Structural optimization: Status and promise

NASA Astrophysics Data System (ADS)

Kamat, Manohar P.

Chapters contained in this book include fundamental concepts of optimum design, mathematical programming methods for constrained optimization, function approximations, approximate reanalysis methods, dual mathematical programming methods for constrained optimization, a generalized optimality criteria method, and a tutorial and survey of multicriteria optimization in engineering. Also included are chapters on the compromise decision support problem and the adaptive linear programming algorithm, sensitivity analyses of discrete and distributed systems, the design sensitivity analysis of nonlinear structures, optimization by decomposition, mixed elements in shape sensitivity analysis of structures based on local criteria, and optimization of stiffened cylindrical shells subjected to destabilizing loads. Other chapters are on applications to fixed-wing aircraft and spacecraft, integrated optimum structural and control design, modeling concurrency in the design of composite structures, and tools for structural optimization. (No individual items are abstracted in this volume)

A globally convergent LCL method for nonlinear optimization.

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

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

2005-01-01

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

Adaptive Constrained Optimal Control Design for Data-Based Nonlinear Discrete-Time Systems With Critic-Only Structure.

PubMed

Luo, Biao; Liu, Derong; Wu, Huai-Ning

2018-06-01

Reinforcement learning has proved to be a powerful tool to solve optimal control problems over the past few years. However, the data-based constrained optimal control problem of nonaffine nonlinear discrete-time systems has rarely been studied yet. To solve this problem, an adaptive optimal control approach is developed by using the value iteration-based Q-learning (VIQL) with the critic-only structure. Most of the existing constrained control methods require the use of a certain performance index and only suit for linear or affine nonlinear systems, which is unreasonable in practice. To overcome this problem, the system transformation is first introduced with the general performance index. Then, the constrained optimal control problem is converted to an unconstrained optimal control problem. By introducing the action-state value function, i.e., Q-function, the VIQL algorithm is proposed to learn the optimal Q-function of the data-based unconstrained optimal control problem. The convergence results of the VIQL algorithm are established with an easy-to-realize initial condition . To implement the VIQL algorithm, the critic-only structure is developed, where only one neural network is required to approximate the Q-function. The converged Q-function obtained from the critic-only VIQL method is employed to design the adaptive constrained optimal controller based on the gradient descent scheme. Finally, the effectiveness of the developed adaptive control method is tested on three examples with computer simulation.

A linearized theory method of constrained optimization for supersonic cruise wing design

NASA Technical Reports Server (NTRS)

Miller, D. S.; Carlson, H. W.; Middleton, W. D.

1976-01-01

A linearized theory wing design and optimization procedure which allows physical realism and practical considerations to be imposed as constraints on the optimum (least drag due to lift) solution is discussed and examples of application are presented. In addition to the usual constraints on lift and pitching moment, constraints are imposed on wing surface ordinates and wing upper surface pressure levels and gradients. The design procedure also provides the capability of including directly in the optimization process the effects of other aircraft components such as a fuselage, canards, and nacelles.

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.

Analytical optimal pulse shapes obtained with the aid of genetic algorithms

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

Guerrero, Rubén D., E-mail: rdguerrerom@unal.edu.co; Arango, Carlos A.; Reyes, Andrés

2015-09-28

We propose a methodology to design optimal pulses for achieving quantum optimal control on molecular systems. Our approach constrains pulse shapes to linear combinations of a fixed number of experimentally relevant pulse functions. Quantum optimal control is obtained by maximizing a multi-target fitness function using genetic algorithms. As a first application of the methodology, we generated an optimal pulse that successfully maximized the yield on a selected dissociation channel of a diatomic molecule. Our pulse is obtained as a linear combination of linearly chirped pulse functions. Data recorded along the evolution of the genetic algorithm contained important information regarding themore » interplay between radiative and diabatic processes. We performed a principal component analysis on these data to retrieve the most relevant processes along the optimal path. Our proposed methodology could be useful for performing quantum optimal control on more complex systems by employing a wider variety of pulse shape functions.« less

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

Dufour, F., E-mail: dufour@math.u-bordeaux1.fr; Prieto-Rumeau, T., E-mail: tprieto@ccia.uned.es

We consider a discrete-time constrained discounted Markov decision process (MDP) with Borel state and action spaces, compact action sets, and lower semi-continuous cost functions. We introduce a set of hypotheses related to a positive weight function which allow us to consider cost functions that might not be bounded below by a constant, and which imply the solvability of the linear programming formulation of the constrained MDP. In particular, we establish the existence of a constrained optimal stationary policy. Our results are illustrated with an application to a fishery management problem.

Finite Element Based Structural Damage Detection Using Artificial Boundary Conditions

DTIC Science & Technology

2007-09-01

C. (2005). Elementary Linear Algebra . New York: John Wiley and Sons. Avitable, Peter (2001, January) Experimental Modal Analysis, A Simple Non...variables under consideration. 3 Frequency sensitivities are the basis for a linear approximation to compute the change in the natural frequencies of a...THEORY The general problem statement for a non- linear constrained optimization problem is: To minimize ( )f x Objective Function Subject to

A one-layer recurrent neural network for constrained pseudoconvex optimization and its application for dynamic portfolio optimization.

PubMed

Liu, Qingshan; Guo, Zhishan; Wang, Jun

2012-02-01

In this paper, a one-layer recurrent neural network is proposed for solving pseudoconvex optimization problems subject to linear equality and bound constraints. Compared with the existing neural networks for optimization (e.g., the projection neural networks), the proposed neural network is capable of solving more general pseudoconvex optimization problems with equality and bound constraints. Moreover, it is capable of solving constrained fractional programming problems as a special case. The convergence of the state variables of the proposed neural network to achieve solution optimality is guaranteed as long as the designed parameters in the model are larger than the derived lower bounds. Numerical examples with simulation results illustrate the effectiveness and characteristics of the proposed neural network. In addition, an application for dynamic portfolio optimization is discussed. Copyright © 2011 Elsevier Ltd. All rights reserved.

Microgrid Optimal Scheduling With Chance-Constrained Islanding Capability

DOE PAGES

Liu, Guodong; Starke, Michael R.; Xiao, B.; ...

2017-01-13

To facilitate the integration of variable renewable generation and improve the resilience of electricity sup-ply in a microgrid, this paper proposes an optimal scheduling strategy for microgrid operation considering constraints of islanding capability. A new concept, probability of successful islanding (PSI), indicating the probability that a microgrid maintains enough spinning reserve (both up and down) to meet local demand and accommodate local renewable generation after instantaneously islanding from the main grid, is developed. The PSI is formulated as mixed-integer linear program using multi-interval approximation taking into account the probability distributions of forecast errors of wind, PV and load. With themore » goal of minimizing the total operating cost while preserving user specified PSI, a chance-constrained optimization problem is formulated for the optimal scheduling of mirogrids and solved by mixed integer linear programming (MILP). Numerical simulations on a microgrid consisting of a wind turbine, a PV panel, a fuel cell, a micro-turbine, a diesel generator and a battery demonstrate the effectiveness of the proposed scheduling strategy. Lastly, we verify the relationship between PSI and various factors.« less

A New Continuous-Time Equality-Constrained Optimization to Avoid Singularity.

PubMed

Quan, Quan; Cai, Kai-Yuan

2016-02-01

In equality-constrained optimization, a standard regularity assumption is often associated with feasible point methods, namely, that the gradients of constraints are linearly independent. In practice, the regularity assumption may be violated. In order to avoid such a singularity, a new projection matrix is proposed based on which a feasible point method to continuous-time, equality-constrained optimization is developed. First, the equality constraint is transformed into a continuous-time dynamical system with solutions that always satisfy the equality constraint. Second, a new projection matrix without singularity is proposed to realize the transformation. An update (or say a controller) is subsequently designed to decrease the objective function along the solutions of the transformed continuous-time dynamical system. The invariance principle is then applied to analyze the behavior of the solution. Furthermore, the proposed method is modified to address cases in which solutions do not satisfy the equality constraint. Finally, the proposed optimization approach is applied to three examples to demonstrate its effectiveness.

Constrained multi-objective optimization of storage ring lattices

NASA Astrophysics Data System (ADS)

Husain, Riyasat; Ghodke, A. D.

2018-03-01

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

An historical survey of computational methods in optimal control.

NASA Technical Reports Server (NTRS)

Polak, E.

1973-01-01

Review of some of the salient theoretical developments in the specific area of optimal control algorithms. The first algorithms for optimal control were aimed at unconstrained problems and were derived by using first- and second-variation methods of the calculus of variations. These methods have subsequently been recognized as gradient, Newton-Raphson, or Gauss-Newton methods in function space. A much more recent addition to the arsenal of unconstrained optimal control algorithms are several variations of conjugate-gradient methods. At first, constrained optimal control problems could only be solved by exterior penalty function methods. Later algorithms specifically designed for constrained problems have appeared. Among these are methods for solving the unconstrained linear quadratic regulator problem, as well as certain constrained minimum-time and minimum-energy problems. Differential-dynamic programming was developed from dynamic programming considerations. The conditional-gradient method, the gradient-projection method, and a couple of feasible directions methods were obtained as extensions or adaptations of related algorithms for finite-dimensional problems. Finally, the so-called epsilon-methods combine the Ritz method with penalty function techniques.

Solving LP Relaxations of Large-Scale Precedence Constrained Problems

NASA Astrophysics Data System (ADS)

Bienstock, Daniel; Zuckerberg, Mark

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

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

NASA Technical Reports Server (NTRS)

Nguyen, Duc T.

1990-01-01

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

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

PubMed Central

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

2012-01-01

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

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

PubMed

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

2012-01-01

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

Interior point techniques for LP and NLP

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

Evtushenko, Y.

By using surjective mapping the initial constrained optimization problem is transformed to a problem in a new space with only equality constraints. For the numerical solution of the latter problem we use the generalized gradient-projection method and Newton`s method. After inverse transformation to the initial space we obtain the family of numerical methods for solving optimization problems with equality and inequality constraints. In the linear programming case after some simplification we obtain Dikin`s algorithm, affine scaling algorithm and generalized primal dual interior point linear programming algorithm.

