loris; Feruglio, Lorenzo; Mozzillo, Raffaele; Corpino, Sabrina

2018-01-01

In recent years, thanks to the increase of the know-how on machine-learning techniques and the advance of the computational capabilities of on-board processing, expensive computing algorithms, such as Model Predictive Control, have begun to spread in space applications even on small on-board processor. The paper presents an algorithm for an optimal fault recovery of a 3U CubeSat, developed in MathWorks Matlab & Simulink environment. This algorithm involves optimization techniques aiming at obtaining the optimal recovery solution, and involves a Model Predictive Control approach for the attitude control. The simulated system is a CubeSat in Low Earth Orbit: the attitude control is performed with three magnetic torquers and a single reaction wheel. The simulation neglects the errors in the attitude determination of the satellite, and focuses on the recovery approach and control method. The optimal recovery approach takes advantage of the properties of magnetic actuation, which gives the possibility of the redistribution of the control action when a fault occurs on a single magnetic torquer, even in absence of redundant actuators. In addition, the paper presents the results of the implementation of Model Predictive approach to control the attitude of the satellite.

Universal approximators for multi-objective direct policy search in water reservoir management problems: a comparative analysis

NASA Astrophysics Data System (ADS)

Giuliani, Matteo; Mason, Emanuele; Castelletti, Andrea; Pianosi, Francesca

2014-05-01

The optimal operation of water resources systems is a wide and challenging problem due to non-linearities in the model and the objectives, high dimensional state-control space, and strong uncertainties in the hydroclimatic regimes. The application of classical optimization techniques (e.g., SDP, Q-learning, gradient descent-based algorithms) is strongly limited by the dimensionality of the system and by the presence of multiple, conflicting objectives. This study presents a novel approach which combines Direct Policy Search (DPS) and Multi-Objective Evolutionary Algorithms (MOEAs) to solve high-dimensional state and control space problems involving multiple objectives. DPS, also known as parameterization-simulation-optimization in the water resources literature, is a simulation-based approach where the reservoir operating policy is first parameterized within a given family of functions and, then, the parameters optimized with respect to the objectives of the management problem. The selection of a suitable class of functions to which the operating policy belong to is a key step, as it might restrict the search for the optimal policy to a subspace of the decision space that does not include the optimal solution. In the water reservoir literature, a number of classes have been proposed. However, many of these rules are based largely on empirical or experimental successes and they were designed mostly via simulation and for single-purpose reservoirs. In a multi-objective context similar rules can not easily inferred from the experience and the use of universal function approximators is generally preferred. In this work, we comparatively analyze two among the most common universal approximators: artificial neural networks (ANN) and radial basis functions (RBF) under different problem settings to estimate their scalability and flexibility in dealing with more and more complex problems. The multi-purpose HoaBinh water reservoir in Vietnam, accounting for hydropower production and flood control, is used as a case study. Preliminary results show that the RBF policy parametrization is more effective than the ANN one. In particular, the approximated Pareto front obtained with RBF control policies successfully explores the full tradeoff space between the two conflicting objectives, while most of the ANN solutions results to be Pareto-dominated by the RBF ones.

A Standard Platform for Testing and Comparison of MDAO Architectures

NASA Technical Reports Server (NTRS)

Gray, Justin S.; Moore, Kenneth T.; Hearn, Tristan A.; Naylor, Bret A.

2012-01-01

The Multidisciplinary Design Analysis and Optimization (MDAO) community has developed a multitude of algorithms and techniques, called architectures, for performing optimizations on complex engineering systems which involve coupling between multiple discipline analyses. These architectures seek to efficiently handle optimizations with computationally expensive analyses including multiple disciplines. We propose a new testing procedure that can provide a quantitative and qualitative means of comparison among architectures. The proposed test procedure is implemented within the open source framework, OpenMDAO, and comparative results are presented for five well-known architectures: MDF, IDF, CO, BLISS, and BLISS-2000. We also demonstrate how using open source soft- ware development methods can allow the MDAO community to submit new problems and architectures to keep the test suite relevant.

Transonic airfoil analysis and design in nonuniform flow

NASA Technical Reports Server (NTRS)

Chang, J. F.; Lan, C. E.

1986-01-01

A nonuniform transonic airfoil code is developed for applications in analysis, inverse design and direct optimization involving an airfoil immersed in propfan slipstream. Problems concerning the numerical stability, convergence, divergence and solution oscillations are discussed. The code is validated by comparing with some known results in incompressible flow. A parametric investigation indicates that the airfoil lift-drag ratio can be increased by decreasing the thickness ratio. A better performance can be achieved if the airfoil is located below the slipstream center. Airfoil characteristics designed by the inverse method and a direct optimization are compared. The airfoil designed with the method of direct optimization exhibits better characteristics and achieves a gain of 22 percent in lift-drag ratio with a reduction of 4 percent in thickness.

Generalized bipartite quantum state discrimination problems with sequential measurements

NASA Astrophysics Data System (ADS)

Nakahira, Kenji; Kato, Kentaro; Usuda, Tsuyoshi Sasaki

2018-02-01

We investigate an optimization problem of finding quantum sequential measurements, which forms a wide class of state discrimination problems with the restriction that only local operations and one-way classical communication are allowed. Sequential measurements from Alice to Bob on a bipartite system are considered. Using the fact that the optimization problem can be formulated as a problem with only Alice's measurement and is convex programming, we derive its dual problem and necessary and sufficient conditions for an optimal solution. Our results are applicable to various practical optimization criteria, including the Bayes criterion, the Neyman-Pearson criterion, and the minimax criterion. In the setting of the problem of finding an optimal global measurement, its dual problem and necessary and sufficient conditions for an optimal solution have been widely used to obtain analytical and numerical expressions for optimal solutions. Similarly, our results are useful to obtain analytical and numerical expressions for optimal sequential measurements. Examples in which our results can be used to obtain an analytical expression for an optimal sequential measurement are provided.

WE-D-303-00: Computational Phantoms

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

Lewis, John; Brigham and Women’s Hospital and Dana-Farber Cancer Institute, Boston, MA

2015-06-15

Modern medical physics deals with complex problems such as 4D radiation therapy and imaging quality optimization. Such problems involve a large number of radiological parameters, and anatomical and physiological breathing patterns. A major challenge is how to develop, test, evaluate and compare various new imaging and treatment techniques, which often involves testing over a large range of radiological parameters as well as varying patient anatomies and motions. It would be extremely challenging, if not impossible, both ethically and practically, to test every combination of parameters and every task on every type of patient under clinical conditions. Computer-based simulation using computationalmore » phantoms offers a practical technique with which to evaluate, optimize, and compare imaging technologies and methods. Within simulation, the computerized phantom provides a virtual model of the patient’s anatomy and physiology. Imaging data can be generated from it as if it was a live patient using accurate models of the physics of the imaging and treatment process. With sophisticated simulation algorithms, it is possible to perform virtual experiments entirely on the computer. By serving as virtual patients, computational phantoms hold great promise in solving some of the most complex problems in modern medical physics. In this proposed symposium, we will present the history and recent developments of computational phantom models, share experiences in their application to advanced imaging and radiation applications, and discuss their promises and limitations. Learning Objectives: Understand the need and requirements of computational phantoms in medical physics research Discuss the developments and applications of computational phantoms Know the promises and limitations of computational phantoms in solving complex problems.« less

An optimization tool for satellite equipment layout

NASA Astrophysics Data System (ADS)

Qin, Zheng; Liang, Yan-gang; Zhou, Jian-ping

2018-01-01

Selection of the satellite equipment layout with performance constraints is a complex task which can be viewed as a constrained multi-objective optimization and a multiple criteria decision making problem. The layout design of a satellite cabin involves the process of locating the required equipment in a limited space, thereby satisfying various behavioral constraints of the interior and exterior environments. The layout optimization of satellite cabin in this paper includes the C.G. offset, the moments of inertia and the space debris impact risk of the system, of which the impact risk index is developed to quantify the risk to a satellite cabin of coming into contact with space debris. In this paper an optimization tool for the integration of CAD software as well as the optimization algorithms is presented, which is developed to automatically find solutions for a three-dimensional layout of equipment in satellite. The effectiveness of the tool is also demonstrated by applying to the layout optimization of a satellite platform.

A Cascade Optimization Strategy for Solution of Difficult Multidisciplinary Design Problems

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Coroneos, Rula M.; Hopkins, Dale A.; Berke, Laszlo

1996-01-01

A research project to comparatively evaluate 10 nonlinear optimization algorithms was recently completed. A conclusion was that no single optimizer could successfully solve all 40 problems in the test bed, even though most optimizers successfully solved at least one-third of the problems. We realized that improved search directions and step lengths, available in the 10 optimizers compared, were not likely to alleviate the convergence difficulties. For the solution of those difficult problems we have devised an alternative approach called cascade optimization strategy. The cascade strategy uses several optimizers, one followed by another in a specified sequence, to solve a problem. A pseudorandom scheme perturbs design variables between the optimizers. The cascade strategy has been tested successfully in the design of supersonic and subsonic aircraft configurations and air-breathing engines for high-speed civil transport applications. These problems could not be successfully solved by an individual optimizer. The cascade optimization strategy, however, generated feasible optimum solutions for both aircraft and engine problems. This paper presents the cascade strategy and solutions to a number of these problems.

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

Incorporation of Fixed Installation Costs into Optimization of Groundwater Remediation with a New Efficient Surrogate Nonlinear Mixed Integer Optimization Algorithm

NASA Astrophysics Data System (ADS)

Shoemaker, Christine; Wan, Ying

2016-04-01

Optimization of nonlinear water resources management issues which have a mixture of fixed (e.g. construction cost for a well) and variable (e.g. cost per gallon of water pumped) costs has been not well addressed because prior algorithms for the resulting nonlinear mixed integer problems have required many groundwater simulations (with different configurations of decision variable), especially when the solution space is multimodal. In particular heuristic methods like genetic algorithms have often been used in the water resources area, but they require so many groundwater simulations that only small systems have been solved. Hence there is a need to have a method that reduces the number of expensive groundwater simulations. A recently published algorithm for nonlinear mixed integer programming using surrogates was shown in this study to greatly reduce the computational effort for obtaining accurate answers to problems involving fixed costs for well construction as well as variable costs for pumping because of a substantial reduction in the number of groundwater simulations required to obtain an accurate answer. Results are presented for a US EPA hazardous waste site. The nonlinear mixed integer surrogate algorithm is general and can be used on other problems arising in hydrology with open source codes in Matlab and python ("pySOT" in Bitbucket).

Rational approximations to rational models: alternative algorithms for category learning.

PubMed

Sanborn, Adam N; Griffiths, Thomas L; Navarro, Daniel J

2010-10-01

Rational models of cognition typically consider the abstract computational problems posed by the environment, assuming that people are capable of optimally solving those problems. This differs from more traditional formal models of cognition, which focus on the psychological processes responsible for behavior. A basic challenge for rational models is thus explaining how optimal solutions can be approximated by psychological processes. We outline a general strategy for answering this question, namely to explore the psychological plausibility of approximation algorithms developed in computer science and statistics. In particular, we argue that Monte Carlo methods provide a source of rational process models that connect optimal solutions to psychological processes. We support this argument through a detailed example, applying this approach to Anderson's (1990, 1991) rational model of categorization (RMC), which involves a particularly challenging computational problem. Drawing on a connection between the RMC and ideas from nonparametric Bayesian statistics, we propose 2 alternative algorithms for approximate inference in this model. The algorithms we consider include Gibbs sampling, a procedure appropriate when all stimuli are presented simultaneously, and particle filters, which sequentially approximate the posterior distribution with a small number of samples that are updated as new data become available. Applying these algorithms to several existing datasets shows that a particle filter with a single particle provides a good description of human inferences.

Modeling crowdsourcing as collective problem solving

NASA Astrophysics Data System (ADS)

Guazzini, Andrea; Vilone, Daniele; Donati, Camillo; Nardi, Annalisa; Levnajić, Zoran

2015-11-01

Crowdsourcing is a process of accumulating the ideas, thoughts or information from many independent participants, with aim to find the best solution for a given challenge. Modern information technologies allow for massive number of subjects to be involved in a more or less spontaneous way. Still, the full potentials of crowdsourcing are yet to be reached. We introduce a modeling framework through which we study the effectiveness of crowdsourcing in relation to the level of collectivism in facing the problem. Our findings reveal an intricate relationship between the number of participants and the difficulty of the problem, indicating the optimal size of the crowdsourced group. We discuss our results in the context of modern utilization of crowdsourcing.

Multi-objective optimization of composite structures. A review

NASA Astrophysics Data System (ADS)

Teters, G. A.; Kregers, A. F.

1996-05-01

Studies performed on the optimization of composite structures by coworkers of the Institute of Polymers Mechanics of the Latvian Academy of Sciences in recent years are reviewed. The possibility of controlling the geometry and anisotropy of laminar composite structures will make it possible to design articles that best satisfy the requirements established for them. Conflicting requirements such as maximum bearing capacity, minimum weight and/or cost, prescribed thermal conductivity and thermal expansion, etc. usually exist for optimal design. This results in the multi-objective compromise optimization of structures. Numerical methods have been developed for solution of problems of multi-objective optimization of composite structures; parameters of the structure of the reinforcement and the geometry of the design are assigned as controlling parameters. Programs designed to run on personal computers have been compiled for multi-objective optimization of the properties of composite materials, plates, and shells. Solutions are obtained for both linear and nonlinear models. The programs make it possible to establish the Pareto compromise region and special multicriterial solutions. The problem of the multi-objective optimization of the elastic moduli of a spatially reinforced fiberglass with stochastic stiffness parameters has been solved. The region of permissible solutions and the Pareto region have been found for the elastic moduli. The dimensions of the scatter ellipse have been determined for a multidimensional Gaussian probability distribution where correlation between the composite's properties being optimized are accounted for. Two types of problems involving the optimization of a laminar rectangular composite plate are considered: the plate is considered elastic and anisotropic in the first case, and viscoelastic properties are accounted for in the second. The angle of reinforcement and the relative amount of fibers in the longitudinal direction are controlling parameters. The optimized properties are the critical stresses, thermal conductivity, and thermal expansion. The properties of a plate are determined by the properties of the components in the composite, eight of which are stochastic. The region of multi-objective compromise solutions is presented, and the parameters of the scatter ellipses of the properties are given.

Practical optimal flight control system design for helicopter aircraft. Volume 2: Software user's guide

NASA Technical Reports Server (NTRS)

Riedel, S. A.

1979-01-01

A method by which modern and classical control theory techniques may be integrated in a synergistic fashion and used in the design of practical flight control systems is presented. A general procedure is developed, and several illustrative examples are included. Emphasis is placed not only on the synthesis of the design, but on the assessment of the results as well. The first step is to establish the differences, distinguishing characteristics and connections between the modern and classical control theory approaches. Ultimately, this uncovers a relationship between bandwidth goals familiar in classical control and cost function weights in the equivalent optimal system. In order to obtain a practical optimal solution, it is also necessary to formulate the problem very carefully, and each choice of state, measurement and output variable must be judiciously considered. Once design goals are established and problem formulation completed, the control system is synthesized in a straightforward manner. Three steps are involved: filter-observer solution, regulator solution, and the combination of those two into the controller. Assessment of the controller permits and examination and expansion of the synthesis results.

Improving delivery routes using combined heuristic and optimization in a consumer goods distribution company

NASA Astrophysics Data System (ADS)

Wibisono, E.; Santoso, A.; Sunaryo, M. A.

2017-11-01

XYZ is a distributor of various consumer goods products. The company plans its delivery routes daily and in order to obtain route construction in a short amount of time, it simplifies the process by assigning drivers based on geographic regions. This approach results in inefficient use of vehicles leading to imbalance workloads. In this paper, we propose a combined method involving heuristic and optimization to obtain better solutions in acceptable computation time. The heuristic is based on a time-oriented, nearest neighbor (TONN) to form clusters if the number of locations is higher than a certain value. The optimization part uses a mathematical modeling formulation based on vehicle routing problem that considers heterogeneous vehicles, time windows, and fixed costs (HVRPTWF) and is used to solve routing problem in clusters. A case study using data from one month of the company’s operations is analyzed, and data from one day of operations are detailed in this paper. The analysis shows that the proposed method results in 24% cost savings on that month, but it can be as high as 54% in a day.

Optimal Prediction in the Retina and Natural Motion Statistics

NASA Astrophysics Data System (ADS)

Salisbury, Jared M.; Palmer, Stephanie E.