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).

Chance-Constrained AC Optimal Power Flow for Distribution Systems With Renewables

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

DallAnese, Emiliano; Baker, Kyri; Summers, Tyler

This paper focuses on distribution systems featuring renewable energy sources (RESs) and energy storage systems, and presents an AC optimal power flow (OPF) approach to optimize system-level performance objectives while coping with uncertainty in both RES generation and loads. The proposed method hinges on a chance-constrained AC OPF formulation where probabilistic constraints are utilized to enforce voltage regulation with prescribed probability. A computationally more affordable convex reformulation is developed by resorting to suitable linear approximations of the AC power-flow equations as well as convex approximations of the chance constraints. The approximate chance constraints provide conservative bounds that hold for arbitrarymore » distributions of the forecasting errors. An adaptive strategy is then obtained by embedding the proposed AC OPF task into a model predictive control framework. Finally, a distributed solver is developed to strategically distribute the solution of the optimization problems across utility and customers.« less

Stability-Constrained Aerodynamic Shape Optimization with Applications to Flying Wings

NASA Astrophysics Data System (ADS)

Mader, Charles Alexander

A set of techniques is developed that allows the incorporation of flight dynamics metrics as an additional discipline in a high-fidelity aerodynamic optimization. Specifically, techniques for including static stability constraints and handling qualities constraints in a high-fidelity aerodynamic optimization are demonstrated. These constraints are developed from stability derivative information calculated using high-fidelity computational fluid dynamics (CFD). Two techniques are explored for computing the stability derivatives from CFD. One technique uses an automatic differentiation adjoint technique (ADjoint) to efficiently and accurately compute a full set of static and dynamic stability derivatives from a single steady solution. The other technique uses a linear regression method to compute the stability derivatives from a quasi-unsteady time-spectral CFD solution, allowing for the computation of static, dynamic and transient stability derivatives. Based on the characteristics of the two methods, the time-spectral technique is selected for further development, incorporated into an optimization framework, and used to conduct stability-constrained aerodynamic optimization. This stability-constrained optimization framework is then used to conduct an optimization study of a flying wing configuration. This study shows that stability constraints have a significant impact on the optimal design of flying wings and that, while static stability constraints can often be satisfied by modifying the airfoil profiles of the wing, dynamic stability constraints can require a significant change in the planform of the aircraft in order for the constraints to be satisfied.

EMG prediction from Motor Cortical Recordings via a Non-Negative Point Process Filter

PubMed Central

Nazarpour, Kianoush; Ethier, Christian; Paninski, Liam; Rebesco, James M.; Miall, R. Chris; Miller, Lee E.

2012-01-01

A constrained point process filtering mechanism for prediction of electromyogram (EMG) signals from multi-channel neural spike recordings is proposed here. Filters from the Kalman family are inherently sub-optimal in dealing with non-Gaussian observations, or a state evolution that deviates from the Gaussianity assumption. To address these limitations, we modeled the non-Gaussian neural spike train observations by using a generalized linear model (GLM) that encapsulates covariates of neural activity, including the neurons’ own spiking history, concurrent ensemble activity, and extrinsic covariates (EMG signals). In order to predict the envelopes of EMGs, we reformulated the Kalman filter (KF) in an optimization framework and utilized a non-negativity constraint. This structure characterizes the non-linear correspondence between neural activity and EMG signals reasonably. The EMGs were recorded from twelve forearm and hand muscles of a behaving monkey during a grip-force task. For the case of limited training data, the constrained point process filter improved the prediction accuracy when compared to a conventional Wiener cascade filter (a linear causal filter followed by a static non-linearity) for different bin sizes and delays between input spikes and EMG output. For longer training data sets, results of the proposed filter and that of the Wiener cascade filter were comparable. PMID:21659018

A method to stabilize linear systems using eigenvalue gradient information

NASA Technical Reports Server (NTRS)

Wieseman, C. D.

1985-01-01

Formal optimization methods and eigenvalue gradient information are used to develop a stabilizing control law for a closed loop linear system that is initially unstable. The method was originally formulated by using direct, constrained optimization methods with the constraints being the real parts of the eigenvalues. However, because of problems in trying to achieve stabilizing control laws, the problem was reformulated to be solved differently. The method described uses the Davidon-Fletcher-Powell minimization technique to solve an indirect, constrained minimization problem in which the performance index is the Kreisselmeier-Steinhauser function of the real parts of all the eigenvalues. The method is applied successfully to solve two different problems: the determination of a fourth-order control law stabilizes a single-input single-output active flutter suppression system and the determination of a second-order control law for a multi-input multi-output lateral-directional flight control system. Various sets of design variables and initial starting points were chosen to show the robustness of the method.

Effect of leading-edge load constraints on the design and performance of supersonic wings

NASA Technical Reports Server (NTRS)

Darden, C. M.

1985-01-01

A theoretical and experimental investigation was conducted to assess the effect of leading-edge load constraints on supersonic wing design and performance. In the effort to delay flow separation and the formation of leading-edge vortices, two constrained, linear-theory optimization approaches were used to limit the loadings on the leading edge of a variable-sweep planform design. Experimental force and moment tests were made on two constrained camber wings, a flat uncambered wing, and an optimum design with no constraints. Results indicate that vortex strength and separation regions were mildest on the severely and moderately constrained wings.

Spacecraft inertia estimation via constrained least squares

NASA Technical Reports Server (NTRS)

Keim, Jason A.; Acikmese, Behcet A.; Shields, Joel F.

2006-01-01

This paper presents a new formulation for spacecraft inertia estimation from test data. Specifically, the inertia estimation problem is formulated as a constrained least squares minimization problem with explicit bounds on the inertia matrix incorporated as LMIs [linear matrix inequalities). The resulting minimization problem is a semidefinite optimization that can be solved efficiently with guaranteed convergence to the global optimum by readily available algorithms. This method is applied to data collected from a robotic testbed consisting of a freely rotating body. The results show that the constrained least squares approach produces more accurate estimates of the inertia matrix than standard unconstrained least squares estimation methods.

Exact and explicit optimal solutions for trajectory planning and control of single-link flexible-joint manipulators

NASA Technical Reports Server (NTRS)

Chen, Guanrong

1991-01-01

An optimal trajectory planning problem for a single-link, flexible joint manipulator is studied. A global feedback-linearization is first applied to formulate the nonlinear inequality-constrained optimization problem in a suitable way. Then, an exact and explicit structural formula for the optimal solution of the problem is derived and the solution is shown to be unique. It turns out that the optimal trajectory planning and control can be done off-line, so that the proposed method is applicable to both theoretical analysis and real time tele-robotics control engineering.

Optimal Control Strategies for Constrained Relative Orbits

DTIC Science & Technology

2007-09-01

the chief. The work assumes the Clohessy - Wiltshire closeness assump- tion between the deputy and chief is valid, however, elliptical chief orbits are...133 Appendix G. A Closed-Form Solution of the Linear Clohessy - Wiltshire Equa- tions...Counterspace . . . . . . . . . . . . . . . . . . . 1 CW Clohessy - Wiltshire . . . . . . . . . . . . . . . . . . . . . . 4 DARPA Defense Advanced Research

Galaxy Redshifts from Discrete Optimization of Correlation Functions

NASA Astrophysics Data System (ADS)

Lee, Benjamin C. G.; Budavári, Tamás; Basu, Amitabh; Rahman, Mubdi

2016-12-01

We propose a new method of constraining the redshifts of individual extragalactic sources based on celestial coordinates and their ensemble statistics. Techniques from integer linear programming (ILP) are utilized to optimize simultaneously for the angular two-point cross- and autocorrelation functions. Our novel formalism introduced here not only transforms the otherwise hopelessly expensive, brute-force combinatorial search into a linear system with integer constraints but also is readily implementable in off-the-shelf solvers. We adopt Gurobi, a commercial optimization solver, and use Python to build the cost function dynamically. The preliminary results on simulated data show potential for future applications to sky surveys by complementing and enhancing photometric redshift estimators. Our approach is the first application of ILP to astronomical analysis.

Impulsive Control for Continuous-Time Markov Decision Processes: A Linear Programming Approach

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

Dufour, F., E-mail: dufour@math.u-bordeaux1.fr; Piunovskiy, A. B., E-mail: piunov@liv.ac.uk

2016-08-15

In this paper, we investigate an optimization problem for continuous-time Markov decision processes with both impulsive and continuous controls. We consider the so-called constrained problem where the objective of the controller is to minimize a total expected discounted optimality criterion associated with a cost rate function while keeping other performance criteria of the same form, but associated with different cost rate functions, below some given bounds. Our model allows multiple impulses at the same time moment. The main objective of this work is to study the associated linear program defined on a space of measures including the occupation measures ofmore » the controlled process and to provide sufficient conditions to ensure the existence of an optimal control.« less

A comparison of optimization algorithms for localized in vivo B0 shimming.

PubMed

Nassirpour, Sahar; Chang, Paul; Fillmer, Ariane; Henning, Anke

2018-02-01

To compare several different optimization algorithms currently used for localized in vivo B 0 shimming, and to introduce a novel, fast, and robust constrained regularized algorithm (ConsTru) for this purpose. Ten different optimization algorithms (including samples from both generic and dedicated least-squares solvers, and a novel constrained regularized inversion method) were implemented and compared for shimming in five different shimming volumes on 66 in vivo data sets from both 7 T and 9.4 T. The best algorithm was chosen to perform single-voxel spectroscopy at 9.4 T in the frontal cortex of the brain on 10 volunteers. The results of the performance tests proved that the shimming algorithm is prone to unstable solutions if it depends on the value of a starting point, and is not regularized to handle ill-conditioned problems. The ConsTru algorithm proved to be the most robust, fast, and efficient algorithm among all of the chosen algorithms. It enabled acquisition of spectra of reproducible high quality in the frontal cortex at 9.4 T. For localized in vivo B 0 shimming, the use of a dedicated linear least-squares solver instead of a generic nonlinear one is highly recommended. Among all of the linear solvers, the constrained regularized method (ConsTru) was found to be both fast and most robust. Magn Reson Med 79:1145-1156, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Fitting aerodynamic forces in the Laplace domain: An application of a nonlinear nongradient technique to multilevel constrained optimization

NASA Technical Reports Server (NTRS)

Tiffany, S. H.; Adams, W. M., Jr.