2016-03-01

Almost all behaviors involve making predictions. Whether an organism is trying to catch prey, avoid predators, or simply move through a complex environment, the organism uses the data it collects through its senses to guide its actions by extracting from these data information about the future state of the world. A key aspect of the prediction problem is that not all features of the past sensory input have predictive power, and representing all features of the external sensory world is prohibitively costly both due to space and metabolic constraints. This leads to the hypothesis that neural systems are optimized for prediction. Here we describe theoretical and computational efforts to define and quantify the efficient representation of the predictive information by the brain. Another important feature of the prediction problem is that the physics of the world is diverse enough to contain a wide range of possible statistical ensembles, yet not all inputs are probable. Thus, the brain might not be a generalized predictive machine; it might have evolved to specifically solve the prediction problems most common in the natural environment. This paper summarizes recent results on predictive coding and optimal predictive information in the retina and suggests approaches for quantifying prediction in response to natural motion. Basic statistics of natural movies reveal that general patterns of spatiotemporal correlation are present across a wide range of scenes, though individual differences in motion type may be important for optimal processing of motion in a given ecological niche.

Asynchronous Incremental Stochastic Dual Descent Algorithm for Network Resource Allocation

NASA Astrophysics Data System (ADS)

Bedi, Amrit Singh; Rajawat, Ketan

2018-05-01

Stochastic network optimization problems entail finding resource allocation policies that are optimum on an average but must be designed in an online fashion. Such problems are ubiquitous in communication networks, where resources such as energy and bandwidth are divided among nodes to satisfy certain long-term objectives. This paper proposes an asynchronous incremental dual decent resource allocation algorithm that utilizes delayed stochastic {gradients} for carrying out its updates. The proposed algorithm is well-suited to heterogeneous networks as it allows the computationally-challenged or energy-starved nodes to, at times, postpone the updates. The asymptotic analysis of the proposed algorithm is carried out, establishing dual convergence under both, constant and diminishing step sizes. It is also shown that with constant step size, the proposed resource allocation policy is asymptotically near-optimal. An application involving multi-cell coordinated beamforming is detailed, demonstrating the usefulness of the proposed algorithm.

An improved CS-LSSVM algorithm-based fault pattern recognition of ship power equipments.

PubMed

Yang, Yifei; Tan, Minjia; Dai, Yuewei

2017-01-01

A ship power equipments' fault monitoring signal usually provides few samples and the data's feature is non-linear in practical situation. This paper adopts the method of the least squares support vector machine (LSSVM) to deal with the problem of fault pattern identification in the case of small sample data. Meanwhile, in order to avoid involving a local extremum and poor convergence precision which are induced by optimizing the kernel function parameter and penalty factor of LSSVM, an improved Cuckoo Search (CS) algorithm is proposed for the purpose of parameter optimization. Based on the dynamic adaptive strategy, the newly proposed algorithm improves the recognition probability and the searching step length, which can effectively solve the problems of slow searching speed and low calculation accuracy of the CS algorithm. A benchmark example demonstrates that the CS-LSSVM algorithm can accurately and effectively identify the fault pattern types of ship power equipments.

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.

An intelligent case-adjustment algorithm for the automated design of population-based quality auditing protocols.

PubMed

Advani, Aneel; Jones, Neil; Shahar, Yuval; Goldstein, Mary K; Musen, Mark A

2004-01-01

We develop a method and algorithm for deciding the optimal approach to creating quality-auditing protocols for guideline-based clinical performance measures. An important element of the audit protocol design problem is deciding which guide-line elements to audit. Specifically, the problem is how and when to aggregate individual patient case-specific guideline elements into population-based quality measures. The key statistical issue involved is the trade-off between increased reliability with more general population-based quality measures versus increased validity from individually case-adjusted but more restricted measures done at a greater audit cost. Our intelligent algorithm for auditing protocol design is based on hierarchically modeling incrementally case-adjusted quality constraints. We select quality constraints to measure using an optimization criterion based on statistical generalizability coefficients. We present results of the approach from a deployed decision support system for a hypertension guideline.

Geodesic regression on orientation distribution functions with its application to an aging study.

PubMed

Du, Jia; Goh, Alvina; Kushnarev, Sergey; Qiu, Anqi

2014-02-15

In this paper, we treat orientation distribution functions (ODFs) derived from high angular resolution diffusion imaging (HARDI) as elements of a Riemannian manifold and present a method for geodesic regression on this manifold. In order to find the optimal regression model, we pose this as a least-squares problem involving the sum-of-squared geodesic distances between observed ODFs and their model fitted data. We derive the appropriate gradient terms and employ gradient descent to find the minimizer of this least-squares optimization problem. In addition, we show how to perform statistical testing for determining the significance of the relationship between the manifold-valued regressors and the real-valued regressands. Experiments on both synthetic and real human data are presented. In particular, we examine aging effects on HARDI via geodesic regression of ODFs in normal adults aged 22 years old and above. © 2013 Elsevier Inc. All rights reserved.

Gradient-based Optimization for Poroelastic and Viscoelastic MR Elastography

PubMed Central

Tan, Likun; McGarry, Matthew D.J.; Van Houten, Elijah E.W.; Ji, Ming; Solamen, Ligin; Weaver, John B.

2017-01-01

We describe an efficient gradient computation for solving inverse problems arising in magnetic resonance elastography (MRE). The algorithm can be considered as a generalized ‘adjoint method’ based on a Lagrangian formulation. One requirement for the classic adjoint method is assurance of the self-adjoint property of the stiffness matrix in the elasticity problem. In this paper, we show this property is no longer a necessary condition in our algorithm, but the computational performance can be as efficient as the classic method, which involves only two forward solutions and is independent of the number of parameters to be estimated. The algorithm is developed and implemented in material property reconstructions using poroelastic and viscoelastic modeling. Various gradient- and Hessian-based optimization techniques have been tested on simulation, phantom and in vivo brain data. The numerical results show the feasibility and the efficiency of the proposed scheme for gradient calculation. PMID:27608454

Solving a class of generalized fractional programming problems using the feasibility of linear programs.

PubMed

Shen, Peiping; Zhang, Tongli; Wang, Chunfeng

2017-01-01

This article presents a new approximation algorithm for globally solving a class of generalized fractional programming problems (P) whose objective functions are defined as an appropriate composition of ratios of affine functions. To solve this problem, the algorithm solves an equivalent optimization problem (Q) via an exploration of a suitably defined nonuniform grid. The main work of the algorithm involves checking the feasibility of linear programs associated with the interesting grid points. It is proved that the proposed algorithm is a fully polynomial time approximation scheme as the ratio terms are fixed in the objective function to problem (P), based on the computational complexity result. In contrast to existing results in literature, the algorithm does not require the assumptions on quasi-concavity or low-rank of the objective function to problem (P). Numerical results are given to illustrate the feasibility and effectiveness of the proposed algorithm.

Inverse problems in complex material design: Applications to non-crystalline solids

NASA Astrophysics Data System (ADS)

Biswas, Parthapratim; Drabold, David; Elliott, Stephen

The design of complex amorphous materials is one of the fundamental problems in disordered condensed-matter science. While impressive developments of ab-initio simulation methods during the past several decades have brought tremendous success in understanding materials property from micro- to mesoscopic length scales, a major drawback is that they fail to incorporate existing knowledge of the materials in simulation methodologies. Since an essential feature of materials design is the synergy between experiment and theory, a properly developed approach to design materials should be able to exploit all available knowledge of the materials from measured experimental data. In this talk, we will address the design of complex disordered materials as an inverse problem involving experimental data and available empirical information. We show that the problem can be posed as a multi-objective non-convex optimization program, which can be addressed using a number of recently-developed bio-inspired global optimization techniques. In particular, we will discuss how a population-based stochastic search procedure can be used to determine the structure of non-crystalline solids (e.g. a-SiH, a-SiO2, amorphous graphene, and Fe and Ni clusters). The work is partially supported by NSF under Grant Nos. DMR 1507166 and 1507670.

An improved exploratory search technique for pure integer linear programming problems

NASA Technical Reports Server (NTRS)

Fogle, F. R.

1990-01-01

The development is documented of a heuristic method for the solution of pure integer linear programming problems. The procedure draws its methodology from the ideas of Hooke and Jeeves type 1 and 2 exploratory searches, greedy procedures, and neighborhood searches. It uses an efficient rounding method to obtain its first feasible integer point from the optimal continuous solution obtained via the simplex method. Since this method is based entirely on simple addition or subtraction of one to each variable of a point in n-space and the subsequent comparison of candidate solutions to a given set of constraints, it facilitates significant complexity improvements over existing techniques. It also obtains the same optimal solution found by the branch-and-bound technique in 44 of 45 small to moderate size test problems. Two example problems are worked in detail to show the inner workings of the method. Furthermore, using an established weighted scheme for comparing computational effort involved in an algorithm, a comparison of this algorithm is made to the more established and rigorous branch-and-bound method. A computer implementation of the procedure, in PC compatible Pascal, is also presented and discussed.

Two-Stage Path Planning Approach for Designing Multiple Spacecraft Reconfiguration Maneuvers

NASA Technical Reports Server (NTRS)

Aoude, Georges S.; How, Jonathan P.; Garcia, Ian M.

2007-01-01

The paper presents a two-stage approach for designing optimal reconfiguration maneuvers for multiple spacecraft. These maneuvers involve well-coordinated and highly-coupled motions of the entire fleet of spacecraft while satisfying an arbitrary number of constraints. This problem is particularly difficult because of the nonlinearity of the attitude dynamics, the non-convexity of some of the constraints, and the coupling between the positions and attitudes of all spacecraft. As a result, the trajectory design must be solved as a single 6N DOF problem instead of N separate 6 DOF problems. The first stage of the solution approach quickly provides a feasible initial solution by solving a simplified version without differential constraints using a bi-directional Rapidly-exploring Random Tree (RRT) planner. A transition algorithm then augments this guess with feasible dynamics that are propagated from the beginning to the end of the trajectory. The resulting output is a feasible initial guess to the complete optimal control problem that is discretized in the second stage using a Gauss pseudospectral method (GPM) and solved using an off-the-shelf nonlinear solver. This paper also places emphasis on the importance of the initialization step in pseudospectral methods in order to decrease their computation times and enable the solution of a more complex class of problems. Several examples are presented and discussed.

Algorithms for bilevel optimization

NASA Technical Reports Server (NTRS)

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

1994-01-01

General multilevel nonlinear optimization problems arise in design of complex systems and can be used as a means of regularization for multi-criteria optimization problems. Here, for clarity in displaying our ideas, we restrict ourselves to general bi-level optimization problems, and we present two solution approaches. Both approaches use a trust-region globalization strategy, and they can be easily extended to handle the general multilevel problem. We make no convexity assumptions, but we do assume that the problem has a nondegenerate feasible set. We consider necessary optimality conditions for the bi-level problem formulations and discuss results that can be extended to obtain multilevel optimization formulations with constraints at each level.

Approximate analysis for repeated eigenvalue problems with applications to controls-structure integrated design

NASA Technical Reports Server (NTRS)

Kenny, Sean P.; Hou, Gene J. W.

1994-01-01

A method for eigenvalue and eigenvector approximate analysis for the case of repeated eigenvalues with distinct first derivatives is presented. The approximate analysis method developed involves a reparameterization of the multivariable structural eigenvalue problem in terms of a single positive-valued parameter. The resulting equations yield first-order approximations to changes in the eigenvalues and the eigenvectors associated with the repeated eigenvalue problem. This work also presents a numerical technique that facilitates the definition of an eigenvector derivative for the case of repeated eigenvalues with repeated eigenvalue derivatives (of all orders). Examples are given which demonstrate the application of such equations for sensitivity and approximate analysis. Emphasis is placed on the application of sensitivity analysis to large-scale structural and controls-structures optimization problems.

Fair Inference on Outcomes

PubMed Central

Nabi, Razieh; Shpitser, Ilya

2017-01-01

In this paper, we consider the problem of fair statistical inference involving outcome variables. Examples include classification and regression problems, and estimating treatment effects in randomized trials or observational data. The issue of fairness arises in such problems where some covariates or treatments are “sensitive,” in the sense of having potential of creating discrimination. In this paper, we argue that the presence of discrimination can be formalized in a sensible way as the presence of an effect of a sensitive covariate on the outcome along certain causal pathways, a view which generalizes (Pearl 2009). A fair outcome model can then be learned by solving a constrained optimization problem. We discuss a number of complications that arise in classical statistical inference due to this view and provide workarounds based on recent work in causal and semi-parametric inference.

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.

A Workflow for Subsurface Pressure Control in Geological CO2 Storage: Optimization of Brine Extraction

NASA Astrophysics Data System (ADS)

Birkholzer, J. T.; Gonzalez-Nicolas, A.; Cihan, A.

2017-12-01

Industrial-scale injection of CO2 into the subsurface increases the fluid pressure in the reservoir, sometimes to the point that the resulting stress increases must be properly controlled to prevent potential damaging impacts such as fault activation, leakage through abandoned wells, or caprock fracturing. Brine extraction is one approach for managing formation pressure, effective stress, and plume movement in response to CO2 injection. However, the management of the extracted brine adds cost to the carbon capture and sequestration operations; therefore optimizing (minimizing) the extraction volume of brine is of great importance. In this study, we apply an adaptive management approach that optimizes extraction rates of brine for pressure control in an integrated optimization framework involving site monitoring, model calibration, and optimization. We investigate the optimization performance as affected by initial site characterization data and introduction of newly acquired data during the injection phase. More accurate initial reservoir characterization data reduce the risk of pressure buildup damage with better estimations of initial extraction rates, which results in better control of pressure during the overall injection time periods. Results also show that low frequencies of model calibration and optimization with the new data, especially at early injection periods, may lead to optimization problems, either that pressure buildup constraints are violated or excessively high extraction rates are proposed. These optimization problems can be eliminated if more frequent data collection and model calibration are conducted, especially at early injection time periods. Approaches such as adaptive pressure management may constitute an effective tool to manage pressure buildup under uncertain and unknown reservoir conditions by minimizing the brine extraction volumes while not exceeding critical pressure buildups of the reservoir.

Direct Method Transcription for a Human-Class Translunar Injection Trajectory Optimization

NASA Technical Reports Server (NTRS)

Witzberger, Kevin E.; Zeiler, Tom

2012-01-01

This paper presents a new trajectory optimization software package developed in the framework of a low-to-high fidelity 3 degrees-of-freedom (DOF)/6-DOF vehicle simulation program named Mission Analysis Simulation Tool in Fortran (MASTIF) and its application to a translunar trajectory optimization problem. The functionality of the developed optimization package is implemented as a new "mode" in generalized settings to make it applicable for a general trajectory optimization problem. In doing so, a direct optimization method using collocation is employed for solving the problem. Trajectory optimization problems in MASTIF are transcribed to a constrained nonlinear programming (NLP) problem and solved with SNOPT, a commercially available NLP solver. A detailed description of the optimization software developed is provided as well as the transcription specifics for the translunar injection (TLI) problem. The analysis includes a 3-DOF trajectory TLI optimization and a 3-DOF vehicle TLI simulation using closed-loop guidance.

An Algorithm for Integrated Subsystem Embodiment and System Synthesis

NASA Technical Reports Server (NTRS)

Lewis, Kemper

1997-01-01

Consider the statement,'A system has two coupled subsystems, one of which dominates the design process. Each subsystem consists of discrete and continuous variables, and is solved using sequential analysis and solution.' To address this type of statement in the design of complex systems, three steps are required, namely, the embodiment of the statement in terms of entities on a computer, the mathematical formulation of subsystem models, and the resulting solution and system synthesis. In complex system decomposition, the subsystems are not isolated, self-supporting entities. Information such as constraints, goals, and design variables may be shared between entities. But many times in engineering problems, full communication and cooperation does not exist, information is incomplete, or one subsystem may dominate the design. Additionally, these engineering problems give rise to mathematical models involving nonlinear functions of both discrete and continuous design variables. In this dissertation an algorithm is developed to handle these types of scenarios for the domain-independent integration of subsystem embodiment, coordination, and system synthesis using constructs from Decision-Based Design, Game Theory, and Multidisciplinary Design Optimization. Implementation of the concept in this dissertation involves testing of the hypotheses using example problems and a motivating case study involving the design of a subsonic passenger aircraft.

ELM Meets Urban Big Data Analysis: Case Studies

PubMed Central

Chen, Huajun; Chen, Jiaoyan

2016-01-01

In the latest years, the rapid progress of urban computing has engendered big issues, which creates both opportunities and challenges. The heterogeneous and big volume of data and the big difference between physical and virtual worlds have resulted in lots of problems in quickly solving practical problems in urban computing. In this paper, we propose a general application framework of ELM for urban computing. We present several real case studies of the framework like smog-related health hazard prediction and optimal retain store placement. Experiments involving urban data in China show the efficiency, accuracy, and flexibility of our proposed framework. PMID:27656203

A mathematical model for the generation and control of a pH gradient in an immobilized enzyme system involving acid generation.