1984-01-01

A technique which employs both linear and nonlinear methods in a multilevel optimization structure to best approximate generalized unsteady aerodynamic forces for arbitrary motion is described. Optimum selection of free parameters is made in a rational function approximation of the aerodynamic forces in the Laplace domain such that a best fit is obtained, in a least squares sense, to tabular data for purely oscillatory motion. The multilevel structure and the corresponding formulation of the objective models are presented which separate the reduction of the fit error into linear and nonlinear problems, thus enabling the use of linear methods where practical. Certain equality and inequality constraints that may be imposed are identified; a brief description of the nongradient, nonlinear optimizer which is used is given; and results which illustrate application of the method are presented.

Optical Correlation of Images With Signal-Dependent Noise Using Constrained-Modulation Filter Devices

NASA Technical Reports Server (NTRS)

Downie, John D.

1995-01-01

Images with signal-dependent noise present challenges beyond those of images with additive white or colored signal-independent noise in terms of designing the optimal 4-f correlation filter that maximizes correlation-peak signal-to-noise ratio, or combinations of correlation-peak metrics. Determining the proper design becomes more difficult when the filter is to be implemented on a constrained-modulation spatial light modulator device. The design issues involved for updatable optical filters for images with signal-dependent film-grain noise and speckle noise are examined. It is shown that although design of the optimal linear filter in the Fourier domain is impossible for images with signal-dependent noise, proper nonlinear preprocessing of the images allows the application of previously developed design rules for optimal filters to be implemented on constrained-modulation devices. Thus the nonlinear preprocessing becomes necessary for correlation in optical systems with current spatial light modulator technology. These results are illustrated with computer simulations of images with signal-dependent noise correlated with binary-phase-only filters and ternary-phase-amplitude filters.

Linearized Alternating Direction Method of Multipliers for Constrained Nonconvex Regularized Optimization

DTIC Science & Technology

2016-11-22

structure of the graph, we replace the ℓ1- norm by the nonconvex Capped -ℓ1 norm , and obtain the Generalized Capped -ℓ1 regularized logistic regression...X. M. Yuan. Linearized augmented lagrangian and alternating direction methods for nuclear norm minimization. Mathematics of Computation, 82(281):301...better approximations of ℓ0- norm theoretically and computationally beyond ℓ1- norm , for example, the compressive sensing (Xiao et al., 2011). The

Missile Guidance Law Based on Robust Model Predictive Control Using Neural-Network Optimization.

PubMed

Li, Zhijun; Xia, Yuanqing; Su, Chun-Yi; Deng, Jun; Fu, Jun; He, Wei

2015-08-01

In this brief, the utilization of robust model-based predictive control is investigated for the problem of missile interception. Treating the target acceleration as a bounded disturbance, novel guidance law using model predictive control is developed by incorporating missile inside constraints. The combined model predictive approach could be transformed as a constrained quadratic programming (QP) problem, which may be solved using a linear variational inequality-based primal-dual neural network over a finite receding horizon. Online solutions to multiple parametric QP problems are used so that constrained optimal control decisions can be made in real time. Simulation studies are conducted to illustrate the effectiveness and performance of the proposed guidance control law for missile interception.

A methodology based on reduced complexity algorithm for system applications using microprocessors

NASA Technical Reports Server (NTRS)

Yan, T. Y.; Yao, K.

1988-01-01

The paper considers a methodology on the analysis and design of a minimum mean-square error criterion linear system incorporating a tapped delay line (TDL) where all the full-precision multiplications in the TDL are constrained to be powers of two. A linear equalizer based on the dispersive and additive noise channel is presented. This microprocessor implementation with optimized power of two TDL coefficients achieves a system performance comparable to the optimum linear equalization with full-precision multiplications for an input data rate of 300 baud.

A generalised optimal linear quadratic tracker with universal applications. Part 2: discrete-time systems

NASA Astrophysics Data System (ADS)

Ebrahimzadeh, Faezeh; Tsai, Jason Sheng-Hong; Chung, Min-Ching; Liao, Ying Ting; Guo, Shu-Mei; Shieh, Leang-San; Wang, Li

2017-01-01

Contrastive to Part 1, Part 2 presents a generalised optimal linear quadratic digital tracker (LQDT) with universal applications for the discrete-time (DT) systems. This includes (1) a generalised optimal LQDT design for the system with the pre-specified trajectories of the output and the control input and additionally with both the input-to-output direct-feedthrough term and known/estimated system disturbances or extra input/output signals; (2) a new optimal filter-shaped proportional plus integral state-feedback LQDT design for non-square non-minimum phase DT systems to achieve a minimum-phase-like tracking performance; (3) a new approach for computing the control zeros of the given non-square DT systems; and (4) a one-learning-epoch input-constrained iterative learning LQDT design for the repetitive DT systems.

A Model-Data Fusion Approach for Constraining Modeled GPP at Global Scales Using GOME2 SIF Data

NASA Astrophysics Data System (ADS)

MacBean, N.; Maignan, F.; Lewis, P.; Guanter, L.; Koehler, P.; Bacour, C.; Peylin, P.; Gomez-Dans, J.; Disney, M.; Chevallier, F.

2015-12-01

Predicting the fate of the ecosystem carbon, C, stocks and their sensitivity to climate change relies heavily on our ability to accurately model the gross carbon fluxes, i.e. photosynthesis and respiration. However, there are large differences in the Gross Primary Productivity (GPP) simulated by different land surface models (LSMs), not only in terms of mean value, but also in terms of phase and amplitude when compared to independent data-based estimates. This strongly limits our ability to provide accurate predictions of carbon-climate feedbacks. One possible source of this uncertainty is from inaccurate parameter values resulting from incomplete model calibration. Solar Induced Fluorescence (SIF) has been shown to have a linear relationship with GPP at the typical spatio-temporal scales used in LSMs (Guanter et al., 2011). New satellite-derived SIF datasets have the potential to constrain LSM parameters related to C uptake at global scales due to their coverage. Here we use SIF data derived from the GOME2 instrument (Köhler et al., 2014) to optimize parameters related to photosynthesis and leaf phenology of the ORCHIDEE LSM, as well as the linear relationship between SIF and GPP. We use a multi-site approach that combines many model grid cells covering a wide spatial distribution within the same optimization (e.g. Kuppel et al., 2014). The parameters are constrained per Plant Functional type as the linear relationship described above varies depending on vegetation structural properties. The relative skill of the optimization is compared to a case where only satellite-derived vegetation index data are used to constrain the model, and to a case where both data streams are used. We evaluate the results using an independent data-driven estimate derived from FLUXNET data (Jung et al., 2011) and with a new atmospheric tracer, Carbonyl sulphide (OCS) following the approach of Launois et al. (ACPD, in review). We show that the optimization reduces the strong positive bias of the ORCHIDEE model and increases the correlation compared to independent estimates. Differences in spatial patterns and gradients between simulated GPP and observed SIF remain largely unchanged however, suggesting that the underlying representation of vegetation type and/or structure and functioning in the model requires further investigation.

Reinforcement learning solution for HJB equation arising in constrained optimal control problem.

PubMed

Luo, Biao; Wu, Huai-Ning; Huang, Tingwen; Liu, Derong

2015-11-01

The constrained optimal control problem depends on the solution of the complicated Hamilton-Jacobi-Bellman equation (HJBE). In this paper, a data-based off-policy reinforcement learning (RL) method is proposed, which learns the solution of the HJBE and the optimal control policy from real system data. One important feature of the off-policy RL is that its policy evaluation can be realized with data generated by other behavior policies, not necessarily the target policy, which solves the insufficient exploration problem. The convergence of the off-policy RL is proved by demonstrating its equivalence to the successive approximation approach. Its implementation procedure is based on the actor-critic neural networks structure, where the function approximation is conducted with linearly independent basis functions. Subsequently, the convergence of the implementation procedure with function approximation is also proved. Finally, its effectiveness is verified through computer simulations. Copyright © 2015 Elsevier Ltd. All rights reserved.

Order-constrained linear optimization.

PubMed

Tidwell, Joe W; Dougherty, Michael R; Chrabaszcz, Jeffrey S; Thomas, Rick P

2017-11-01

Despite the fact that data and theories in the social, behavioural, and health sciences are often represented on an ordinal scale, there has been relatively little emphasis on modelling ordinal properties. The most common analytic framework used in psychological science is the general linear model, whose variants include ANOVA, MANOVA, and ordinary linear regression. While these methods are designed to provide the best fit to the metric properties of the data, they are not designed to maximally model ordinal properties. In this paper, we develop an order-constrained linear least-squares (OCLO) optimization algorithm that maximizes the linear least-squares fit to the data conditional on maximizing the ordinal fit based on Kendall's τ. The algorithm builds on the maximum rank correlation estimator (Han, 1987, Journal of Econometrics, 35, 303) and the general monotone model (Dougherty & Thomas, 2012, Psychological Review, 119, 321). Analyses of simulated data indicate that when modelling data that adhere to the assumptions of ordinary least squares, OCLO shows minimal bias, little increase in variance, and almost no loss in out-of-sample predictive accuracy. In contrast, under conditions in which data include a small number of extreme scores (fat-tailed distributions), OCLO shows less bias and variance, and substantially better out-of-sample predictive accuracy, even when the outliers are removed. We show that the advantages of OCLO over ordinary least squares in predicting new observations hold across a variety of scenarios in which researchers must decide to retain or eliminate extreme scores when fitting data. © 2017 The British Psychological Society.

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.