PubMed

Chen, G; Fournier, R L; Varanasi, S

1998-02-20

An optimal pH control technique has been developed for multistep enzymatic synthesis reactions where the optimal pH differs by several units for each step. This technique separates an acidic environment from a basic environment by the hydrolysis of urea within a thin layer of immobilized urease. With this technique, a two-step enzymatic reaction can take place simultaneously, in proximity to each other, and at their respective optimal pH. Because a reaction system involving an acid generation represents a more challenging test of this pH control technique, a number of factors that affect the generation of such a pH gradient are considered in this study. The mathematical model proposed is based on several simplifying assumptions and represents a first attempt to provide an analysis of this complex problem. The results show that, by choosing appropriate parameters, the pH control technique still can generate the desired pH gradient even if there is an acid-generating reaction in the system. Copyright 1998 John Wiley & Sons, Inc.

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.

Jerk Minimization Method for Vibration Control in Buildings

NASA Technical Reports Server (NTRS)

Abatan, Ayo O.; Yao, Leummim

1997-01-01

In many vibration minimization control problems for high rise buildings subject to strong earthquake loads, the emphasis has been on a combination of minimizing the displacement, the velocity and the acceleration of the motion of the building. In most cases, the accelerations that are involved are not necessarily large but the change in them (jerk) are abrupt. These changes in magnitude or direction are responsible for most building damage and also create discomfort like motion sickness for inhabitants of these structures because of the element of surprise. We propose a method of minimizing also the jerk which is the sudden change in acceleration or the derivative of the acceleration using classical linear quadratic optimal controls. This was done through the introduction of a quadratic performance index involving the cost due to the jerk; a special change of variable; and using the jerk as a control variable. The values of the optimal control are obtained using the Riccati equation.

Multidisciplinary Optimization of a Transport Aircraft Wing using Particle Swarm Optimization

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, Jaroslaw; Venter, Gerhard

2002-01-01

The purpose of this paper is to demonstrate the application of particle swarm optimization to a realistic multidisciplinary optimization test problem. The paper's new contributions to multidisciplinary optimization is the application of a new algorithm for dealing with the unique challenges associated with multidisciplinary optimization problems, and recommendations as to the utility of the algorithm in future multidisciplinary optimization applications. The selected example is a bi-level optimization problem that demonstrates severe numerical noise and has a combination of continuous and truly discrete design variables. The use of traditional gradient-based optimization algorithms is thus not practical. The numerical results presented indicate that the particle swarm optimization algorithm is able to reliably find the optimum design for the problem presented here. The algorithm is capable of dealing with the unique challenges posed by multidisciplinary optimization as well as the numerical noise and truly discrete variables present in the current example problem.

Mesh refinement strategy for optimal control problems

NASA Astrophysics Data System (ADS)

Paiva, L. T.; Fontes, F. A. C. C.

2013-10-01

Direct methods are becoming the most used technique to solve nonlinear optimal control problems. Regular time meshes having equidistant spacing are frequently used. However, in some cases these meshes cannot cope accurately with nonlinear behavior. One way to improve the solution is to select a new mesh with a greater number of nodes. Another way, involves adaptive mesh refinement. In this case, the mesh nodes have non equidistant spacing which allow a non uniform nodes collocation. In the method presented in this paper, a time mesh refinement strategy based on the local error is developed. After computing a solution in a coarse mesh, the local error is evaluated, which gives information about the subintervals of time domain where refinement is needed. This procedure is repeated until the local error reaches a user-specified threshold. The technique is applied to solve the car-like vehicle problem aiming minimum consumption. The approach developed in this paper leads to results with greater accuracy and yet with lower overall computational time as compared to using a time meshes having equidistant spacing.

A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models

NASA Technical Reports Server (NTRS)

Giunta, Anthony A.; Watson, Layne T.

1998-01-01

Two methods of creating approximation models are compared through the calculation of the modeling accuracy on test problems involving one, five, and ten independent variables. Here, the test problems are representative of the modeling challenges typically encountered in realistic engineering optimization problems. The first approximation model is a quadratic polynomial created using the method of least squares. This type of polynomial model has seen considerable use in recent engineering optimization studies due to its computational simplicity and ease of use. However, quadratic polynomial models may be of limited accuracy when the response data to be modeled have multiple local extrema. The second approximation model employs an interpolation scheme known as kriging developed in the fields of spatial statistics and geostatistics. This class of interpolating model has the flexibility to model response data with multiple local extrema. However, this flexibility is obtained at an increase in computational expense and a decrease in ease of use. The intent of this study is to provide an initial exploration of the accuracy and modeling capabilities of these two approximation methods.

Optimal recombination in genetic algorithms for flowshop scheduling problems

NASA Astrophysics Data System (ADS)

Kovalenko, Julia

2016-10-01

The optimal recombination problem consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. We prove NP-hardness of the optimal recombination for various variants of the flowshop scheduling problem with makespan criterion and criterion of maximum lateness. An algorithm for solving the optimal recombination problem for permutation flowshop problems is built, using enumeration of prefect matchings in a special bipartite graph. The algorithm is adopted for the classical flowshop scheduling problem and for the no-wait flowshop problem. It is shown that the optimal recombination problem for the permutation flowshop scheduling problem is solvable in polynomial time for almost all pairs of parent solutions as the number of jobs tends to infinity.

Photovoltaic design optimization for terrestrial applications

NASA Technical Reports Server (NTRS)

Ross, R. G., Jr.

1978-01-01

As part of the Jet Propulsion Laboratory's Low-Cost Solar Array Project, a comprehensive program of module cost-optimization has been carried out. The objective of these studies has been to define means of reducing the cost and improving the utility and reliability of photovoltaic modules for the broad spectrum of terrestrial applications. This paper describes one of the methods being used for module optimization, including the derivation of specific equations which allow the optimization of various module design features. The method is based on minimizing the life-cycle cost of energy for the complete system. Comparison of the life-cycle energy cost with the marginal cost of energy each year allows the logical plant lifetime to be determined. The equations derived allow the explicit inclusion of design parameters such as tracking, site variability, and module degradation with time. An example problem involving the selection of an optimum module glass substrate is presented.

Design Methods and Optimization for Morphing Aircraft

NASA Technical Reports Server (NTRS)

Crossley, William A.

2005-01-01

This report provides a summary of accomplishments made during this research effort. The major accomplishments are in three areas. The first is the use of a multiobjective optimization strategy to help identify potential morphing features that uses an existing aircraft sizing code to predict the weight, size and performance of several fixed-geometry aircraft that are Pareto-optimal based upon on two competing aircraft performance objectives. The second area has been titled morphing as an independent variable and formulates the sizing of a morphing aircraft as an optimization problem in which the amount of geometric morphing for various aircraft parameters are included as design variables. This second effort consumed most of the overall effort on the project. The third area involved a more detailed sizing study of a commercial transport aircraft that would incorporate a morphing wing to possibly enable transatlantic point-to-point passenger service.

Bioeconomic analysis supports the endangered species act.

PubMed

Salau, Kehinde R; Fenichel, Eli P

2015-10-01

The United States Endangered Species Act (ESA) was enacted to protect and restore declining fish, wildlife, and plant populations. The ESA mandates endangered species protection irrespective of costs. This translates to the restriction of activities that harm endangered populations. We discuss criticisms of the ESA in the context of public land management and examine under what circumstance banning non-conservation activity on multiple use federal lands can be socially optimal. We develop a bioeconomic model to frame the species management problem under the ESA and identify scenarios where ESA-imposed regulations emerge as optimal strategies. Results suggest that banning harmful activities is a preferred strategy when valued endangered species are in decline or exposed to poor habitat quality. However, it is not optimal to sustain such a strategy in perpetuity. An optimal plan involves a switch to land-use practices characteristic of habitat conservation plans.

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

Reister, D.B.; Pin, F.G.

This paper addresses the problem of time-optional motions for a mobile platform in a planar environment. The platform has two non-steerable independently driven wheels. The overall mission of the robot is expressed in terms of a sequence of via points at which the platform must be at rest in a given configuration (position and orientation). The objective is to plan time-optimal trajectories between these configurations assuming an unobstructed environment. Using Pontryagin's maximum principle (PMP), we formally demonstrate that all time optimal motions of the platform for this problem occur for bang-bang controls on the wheels (at each instant, the accelerationmore » on each wheel is either at its upper or lower limit). The PMP, however, only provides necessary conditions for time optimality. To find the time optimal robot trajectories, we first parameterize the bang-bang trajectories using the switch times on the wheels (the times at which the wheel accelerations change sign). With this parameterization, we can fully search the robot trajectory space and find the switch times that will produce particular paths to a desired final configuration of the platform. We show numerically that robot trajectories with three switch times (two on one wheel, one on the other) can reach any position, while trajectories with four switch times can reach any configuration. By numerical comparison with other trajectories involving similar or greater numbers of switch times, we then identify the sets of time-optimal trajectories. These are uniquely defined using ranges of the parameters, and consist of subsets of trajectories with three switch times for the problem when the final orientation of the robot is not specified, and four switch times when a full final configuration is specified. We conclude with a description of the use of the method for trajectory planning for one of our robots.« less

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

Reister, D.B.; Pin, F.G.

This paper addresses the problem of time-optional motions for a mobile platform in a planar environment. The platform has two non-steerable independently driven wheels. The overall mission of the robot is expressed in terms of a sequence of via points at which the platform must be at rest in a given configuration (position and orientation). The objective is to plan time-optimal trajectories between these configurations assuming an unobstructed environment. Using Pontryagin`s maximum principle (PMP), we formally demonstrate that all time optimal motions of the platform for this problem occur for bang-bang controls on the wheels (at each instant, the accelerationmore » on each wheel is either at its upper or lower limit). The PMP, however, only provides necessary conditions for time optimality. To find the time optimal robot trajectories, we first parameterize the bang-bang trajectories using the switch times on the wheels (the times at which the wheel accelerations change sign). With this parameterization, we can fully search the robot trajectory space and find the switch times that will produce particular paths to a desired final configuration of the platform. We show numerically that robot trajectories with three switch times (two on one wheel, one on the other) can reach any position, while trajectories with four switch times can reach any configuration. By numerical comparison with other trajectories involving similar or greater numbers of switch times, we then identify the sets of time-optimal trajectories. These are uniquely defined using ranges of the parameters, and consist of subsets of trajectories with three switch times for the problem when the final orientation of the robot is not specified, and four switch times when a full final configuration is specified. We conclude with a description of the use of the method for trajectory planning for one of our robots.« less

Backtracking search algorithm in CVRP models for efficient solid waste collection and route optimization.

PubMed

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

2017-03-01

Waste collection is an important part of waste management that involves different issues, including environmental, economic, and social, among others. Waste collection optimization can reduce the waste collection budget and environmental emissions by reducing the collection route distance. This paper presents a modified Backtracking Search Algorithm (BSA) in capacitated vehicle routing problem (CVRP) models with the smart bin concept to find the best optimized waste collection route solutions. The objective function minimizes the sum of the waste collection route distances. The study introduces the concept of the threshold waste level (TWL) of waste bins to reduce the number of bins to be emptied by finding an optimal range, thus minimizing the distance. A scheduling model is also introduced to compare the feasibility of the proposed model with that of the conventional collection system in terms of travel distance, collected waste, fuel consumption, fuel cost, efficiency and CO 2 emission. The optimal TWL was found to be between 70% and 75% of the fill level of waste collection nodes and had the maximum tightness value for different problem cases. The obtained results for four days show a 36.80% distance reduction for 91.40% of the total waste collection, which eventually increases the average waste collection efficiency by 36.78% and reduces the fuel consumption, fuel cost and CO 2 emission by 50%, 47.77% and 44.68%, respectively. Thus, the proposed optimization model can be considered a viable tool for optimizing waste collection routes to reduce economic costs and environmental impacts. Copyright © 2017 Elsevier Ltd. All rights reserved.

Human motion planning based on recursive dynamics and optimal control techniques

NASA Technical Reports Server (NTRS)

Lo, Janzen; Huang, Gang; Metaxas, Dimitris

2002-01-01

This paper presents an efficient optimal control and recursive dynamics-based computer animation system for simulating and controlling the motion of articulated figures. A quasi-Newton nonlinear programming technique (super-linear convergence) is implemented to solve minimum torque-based human motion-planning problems. The explicit analytical gradients needed in the dynamics are derived using a matrix exponential formulation and Lie algebra. Cubic spline functions are used to make the search space for an optimal solution finite. Based on our formulations, our method is well conditioned and robust, in addition to being computationally efficient. To better illustrate the efficiency of our method, we present results of natural looking and physically correct human motions for a variety of human motion tasks involving open and closed loop kinematic chains.

An application of different dioids in public key cryptography

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

Durcheva, Mariana I., E-mail: mdurcheva66@gmail.com

2014-11-18

Dioids provide a natural framework for analyzing a broad class of discrete event dynamical systems such as the design and analysis of bus and railway timetables, scheduling of high-throughput industrial processes, solution of combinatorial optimization problems, the analysis and improvement of flow systems in communication networks. They have appeared in several branches of mathematics such as functional analysis, optimization, stochastic systems and dynamic programming, tropical geometry, fuzzy logic. In this paper we show how to involve dioids in public key cryptography. The main goal is to create key – exchange protocols based on dioids. Additionally the digital signature scheme ismore » presented.« less

An optimal brain can be composed of conflicting agents

PubMed Central

Livnat, Adi; Pippenger, Nicholas

2006-01-01

Many behaviors have been attributed to internal conflict within the animal and human mind. However, internal conflict has not been reconciled with evolutionary principles, in that it appears maladaptive relative to a seamless decision-making process. We study this problem through a mathematical analysis of decision-making structures. We find that, under natural physiological limitations, an optimal decision-making system can involve “selfish” agents that are in conflict with one another, even though the system is designed for a single purpose. It follows that conflict can emerge within a collective even when natural selection acts on the level of the collective only. PMID:16492775

Optimal Sampling to Provide User-Specific Climate Information.

NASA Astrophysics Data System (ADS)

Panturat, Suwanna

The types of weather-related world problems which are of socio-economic importance selected in this study as representative of three different levels of user groups include: (i) a regional problem concerned with air pollution plumes which lead to acid rain in the north eastern United States, (ii) a state-level problem in the form of winter wheat production in Oklahoma, and (iii) an individual-level problem involving reservoir management given errors in rainfall estimation at Lake Ellsworth, upstream from Lawton, Oklahoma. The study is aimed at designing optimal sampling networks which are based on customer value systems and also abstracting from data sets that information which is most cost-effective in reducing the climate-sensitive aspects of a given user problem. Three process models being used in this study to interpret climate variability in terms of the variables of importance to the user comprise: (i) the HEFFTER-SAMSON diffusion model as the climate transfer function for acid rain, (ii) the CERES-MAIZE plant process model for winter wheat production and (iii) the AGEHYD streamflow model selected as "a black box" for reservoir management. A state-of-the-art Non Linear Program (NLP) algorithm for minimizing an objective function is employed to determine the optimal number and location of various sensors. Statistical quantities considered in determining sensor locations including Bayes Risk, the chi-squared value, the probability of the Type I error (alpha) and the probability of the Type II error (beta) and the noncentrality parameter delta^2. Moreover, the number of years required to detect a climate change resulting in a given bushel per acre change in mean wheat production is determined; the number of seasons of observations required to reduce the standard deviation of the error variance of the ambient sulfur dioxide to less than a certain percent of the mean is found; and finally the policy of maintaining pre-storm flood pools at selected levels is examined given information from the optimal sampling network as defined by the study.

Minimum fuel coplanar aeroassisted orbital transfer using collocation and nonlinear programming

NASA Technical Reports Server (NTRS)

Shi, Yun Yuan; Young, D. H.

1991-01-01

The fuel optimal control problem arising in coplanar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) without plane change. The basic approach here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the coplanar aeroassisted HEO to LEO orbit transfer consists of three phases. In the first phase, the transfer begins with a deorbit impulse at HEO which injects the vehicle into a elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and drag modulation to satisfy heating constraints and to exit the atmosphere with the desired flight path angle and velocity so that the apogee of the exit orbit is the altitude of the desired LEO. Finally, the second impulse is required to circularize the orbit at LEO. The performance index is maximum final mass. Simulation results show that the coplanar aerocapture is quite different from the case where orbital plane changes are made inside the atmosphere. In the latter case, the vehicle has to penetrate deeper into the atmosphere to perform the desired orbital plane change. For the coplanar case, the vehicle needs only to penetrate the atmosphere deep enough to reduce the exit velocity so the vehicle can be captured at the desired LEO. The peak heating rates are lower and the entry corridor is wider. From the thermal protection point of view, the coplanar transfer may be desirable. Parametric studies also show the maximum peak heating rates and the entry corridor width are functions of maximum lift coefficient. The problem is solved using a direct optimization technique which uses piecewise polynomial representation for the states and controls and collocation to represent the differential equations. This converts the optimal control problem into a nonlinear programming problem which is solved numerically by using a modified version of NPSOL. Solutions were obtained for the described problem for cases with and without heating constraints. The method appears to be more robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

LDRD Final Report: Global Optimization for Engineering Science Problems

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

HART,WILLIAM E.

1999-12-01

For a wide variety of scientific and engineering problems the desired solution corresponds to an optimal set of objective function parameters, where the objective function measures a solution's quality. The main goal of the LDRD ''Global Optimization for Engineering Science Problems'' was the development of new robust and efficient optimization algorithms that can be used to find globally optimal solutions to complex optimization problems. This SAND report summarizes the technical accomplishments of this LDRD, discusses lessons learned and describes open research issues.

Optimal replenishment and credit policy in supply chain inventory model under two levels of trade credit with time- and credit-sensitive demand involving default risk

NASA Astrophysics Data System (ADS)

Mahata, Puspita; Mahata, Gour Chandra; Kumar De, Sujit

2018-03-01

Traditional supply chain inventory modes with trade credit usually only assumed that the up-stream suppliers offered the down-stream retailers a fixed credit period. However, in practice the retailers will also provide a credit period to customers to promote the market competition. In this paper, we formulate an optimal supply chain inventory model under two levels of trade credit policy with default risk consideration. Here, the demand is assumed to be credit-sensitive and increasing function of time. The major objective is to determine the retailer's optimal credit period and cycle time such that the total profit per unit time is maximized. The existence and uniqueness of the optimal solution to the presented model are examined, and an easy method is also shown to find the optimal inventory policies of the considered problem. Finally, numerical examples and sensitive analysis are presented to illustrate the developed model and to provide some managerial insights.

Research on NC laser combined cutting optimization model of sheet metal parts

NASA Astrophysics Data System (ADS)

Wu, Z. Y.; Zhang, Y. L.; Li, L.; Wu, L. H.; Liu, N. B.

2017-09-01

The optimization problem for NC laser combined cutting of sheet metal parts was taken as the research object in this paper. The problem included two contents: combined packing optimization and combined cutting path optimization. In the problem of combined packing optimization, the method of “genetic algorithm + gravity center NFP + geometric transformation” was used to optimize the packing of sheet metal parts. In the problem of combined cutting path optimization, the mathematical model of cutting path optimization was established based on the parts cutting constraint rules of internal contour priority and cross cutting. The model played an important role in the optimization calculation of NC laser combined cutting.

Quadratic constrained mixed discrete optimization with an adiabatic quantum optimizer

NASA Astrophysics Data System (ADS)

Chandra, Rishabh; Jacobson, N. Tobias; Moussa, Jonathan E.; Frankel, Steven H.; Kais, Sabre

2014-07-01

We extend the family of problems that may be implemented on an adiabatic quantum optimizer (AQO). When a quadratic optimization problem has at least one set of discrete controls and the constraints are linear, we call this a quadratic constrained mixed discrete optimization (QCMDO) problem. QCMDO problems are NP-hard, and no efficient classical algorithm for their solution is known. Included in the class of QCMDO problems are combinatorial optimization problems constrained by a linear partial differential equation (PDE) or system of linear PDEs. An essential complication commonly encountered in solving this type of problem is that the linear constraint may introduce many intermediate continuous variables into the optimization while the computational cost grows exponentially with problem size. We resolve this difficulty by developing a constructive mapping from QCMDO to quadratic unconstrained binary optimization (QUBO) such that the size of the QUBO problem depends only on the number of discrete control variables. With a suitable embedding, taking into account the physical constraints of the realizable coupling graph, the resulting QUBO problem can be implemented on an existing AQO. The mapping itself is efficient, scaling cubically with the number of continuous variables in the general case and linearly in the PDE case if an efficient preconditioner is available.

An Enhanced Memetic Algorithm for Single-Objective Bilevel Optimization Problems.

PubMed

Islam, Md Monjurul; Singh, Hemant Kumar; Ray, Tapabrata; Sinha, Ankur

2017-01-01

Bilevel optimization, as the name reflects, deals with optimization at two interconnected hierarchical levels. The aim is to identify the optimum of an upper-level  leader problem, subject to the optimality of a lower-level follower problem. Several problems from the domain of engineering, logistics, economics, and transportation have an inherent nested structure which requires them to be modeled as bilevel optimization problems. Increasing size and complexity of such problems has prompted active theoretical and practical interest in the design of efficient algorithms for bilevel optimization. Given the nested nature of bilevel problems, the computational effort (number of function evaluations) required to solve them is often quite high. In this article, we explore the use of a Memetic Algorithm (MA) to solve bilevel optimization problems. While MAs have been quite successful in solving single-level optimization problems, there have been relatively few studies exploring their potential for solving bilevel optimization problems. MAs essentially attempt to combine advantages of global and local search strategies to identify optimum solutions with low computational cost (function evaluations). The approach introduced in this article is a nested Bilevel Memetic Algorithm (BLMA). At both upper and lower levels, either a global or a local search method is used during different phases of the search. The performance of BLMA is presented on twenty-five standard test problems and two real-life applications. The results are compared with other established algorithms to demonstrate the efficacy of the proposed approach.

Optimal Price Decision Problem for Simultaneous Multi-article Auction and Its Optimal Price Searching Method by Particle Swarm Optimization

NASA Astrophysics Data System (ADS)

Masuda, Kazuaki; Aiyoshi, Eitaro

We propose a method for solving optimal price decision problems for simultaneous multi-article auctions. An auction problem, originally formulated as a combinatorial problem, determines both every seller's whether or not to sell his/her article and every buyer's which article(s) to buy, so that the total utility of buyers and sellers will be maximized. Due to the duality theory, we transform it equivalently into a dual problem in which Lagrange multipliers are interpreted as articles' transaction price. As the dual problem is a continuous optimization problem with respect to the multipliers (i.e., the transaction prices), we propose a numerical method to solve it by applying heuristic global search methods. In this paper, Particle Swarm Optimization (PSO) is used to solve the dual problem, and experimental results are presented to show the validity of the proposed method.

Techniques for shuttle trajectory optimization

NASA Technical Reports Server (NTRS)

Edge, E. R.; Shieh, C. J.; Powers, W. F.

1973-01-01

The application of recently developed function-space Davidon-type techniques to the shuttle ascent trajectory optimization problem is discussed along with an investigation of the recently developed PRAXIS algorithm for parameter optimization. At the outset of this analysis, the major deficiency of the function-space algorithms was their potential storage problems. Since most previous analyses of the methods were with relatively low-dimension problems, no storage problems were encountered. However, in shuttle trajectory optimization, storage is a problem, and this problem was handled efficiently. Topics discussed include: the shuttle ascent model and the development of the particular optimization equations; the function-space algorithms; the operation of the algorithm and typical simulations; variable final-time problem considerations; and a modification of Powell's algorithm.

WE-D-303-01: Development and Application of Digital Human Phantoms

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

Segars, P.

2015-06-15

Modern medical physics deals with complex problems such as 4D radiation therapy and imaging quality optimization. Such problems involve a large number of radiological parameters, and anatomical and physiological breathing patterns. A major challenge is how to develop, test, evaluate and compare various new imaging and treatment techniques, which often involves testing over a large range of radiological parameters as well as varying patient anatomies and motions. It would be extremely challenging, if not impossible, both ethically and practically, to test every combination of parameters and every task on every type of patient under clinical conditions. Computer-based simulation using computationalmore » phantoms offers a practical technique with which to evaluate, optimize, and compare imaging technologies and methods. Within simulation, the computerized phantom provides a virtual model of the patient’s anatomy and physiology. Imaging data can be generated from it as if it was a live patient using accurate models of the physics of the imaging and treatment process. With sophisticated simulation algorithms, it is possible to perform virtual experiments entirely on the computer. By serving as virtual patients, computational phantoms hold great promise in solving some of the most complex problems in modern medical physics. In this proposed symposium, we will present the history and recent developments of computational phantom models, share experiences in their application to advanced imaging and radiation applications, and discuss their promises and limitations. Learning Objectives: Understand the need and requirements of computational phantoms in medical physics research Discuss the developments and applications of computational phantoms Know the promises and limitations of computational phantoms in solving complex problems.« less

On l(1): Optimal decentralized performance

NASA Technical Reports Server (NTRS)

Sourlas, Dennis; Manousiouthakis, Vasilios

1993-01-01

In this paper, the Manousiouthakis parametrization of all decentralized stabilizing controllers is employed in mathematically formulating the l(sup 1) optimal decentralized controller synthesis problem. The resulting optimization problem is infinite dimensional and therefore not directly amenable to computations. It is shown that finite dimensional optimization problems that have value arbitrarily close to the infinite dimensional one can be constructed. Based on this result, an algorithm that solves the l(sup 1) decentralized performance problems is presented. A global optimization approach to the solution of the infinite dimensional approximating problems is also discussed.

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

Chandrasekhar equations for infinite dimensional systems. Part 2: Unbounded input and output case

NASA Technical Reports Server (NTRS)

Ito, Kazufumi; Powers, Robert K.

1987-01-01

A set of equations known as Chandrasekhar equations arising in the linear quadratic optimal control problem is considered. In this paper, we consider the linear time-invariant system defined in Hilbert spaces involving unbounded input and output operators. For a general class of such systems, the Chandrasekhar equations are derived and the existence, uniqueness, and regularity of the results of their solutions established.

An Empirical Comparison of Seven Iterative and Evolutionary Function Optimization Heuristics

NASA Technical Reports Server (NTRS)

Baluja, Shumeet

1995-01-01

This report is a repository of the results obtained from a large scale empirical comparison of seven iterative and evolution-based optimization heuristics. Twenty-seven static optimization problems, spanning six sets of problem classes which are commonly explored in genetic algorithm literature, are examined. The problem sets include job-shop scheduling, traveling salesman, knapsack, binpacking, neural network weight optimization, and standard numerical optimization. The search spaces in these problems range from 2368 to 22040. The results indicate that using genetic algorithms for the optimization of static functions does not yield a benefit, in terms of the final answer obtained, over simpler optimization heuristics. Descriptions of the algorithms tested and the encodings of the problems are described in detail for reproducibility.

A multiobjective optimization framework for multicontaminant industrial water network design.

PubMed

Boix, Marianne; Montastruc, Ludovic; Pibouleau, Luc; Azzaro-Pantel, Catherine; Domenech, Serge

2011-07-01

The optimal design of multicontaminant industrial water networks according to several objectives is carried out in this paper. The general formulation of the water allocation problem (WAP) is given as a set of nonlinear equations with binary variables representing the presence of interconnections in the network. For optimization purposes, three antagonist objectives are considered: F(1), the freshwater flow-rate at the network entrance, F(2), the water flow-rate at inlet of regeneration units, and F(3), the number of interconnections in the network. The multiobjective problem is solved via a lexicographic strategy, where a mixed-integer nonlinear programming (MINLP) procedure is used at each step. The approach is illustrated by a numerical example taken from the literature involving five processes, one regeneration unit and three contaminants. The set of potential network solutions is provided in the form of a Pareto front. Finally, the strategy for choosing the best network solution among those given by Pareto fronts is presented. This Multiple Criteria Decision Making (MCDM) problem is tackled by means of two approaches: a classical TOPSIS analysis is first implemented and then an innovative strategy based on the global equivalent cost (GEC) in freshwater that turns out to be more efficient for choosing a good network according to a practical point of view. Copyright © 2011 Elsevier Ltd. All rights reserved.

The role of adaptive management as an operational approach for resource management agencies

USGS Publications Warehouse

Johnson, B.L.

1999-01-01

In making resource management decisions, agencies use a variety of approaches that involve different levels of political concern, historical precedence, data analyses, and evaluation. Traditional decision-making approaches have often failed to achieve objectives for complex problems in large systems, such as the Everglades or the Colorado River. I contend that adaptive management is the best approach available to agencies for addressing this type of complex problem, although its success has been limited thus far. Traditional decision-making approaches have been fairly successful at addressing relatively straightforward problems in small, replicated systems, such as management of trout in small streams or pulp production in forests. However, this success may be jeopardized as more users place increasing demands on these systems. Adaptive management has received little attention from agencies for addressing problems in small-scale systems, but I suggest that it may be a useful approach for creating a holistic view of common problems and developing guidelines that can then be used in simpler, more traditional approaches to management. Although adaptive management may be more expensive to initiate than traditional approaches, it may be less expensive in the long run if it leads to more effective management. The overall goal of adaptive management is not to maintain an optimal condition of the resource, but to develop an optimal management capacity. This is accomplished by maintaining ecological resilience that allows the system to react to inevitable stresses, and generating flexibility in institutions and stakeholders that allows managers to react when conditions change. The result is that, rather than managing for a single, optimal state, we manage within a range of acceptable outcomes while avoiding catastrophes and irreversible negative effects. Copyright ?? 1999 by The Resilience Alliance.

Autonomous Modelling of X-ray Spectra Using Robust Global Optimization Methods

NASA Astrophysics Data System (ADS)

Rogers, Adam; Safi-Harb, Samar; Fiege, Jason

2015-08-01

The standard approach to model fitting in X-ray astronomy is by means of local optimization methods. However, these local optimizers suffer from a number of problems, such as a tendency for the fit parameters to become trapped in local minima, and can require an involved process of detailed user intervention to guide them through the optimization process. In this work we introduce a general GUI-driven global optimization method for fitting models to X-ray data, written in MATLAB, which searches for optimal models with minimal user interaction. We directly interface with the commonly used XSPEC libraries to access the full complement of pre-existing spectral models that describe a wide range of physics appropriate for modelling astrophysical sources, including supernova remnants and compact objects. Our algorithm is powered by the Ferret genetic algorithm and Locust particle swarm optimizer from the Qubist Global Optimization Toolbox, which are robust at finding families of solutions and identifying degeneracies. This technique will be particularly instrumental for multi-parameter models and high-fidelity data. In this presentation, we provide details of the code and use our techniques to analyze X-ray data obtained from a variety of astrophysical sources.

Application of heuristic satellite plan synthesis algorithms to requirements of the WARC-88 allotment plan

NASA Technical Reports Server (NTRS)

Heyward, Ann O.; Reilly, Charles H.; Walton, Eric K.; Mata, Fernando; Olen, Carl

1990-01-01

Creation of an Allotment Plan for the Fixed Satellite Service at the 1988 Space World Administrative Radio Conference (WARC) represented a complex satellite plan synthesis problem, involving a large number of planned and existing systems. Solutions to this problem at WARC-88 required the use of both automated and manual procedures to develop an acceptable set of system positions. Development of an Allotment Plan may also be attempted through solution of an optimization problem, known as the Satellite Location Problem (SLP). Three automated heuristic procedures, developed specifically to solve SLP, are presented. The heuristics are then applied to two specific WARC-88 scenarios. Solutions resulting from the fully automated heuristics are then compared with solutions obtained at WARC-88 through a combination of both automated and manual planning efforts.

Solving the vehicle routing problem by a hybrid meta-heuristic algorithm

NASA Astrophysics Data System (ADS)

Yousefikhoshbakht, Majid; Khorram, Esmaile

2012-08-01

The vehicle routing problem (VRP) is one of the most important combinational optimization problems that has nowadays received much attention because of its real application in industrial and service problems. The VRP involves routing a fleet of vehicles, each of them visiting a set of nodes such that every node is visited by exactly one vehicle only once. So, the objective is to minimize the total distance traveled by all the vehicles. This paper presents a hybrid two-phase algorithm called sweep algorithm (SW) + ant colony system (ACS) for the classical VRP. At the first stage, the VRP is solved by the SW, and at the second stage, the ACS and 3-opt local search are used for improving the solutions. Extensive computational tests on standard instances from the literature confirm the effectiveness of the presented approach.

An efficient assisted history matching and uncertainty quantification workflow using Gaussian processes proxy models and variogram based sensitivity analysis: GP-VARS

NASA Astrophysics Data System (ADS)

Rana, Sachin; Ertekin, Turgay; King, Gregory R.