Optimization of constrained density functional theory

NASA Astrophysics Data System (ADS)

O'Regan, David D.; Teobaldi, Gilberto

2016-07-01

Constrained density functional theory (cDFT) is a versatile electronic structure method that enables ground-state calculations to be performed subject to physical constraints. It thereby broadens their applicability and utility. Automated Lagrange multiplier optimization is necessary for multiple constraints to be applied efficiently in cDFT, for it to be used in tandem with geometry optimization, or with molecular dynamics. In order to facilitate this, we comprehensively develop the connection between cDFT energy derivatives and response functions, providing a rigorous assessment of the uniqueness and character of cDFT stationary points while accounting for electronic interactions and screening. In particular, we provide a nonperturbative proof that stable stationary points of linear density constraints occur only at energy maxima with respect to their Lagrange multipliers. We show that multiple solutions, hysteresis, and energy discontinuities may occur in cDFT. Expressions are derived, in terms of convenient by-products of cDFT optimization, for quantities such as the dielectric function and a condition number quantifying ill definition in multiple constraint cDFT.

Level-Set Topology Optimization with Aeroelastic Constraints

NASA Technical Reports Server (NTRS)

Dunning, Peter D.; Stanford, Bret K.; Kim, H. Alicia

2015-01-01

Level-set topology optimization is used to design a wing considering skin buckling under static aeroelastic trim loading, as well as dynamic aeroelastic stability (flutter). The level-set function is defined over the entire 3D volume of a transport aircraft wing box. Therefore, the approach is not limited by any predefined structure and can explore novel configurations. The Sequential Linear Programming (SLP) level-set method is used to solve the constrained optimization problems. The proposed method is demonstrated using three problems with mass, linear buckling and flutter objective and/or constraints. A constraint aggregation method is used to handle multiple buckling constraints in the wing skins. A continuous flutter constraint formulation is used to handle difficulties arising from discontinuities in the design space caused by a switching of the critical flutter mode.

Advanced Computational Methods for Security Constrained Financial Transmission Rights: Structure and Parallelism

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

Elbert, Stephen T.; Kalsi, Karanjit; Vlachopoulou, Maria

Financial Transmission Rights (FTRs) help power market participants reduce price risks associated with transmission congestion. FTRs are issued based on a process of solving a constrained optimization problem with the objective to maximize the FTR social welfare under power flow security constraints. Security constraints for different FTR categories (monthly, seasonal or annual) are usually coupled and the number of constraints increases exponentially with the number of categories. Commercial software for FTR calculation can only provide limited categories of FTRs due to the inherent computational challenges mentioned above. In this paper, a novel non-linear dynamical system (NDS) approach is proposed tomore » solve the optimization problem. The new formulation and performance of the NDS solver is benchmarked against widely used linear programming (LP) solvers like CPLEX™ and tested on large-scale systems using data from the Western Electricity Coordinating Council (WECC). The NDS is demonstrated to outperform the widely used CPLEX algorithms while exhibiting superior scalability. Furthermore, the NDS based solver can be easily parallelized which results in significant computational improvement.« less

Digital robust active control law synthesis for large order systems using constrained optimization

NASA Technical Reports Server (NTRS)

Mukhopadhyay, Vivek

1987-01-01

This paper presents a direct digital control law synthesis procedure for a large order, sampled data, linear feedback system using constrained optimization techniques to meet multiple design requirements. A linear quadratic Gaussian type cost function is minimized while satisfying a set of constraints on the design loads and responses. General expressions for gradients of the cost function and constraints, with respect to the digital control law design variables are derived analytically and computed by solving a set of discrete Liapunov equations. The designer can choose the structure of the control law and the design variables, hence a stable classical control law as well as an estimator-based full or reduced order control law can be used as an initial starting point. Selected design responses can be treated as constraints instead of lumping them into the cost function. This feature can be used to modify a control law, to meet individual root mean square response limitations as well as minimum single value restrictions. Low order, robust digital control laws were synthesized for gust load alleviation of a flexible remotely piloted drone aircraft.

Helicopter Control Energy Reduction Using Moving Horizontal Tail

PubMed Central

Oktay, Tugrul; Sal, Firat

2015-01-01

Helicopter moving horizontal tail (i.e., MHT) strategy is applied in order to save helicopter flight control system (i.e., FCS) energy. For this intention complex, physics-based, control-oriented nonlinear helicopter models are used. Equations of MHT are integrated into these models and they are together linearized around straight level flight condition. A specific variance constrained control strategy, namely, output variance constrained Control (i.e., OVC) is utilized for helicopter FCS. Control energy savings due to this MHT idea with respect to a conventional helicopter are calculated. Parameters of helicopter FCS and dimensions of MHT are simultaneously optimized using a stochastic optimization method, namely, simultaneous perturbation stochastic approximation (i.e., SPSA). In order to observe improvement in behaviors of classical controls closed loop analyses are done. PMID:26180841

Optimal vibration control of a rotating plate with self-sensing active constrained layer damping

NASA Astrophysics Data System (ADS)

Xie, Zhengchao; Wong, Pak Kin; Lo, Kin Heng

2012-04-01

This paper proposes a finite element model for optimally controlled constrained layer damped (CLD) rotating plate with self-sensing technique and frequency-dependent material property in both the time and frequency domain. Constrained layer damping with viscoelastic material can effectively reduce the vibration in rotating structures. However, most existing research models use complex modulus approach to model viscoelastic material, and an additional iterative approach which is only available in frequency domain has to be used to include the material's frequency dependency. It is meaningful to model the viscoelastic damping layer in rotating part by using the anelastic displacement fields (ADF) in order to include the frequency dependency in both the time and frequency domain. Also, unlike previous ones, this finite element model treats all three layers as having the both shear and extension strains, so all types of damping are taken into account. Thus, in this work, a single layer finite element is adopted to model a three-layer active constrained layer damped rotating plate in which the constraining layer is made of piezoelectric material to work as both the self-sensing sensor and actuator under an linear quadratic regulation (LQR) controller. After being compared with verified data, this newly proposed finite element model is validated and could be used for future research.

Advanced Computational Methods for Security Constrained Financial Transmission Rights

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

Kalsi, Karanjit; Elbert, Stephen T.; Vlachopoulou, Maria

Financial Transmission Rights (FTRs) are financial insurance tools to help power market participants reduce price risks associated with transmission congestion. FTRs are issued based on a process of solving a constrained optimization problem with the objective to maximize the FTR social welfare under power flow security constraints. Security constraints for different FTR categories (monthly, seasonal or annual) are usually coupled and the number of constraints increases exponentially with the number of categories. Commercial software for FTR calculation can only provide limited categories of FTRs due to the inherent computational challenges mentioned above. In this paper, first an innovative mathematical reformulationmore » of the FTR problem is presented which dramatically improves the computational efficiency of optimization problem. After having re-formulated the problem, a novel non-linear dynamic system (NDS) approach is proposed to solve the optimization problem. The new formulation and performance of the NDS solver is benchmarked against widely used linear programming (LP) solvers like CPLEX™ and tested on both standard IEEE test systems and large-scale systems using data from the Western Electricity Coordinating Council (WECC). The performance of the NDS is demonstrated to be comparable and in some cases is shown to outperform the widely used CPLEX algorithms. The proposed formulation and NDS based solver is also easily parallelizable enabling further computational improvement.« less

Mathematical programming models for the economic design and assessment of wind energy conversion systems

NASA Astrophysics Data System (ADS)

Reinert, K. A.

The use of linear decision rules (LDR) and chance constrained programming (CCP) to optimize the performance of wind energy conversion clusters coupled to storage systems is described. Storage is modelled by LDR and output by CCP. The linear allocation rule and linear release rule prescribe the size and optimize a storage facility with a bypass. Chance constraints are introduced to explicitly treat reliability in terms of an appropriate value from an inverse cumulative distribution function. Details of deterministic programming structure and a sample problem involving a 500 kW and a 1.5 MW WECS are provided, considering an installed cost of $1/kW. Four demand patterns and three levels of reliability are analyzed for optimizing the generator choice and the storage configuration for base load and peak operating conditions. Deficiencies in ability to predict reliability and to account for serial correlations are noted in the model, which is concluded useful for narrowing WECS design options.

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

Luo, Yousong, E-mail: yousong.luo@rmit.edu.au

This paper deals with a class of optimal control problems governed by an initial-boundary value problem of a parabolic equation. The case of semi-linear boundary control is studied where the control is applied to the system via the Wentzell boundary condition. The differentiability of the state variable with respect to the control is established and hence a necessary condition is derived for the optimal solution in the case of both unconstrained and constrained problems. The condition is also sufficient for the unconstrained convex problems. A second order condition is also derived.

Nonlinear programming extensions to rational function approximation methods for unsteady aerodynamic forces

NASA Technical Reports Server (NTRS)

Tiffany, Sherwood H.; Adams, William M., Jr.

1988-01-01

The approximation of unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft are discussed. Two methods of formulating these approximations are extended to include the same flexibility in constraining the approximations and the same methodology in optimizing nonlinear parameters as another currently used extended least-squares method. Optimal selection of nonlinear parameters is made in each of the three methods by use of the same nonlinear, nongradient optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is lower order than that required when no optimization of the nonlinear terms is performed. The free linear parameters are determined using the least-squares matrix techniques of a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from different approaches are described and results are presented that show comparative evaluations from application of each of the extended methods to a numerical example.

Digital robust active control law synthesis for large order flexible structure using parameter optimization

NASA Technical Reports Server (NTRS)

Mukhopadhyay, V.

1988-01-01

A generic procedure for the parameter optimization of a digital control law for a large-order flexible flight vehicle or large space structure modeled as a sampled data system is presented. A linear quadratic Guassian type cost function was minimized, while satisfying a set of constraints on the steady-state rms values of selected design responses, using a constrained optimization technique to meet multiple design requirements. Analytical expressions for the gradients of the cost function and the design constraints on mean square responses with respect to the control law design variables are presented.

On the functional optimization of a certain class of nonstationary spatial functions

USGS Publications Warehouse

Christakos, G.; Paraskevopoulos, P.N.

1987-01-01

Procedures are developed in order to obtain optimal estimates of linear functionals for a wide class of nonstationary spatial functions. These procedures rely on well-established constrained minimum-norm criteria, and are applicable to multidimensional phenomena which are characterized by the so-called hypothesis of inherentity. The latter requires elimination of the polynomial, trend-related components of the spatial function leading to stationary quantities, and also it generates some interesting mathematics within the context of modelling and optimization in several dimensions. The arguments are illustrated using various examples, and a case study computed in detail. ?? 1987 Plenum Publishing Corporation.

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.

Closed-form solutions for linear regulator-design of mechanical systems including optimal weighting matrix selection

NASA Technical Reports Server (NTRS)

Hanks, Brantley R.; Skelton, Robert E.

1991-01-01

This paper addresses the restriction of Linear Quadratic Regulator (LQR) solutions to the algebraic Riccati Equation to design spaces which can be implemented as passive structural members and/or dampers. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical systems. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist. Some examples of simple spring mass systems are shown to illustrate key points.

On the optimization of electromagnetic geophysical data: Application of the PSO algorithm

NASA Astrophysics Data System (ADS)

Godio, A.; Santilano, A.

2018-01-01

Particle Swarm optimization (PSO) algorithm resolves constrained multi-parameter problems and is suitable for simultaneous optimization of linear and nonlinear problems, with the assumption that forward modeling is based on good understanding of ill-posed problem for geophysical inversion. We apply PSO for solving the geophysical inverse problem to infer an Earth model, i.e. the electrical resistivity at depth, consistent with the observed geophysical data. The method doesn't require an initial model and can be easily constrained, according to external information for each single sounding. The optimization process to estimate the model parameters from the electromagnetic soundings focuses on the discussion of the objective function to be minimized. We discuss the possibility to introduce in the objective function vertical and lateral constraints, with an Occam-like regularization. A sensitivity analysis allowed us to check the performance of the algorithm. The reliability of the approach is tested on synthetic, real Audio-Magnetotelluric (AMT) and Long Period MT data. The method appears able to solve complex problems and allows us to estimate the a posteriori distribution of the model parameters.

Digital robust control law synthesis using constrained optimization

NASA Technical Reports Server (NTRS)

Mukhopadhyay, Vivekananda

1989-01-01

Development of digital robust control laws for active control of high performance flexible aircraft and large space structures is a research area of significant practical importance. The flexible system is typically modeled by a large order state space system of equations in order to accurately represent the dynamics. The active control law must satisy multiple conflicting design requirements and maintain certain stability margins, yet should be simple enough to be implementable on an onboard digital computer. Described here is an application of a generic digital control law synthesis procedure for such a system, using optimal control theory and constrained optimization technique. A linear quadratic Gaussian type cost function is minimized by updating the free parameters of the digital control law, while trying to satisfy a set of constraints on the design loads, responses and stability margins. Analytical expressions for the gradients of the cost function and the constraints with respect to the control law design variables are used to facilitate rapid numerical convergence. These gradients can be used for sensitivity study and may be integrated into a simultaneous structure and control optimization scheme.

Chance-Constrained AC Optimal Power Flow: Reformulations and Efficient Algorithms

DOE PAGES

Roald, Line Alnaes; Andersson, Goran

2017-08-29

Higher levels of renewable electricity generation increase uncertainty in power system operation. To ensure secure system operation, new tools that account for this uncertainty are required. Here, in this paper, we adopt a chance-constrained AC optimal power flow formulation, which guarantees that generation, power flows and voltages remain within their bounds with a pre-defined probability. We then discuss different chance-constraint reformulations and solution approaches for the problem. Additionally, we first discuss an analytical reformulation based on partial linearization, which enables us to obtain a tractable representation of the optimization problem. We then provide an efficient algorithm based on an iterativemore » solution scheme which alternates between solving a deterministic AC OPF problem and assessing the impact of uncertainty. This more flexible computational framework enables not only scalable implementations, but also alternative chance-constraint reformulations. In particular, we suggest two sample based reformulations that do not require any approximation or relaxation of the AC power flow equations.« less

Nonlinear programming extensions to rational function approximations of unsteady aerodynamics

NASA Technical Reports Server (NTRS)

Tiffany, Sherwood H.; Adams, William M., Jr.

1987-01-01

This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.

Dynamic optimization and its relation to classical and quantum constrained systems

NASA Astrophysics Data System (ADS)

Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo

2017-08-01

We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum frameworks. Classically, the dynamic optimization problem is equivalent to a classical mechanics constrained system, so we must use the Dirac method to analyze it in a correct way. We find that there are two second-class constraints in the model: one fix the momenta associated with the control variables, and the other is a reminder of the optimal control law. The dynamic evolution of this constrained system is given by the Dirac's bracket of the canonical variables with the Hamiltonian. This dynamic results to be identical to the unconstrained one given by the Pontryagin equations, which are the correct classical equations of motion for our physical optimization problem. In the same Pontryagin scheme, by imposing a closed-loop λ-strategy, the optimality condition for the action gives a consistency relation, which is associated to the Hamilton-Jacobi-Bellman equation of the dynamic programming method. A similar result is achieved by quantizing the classical model. By setting the wave function Ψ(x , t) =e iS(x , t) in the quantum Schrödinger equation, a non-linear partial equation is obtained for the S function. For the right-hand side quantization, this is the Hamilton-Jacobi-Bellman equation, when S(x , t) is identified with the optimal value function. Thus, the Hamilton-Jacobi-Bellman equation in Bellman's maximum principle, can be interpreted as the quantum approach of the optimization problem.

State transformations and Hamiltonian structures for optimal control in discrete systems

NASA Astrophysics Data System (ADS)

Sieniutycz, S.

2006-04-01

Preserving usual definition of Hamiltonian H as the scalar product of rates and generalized momenta we investigate two basic classes of discrete optimal control processes governed by the difference rather than differential equations for the state transformation. The first class, linear in the time interval θ, secures the constancy of optimal H and satisfies a discrete Hamilton-Jacobi equation. The second class, nonlinear in θ, does not assure the constancy of optimal H and satisfies only a relationship that may be regarded as an equation of Hamilton-Jacobi type. The basic question asked is if and when Hamilton's canonical structures emerge in optimal discrete systems. For a constrained discrete control, general optimization algorithms are derived that constitute powerful theoretical and computational tools when evaluating extremum properties of constrained physical systems. The mathematical basis is Bellman's method of dynamic programming (DP) and its extension in the form of the so-called Carathéodory-Boltyanski (CB) stage optimality criterion which allows a variation of the terminal state that is otherwise fixed in Bellman's method. For systems with unconstrained intervals of the holdup time θ two powerful optimization algorithms are obtained: an unconventional discrete algorithm with a constant H and its counterpart for models nonlinear in θ. We also present the time-interval-constrained extension of the second algorithm. The results are general; namely, one arrives at: discrete canonical equations of Hamilton, maximum principles, and (at the continuous limit of processes with free intervals of time) the classical Hamilton-Jacobi theory, along with basic results of variational calculus. A vast spectrum of applications and an example are briefly discussed with particular attention paid to models nonlinear in the time interval θ.

PI controller design of a wind turbine: evaluation of the pole-placement method and tuning using constrained optimization

NASA Astrophysics Data System (ADS)

Mirzaei, Mahmood; Tibaldi, Carlo; Hansen, Morten H.

2016-09-01

PI/PID controllers are the most common wind turbine controllers. Normally a first tuning is obtained using methods such as pole-placement or Ziegler-Nichols and then extensive aeroelastic simulations are used to obtain the best tuning in terms of regulation of the outputs and reduction of the loads. In the traditional tuning approaches, the properties of different open loop and closed loop transfer functions of the system are not normally considered. In this paper, an assessment of the pole-placement tuning method is presented based on robustness measures. Then a constrained optimization setup is suggested to automatically tune the wind turbine controller subject to robustness constraints. The properties of the system such as the maximum sensitivity and complementary sensitivity functions (Ms and Mt ), along with some of the responses of the system, are used to investigate the controller performance and formulate the optimization problem. The cost function is the integral absolute error (IAE) of the rotational speed from a disturbance modeled as a step in wind speed. Linearized model of the DTU 10-MW reference wind turbine is obtained using HAWCStab2. Thereafter, the model is reduced with model order reduction. The trade-off curves are given to assess the tunings of the poles- placement method and a constrained optimization problem is solved to find the best tuning.

SLFP: a stochastic linear fractional programming approach for sustainable waste management.

PubMed

Zhu, H; Huang, G H

2011-12-01

A stochastic linear fractional programming (SLFP) approach is developed for supporting sustainable municipal solid waste management under uncertainty. The SLFP method can solve ratio optimization problems associated with random information, where chance-constrained programming is integrated into a linear fractional programming framework. It has advantages in: (1) comparing objectives of two aspects, (2) reflecting system efficiency, (3) dealing with uncertainty expressed as probability distributions, and (4) providing optimal-ratio solutions under different system-reliability conditions. The method is applied to a case study of waste flow allocation within a municipal solid waste (MSW) management system. The obtained solutions are useful for identifying sustainable MSW management schemes with maximized system efficiency under various constraint-violation risks. The results indicate that SLFP can support in-depth analysis of the interrelationships among system efficiency, system cost and system-failure risk. Copyright © 2011 Elsevier Ltd. All rights reserved.

Method for hue plane preserving color correction.