2018-05-01

Reservoir history matching is frequently viewed as an optimization problem which involves minimizing misfit between simulated and observed data. Many gradient and evolutionary strategy based optimization algorithms have been proposed to solve this problem which typically require a large number of numerical simulations to find feasible solutions. Therefore, a new methodology referred to as GP-VARS is proposed in this study which uses forward and inverse Gaussian processes (GP) based proxy models combined with a novel application of variogram analysis of response surface (VARS) based sensitivity analysis to efficiently solve high dimensional history matching problems. Empirical Bayes approach is proposed to optimally train GP proxy models for any given data. The history matching solutions are found via Bayesian optimization (BO) on forward GP models and via predictions of inverse GP model in an iterative manner. An uncertainty quantification method using MCMC sampling in conjunction with GP model is also presented to obtain a probabilistic estimate of reservoir properties and estimated ultimate recovery (EUR). An application of the proposed GP-VARS methodology on PUNQ-S3 reservoir is presented in which it is shown that GP-VARS provides history match solutions in approximately four times less numerical simulations as compared to the differential evolution (DE) algorithm. Furthermore, a comparison of uncertainty quantification results obtained by GP-VARS, EnKF and other previously published methods shows that the P50 estimate of oil EUR obtained by GP-VARS is in close agreement to the true values for the PUNQ-S3 reservoir.

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.

Multiobjective optimization of temporal processes.

PubMed

Song, Zhe; Kusiak, Andrew

2010-06-01

This paper presents a dynamic predictive-optimization framework of a nonlinear temporal process. Data-mining (DM) and evolutionary strategy algorithms are integrated in the framework for solving the optimization model. DM algorithms learn dynamic equations from the process data. An evolutionary strategy algorithm is then applied to solve the optimization problem guided by the knowledge extracted by the DM algorithm. The concept presented in this paper is illustrated with the data from a power plant, where the goal is to maximize the boiler efficiency and minimize the limestone consumption. This multiobjective optimization problem can be either transformed into a single-objective optimization problem through preference aggregation approaches or into a Pareto-optimal optimization problem. The computational results have shown the effectiveness of the proposed optimization framework.

Optimization of Straight Cylindrical Turning Using Artificial Bee Colony (ABC) Algorithm

NASA Astrophysics Data System (ADS)

Prasanth, Rajanampalli Seshasai Srinivasa; Hans Raj, Kandikonda

2017-04-01

Artificial bee colony (ABC) algorithm, that mimics the intelligent foraging behavior of honey bees, is increasingly gaining acceptance in the field of process optimization, as it is capable of handling nonlinearity, complexity and uncertainty. Straight cylindrical turning is a complex and nonlinear machining process which involves the selection of appropriate cutting parameters that affect the quality of the workpiece. This paper presents the estimation of optimal cutting parameters of the straight cylindrical turning process using the ABC algorithm. The ABC algorithm is first tested on four benchmark problems of numerical optimization and its performance is compared with genetic algorithm (GA) and ant colony optimization (ACO) algorithm. Results indicate that, the rate of convergence of ABC algorithm is better than GA and ACO. Then, the ABC algorithm is used to predict optimal cutting parameters such as cutting speed, feed rate, depth of cut and tool nose radius to achieve good surface finish. Results indicate that, the ABC algorithm estimated a comparable surface finish when compared with real coded genetic algorithm and differential evolution algorithm.

Modeling, simulation and optimization approaches for design of lightweight car body structures

NASA Astrophysics Data System (ADS)

Kiani, Morteza

Simulation-based design optimization and finite element method are used in this research to investigate weight reduction of car body structures made of metallic and composite materials under different design criteria. Besides crashworthiness in full frontal, offset frontal, and side impact scenarios, vibration frequencies, static stiffness, and joint rigidity are also considered. Energy absorption at the component level is used to study the effectiveness of carbon fiber reinforced polymer (CFRP) composite material with consideration of different failure criteria. A global-local design strategy is introduced and applied to multi-objective optimization of car body structures with CFRP components. Multiple example problems involving the analysis of full-vehicle crash and body-in-white models are used to examine the effect of material substitution and the choice of design criteria on weight reduction. The results of this study show that car body structures that are optimized for crashworthiness alone may not meet the vibration criterion. Moreover, optimized car body structures with CFRP components can be lighter with superior crashworthiness than the baseline and optimized metallic structures.

Multivariable frequency domain identification via 2-norm minimization

NASA Technical Reports Server (NTRS)

Bayard, David S.

1992-01-01

The author develops a computational approach to multivariable frequency domain identification, based on 2-norm minimization. In particular, a Gauss-Newton (GN) iteration is developed to minimize the 2-norm of the error between frequency domain data and a matrix fraction transfer function estimate. To improve the global performance of the optimization algorithm, the GN iteration is initialized using the solution to a particular sequentially reweighted least squares problem, denoted as the SK iteration. The least squares problems which arise from both the SK and GN iterations are shown to involve sparse matrices with identical block structure. A sparse matrix QR factorization method is developed to exploit the special block structure, and to efficiently compute the least squares solution. A numerical example involving the identification of a multiple-input multiple-output (MIMO) plant having 286 unknown parameters is given to illustrate the effectiveness of the algorithm.

Composition of web services using Markov decision processes and dynamic programming.

PubMed

Uc-Cetina, Víctor; Moo-Mena, Francisco; Hernandez-Ucan, Rafael

2015-01-01

We propose a Markov decision process model for solving the Web service composition (WSC) problem. Iterative policy evaluation, value iteration, and policy iteration algorithms are used to experimentally validate our approach, with artificial and real data. The experimental results show the reliability of the model and the methods employed, with policy iteration being the best one in terms of the minimum number of iterations needed to estimate an optimal policy, with the highest Quality of Service attributes. Our experimental work shows how the solution of a WSC problem involving a set of 100,000 individual Web services and where a valid composition requiring the selection of 1,000 services from the available set can be computed in the worst case in less than 200 seconds, using an Intel Core i5 computer with 6 GB RAM. Moreover, a real WSC problem involving only 7 individual Web services requires less than 0.08 seconds, using the same computational power. Finally, a comparison with two popular reinforcement learning algorithms, sarsa and Q-learning, shows that these algorithms require one or two orders of magnitude and more time than policy iteration, iterative policy evaluation, and value iteration to handle WSC problems of the same complexity.

Improving stability and strength characteristics of framed structures with nonlinear behavior

NASA Technical Reports Server (NTRS)

Pezeshk, Shahram

1990-01-01

In this paper an optimal design procedure is introduced to improve the overall performance of nonlinear framed structures. The design methodology presented here is a multiple-objective optimization procedure whose objective functions involve the buckling eigenvalues and eigenvectors of the structure. A constant volume with bounds on the design variables is used in conjunction with an optimality criterion approach. The method provides a general tool for solving complex design problems and generally leads to structures with better limit strength and stability. Many algorithms have been developed to improve the limit strength of structures. In most applications geometrically linear analysis is employed with the consequence that overall strength of the design is overestimated. Directly optimizing the limit load of the structure would require a full nonlinear analysis at each iteration which would be prohibitively expensive. The objective of this paper is to develop an algorithm that can improve the limit-load of geometrically nonlinear framed structures while avoiding the nonlinear analysis. One of the novelties of the new design methodology is its ability to efficiently model and design structures under multiple loading conditions. These loading conditions can be different factored loads or any kind of loads that can be applied to the structure simultaneously or independently. Attention is focused on optimal design of space framed structures. Three-dimensional design problems are more complicated to carry out, but they yield insight into real behavior of the structure and can help avoiding some of the problems that might appear in planar design procedure such as the need for out-of-plane buckling constraint. Although researchers in the field of structural engineering generally agree that optimum design of three-dimension building frames especially in the seismic regions would be beneficial, methods have been slow to emerge. Most of the research in this area has dealt with the optimization of truss and plane frame structures.

Minimal entropy probability paths between genome families.

PubMed

Ahlbrandt, Calvin; Benson, Gary; Casey, William

2004-05-01

We develop a metric for probability distributions with applications to biological sequence analysis. Our distance metric is obtained by minimizing a functional defined on the class of paths over probability measures on N categories. The underlying mathematical theory is connected to a constrained problem in the calculus of variations. The solution presented is a numerical solution, which approximates the true solution in a set of cases called rich paths where none of the components of the path is zero. The functional to be minimized is motivated by entropy considerations, reflecting the idea that nature might efficiently carry out mutations of genome sequences in such a way that the increase in entropy involved in transformation is as small as possible. We characterize sequences by frequency profiles or probability vectors, in the case of DNA where N is 4 and the components of the probability vector are the frequency of occurrence of each of the bases A, C, G and T. Given two probability vectors a and b, we define a distance function based as the infimum of path integrals of the entropy function H( p) over all admissible paths p(t), 0 < or = t< or =1, with p(t) a probability vector such that p(0)=a and p(1)=b. If the probability paths p(t) are parameterized as y(s) in terms of arc length s and the optimal path is smooth with arc length L, then smooth and "rich" optimal probability paths may be numerically estimated by a hybrid method of iterating Newton's method on solutions of a two point boundary value problem, with unknown distance L between the abscissas, for the Euler-Lagrange equations resulting from a multiplier rule for the constrained optimization problem together with linear regression to improve the arc length estimate L. Matlab code for these numerical methods is provided which works only for "rich" optimal probability vectors. These methods motivate a definition of an elementary distance function which is easier and faster to calculate, works on non-rich vectors, does not involve variational theory and does not involve differential equations, but is a better approximation of the minimal entropy path distance than the distance //b-a//(2). We compute minimal entropy distance matrices for examples of DNA myostatin genes and amino-acid sequences across several species. Output tree dendograms for our minimal entropy metric are compared with dendograms based on BLAST and BLAST identity scores.

Social Emotional Optimization Algorithm for Nonlinear Constrained Optimization Problems

NASA Astrophysics Data System (ADS)

Xu, Yuechun; Cui, Zhihua; Zeng, Jianchao

Nonlinear programming problem is one important branch in operational research, and has been successfully applied to various real-life problems. In this paper, a new approach called Social emotional optimization algorithm (SEOA) is used to solve this problem which is a new swarm intelligent technique by simulating the human behavior guided by emotion. Simulation results show that the social emotional optimization algorithm proposed in this paper is effective and efficiency for the nonlinear constrained programming problems.

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.

Primer Vector Optimization: Survey of Theory, new Analysis and Applications

NASA Astrophysics Data System (ADS)

Guzman

This paper presents a preliminary study in developing a set of optimization tools for orbit rendezvous, transfer and station keeping. This work is part of a large scale effort undergoing at NASA Goddard Space Flight Center and a.i. solutions, Inc. to build generic methods, which will enable missions with tight fuel budgets. Since no single optimization technique can solve efficiently all existing problems, a library of tools where the user could pick the method most suited for the particular mission is envisioned. The first trajectory optimization technique explored is Lawden's primer vector theory [Ref. 1]. Primer vector theory can be considered as a byproduct of applying Calculus of Variations (COV) techniques to the problem of minimizing the fuel usage of impulsive trajectories. For an n-impulse trajectory, it involves the solution of n-1 two-point boundary value problems. In this paper, we look at some of the different formulations of the primer vector (dependent on the frame employed and on the force model). Also, the applicability of primer vector theory is examined in effort to understand when and why the theory can fail. Specifically, since COV is based on "small variations", singularities in the linearized (variational) equations of motion along the arcs must be taken into account. These singularities are a recurring problem in analyzes that employ "small variations" [Refs. 2, 3]. For example, singularities in the (2-body problem) variational equations along elliptic arcs occur when [Ref. 4], 1) the difference between the initial and final times is a multiple of the reference orbit period, 2) the difference between the initial and final true anomalies are given by k, for k= 0, 1, 2, 3,..., note that this cover the 3) the time of flight is a minimum for the given difference in true anomaly. For the N-body problem, the situation is more complex and is still under investigation. Several examples, such as the initialization of an orbit (ascent trajectory) and rotation of the line of apsides, are utilized as test cases. Recommendations, future work, and the possible addition of other optimization techniques are also discussed. References: [1] Lawden D.F., Optimal Trajectories for Space Navigation, Butterworths, London, 1963. [2] Wilson, R.S., Howell, K.C., and, Lo, M, "Optimization of Insertion Cost for Transfer Trajectories to Libration Point Orbits", AIAA/AAS Astrodynamics Specialist Conference, AAS 99-041, Girdwood, Alaska, August 16-19, 1999. [3] Goodson, T, "Monte-Carlo Maneuver Analysis for the Microwave Anisotropy Probe", AAS/AIAA Astrodynamics Specialist Conference, AAS 01-331, Quebec City, Canada, July 30 - August 2, 2001. [4] Stern, R.G., "Singularities in the Analytic Solution of the Linearized Variational Equations of Elliptical Motion", Report RE-8, May 1964, Experimental Astronomy Lab., Massachusetts Institute of Technology, Cambridge, Massachusetts.

Optimality conditions for the numerical solution of optimization problems with PDE constraints :

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

Aguilo Valentin, Miguel Alejandro; Ridzal, Denis

2014-03-01

A theoretical framework for the numerical solution of partial di erential equation (PDE) constrained optimization problems is presented in this report. This theoretical framework embodies the fundamental infrastructure required to e ciently implement and solve this class of problems. Detail derivations of the optimality conditions required to accurately solve several parameter identi cation and optimal control problems are also provided in this report. This will allow the reader to further understand how the theoretical abstraction presented in this report translates to the application.

FRANOPP: Framework for analysis and optimization problems user's guide

NASA Technical Reports Server (NTRS)

Riley, K. M.

1981-01-01

Framework for analysis and optimization problems (FRANOPP) is a software aid for the study and solution of design (optimization) problems which provides the driving program and plotting capability for a user generated programming system. In addition to FRANOPP, the programming system also contains the optimization code CONMIN, and two user supplied codes, one for analysis and one for output. With FRANOPP the user is provided with five options for studying a design problem. Three of the options utilize the plot capability and present an indepth study of the design problem. The study can be focused on a history of the optimization process or on the interaction of variables within the design problem.

Evaluation of Genetic Algorithm Concepts Using Model Problems. Part 2; Multi-Objective Optimization

NASA Technical Reports Server (NTRS)

Holst, Terry L.; Pulliam, Thomas H.

2003-01-01

A genetic algorithm approach suitable for solving multi-objective optimization problems is described and evaluated using a series of simple model problems. Several new features including a binning selection algorithm and a gene-space transformation procedure are included. The genetic algorithm is suitable for finding pareto optimal solutions in search spaces that are defined by any number of genes and that contain any number of local extrema. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all optimization problems attempted. The binning algorithm generally provides pareto front quality enhancements and moderate convergence efficiency improvements for most of the model problems. The gene-space transformation procedure provides a large convergence efficiency enhancement for problems with non-convoluted pareto fronts and a degradation in efficiency for problems with convoluted pareto fronts. The most difficult problems --multi-mode search spaces with a large number of genes and convoluted pareto fronts-- require a large number of function evaluations for GA convergence, but always converge.

A multi-objective approach to solid waste management.

PubMed

Galante, Giacomo; Aiello, Giuseppe; Enea, Mario; Panascia, Enrico

2010-01-01

The issue addressed in this paper consists in the localization and dimensioning of transfer stations, which constitute a necessary intermediate level in the logistic chain of the solid waste stream, from municipalities to the incinerator. Contextually, the determination of the number and type of vehicles involved is carried out in an integrated optimization approach. The model considers both initial investment and operative costs related to transportation and transfer stations. Two conflicting objectives are evaluated, the minimization of total cost and the minimization of environmental impact, measured by pollution. The design of the integrated waste management system is hence approached in a multi-objective optimization framework. To determine the best means of compromise, goal programming, weighted sum and fuzzy multi-objective techniques have been employed. The proposed analysis highlights how different attitudes of the decision maker towards the logic and structure of the problem result in the employment of different methodologies and the obtaining of different results. The novel aspect of the paper lies in the proposal of an effective decision support system for operative waste management, rather than a further contribution to the transportation problem. The model was applied to the waste management of optimal territorial ambit (OTA) of Palermo (Italy). 2010 Elsevier Ltd. All rights reserved.

Choosing the optimal wind turbine variant using the ”ELECTRE” method

NASA Astrophysics Data System (ADS)

Ţişcă, I. A.; Anuşca, D.; Dumitrescu, C. D.