PubMed

Mackiewicz, Michal; Andersen, Casper F; Finlayson, Graham

2016-11-01

Hue plane preserving color correction (HPPCC), introduced by Andersen and Hardeberg [Proceedings of the 13th Color and Imaging Conference (CIC) (2005), pp. 141-146], maps device-dependent color values (RGB) to colorimetric color values (XYZ) using a set of linear transforms, realized by white point preserving 3×3 matrices, where each transform is learned and applied in a subregion of color space, defined by two adjacent hue planes. The hue plane delimited subregions of camera RGB values are mapped to corresponding hue plane delimited subregions of estimated colorimetric XYZ values. Hue planes are geometrical half-planes, where each is defined by the neutral axis and a chromatic color in a linear color space. The key advantage of the HPPCC method is that, while offering an estimation accuracy of higher order methods, it maintains the linear colorimetric relations of colors in hue planes. As a significant result, it therefore also renders the colorimetric estimates invariant to exposure and shading of object reflection. In this paper, we present a new flexible and robust version of HPPCC using constrained least squares in the optimization, where the subregions can be chosen freely in number and position in order to optimize the results while constraining transform continuity at the subregion boundaries. The method is compared to a selection of other state-of-the-art characterization methods, and the results show that it outperforms the original HPPCC method.

Control of linear uncertain systems utilizing mismatched state observers

NASA Technical Reports Server (NTRS)

Goldstein, B.

1972-01-01

The control of linear continuous dynamical systems is investigated as a problem of limited state feedback control. The equations which describe the structure of an observer are developed constrained to time-invarient systems. The optimal control problem is formulated, accounting for the uncertainty in the design parameters. Expressions for bounds on closed loop stability are also developed. The results indicate that very little uncertainty may be tolerated before divergence occurs in the recursive computation algorithms, and the derived stability bound yields extremely conservative estimates of regions of allowable parameter variations.

Constrained optimization via simulation models for new product innovation

NASA Astrophysics Data System (ADS)

Pujowidianto, Nugroho A.

2017-11-01

We consider the problem of constrained optimization where the decision makers aim to optimize the primary performance measure while constraining the secondary performance measures. This paper provides a brief overview of stochastically constrained optimization via discrete event simulation. Most review papers tend to be methodology-based. This review attempts to be problem-based as decision makers may have already decided on the problem formulation. We consider constrained optimization models as there are usually constraints on secondary performance measures as trade-off in new product development. It starts by laying out different possible methods and the reasons using constrained optimization via simulation models. It is then followed by the review of different simulation optimization approach to address constrained optimization depending on the number of decision variables, the type of constraints, and the risk preferences of the decision makers in handling uncertainties.

Linear Approximation to Optimal Control Allocation for Rocket Nozzles with Elliptical Constraints

NASA Technical Reports Server (NTRS)

Orr, Jeb S.; Wall, Johnm W.

2011-01-01

In this paper we present a straightforward technique for assessing and realizing the maximum control moment effectiveness for a launch vehicle with multiple constrained rocket nozzles, where elliptical deflection limits in gimbal axes are expressed as an ensemble of independent quadratic constraints. A direct method of determining an approximating ellipsoid that inscribes the set of attainable angular accelerations is derived. In the case of a parameterized linear generalized inverse, the geometry of the attainable set is computationally expensive to obtain but can be approximated to a high degree of accuracy with the proposed method. A linear inverse can then be optimized to maximize the volume of the true attainable set by maximizing the volume of the approximating ellipsoid. The use of a linear inverse does not preclude the use of linear methods for stability analysis and control design, preferred in practice for assessing the stability characteristics of the inertial and servoelastic coupling appearing in large boosters. The present techniques are demonstrated via application to the control allocation scheme for a concept heavy-lift launch vehicle.

Convex optimisation approach to constrained fuel optimal control of spacecraft in close relative motion

NASA Astrophysics Data System (ADS)

Massioni, Paolo; Massari, Mauro

2018-05-01

This paper describes an interesting and powerful approach to the constrained fuel-optimal control of spacecraft in close relative motion. The proposed approach is well suited for problems under linear dynamic equations, therefore perfectly fitting to the case of spacecraft flying in close relative motion. If the solution of the optimisation is approximated as a polynomial with respect to the time variable, then the problem can be approached with a technique developed in the control engineering community, known as "Sum Of Squares" (SOS), and the constraints can be reduced to bounds on the polynomials. Such a technique allows rewriting polynomial bounding problems in the form of convex optimisation problems, at the cost of a certain amount of conservatism. The principles of the techniques are explained and some application related to spacecraft flying in close relative motion are shown.

A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm

NASA Technical Reports Server (NTRS)

Ortiz, Francisco

2004-01-01

COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions is performed in this study. Also, a response surface approach to robust design is used to develop a new penalty function approach. This new penalty function approach is then compared with the other existing penalty functions.

Computer object segmentation by nonlinear image enhancement, multidimensional clustering, and geometrically constrained contour optimization

NASA Astrophysics Data System (ADS)

Bruynooghe, Michel M.

1998-04-01

In this paper, we present a robust method for automatic object detection and delineation in noisy complex images. The proposed procedure is a three stage process that integrates image segmentation by multidimensional pixel clustering and geometrically constrained optimization of deformable contours. The first step is to enhance the original image by nonlinear unsharp masking. The second step is to segment the enhanced image by multidimensional pixel clustering, using our reducible neighborhoods clustering algorithm that has a very interesting theoretical maximal complexity. Then, candidate objects are extracted and initially delineated by an optimized region merging algorithm, that is based on ascendant hierarchical clustering with contiguity constraints and on the maximization of average contour gradients. The third step is to optimize the delineation of previously extracted and initially delineated objects. Deformable object contours have been modeled by cubic splines. An affine invariant has been used to control the undesired formation of cusps and loops. Non linear constrained optimization has been used to maximize the external energy. This avoids the difficult and non reproducible choice of regularization parameters, that are required by classical snake models. The proposed method has been applied successfully to the detection of fine and subtle microcalcifications in X-ray mammographic images, to defect detection by moire image analysis, and to the analysis of microrugosities of thin metallic films. The later implementation of the proposed method on a digital signal processor associated to a vector coprocessor would allow the design of a real-time object detection and delineation system for applications in medical imaging and in industrial computer vision.

An algorithm for the solution of dynamic linear programs

NASA Technical Reports Server (NTRS)

Psiaki, Mark L.

1989-01-01

The algorithm's objective is to efficiently solve Dynamic Linear Programs (DLP) by taking advantage of their special staircase structure. This algorithm constitutes a stepping stone to an improved algorithm for solving Dynamic Quadratic Programs, which, in turn, would make the nonlinear programming method of Successive Quadratic Programs more practical for solving trajectory optimization problems. The ultimate goal is to being trajectory optimization solution speeds into the realm of real-time control. The algorithm exploits the staircase nature of the large constraint matrix of the equality-constrained DLPs encountered when solving inequality-constrained DLPs by an active set approach. A numerically-stable, staircase QL factorization of the staircase constraint matrix is carried out starting from its last rows and columns. The resulting recursion is like the time-varying Riccati equation from multi-stage LQR theory. The resulting factorization increases the efficiency of all of the typical LP solution operations over that of a dense matrix LP code. At the same time numerical stability is ensured. The algorithm also takes advantage of dynamic programming ideas about the cost-to-go by relaxing active pseudo constraints in a backwards sweeping process. This further decreases the cost per update of the LP rank-1 updating procedure, although it may result in more changes of the active set that if pseudo constraints were relaxed in a non-stagewise fashion. The usual stability of closed-loop Linear/Quadratic optimally-controlled systems, if it carries over to strictly linear cost functions, implies that the saving due to reduced factor update effort may outweigh the cost of an increased number of updates. An aerospace example is presented in which a ground-to-ground rocket's distance is maximized. This example demonstrates the applicability of this class of algorithms to aerospace guidance. It also sheds light on the efficacy of the proposed pseudo constraint relaxation scheme.

Digital Image Restoration Under a Regression Model - The Unconstrained, Linear Equality and Inequality Constrained Approaches

DTIC Science & Technology

1974-01-01

REGRESSION MODEL - THE UNCONSTRAINED, LINEAR EQUALITY AND INEQUALITY CONSTRAINED APPROACHES January 1974 Nelson Delfino d’Avila Mascarenha;? Image...Report 520 DIGITAL IMAGE RESTORATION UNDER A REGRESSION MODEL THE UNCONSTRAINED, LINEAR EQUALITY AND INEQUALITY CONSTRAINED APPROACHES January...a two- dimensional form adequately describes the linear model . A dis- cretization is performed by using quadrature methods. By trans

Stochastic Control of Energy Efficient Buildings: A Semidefinite Programming Approach

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

Ma, Xiao; Dong, Jin; Djouadi, Seddik M

2015-01-01

The key goal in energy efficient buildings is to reduce energy consumption of Heating, Ventilation, and Air- Conditioning (HVAC) systems while maintaining a comfortable temperature and humidity in the building. This paper proposes a novel stochastic control approach for achieving joint performance and power control of HVAC. We employ a constrained Stochastic Linear Quadratic Control (cSLQC) by minimizing a quadratic cost function with a disturbance assumed to be Gaussian. The problem is formulated to minimize the expected cost subject to a linear constraint and a probabilistic constraint. By using cSLQC, the problem is reduced to a semidefinite optimization problem, wheremore » the optimal control can be computed efficiently by Semidefinite programming (SDP). Simulation results are provided to demonstrate the effectiveness and power efficiency by utilizing the proposed control approach.« less

Nonlinear Recurrent Neural Network Predictive Control for Energy Distribution of a Fuel Cell Powered Robot

PubMed Central

Chen, Qihong; Long, Rong; Quan, Shuhai

2014-01-01

This paper presents a neural network predictive control strategy to optimize power distribution for a fuel cell/ultracapacitor hybrid power system of a robot. We model the nonlinear power system by employing time variant auto-regressive moving average with exogenous (ARMAX), and using recurrent neural network to represent the complicated coefficients of the ARMAX model. Because the dynamic of the system is viewed as operating- state- dependent time varying local linear behavior in this frame, a linear constrained model predictive control algorithm is developed to optimize the power splitting between the fuel cell and ultracapacitor. The proposed algorithm significantly simplifies implementation of the controller and can handle multiple constraints, such as limiting substantial fluctuation of fuel cell current. Experiment and simulation results demonstrate that the control strategy can optimally split power between the fuel cell and ultracapacitor, limit the change rate of the fuel cell current, and so as to extend the lifetime of the fuel cell. PMID:24707206

Optimal Attack Strategies Subject to Detection Constraints Against Cyber-Physical Systems

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

Chen, Yuan; Kar, Soummya; Moura, Jose M. F.