2017-08-01

This paper presents a method of choosing the “optimal” alternative, both under certainty and under uncertainty, based on relevant analysis criteria. Taking into account that a product can be assimilated to a system and that the reliability of the system depends on the reliability of its components, the choice of product (the appropriate system decision) can be done using the “ELECTRE” method and depending on the level of reliability of each product. In the paper, the “ELECTRE” method is used in choosing the optimal version of a wind turbine required to equip a wind farm in western Romania. The problems to be solved are related to the current situation of wind turbines that involves reliability problems. A set of criteria has been proposed to compare two or more products from a range of available products: Operating conditions, Environmental conditions during operation, Time requirements. Using the ELECTRE hierarchical mathematical method it was established that on the basis of the obtained coefficients of concordance the optimal variant of the wind turbine and the order of preference of the variants are determined, the values chosen as limits being arbitrary.

A multi-objective approach to solid waste management

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

Galante, Giacomo, E-mail: galante@dtpm.unipa.i; Aiello, Giuseppe; Enea, Mario

2010-08-15

The issue addressed in this paper consists in the localization and dimensioning of transfer stations, which constitute a necessary intermediate level in the logistic chain of the solid waste stream, from municipalities to the incinerator. Contextually, the determination of the number and type of vehicles involved is carried out in an integrated optimization approach. The model considers both initial investment and operative costs related to transportation and transfer stations. Two conflicting objectives are evaluated, the minimization of total cost and the minimization of environmental impact, measured by pollution. The design of the integrated waste management system is hence approached inmore » a multi-objective optimization framework. To determine the best means of compromise, goal programming, weighted sum and fuzzy multi-objective techniques have been employed. The proposed analysis highlights how different attitudes of the decision maker towards the logic and structure of the problem result in the employment of different methodologies and the obtaining of different results. The novel aspect of the paper lies in the proposal of an effective decision support system for operative waste management, rather than a further contribution to the transportation problem. The model was applied to the waste management of optimal territorial ambit (OTA) of Palermo (Italy).« less

Unified anomaly suppression and boundary extraction in laser radar range imagery based on a joint curve-evolution and expectation-maximization algorithm.

PubMed

Feng, Haihua; Karl, William Clem; Castañon, David A

2008-05-01

In this paper, we develop a new unified approach for laser radar range anomaly suppression, range profiling, and segmentation. This approach combines an object-based hybrid scene model for representing the range distribution of the field and a statistical mixture model for the range data measurement noise. The image segmentation problem is formulated as a minimization problem which jointly estimates the target boundary together with the target region range variation and background range variation directly from the noisy and anomaly-filled range data. This formulation allows direct incorporation of prior information concerning the target boundary, target ranges, and background ranges into an optimal reconstruction process. Curve evolution techniques and a generalized expectation-maximization algorithm are jointly employed as an efficient solver for minimizing the objective energy, resulting in a coupled pair of object and intensity optimization tasks. The method directly and optimally extracts the target boundary, avoiding a suboptimal two-step process involving image smoothing followed by boundary extraction. Experiments are presented demonstrating that the proposed approach is robust to anomalous pixels (missing data) and capable of producing accurate estimation of the target boundary and range values from noisy data.

Wireless Sensor Network Optimization: Multi-Objective Paradigm.

PubMed

Iqbal, Muhammad; Naeem, Muhammad; Anpalagan, Alagan; Ahmed, Ashfaq; Azam, Muhammad

2015-07-20

Optimization problems relating to wireless sensor network planning, design, deployment and operation often give rise to multi-objective optimization formulations where multiple desirable objectives compete with each other and the decision maker has to select one of the tradeoff solutions. These multiple objectives may or may not conflict with each other. Keeping in view the nature of the application, the sensing scenario and input/output of the problem, the type of optimization problem changes. To address different nature of optimization problems relating to wireless sensor network design, deployment, operation, planing and placement, there exist a plethora of optimization solution types. We review and analyze different desirable objectives to show whether they conflict with each other, support each other or they are design dependent. We also present a generic multi-objective optimization problem relating to wireless sensor network which consists of input variables, required output, objectives and constraints. A list of constraints is also presented to give an overview of different constraints which are considered while formulating the optimization problems in wireless sensor networks. Keeping in view the multi facet coverage of this article relating to multi-objective optimization, this will open up new avenues of research in the area of multi-objective optimization relating to wireless sensor networks.

Adaptive infinite impulse response system identification using modified-interior search algorithm with Lèvy flight.

PubMed

Kumar, Manjeet; Rawat, Tarun Kumar; Aggarwal, Apoorva

2017-03-01

In this paper, a new meta-heuristic optimization technique, called interior search algorithm (ISA) with Lèvy flight is proposed and applied to determine the optimal parameters of an unknown infinite impulse response (IIR) system for the system identification problem. ISA is based on aesthetics, which is commonly used in interior design and decoration processes. In ISA, composition phase and mirror phase are applied for addressing the nonlinear and multimodal system identification problems. System identification using modified-ISA (M-ISA) based method involves faster convergence, single parameter tuning and does not require derivative information because it uses a stochastic random search using the concepts of Lèvy flight. A proper tuning of control parameter has been performed in order to achieve a balance between intensification and diversification phases. In order to evaluate the performance of the proposed method, mean square error (MSE), computation time and percentage improvement are considered as the performance measure. To validate the performance of M-ISA based method, simulations has been carried out for three benchmarked IIR systems using same order and reduced order system. Genetic algorithm (GA), particle swarm optimization (PSO), cat swarm optimization (CSO), cuckoo search algorithm (CSA), differential evolution using wavelet mutation (DEWM), firefly algorithm (FFA), craziness based particle swarm optimization (CRPSO), harmony search (HS) algorithm, opposition based harmony search (OHS) algorithm, hybrid particle swarm optimization-gravitational search algorithm (HPSO-GSA) and ISA are also used to model the same examples and simulation results are compared. Obtained results confirm the efficiency of the proposed method. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

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.

Automatic blocking of nested loops

NASA Technical Reports Server (NTRS)

Schreiber, Robert; Dongarra, Jack J.

1990-01-01

Blocked algorithms have much better properties of data locality and therefore can be much more efficient than ordinary algorithms when a memory hierarchy is involved. On the other hand, they are very difficult to write and to tune for particular machines. The reorganization is considered of nested loops through the use of known program transformations in order to create blocked algorithms automatically. The program transformations used are strip mining, loop interchange, and a variant of loop skewing in which invertible linear transformations (with integer coordinates) of the loop indices are allowed. Some problems are solved concerning the optimal application of these transformations. It is shown, in a very general setting, how to choose a nearly optimal set of transformed indices. It is then shown, in one particular but rather frequently occurring situation, how to choose an optimal set of block sizes.

Uncertainty Aware Structural Topology Optimization Via a Stochastic Reduced Order Model Approach

NASA Technical Reports Server (NTRS)

Aguilo, Miguel A.; Warner, James E.

2017-01-01

This work presents a stochastic reduced order modeling strategy for the quantification and propagation of uncertainties in topology optimization. Uncertainty aware optimization problems can be computationally complex due to the substantial number of model evaluations that are necessary to accurately quantify and propagate uncertainties. This computational complexity is greatly magnified if a high-fidelity, physics-based numerical model is used for the topology optimization calculations. Stochastic reduced order model (SROM) methods are applied here to effectively 1) alleviate the prohibitive computational cost associated with an uncertainty aware topology optimization problem; and 2) quantify and propagate the inherent uncertainties due to design imperfections. A generic SROM framework that transforms the uncertainty aware, stochastic topology optimization problem into a deterministic optimization problem that relies only on independent calls to a deterministic numerical model is presented. This approach facilitates the use of existing optimization and modeling tools to accurately solve the uncertainty aware topology optimization problems in a fraction of the computational demand required by Monte Carlo methods. Finally, an example in structural topology optimization is presented to demonstrate the effectiveness of the proposed uncertainty aware structural topology optimization approach.

A Kind of Nonlinear Programming Problem Based on Mixed Fuzzy Relation Equations Constraints

NASA Astrophysics Data System (ADS)

Li, Jinquan; Feng, Shuang; Mi, Honghai

In this work, a kind of nonlinear programming problem with non-differential objective function and under the constraints expressed by a system of mixed fuzzy relation equations is investigated. First, some properties of this kind of optimization problem are obtained. Then, a polynomial-time algorithm for this kind of optimization problem is proposed based on these properties. Furthermore, we show that this algorithm is optimal for the considered optimization problem in this paper. Finally, numerical examples are provided to illustrate our algorithms.

Common aero vehicle autonomous reentry trajectory optimization satisfying waypoint and no-fly zone constraints

NASA Astrophysics Data System (ADS)

Jorris, Timothy R.

2007-12-01

To support the Air Force's Global Reach concept, a Common Aero Vehicle is being designed to support the Global Strike mission. "Waypoints" are specified for reconnaissance or multiple payload deployments and "no-fly zones" are specified for geopolitical restrictions or threat avoidance. Due to time critical targets and multiple scenario analysis, an autonomous solution is preferred over a time-intensive, manually iterative one. Thus, a real-time or near real-time autonomous trajectory optimization technique is presented to minimize the flight time, satisfy terminal and intermediate constraints, and remain within the specified vehicle heating and control limitations. This research uses the Hypersonic Cruise Vehicle (HCV) as a simplified two-dimensional platform to compare multiple solution techniques. The solution techniques include a unique geometric approach developed herein, a derived analytical dynamic optimization technique, and a rapidly emerging collocation numerical approach. This up-and-coming numerical technique is a direct solution method involving discretization then dualization, with pseudospectral methods and nonlinear programming used to converge to the optimal solution. This numerical approach is applied to the Common Aero Vehicle (CAV) as the test platform for the full three-dimensional reentry trajectory optimization problem. The culmination of this research is the verification of the optimality of this proposed numerical technique, as shown for both the two-dimensional and three-dimensional models. Additionally, user implementation strategies are presented to improve accuracy and enhance solution convergence. Thus, the contributions of this research are the geometric approach, the user implementation strategies, and the determination and verification of a numerical solution technique for the optimal reentry trajectory problem that minimizes time to target while satisfying vehicle dynamics and control limitation, and heating, waypoint, and no-fly zone constraints.

A Galerkin method for the estimation of parameters in hybrid systems governing the vibration of flexible beams with tip bodies

NASA Technical Reports Server (NTRS)

Banks, H. T.; Rosen, I. G.

1985-01-01

An approximation scheme is developed for the identification of hybrid systems describing the transverse vibrations of flexible beams with attached tip bodies. In particular, problems involving the estimation of functional parameters are considered. The identification problem is formulated as a least squares fit to data subject to the coupled system of partial and ordinary differential equations describing the transverse displacement of the beam and the motion of the tip bodies respectively. A cubic spline-based Galerkin method applied to the state equations in weak form and the discretization of the admissible parameter space yield a sequence of approximating finite dimensional identification problems. It is shown that each of the approximating problems admits a solution and that from the resulting sequence of optimal solutions a convergent subsequence can be extracted, the limit of which is a solution to the original identification problem. The approximating identification problems can be solved using standard techniques and readily available software.

Fast Optimization for Aircraft Descent and Approach Trajectory

NASA Technical Reports Server (NTRS)

Luchinsky, Dmitry G.; Schuet, Stefan; Brenton, J.; Timucin, Dogan; Smith, David; Kaneshige, John

2017-01-01

We address problem of on-line scheduling of the aircraft descent and approach trajectory. We formulate a general multiphase optimal control problem for optimization of the descent trajectory and review available methods of its solution. We develop a fast algorithm for solution of this problem using two key components: (i) fast inference of the dynamical and control variables of the descending trajectory from the low dimensional flight profile data and (ii) efficient local search for the resulting reduced dimensionality non-linear optimization problem. We compare the performance of the proposed algorithm with numerical solution obtained using optimal control toolbox General Pseudospectral Optimal Control Software. We present results of the solution of the scheduling problem for aircraft descent using novel fast algorithm and discuss its future applications.

Research on cutting path optimization of sheet metal parts based on ant colony algorithm

NASA Astrophysics Data System (ADS)

Wu, Z. Y.; Ling, H.; Li, L.; Wu, L. H.; Liu, N. B.

2017-09-01

In view of the disadvantages of the current cutting path optimization methods of sheet metal parts, a new method based on ant colony algorithm was proposed in this paper. The cutting path optimization problem of sheet metal parts was taken as the research object. The essence and optimization goal of the optimization problem were presented. The traditional serial cutting constraint rule was improved. The cutting constraint rule with cross cutting was proposed. The contour lines of parts were discretized and the mathematical model of cutting path optimization was established. Thus the problem was converted into the selection problem of contour lines of parts. Ant colony algorithm was used to solve the problem. The principle and steps of the algorithm were analyzed.

Shape optimization using a NURBS-based interface-enriched generalized FEM

DOE PAGES

Najafi, Ahmad R.; Safdari, Masoud; Tortorelli, Daniel A.; ...

2016-11-26

This study presents a gradient-based shape optimization over a fixed mesh using a non-uniform rational B-splines-based interface-enriched generalized finite element method, applicable to multi-material structures. In the proposed method, non-uniform rational B-splines are used to parameterize the design geometry precisely and compactly by a small number of design variables. An analytical shape sensitivity analysis is developed to compute derivatives of the objective and constraint functions with respect to the design variables. Subtle but important new terms involve the sensitivity of shape functions and their spatial derivatives. As a result, verification and illustrative problems are solved to demonstrate the precision andmore » capability of the method.« less

Optimized Hyperthermia Treatment of Prostate Cancer Using a Novel Intracavitary Ultrasound Array

DTIC Science & Technology

2005-01-01

many problems Introduction involved with transducer fabrication. Focused ultrasound surgery ( FUS ) has been shown to give promising results in treating...low frequencies are used) (Hutchinson 1997). With focused ultrasound ( FUS ), tissue is noninvasively necrosed by elevating the temperature at the focal...curved 1.5 dimensional (1.5-D) array that could, but had of a 1.75 dimensional (1.75-D) tapered ultrasound phased array restrictions to the focusing

Design Optimization and Characterization of Helicoidal Composites with Enhanced Impact Resistance

DTIC Science & Technology

2011-01-12

mitigating the delamination problem. The reinforcement can be achieved by many methods such as stitching, braiding , z-fibers/z-rods, fiber waviness or...that act perpendicular to the plane of the laminate. Some of these methods involve stitching, braiding , or weaving fibers together. Other methods use...temperature channels in the autoclave and attaching vacuum connector to the vacuum hose for inspecting the sealing system. For curing the composite, the

Large-scale structural optimization

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, J.

1983-01-01

Problems encountered by aerospace designers in attempting to optimize whole aircraft are discussed, along with possible solutions. Large scale optimization, as opposed to component-by-component optimization, is hindered by computational costs, software inflexibility, concentration on a single, rather than trade-off, design methodology and the incompatibility of large-scale optimization with single program, single computer methods. The software problem can be approached by placing the full analysis outside of the optimization loop. Full analysis is then performed only periodically. Problem-dependent software can be removed from the generic code using a systems programming technique, and then embody the definitions of design variables, objective function and design constraints. Trade-off algorithms can be used at the design points to obtain quantitative answers. Finally, decomposing the large-scale problem into independent subproblems allows systematic optimization of the problems by an organization of people and machines.

Application of the gravity search algorithm to multi-reservoir operation optimization

NASA Astrophysics Data System (ADS)

Bozorg-Haddad, Omid; Janbaz, Mahdieh; Loáiciga, Hugo A.

2016-12-01

Complexities in river discharge, variable rainfall regime, and drought severity merit the use of advanced optimization tools in multi-reservoir operation. The gravity search algorithm (GSA) is an evolutionary optimization algorithm based on the law of gravity and mass interactions. This paper explores the GSA's efficacy for solving benchmark functions, single reservoir, and four-reservoir operation optimization problems. The GSA's solutions are compared with those of the well-known genetic algorithm (GA) in three optimization problems. The results show that the GSA's results are closer to the optimal solutions than the GA's results in minimizing the benchmark functions. The average values of the objective function equal 1.218 and 1.746 with the GSA and GA, respectively, in solving the single-reservoir hydropower operation problem. The global solution equals 1.213 for this same problem. The GSA converged to 99.97% of the global solution in its average-performing history, while the GA converged to 97% of the global solution of the four-reservoir problem. Requiring fewer parameters for algorithmic implementation and reaching the optimal solution in fewer number of functional evaluations are additional advantages of the GSA over the GA. The results of the three optimization problems demonstrate a superior performance of the GSA for optimizing general mathematical problems and the operation of reservoir systems.