This paper studies an attacker against a cyberphysical system (CPS) whose goal is to move the state of a CPS to a target state while ensuring that his or her probability of being detected does not exceed a given bound. The attacker’s probability of being detected is related to the nonnegative bias induced by his or her attack on the CPS’s detection statistic. We formulate a linear quadratic cost function that captures the attacker’s control goal and establish constraints on the induced bias that reflect the attacker’s detection-avoidance objectives. When the attacker is constrained to be detected at the false-alarmmore » rate of the detector, we show that the optimal attack strategy reduces to a linear feedback of the attacker’s state estimate. In the case that the attacker’s bias is upper bounded by a positive constant, we provide two algorithms – an optimal algorithm and a sub-optimal, less computationally intensive algorithm – to find suitable attack sequences. Lastly, we illustrate our attack strategies in numerical examples based on a remotely-controlled helicopter under attack.« less

Optimal Attack Strategies Subject to Detection Constraints Against Cyber-Physical Systems

DOE PAGES

Chen, Yuan; Kar, Soummya; Moura, Jose M. F.

2017-03-31

This paper studies an attacker against a cyberphysical system (CPS) whose goal is to move the state of a CPS to a target state while ensuring that his or her probability of being detected does not exceed a given bound. The attacker’s probability of being detected is related to the nonnegative bias induced by his or her attack on the CPS’s detection statistic. We formulate a linear quadratic cost function that captures the attacker’s control goal and establish constraints on the induced bias that reflect the attacker’s detection-avoidance objectives. When the attacker is constrained to be detected at the false-alarmmore » rate of the detector, we show that the optimal attack strategy reduces to a linear feedback of the attacker’s state estimate. In the case that the attacker’s bias is upper bounded by a positive constant, we provide two algorithms – an optimal algorithm and a sub-optimal, less computationally intensive algorithm – to find suitable attack sequences. Lastly, we illustrate our attack strategies in numerical examples based on a remotely-controlled helicopter under attack.« less

Blind Channel Equalization with Colored Source Based on Constrained Optimization Methods

NASA Astrophysics Data System (ADS)

Wang, Yunhua; DeBrunner, Linda; DeBrunner, Victor; Zhou, Dayong

2008-12-01

Tsatsanis and Xu have applied the constrained minimum output variance (CMOV) principle to directly blind equalize a linear channel—a technique that has proven effective with white inputs. It is generally assumed in the literature that their CMOV method can also effectively equalize a linear channel with a colored source. In this paper, we prove that colored inputs will cause the equalizer to incorrectly converge due to inadequate constraints. We also introduce a new blind channel equalizer algorithm that is based on the CMOV principle, but with a different constraint that will correctly handle colored sources. Our proposed algorithm works for channels with either white or colored inputs and performs equivalently to the trained minimum mean-square error (MMSE) equalizer under high SNR. Thus, our proposed algorithm may be regarded as an extension of the CMOV algorithm proposed by Tsatsanis and Xu. We also introduce several methods to improve the performance of our introduced algorithm in the low SNR condition. Simulation results show the superior performance of our proposed methods.

An Optimization-based Atomistic-to-Continuum Coupling Method

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

Olson, Derek; Bochev, Pavel B.; Luskin, Mitchell

2014-08-21

In this paper, we present a new optimization-based method for atomistic-to-continuum (AtC) coupling. The main idea is to cast the latter as a constrained optimization problem with virtual Dirichlet controls on the interfaces between the atomistic and continuum subdomains. The optimization objective is to minimize the error between the atomistic and continuum solutions on the overlap between the two subdomains, while the atomistic and continuum force balance equations provide the constraints. Separation, rather then blending of the atomistic and continuum problems, and their subsequent use as constraints in the optimization problem distinguishes our approach from the existing AtC formulations. Finally,more » we present and analyze the method in the context of a one-dimensional chain of atoms modeled using a linearized two-body potential with next-nearest neighbor interactions.« less

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.

Efficient and Accurate Optimal Linear Phase FIR Filter Design Using Opposition-Based Harmony Search Algorithm

PubMed Central

Saha, S. K.; Dutta, R.; Choudhury, R.; Kar, R.; Mandal, D.; Ghoshal, S. P.

2013-01-01

In this paper, opposition-based harmony search has been applied for the optimal design of linear phase FIR filters. RGA, PSO, and DE have also been adopted for the sake of comparison. The original harmony search algorithm is chosen as the parent one, and opposition-based approach is applied. During the initialization, randomly generated population of solutions is chosen, opposite solutions are also considered, and the fitter one is selected as a priori guess. In harmony memory, each such solution passes through memory consideration rule, pitch adjustment rule, and then opposition-based reinitialization generation jumping, which gives the optimum result corresponding to the least error fitness in multidimensional search space of FIR filter design. Incorporation of different control parameters in the basic HS algorithm results in the balancing of exploration and exploitation of search space. Low pass, high pass, band pass, and band stop FIR filters are designed with the proposed OHS and other aforementioned algorithms individually for comparative optimization performance. A comparison of simulation results reveals the optimization efficacy of the OHS over the other optimization techniques for the solution of the multimodal, nondifferentiable, nonlinear, and constrained FIR filter design problems. PMID:23844390

Efficient and accurate optimal linear phase FIR filter design using opposition-based harmony search algorithm.

PubMed

Saha, S K; Dutta, R; Choudhury, R; Kar, R; Mandal, D; Ghoshal, S P

2013-01-01

In this paper, opposition-based harmony search has been applied for the optimal design of linear phase FIR filters. RGA, PSO, and DE have also been adopted for the sake of comparison. The original harmony search algorithm is chosen as the parent one, and opposition-based approach is applied. During the initialization, randomly generated population of solutions is chosen, opposite solutions are also considered, and the fitter one is selected as a priori guess. In harmony memory, each such solution passes through memory consideration rule, pitch adjustment rule, and then opposition-based reinitialization generation jumping, which gives the optimum result corresponding to the least error fitness in multidimensional search space of FIR filter design. Incorporation of different control parameters in the basic HS algorithm results in the balancing of exploration and exploitation of search space. Low pass, high pass, band pass, and band stop FIR filters are designed with the proposed OHS and other aforementioned algorithms individually for comparative optimization performance. A comparison of simulation results reveals the optimization efficacy of the OHS over the other optimization techniques for the solution of the multimodal, nondifferentiable, nonlinear, and constrained FIR filter design problems.

Computational wing optimization and comparisons with experiment for a semi-span wing model

NASA Technical Reports Server (NTRS)

Waggoner, E. G.; Haney, H. P.; Ballhaus, W. F.

1978-01-01

A computational wing optimization procedure was developed and verified by an experimental investigation of a semi-span variable camber wing model in the NASA Ames Research Center 14 foot transonic wind tunnel. The Bailey-Ballhaus transonic potential flow analysis and Woodward-Carmichael linear theory codes were linked to Vanderplaats constrained minimization routine to optimize model configurations at several subsonic and transonic design points. The 35 deg swept wing is characterized by multi-segmented leading and trailing edge flaps whose hinge lines are swept relative to the leading and trailing edges of the wing. By varying deflection angles of the flap segments, camber and twist distribution can be optimized for different design conditions. Results indicate that numerical optimization can be both an effective and efficient design tool. The optimized configurations had as good or better lift to drag ratios at the design points as the best designs previously tested during an extensive parametric study.

On optimal infinite impulse response edge detection filters

NASA Technical Reports Server (NTRS)

Sarkar, Sudeep; Boyer, Kim L.

1991-01-01

The authors outline the design of an optimal, computationally efficient, infinite impulse response edge detection filter. The optimal filter is computed based on Canny's high signal to noise ratio, good localization criteria, and a criterion on the spurious response of the filter to noise. An expression for the width of the filter, which is appropriate for infinite-length filters, is incorporated directly in the expression for spurious responses. The three criteria are maximized using the variational method and nonlinear constrained optimization. The optimal filter parameters are tabulated for various values of the filter performance criteria. A complete methodology for implementing the optimal filter using approximating recursive digital filtering is presented. The approximating recursive digital filter is separable into two linear filters operating in two orthogonal directions. The implementation is very simple and computationally efficient, has a constant time of execution for different sizes of the operator, and is readily amenable to real-time hardware implementation.

Design of a candidate flutter suppression control law for DAST ARW-2. [Drones for Aerodynamic and Structural Testing Aeroelastic Research Wing

NASA Technical Reports Server (NTRS)

Adams, W. M., Jr.; Tiffany, S. H.

1983-01-01

A control law is developed to suppress symmetric flutter for a mathematical model of an aeroelastic research vehicle. An implementable control law is attained by including modified LQG (linear quadratic Gaussian) design techniques, controller order reduction, and gain scheduling. An alternate (complementary) design approach is illustrated for one flight condition wherein nongradient-based constrained optimization techniques are applied to maximize controller robustness.

Structured Kernel Dictionary Learning with Correlation Constraint for Object Recognition.

PubMed

Wang, Zhengjue; Wang, Yinghua; Liu, Hongwei; Zhang, Hao

2017-06-21

In this paper, we propose a new discriminative non-linear dictionary learning approach, called correlation constrained structured kernel KSVD, for object recognition. The objective function for dictionary learning contains a reconstructive term and a discriminative term. In the reconstructive term, signals are implicitly non-linearly mapped into a space, where a structured kernel dictionary, each sub-dictionary of which lies in the span of the mapped signals from the corresponding class, is established. In the discriminative term, by analyzing the classification mechanism, the correlation constraint is proposed in kernel form, constraining the correlations between different discriminative codes, and restricting the coefficient vectors to be transformed into a feature space, where the features are highly correlated inner-class and nearly independent between-classes. The objective function is optimized by the proposed structured kernel KSVD. During the classification stage, the specific form of the discriminative feature is needless to be known, while the inner product of the discriminative feature with kernel matrix embedded is available, and is suitable for a linear SVM classifier. Experimental results demonstrate that the proposed approach outperforms many state-of-the-art dictionary learning approaches for face, scene and synthetic aperture radar (SAR) vehicle target recognition.