Discrete particle swarm optimization to solve multi-objective limited-wait hybrid flow shop scheduling problem

NASA Astrophysics Data System (ADS)

Santosa, B.; Siswanto, N.; Fiqihesa

2018-04-01

This paper proposes a discrete Particle Swam Optimization (PSO) to solve limited-wait hybrid flowshop scheduing problem with multi objectives. Flow shop schedulimg represents the condition when several machines are arranged in series and each job must be processed at each machine with same sequence. The objective functions are minimizing completion time (makespan), total tardiness time, and total machine idle time. Flow shop scheduling model always grows to cope with the real production system accurately. Since flow shop scheduling is a NP-Hard problem then the most suitable method to solve is metaheuristics. One of metaheuristics algorithm is Particle Swarm Optimization (PSO), an algorithm which is based on the behavior of a swarm. Originally, PSO was intended to solve continuous optimization problems. Since flow shop scheduling is a discrete optimization problem, then, we need to modify PSO to fit the problem. The modification is done by using probability transition matrix mechanism. While to handle multi objectives problem, we use Pareto Optimal (MPSO). The results of MPSO is better than the PSO because the MPSO solution set produced higher probability to find the optimal solution. Besides the MPSO solution set is closer to the optimal solution

Multi-objective optimization of combustion, performance and emission parameters in a jatropha biodiesel engine using Non-dominated sorting genetic algorithm-II

NASA Astrophysics Data System (ADS)

Dhingra, Sunil; Bhushan, Gian; Dubey, Kashyap Kumar

2014-03-01

The present work studies and identifies the different variables that affect the output parameters involved in a single cylinder direct injection compression ignition (CI) engine using jatropha biodiesel. Response surface methodology based on Central composite design (CCD) is used to design the experiments. Mathematical models are developed for combustion parameters (Brake specific fuel consumption (BSFC) and peak cylinder pressure (Pmax)), performance parameter brake thermal efficiency (BTE) and emission parameters (CO, NO x , unburnt HC and smoke) using regression techniques. These regression equations are further utilized for simultaneous optimization of combustion (BSFC, Pmax), performance (BTE) and emission (CO, NO x , HC, smoke) parameters. As the objective is to maximize BTE and minimize BSFC, Pmax, CO, NO x , HC, smoke, a multiobjective optimization problem is formulated. Nondominated sorting genetic algorithm-II is used in predicting the Pareto optimal sets of solution. Experiments are performed at suitable optimal solutions for predicting the combustion, performance and emission parameters to check the adequacy of the proposed model. The Pareto optimal sets of solution can be used as guidelines for the end users to select optimal combination of engine output and emission parameters depending upon their own requirements.

Constraint Optimization Literature Review

DTIC Science & Technology

2015-11-01

COPs. 15. SUBJECT TERMS high-performance computing, mobile ad hoc network, optimization, constraint, satisfaction 16. SECURITY CLASSIFICATION OF: 17...Optimization Problems 1 2.1 Constraint Satisfaction Problems 1 2.2 Constraint Optimization Problems 3 3. Constraint Optimization Algorithms 9 3.1...Constraint Satisfaction Algorithms 9 3.1.1 Brute-Force search 9 3.1.2 Constraint Propagation 10 3.1.3 Depth-First Search 13 3.1.4 Local Search 18

Design consideration in constructing high performance embedded Knowledge-Based Systems (KBS)

NASA Technical Reports Server (NTRS)

Dalton, Shelly D.; Daley, Philip C.

1988-01-01

As the hardware trends for artificial intelligence (AI) involve more and more complexity, the process of optimizing the computer system design for a particular problem will also increase in complexity. Space applications of knowledge based systems (KBS) will often require an ability to perform both numerically intensive vector computations and real time symbolic computations. Although parallel machines can theoretically achieve the speeds necessary for most of these problems, if the application itself is not highly parallel, the machine's power cannot be utilized. A scheme is presented which will provide the computer systems engineer with a tool for analyzing machines with various configurations of array, symbolic, scaler, and multiprocessors. High speed networks and interconnections make customized, distributed, intelligent systems feasible for the application of AI in space. The method presented can be used to optimize such AI system configurations and to make comparisons between existing computer systems. It is an open question whether or not, for a given mission requirement, a suitable computer system design can be constructed for any amount of money.

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

Jonkman, Jason; Annoni, Jennifer; Hayman, Greg

This paper presents the development of FAST.Farm, a new multiphysics tool applicable to engineering problems in research and industry involving wind farm performance and cost optimization that is needed to address the current underperformance, failures, and expenses plaguing the wind industry. Achieving wind cost-of-energy targets - which requires improvements in wind farm performance and reliability, together with reduced uncertainty and expenditures - has been eluded by the complicated nature of the wind farm design problem, especially the sophisticated interaction between atmospheric phenomena and wake dynamics and array effects. FAST.Farm aims to balance the need for accurate modeling of the relevantmore » physics for predicting power performance and loads while maintaining low computational cost to support a highly iterative and probabilistic design process and system-wide optimization. FAST.Farm makes use of FAST to model the aero-hydro-servo-elastics of distinct turbines in the wind farm, and it is based on some of the principles of the Dynamic Wake Meandering (DWM) model, but avoids many of the limitations of existing DWM implementations.« less

A Mathematical Formulation of the SCOLE Control Problem. Part 2: Optimal Compensator Design

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1988-01-01

The study initiated in Part 1 of this report is concluded and optimal feedback control (compensator) design for stability augmentation is considered, following the mathematical formulation developed in Part 1. Co-located (rate) sensors and (force and moment) actuators are assumed, and allowing for both sensor and actuator noise, stabilization is formulated as a stochastic regulator problem. Specializing the general theory developed by the author, a complete, closed form solution (believed to be new with this report) is obtained, taking advantage of the fact that the inherent structural damping is light. In particular, it is possible to solve in closed form the associated infinite-dimensional steady-state Riccati equations. The SCOLE model involves associated partial differential equations in a single space variable, but the compensator design theory developed is far more general since it is given in the abstract wave equation formulation. The results thus hold for any multibody system so long as the basic model is linear.

Visualization for Hyper-Heuristics: Back-End Processing

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

Simon, Luke

Modern society is faced with increasingly complex problems, many of which can be formulated as generate-and-test optimization problems. Yet, general-purpose optimization algorithms may sometimes require too much computational time. In these instances, hyperheuristics may be used. Hyper-heuristics automate the design of algorithms to create a custom algorithm for a particular scenario, finding the solution significantly faster than its predecessor. However, it may be difficult to understand exactly how a design was derived and why it should be trusted. This project aims to address these issues by creating an easy-to-use graphical user interface (GUI) for hyper-heuristics and an easy-to-understand scientific visualizationmore » for the produced solutions. To support the development of this GUI, my portion of the research involved developing algorithms that would allow for parsing of the data produced by the hyper-heuristics. This data would then be sent to the front-end, where it would be displayed to the end user.« less

Integration of QFD, AHP, and LPP methods in supplier development problems under uncertainty

NASA Astrophysics Data System (ADS)

Shad, Zahra; Roghanian, Emad; Mojibian, Fatemeh

2014-04-01

Quality function deployment (QFD) is a customer-driven approach, widely used to develop or process new product to maximize customer satisfaction. Last researches used linear physical programming (LPP) procedure to optimize QFD; however, QFD issue involved uncertainties, or fuzziness, which requires taking them into account for more realistic study. In this paper, a set of fuzzy data is used to address linguistic values parameterized by triangular fuzzy numbers. Proposed integrated approach including analytic hierarchy process (AHP), QFD, and LPP to maximize overall customer satisfaction under uncertain conditions and apply them in the supplier development problem. The fuzzy AHP approach is adopted as a powerful method to obtain the relationship between the customer requirements and engineering characteristics (ECs) to construct house of quality in QFD method. LPP is used to obtain the optimal achievement level of the ECs and subsequently the customer satisfaction level under different degrees of uncertainty. The effectiveness of proposed method will be illustrated by an example.

Multiobjective Genetic Algorithm applied to dengue control.

PubMed

Florentino, Helenice O; Cantane, Daniela R; Santos, Fernando L P; Bannwart, Bettina F

2014-12-01

Dengue fever is an infectious disease caused by a virus of the Flaviridae family and transmitted to the person by a mosquito of the genus Aedes aegypti. This disease has been a global public health problem because a single mosquito can infect up to 300 people and between 50 and 100 million people are infected annually on all continents. Thus, dengue fever is currently a subject of research, whether in the search for vaccines and treatments for the disease or efficient and economical forms of mosquito control. The current study aims to study techniques of multiobjective optimization to assist in solving problems involving the control of the mosquito that transmits dengue fever. The population dynamics of the mosquito is studied in order to understand the epidemic phenomenon and suggest strategies of multiobjective programming for mosquito control. A Multiobjective Genetic Algorithm (MGA_DENGUE) is proposed to solve the optimization model treated here and we discuss the computational results obtained from the application of this technique. Copyright © 2014 Elsevier Inc. All rights reserved.

Fine-grained parallelization of fitness functions in bioinformatics optimization problems: gene selection for cancer classification and biclustering of gene expression data.

PubMed

Gomez-Pulido, Juan A; Cerrada-Barrios, Jose L; Trinidad-Amado, Sebastian; Lanza-Gutierrez, Jose M; Fernandez-Diaz, Ramon A; Crawford, Broderick; Soto, Ricardo

2016-08-31

Metaheuristics are widely used to solve large combinatorial optimization problems in bioinformatics because of the huge set of possible solutions. Two representative problems are gene selection for cancer classification and biclustering of gene expression data. In most cases, these metaheuristics, as well as other non-linear techniques, apply a fitness function to each possible solution with a size-limited population, and that step involves higher latencies than other parts of the algorithms, which is the reason why the execution time of the applications will mainly depend on the execution time of the fitness function. In addition, it is usual to find floating-point arithmetic formulations for the fitness functions. This way, a careful parallelization of these functions using the reconfigurable hardware technology will accelerate the computation, specially if they are applied in parallel to several solutions of the population. A fine-grained parallelization of two floating-point fitness functions of different complexities and features involved in biclustering of gene expression data and gene selection for cancer classification allowed for obtaining higher speedups and power-reduced computation with regard to usual microprocessors. The results show better performances using reconfigurable hardware technology instead of usual microprocessors, in computing time and power consumption terms, not only because of the parallelization of the arithmetic operations, but also thanks to the concurrent fitness evaluation for several individuals of the population in the metaheuristic. This is a good basis for building accelerated and low-energy solutions for intensive computing scenarios.

Advanced Modeling System for Optimization of Wind Farm Layout and Wind Turbine Sizing Using a Multi-Level Extended Pattern Search Algorithm

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

DuPont, Bryony; Cagan, Jonathan; Moriarty, Patrick

This paper presents a system of modeling advances that can be applied in the computational optimization of wind plants. These modeling advances include accurate cost and power modeling, partial wake interaction, and the effects of varying atmospheric stability. To validate the use of this advanced modeling system, it is employed within an Extended Pattern Search (EPS)-Multi-Agent System (MAS) optimization approach for multiple wind scenarios. The wind farm layout optimization problem involves optimizing the position and size of wind turbines such that the aerodynamic effects of upstream turbines are reduced, which increases the effective wind speed and resultant power at eachmore » turbine. The EPS-MAS optimization algorithm employs a profit objective, and an overarching search determines individual turbine positions, with a concurrent EPS-MAS determining the optimal hub height and rotor diameter for each turbine. Two wind cases are considered: (1) constant, unidirectional wind, and (2) three discrete wind speeds and varying wind directions, each of which have a probability of occurrence. Results show the advantages of applying the series of advanced models compared to previous application of an EPS with less advanced models to wind farm layout optimization, and imply best practices for computational optimization of wind farms with improved accuracy.« less

Heuristic query optimization for query multiple table and multiple clausa on mobile finance application

NASA Astrophysics Data System (ADS)

Indrayana, I. N. E.; P, N. M. Wirasyanti D.; Sudiartha, I. KG

2018-01-01

Mobile application allow many users to access data from the application without being limited to space, space and time. Over time the data population of this application will increase. Data access time will cause problems if the data record has reached tens of thousands to millions of records.The objective of this research is to maintain the performance of data execution for large data records. One effort to maintain data access time performance is to apply query optimization method. The optimization used in this research is query heuristic optimization method. The built application is a mobile-based financial application using MySQL database with stored procedure therein. This application is used by more than one business entity in one database, thus enabling rapid data growth. In this stored procedure there is an optimized query using heuristic method. Query optimization is performed on a “Select” query that involves more than one table with multiple clausa. Evaluation is done by calculating the average access time using optimized and unoptimized queries. Access time calculation is also performed on the increase of population data in the database. The evaluation results shown the time of data execution with query heuristic optimization relatively faster than data execution time without using query optimization.

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

Koniges, A.E.; Craddock, G.G.; Schnack, D.D.

The purpose of the workshop was to assemble workers, both within and outside of the fusion-related computations areas, for discussion regarding the issues of dynamically adaptive gridding. There were three invited talks related to adaptive gridding application experiences in various related fields of computational fluid dynamics (CFD), and nine short talks reporting on the progress of adaptive techniques in the specific areas of scrape-off-layer (SOL) modeling and magnetohydrodynamic (MHD) stability. Adaptive mesh methods have been successful in a number of diverse fields of CFD for over a decade. The method involves dynamic refinement of computed field profiles in a waymore » that disperses uniformly the numerical errors associated with discrete approximations. Because the process optimizes computational effort, adaptive mesh methods can be used to study otherwise the intractable physical problems that involve complex boundary shapes or multiple spatial/temporal scales. Recent results indicate that these adaptive techniques will be required for tokamak fluid-based simulations involving the diverted tokamak SOL modeling and MHD simulations problems related to the highest priority ITER relevant issues.Individual papers are indexed separately on the energy data bases.« less

Comparison of Optimal Design Methods in Inverse Problems

PubMed Central

Banks, H. T.; Holm, Kathleen; Kappel, Franz

2011-01-01

Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher Information Matrix (FIM). A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criteria with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model [13], the standard harmonic oscillator model [13] and a popular glucose regulation model [16, 19, 29]. PMID:21857762

Multiobjective optimization approach: thermal food processing.

PubMed

Abakarov, A; Sushkov, Y; Almonacid, S; Simpson, R

2009-01-01

The objective of this study was to utilize a multiobjective optimization technique for the thermal sterilization of packaged foods. The multiobjective optimization approach used in this study is based on the optimization of well-known aggregating functions by an adaptive random search algorithm. The applicability of the proposed approach was illustrated by solving widely used multiobjective test problems taken from the literature. The numerical results obtained for the multiobjective test problems and for the thermal processing problem show that the proposed approach can be effectively used for solving multiobjective optimization problems arising in the food engineering field.

Self-Directed Cooperative Planetary Rovers

NASA Technical Reports Server (NTRS)

Zilberstein, Shlomo; Morris, Robert (Technical Monitor)

2003-01-01

The project is concerned with the development of decision-theoretic techniques to optimize the scientific return of planetary rovers. Planetary rovers are small unmanned vehicles equipped with cameras and a variety of sensors used for scientific experiments. They must operate under tight constraints over such resources as operation time, power, storage capacity, and communication bandwidth. Moreover, the limited computational resources of the rover limit the complexity of on-line planning and scheduling. We have developed a comprehensive solution to this problem that involves high-level tools to describe a mission; a compiler that maps a mission description and additional probabilistic models of the components of the rover into a Markov decision problem; and algorithms for solving the rover control problem that are sensitive to the limited computational resources and high-level of uncertainty in this domain.

Neural architecture design based on extreme learning machine.

PubMed

Bueno-Crespo, Andrés; García-Laencina, Pedro J; Sancho-Gómez, José-Luis

2013-12-01

Selection of the optimal neural architecture to solve a pattern classification problem entails to choose the relevant input units, the number of hidden neurons and its corresponding interconnection weights. This problem has been widely studied in many research works but their solutions usually involve excessive computational cost in most of the problems and they do not provide a unique solution. This paper proposes a new technique to efficiently design the MultiLayer Perceptron (MLP) architecture for classification using the Extreme Learning Machine (ELM) algorithm. The proposed method provides a high generalization capability and a unique solution for the architecture design. Moreover, the selected final network only retains those input connections that are relevant for the classification task. Experimental results show these advantages. Copyright © 2013 Elsevier Ltd. All rights reserved.

Synergetic motor control paradigm for optimizing energy efficiency of multijoint reaching via tacit learning

PubMed Central

Hayashibe, Mitsuhiro; Shimoda, Shingo

2014-01-01

A human motor system can improve its behavior toward optimal movement. The skeletal system has more degrees of freedom than the task dimensions, which incurs an ill-posed problem. The multijoint system involves complex interaction torques between joints. To produce optimal motion in terms of energy consumption, the so-called cost function based optimization has been commonly used in previous works.Even if it is a fact that an optimal motor pattern is employed phenomenologically, there is no evidence that shows the existence of a physiological process that is similar to such a mathematical optimization in our central nervous system.In this study, we aim to find a more primitive computational mechanism with a modular configuration to realize adaptability and optimality without prior knowledge of system dynamics.We propose a novel motor control paradigm based on tacit learning with task space feedback. The motor command accumulation during repetitive environmental interactions, play a major role in the learning process. It is applied to a vertical cyclic reaching which involves complex interaction torques.We evaluated whether the proposed paradigm can learn how to optimize solutions with a 3-joint, planar biomechanical model. The results demonstrate that the proposed method was valid for acquiring motor synergy and resulted in energy efficient solutions for different load conditions. The case in feedback control is largely affected by the interaction torques. In contrast, the trajectory is corrected over time with tacit learning toward optimal solutions.Energy efficient solutions were obtained by the emergence of motor synergy. During learning, the contribution from feedforward controller is augmented and the one from the feedback controller is significantly minimized down to 12% for no load at hand, 16% for a 0.5 kg load condition.The proposed paradigm could provide an optimization process in redundant system with dynamic-model-free and cost-function-free approach. PMID:24616695

Synergetic motor control paradigm for optimizing energy efficiency of multijoint reaching via tacit learning.

PubMed

Hayashibe, Mitsuhiro; Shimoda, Shingo

2014-01-01

A human motor system can improve its behavior toward optimal movement. The skeletal system has more degrees of freedom than the task dimensions, which incurs an ill-posed problem. The multijoint system involves complex interaction torques between joints. To produce optimal motion in terms of energy consumption, the so-called cost function based optimization has been commonly used in previous works.Even if it is a fact that an optimal motor pattern is employed phenomenologically, there is no evidence that shows the existence of a physiological process that is similar to such a mathematical optimization in our central nervous system.In this study, we aim to find a more primitive computational mechanism with a modular configuration to realize adaptability and optimality without prior knowledge of system dynamics.We propose a novel motor control paradigm based on tacit learning with task space feedback. The motor command accumulation during repetitive environmental interactions, play a major role in the learning process. It is applied to a vertical cyclic reaching which involves complex interaction torques.We evaluated whether the proposed paradigm can learn how to optimize solutions with a 3-joint, planar biomechanical model. The results demonstrate that the proposed method was valid for acquiring motor synergy and resulted in energy efficient solutions for different load conditions. The case in feedback control is largely affected by the interaction torques. In contrast, the trajectory is corrected over time with tacit learning toward optimal solutions.Energy efficient solutions were obtained by the emergence of motor synergy. During learning, the contribution from feedforward controller is augmented and the one from the feedback controller is significantly minimized down to 12% for no load at hand, 16% for a 0.5 kg load condition.The proposed paradigm could provide an optimization process in redundant system with dynamic-model-free and cost-function-free approach.

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.

The coral reefs optimization algorithm: a novel metaheuristic for efficiently solving optimization problems.

PubMed

Salcedo-Sanz, S; Del Ser, J; Landa-Torres, I; Gil-López, S; Portilla-Figueras, J A

2014-01-01

This paper presents a novel bioinspired algorithm to tackle complex optimization problems: the coral reefs optimization (CRO) algorithm. The CRO algorithm artificially simulates a coral reef, where different corals (namely, solutions to the optimization problem considered) grow and reproduce in coral colonies, fighting by choking out other corals for space in the reef. This fight for space, along with the specific characteristics of the corals' reproduction, produces a robust metaheuristic algorithm shown to be powerful for solving hard optimization problems. In this research the CRO algorithm is tested in several continuous and discrete benchmark problems, as well as in practical application scenarios (i.e., optimum mobile network deployment and off-shore wind farm design). The obtained results confirm the excellent performance of the proposed algorithm and open line of research for further application of the algorithm to real-world problems.

The Coral Reefs Optimization Algorithm: A Novel Metaheuristic for Efficiently Solving Optimization Problems

PubMed Central

Salcedo-Sanz, S.; Del Ser, J.; Landa-Torres, I.; Gil-López, S.; Portilla-Figueras, J. A.

2014-01-01

This paper presents a novel bioinspired algorithm to tackle complex optimization problems: the coral reefs optimization (CRO) algorithm. The CRO algorithm artificially simulates a coral reef, where different corals (namely, solutions to the optimization problem considered) grow and reproduce in coral colonies, fighting by choking out other corals for space in the reef. This fight for space, along with the specific characteristics of the corals' reproduction, produces a robust metaheuristic algorithm shown to be powerful for solving hard optimization problems. In this research the CRO algorithm is tested in several continuous and discrete benchmark problems, as well as in practical application scenarios (i.e., optimum mobile network deployment and off-shore wind farm design). The obtained results confirm the excellent performance of the proposed algorithm and open line of research for further application of the algorithm to real-world problems. PMID:25147860

Anatomy of the Attraction Basins: Breaking with the Intuition.

PubMed

Hernando, Leticia; Mendiburu, Alexander; Lozano, Jose A

2018-05-22

Solving combinatorial optimization problems efficiently requires the development of algorithms that consider the specific properties of the problems. In this sense, local search algorithms are designed over a neighborhood structure that partially accounts for these properties. Considering a neighborhood, the space is usually interpreted as a natural landscape, with valleys and mountains. Under this perception, it is commonly believed that, if maximizing, the solutions located in the slopes of the same mountain belong to the same attraction basin, with the peaks of the mountains being the local optima. Unfortunately, this is a widespread erroneous visualization of a combinatorial landscape. Thus, our aim is to clarify this aspect, providing a detailed analysis of, first, the existence of plateaus where the local optima are involved, and second, the properties that define the topology of the attraction basins, picturing a reliable visualization of the landscapes. Some of the features explored in this paper have never been examined before. Hence, new findings about the structure of the attraction basins are shown. The study is focused on instances of permutation-based combinatorial optimization problems considering the 2-exchange and the insert neighborhoods. As a consequence of this work, we break away from the extended belief about the anatomy of attraction basins.

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.

A mixed integer linear programming model to reconstruct phylogenies from single nucleotide polymorphism haplotypes under the maximum parsimony criterion

PubMed Central

2013-01-01

Background Phylogeny estimation from aligned haplotype sequences has attracted more and more attention in the recent years due to its importance in analysis of many fine-scale genetic data. Its application fields range from medical research, to drug discovery, to epidemiology, to population dynamics. The literature on molecular phylogenetics proposes a number of criteria for selecting a phylogeny from among plausible alternatives. Usually, such criteria can be expressed by means of objective functions, and the phylogenies that optimize them are referred to as optimal. One of the most important estimation criteria is the parsimony which states that the optimal phylogeny T∗for a set H of n haplotype sequences over a common set of variable loci is the one that satisfies the following requirements: (i) it has the shortest length and (ii) it is such that, for each pair of distinct haplotypes hi,hj∈H, the sum of the edge weights belonging to the path from hi to hj in T∗ is not smaller than the observed number of changes between hi and hj. Finding the most parsimonious phylogeny for H involves solving an optimization problem, called the Most Parsimonious Phylogeny Estimation Problem (MPPEP), which is NP-hard in many of its versions. Results In this article we investigate a recent version of the MPPEP that arises when input data consist of single nucleotide polymorphism haplotypes extracted from a population of individuals on a common genomic region. Specifically, we explore the prospects for improving on the implicit enumeration strategy of implicit enumeration strategy used in previous work using a novel problem formulation and a series of strengthening valid inequalities and preliminary symmetry breaking constraints to more precisely bound the solution space and accelerate implicit enumeration of possible optimal phylogenies. We present the basic formulation and then introduce a series of provable valid constraints to reduce the solution space. We then prove that these constraints can often lead to significant reductions in the gap between the optimal solution and its non-integral linear programming bound relative to the prior art as well as often substantially faster processing of moderately hard problem instances. Conclusion We provide an indication of the conditions under which such an optimal enumeration approach is likely to be feasible, suggesting that these strategies are usable for relatively large numbers of taxa, although with stricter limits on numbers of variable sites. The work thus provides methodology suitable for provably optimal solution of some harder instances that resist all prior approaches. PMID:23343437

Identification of the heat transfer coefficient in the two-dimensional model of binary alloy solidification

NASA Astrophysics Data System (ADS)

Hetmaniok, Edyta; Hristov, Jordan; Słota, Damian; Zielonka, Adam

2017-05-01

The paper presents the procedure for solving the inverse problem for the binary alloy solidification in a two-dimensional space. This is a continuation of some previous works of the authors investigating a similar problem but in the one-dimensional domain. Goal of the problem consists in identification of the heat transfer coefficient on boundary of the region and in reconstruction of the temperature distribution inside the considered region in case when the temperature measurements in selected points of the alloy are known. Mathematical model of the problem is based on the heat conduction equation with the substitute thermal capacity and with the liquidus and solidus temperatures varying in dependance on the concentration of the alloy component. For describing this concentration the Scheil model is used. Investigated procedure involves also the parallelized Ant Colony Optimization algorithm applied for minimizing a functional expressing the error of approximate solution.

Heuristic rules embedded genetic algorithm for in-core fuel management optimization

NASA Astrophysics Data System (ADS)

Alim, Fatih

The objective of this study was to develop a unique methodology and a practical tool for designing loading pattern (LP) and burnable poison (BP) pattern for a given Pressurized Water Reactor (PWR) core. Because of the large number of possible combinations for the fuel assembly (FA) loading in the core, the design of the core configuration is a complex optimization problem. It requires finding an optimal FA arrangement and BP placement in order to achieve maximum cycle length while satisfying the safety constraints. Genetic Algorithms (GA) have been already used to solve this problem for LP optimization for both PWR and Boiling Water Reactor (BWR). The GA, which is a stochastic method works with a group of solutions and uses random variables to make decisions. Based on the theories of evaluation, the GA involves natural selection and reproduction of the individuals in the population for the next generation. The GA works by creating an initial population, evaluating it, and then improving the population by using the evaluation operators. To solve this optimization problem, a LP optimization package, GARCO (Genetic Algorithm Reactor Code Optimization) code is developed in the framework of this thesis. This code is applicable for all types of PWR cores having different geometries and structures with an unlimited number of FA types in the inventory. To reach this goal, an innovative GA is developed by modifying the classical representation of the genotype. To obtain the best result in a shorter time, not only the representation is changed but also the algorithm is changed to use in-core fuel management heuristics rules. The improved GA code was tested to demonstrate and verify the advantages of the new enhancements. The developed methodology is explained in this thesis and preliminary results are shown for the VVER-1000 reactor hexagonal geometry core and the TMI-1 PWR. The improved GA code was tested to verify the advantages of new enhancements. The core physics code used for VVER in this research is Moby-Dick, which was developed to analyze the VVER by SKODA Inc. The SIMULATE-3 code, which is an advanced two-group nodal code, is used to analyze the TMI-1.

Wireless Sensor Network Optimization: Multi-Objective Paradigm

PubMed Central

Iqbal, Muhammad; Naeem, Muhammad; Anpalagan, Alagan; Ahmed, Ashfaq; Azam, Muhammad

2015-01-01

Optimization problems relating to wireless sensor network planning, design, deployment and operation often give rise to multi-objective optimization formulations where multiple desirable objectives compete with each other and the decision maker has to select one of the tradeoff solutions. These multiple objectives may or may not conflict with each other. Keeping in view the nature of the application, the sensing scenario and input/output of the problem, the type of optimization problem changes. To address different nature of optimization problems relating to wireless sensor network design, deployment, operation, planing and placement, there exist a plethora of optimization solution types. We review and analyze different desirable objectives to show whether they conflict with each other, support each other or they are design dependent. We also present a generic multi-objective optimization problem relating to wireless sensor network which consists of input variables, required output, objectives and constraints. A list of constraints is also presented to give an overview of different constraints which are considered while formulating the optimization problems in wireless sensor networks. Keeping in view the multi facet coverage of this article relating to multi-objective optimization, this will open up new avenues of research in the area of multi-objective optimization relating to wireless sensor networks. PMID:26205271

Cost component analysis.

PubMed

Lörincz, András; Póczos, Barnabás

2003-06-01

In optimizations the dimension of the problem may severely, sometimes exponentially increase optimization time. Parametric function approximatiors (FAPPs) have been suggested to overcome this problem. Here, a novel FAPP, cost component analysis (CCA) is described. In CCA, the search space is resampled according to the Boltzmann distribution generated by the energy landscape. That is, CCA converts the optimization problem to density estimation. Structure of the induced density is searched by independent component analysis (ICA). The advantage of CCA is that each independent ICA component can be optimized separately. In turn, (i) CCA intends to partition the original problem into subproblems and (ii) separating (partitioning) the original optimization problem into subproblems may serve interpretation. Most importantly, (iii) CCA may give rise to high gains in optimization time. Numerical simulations illustrate the working of the algorithm.

The design of multirate digital control systems

NASA Technical Reports Server (NTRS)

Berg, M. C.

1986-01-01

The successive loop closures synthesis method is the only method for multirate (MR) synthesis in common use. A new method for MR synthesis is introduced which requires a gradient-search solution to a constrained optimization problem. Some advantages of this method are that the control laws for all control loops are synthesized simultaneously, taking full advantage of all cross-coupling effects, and that simple, low-order compensator structures are easily accomodated. The algorithm and associated computer program for solving the constrained optimization problem are described. The successive loop closures , optimal control, and constrained optimization synthesis methods are applied to two example design problems. A series of compensator pairs are synthesized for each example problem. The succesive loop closure, optimal control, and constrained optimization synthesis methods are compared, in the context of the two design problems.

The optimal location of piezoelectric actuators and sensors for vibration control of plates

NASA Astrophysics Data System (ADS)

Kumar, K. Ramesh; Narayanan, S.

2007-12-01

This paper considers the optimal placement of collocated piezoelectric actuator-sensor pairs on a thin plate using a model-based linear quadratic regulator (LQR) controller. LQR performance is taken as objective for finding the optimal location of sensor-actuator pairs. The problem is formulated using the finite element method (FEM) as multi-input-multi-output (MIMO) model control. The discrete optimal sensor and actuator location problem is formulated in the framework of a zero-one optimization problem. A genetic algorithm (GA) is used to solve the zero-one optimization problem. Different classical control strategies like direct proportional feedback, constant-gain negative velocity feedback and the LQR optimal control scheme are applied to study the control effectiveness.

Portfolio optimization in enhanced index tracking with goal programming approach

NASA Astrophysics Data System (ADS)

Siew, Lam Weng; Jaaman, Saiful Hafizah Hj.; Ismail, Hamizun bin

2014-09-01

Enhanced index tracking is a popular form of passive fund management in stock market. Enhanced index tracking aims to generate excess return over the return achieved by the market index without purchasing all of the stocks that make up the index. This can be done by establishing an optimal portfolio to maximize the mean return and minimize the risk. The objective of this paper is to determine the portfolio composition and performance using goal programming approach in enhanced index tracking and comparing it to the market index. Goal programming is a branch of multi-objective optimization which can handle decision problems that involve two different goals in enhanced index tracking, a trade-off between maximizing the mean return and minimizing the risk. The results of this study show that the optimal portfolio with goal programming approach is able to outperform the Malaysia market index which is FTSE Bursa Malaysia Kuala Lumpur Composite Index because of higher mean return and lower risk without purchasing all the stocks in the market index.

Stochastic Averaging for Constrained Optimization With Application to Online Resource Allocation

NASA Astrophysics Data System (ADS)

Chen, Tianyi; Mokhtari, Aryan; Wang, Xin; Ribeiro, Alejandro; Giannakis, Georgios B.

2017-06-01

Existing approaches to resource allocation for nowadays stochastic networks are challenged to meet fast convergence and tolerable delay requirements. The present paper leverages online learning advances to facilitate stochastic resource allocation tasks. By recognizing the central role of Lagrange multipliers, the underlying constrained optimization problem is formulated as a machine learning task involving both training and operational modes, with the goal of learning the sought multipliers in a fast and efficient manner. To this end, an order-optimal offline learning approach is developed first for batch training, and it is then generalized to the online setting with a procedure termed learn-and-adapt. The novel resource allocation protocol permeates benefits of stochastic approximation and statistical learning to obtain low-complexity online updates with learning errors close to the statistical accuracy limits, while still preserving adaptation performance, which in the stochastic network optimization context guarantees queue stability. Analysis and simulated tests demonstrate that the proposed data-driven approach improves the delay and convergence performance of existing resource allocation schemes.