A Sequential Linear Quadratic Approach for Constrained Nonlinear Optimal Control with Adaptive Time Discretization and Application to Higher Elevation Mars Landing Problem

NASA Astrophysics Data System (ADS)

Sandhu, Amit

A sequential quadratic programming method is proposed for solving nonlinear optimal control problems subject to general path constraints including mixed state-control and state only constraints. The proposed algorithm further develops on the approach proposed in [1] with objective to eliminate the use of a high number of time intervals for arriving at an optimal solution. This is done by introducing an adaptive time discretization to allow formation of a desirable control profile without utilizing a lot of intervals. The use of fewer time intervals reduces the computation time considerably. This algorithm is further used in this thesis to solve a trajectory planning problem for higher elevation Mars landing.

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

Dall'Anese, Emiliano; Baker, Kyri; Summers, Tyler

The paper focuses on distribution systems featuring renewable energy sources and energy storage devices, and develops an optimal power flow (OPF) approach to optimize the system operation in spite of forecasting errors. The proposed method builds on a chance-constrained multi-period AC OPF formulation, where probabilistic constraints are utilized to enforce voltage regulation with a prescribed probability. To enable a computationally affordable solution approach, a convex reformulation of the OPF task is obtained by resorting to i) pertinent linear approximations of the power flow equations, and ii) convex approximations of the chance constraints. Particularly, the approximate chance constraints provide conservative boundsmore » that hold for arbitrary distributions of the forecasting errors. An adaptive optimization strategy is then obtained by embedding the proposed OPF task into a model predictive control framework.« less

A Proposal of a Fast Computation Method for Thermal Capacity and Voltage ATC by Means of Homotopy Functions

NASA Astrophysics Data System (ADS)

Zoka, Yoshifumi; Yorino, Naoto; Kawano, Koki; Suenari, Hiroyasu

This paper proposes a fast computation method for Available Transfer Capability (ATC) with respect to thermal and voltage magnitude limits. In the paper, ATC is formulated as an optimization problem. In order to obtain the efficiency for the N-1 outage contingency calculations, linear sensitivity methods are applied for screening and ranking all contingency selections with respect to the thermal and voltage magnitude limits margin to identify the severest case. In addition, homotopy functions are used for the generator QV constrains to reduce the maximum error of the linear estimation. Then, the Primal-Dual Interior Point Method (PDIPM) is used to solve the optimization problem for the severest case only, in which the solutions of ATC can be obtained efficiently. The effectiveness of the proposed method is demonstrated through IEEE 30, 57, 118-bus systems.

Force sensing using 3D displacement measurements in linear elastic bodies

NASA Astrophysics Data System (ADS)

Feng, Xinzeng; Hui, Chung-Yuen

2016-07-01

In cell traction microscopy, the mechanical forces exerted by a cell on its environment is usually determined from experimentally measured displacement by solving an inverse problem in elasticity. In this paper, an innovative numerical method is proposed which finds the "optimal" traction to the inverse problem. When sufficient regularization is applied, we demonstrate that the proposed method significantly improves the widely used approach using Green's functions. Motivated by real cell experiments, the equilibrium condition of a slowly migrating cell is imposed as a set of equality constraints on the unknown traction. Our validation benchmarks demonstrate that the numeric solution to the constrained inverse problem well recovers the actual traction when the optimal regularization parameter is used. The proposed method can thus be applied to study general force sensing problems, which utilize displacement measurements to sense inaccessible forces in linear elastic bodies with a priori constraints.

Optimal Policy of Cross-Layer Design for Channel Access and Transmission Rate Adaptation in Cognitive Radio Networks

NASA Astrophysics Data System (ADS)

He, Hao; Wang, Jun; Zhu, Jiang; Li, Shaoqian

2010-12-01

In this paper, we investigate the cross-layer design of joint channel access and transmission rate adaptation in CR networks with multiple channels for both centralized and decentralized cases. Our target is to maximize the throughput of CR network under transmission power constraint by taking spectrum sensing errors into account. In centralized case, this problem is formulated as a special constrained Markov decision process (CMDP), which can be solved by standard linear programming (LP) method. As the complexity of finding the optimal policy by LP increases exponentially with the size of action space and state space, we further apply action set reduction and state aggregation to reduce the complexity without loss of optimality. Meanwhile, for the convenience of implementation, we also consider the pure policy design and analyze the corresponding characteristics. In decentralized case, where only local information is available and there is no coordination among the CR users, we prove the existence of the constrained Nash equilibrium and obtain the optimal decentralized policy. Finally, in the case that the traffic load parameters of the licensed users are unknown for the CR users, we propose two methods to estimate the parameters for two different cases. Numerical results validate the theoretic analysis.

Algorithm-enabled exploration of image-quality potential of cone-beam CT in image-guided radiation therapy

NASA Astrophysics Data System (ADS)

Han, Xiao; Pearson, Erik; Pelizzari, Charles; Al-Hallaq, Hania; Sidky, Emil Y.; Bian, Junguo; Pan, Xiaochuan

2015-06-01

Kilo-voltage (KV) cone-beam computed tomography (CBCT) unit mounted onto a linear accelerator treatment system, often referred to as on-board imager (OBI), plays an increasingly important role in image-guided radiation therapy. While the FDK algorithm is currently used for reconstructing images from clinical OBI data, optimization-based reconstruction has also been investigated for OBI CBCT. An optimization-based reconstruction involves numerous parameters, which can significantly impact reconstruction properties (or utility). The success of an optimization-based reconstruction for a particular class of practical applications thus relies strongly on appropriate selection of parameter values. In the work, we focus on tailoring the constrained-TV-minimization-based reconstruction, an optimization-based reconstruction previously shown of some potential for CBCT imaging conditions of practical interest, to OBI imaging through appropriate selection of parameter values. In particular, for given real data of phantoms and patient collected with OBI CBCT, we first devise utility metrics specific to OBI-quality-assurance tasks and then apply them to guiding the selection of parameter values in constrained-TV-minimization-based reconstruction. The study results show that the reconstructions are with improvement, relative to clinical FDK reconstruction, in both visualization and quantitative assessments in terms of the devised utility metrics.

Optimizing cost-efficiency in mean exposure assessment - cost functions reconsidered

PubMed Central

2011-01-01

Background Reliable exposure data is a vital concern in medical epidemiology and intervention studies. The present study addresses the needs of the medical researcher to spend monetary resources devoted to exposure assessment with an optimal cost-efficiency, i.e. obtain the best possible statistical performance at a specified budget. A few previous studies have suggested mathematical optimization procedures based on very simple cost models; this study extends the methodology to cover even non-linear cost scenarios. Methods Statistical performance, i.e. efficiency, was assessed in terms of the precision of an exposure mean value, as determined in a hierarchical, nested measurement model with three stages. Total costs were assessed using a corresponding three-stage cost model, allowing costs at each stage to vary non-linearly with the number of measurements according to a power function. Using these models, procedures for identifying the optimally cost-efficient allocation of measurements under a constrained budget were developed, and applied on 225 scenarios combining different sizes of unit costs, cost function exponents, and exposure variance components. Results Explicit mathematical rules for identifying optimal allocation could be developed when cost functions were linear, while non-linear cost functions implied that parts of or the entire optimization procedure had to be carried out using numerical methods. For many of the 225 scenarios, the optimal strategy consisted in measuring on only one occasion from each of as many subjects as allowed by the budget. Significant deviations from this principle occurred if costs for recruiting subjects were large compared to costs for setting up measurement occasions, and, at the same time, the between-subjects to within-subject variance ratio was small. In these cases, non-linearities had a profound influence on the optimal allocation and on the eventual size of the exposure data set. Conclusions The analysis procedures developed in the present study can be used for informed design of exposure assessment strategies, provided that data are available on exposure variability and the costs of collecting and processing data. The present shortage of empirical evidence on costs and appropriate cost functions however impedes general conclusions on optimal exposure measurement strategies in different epidemiologic scenarios. PMID:21600023

Optimizing cost-efficiency in mean exposure assessment--cost functions reconsidered.

PubMed

Mathiassen, Svend Erik; Bolin, Kristian

2011-05-21

Reliable exposure data is a vital concern in medical epidemiology and intervention studies. The present study addresses the needs of the medical researcher to spend monetary resources devoted to exposure assessment with an optimal cost-efficiency, i.e. obtain the best possible statistical performance at a specified budget. A few previous studies have suggested mathematical optimization procedures based on very simple cost models; this study extends the methodology to cover even non-linear cost scenarios. Statistical performance, i.e. efficiency, was assessed in terms of the precision of an exposure mean value, as determined in a hierarchical, nested measurement model with three stages. Total costs were assessed using a corresponding three-stage cost model, allowing costs at each stage to vary non-linearly with the number of measurements according to a power function. Using these models, procedures for identifying the optimally cost-efficient allocation of measurements under a constrained budget were developed, and applied on 225 scenarios combining different sizes of unit costs, cost function exponents, and exposure variance components. Explicit mathematical rules for identifying optimal allocation could be developed when cost functions were linear, while non-linear cost functions implied that parts of or the entire optimization procedure had to be carried out using numerical methods.For many of the 225 scenarios, the optimal strategy consisted in measuring on only one occasion from each of as many subjects as allowed by the budget. Significant deviations from this principle occurred if costs for recruiting subjects were large compared to costs for setting up measurement occasions, and, at the same time, the between-subjects to within-subject variance ratio was small. In these cases, non-linearities had a profound influence on the optimal allocation and on the eventual size of the exposure data set. The analysis procedures developed in the present study can be used for informed design of exposure assessment strategies, provided that data are available on exposure variability and the costs of collecting and processing data. The present shortage of empirical evidence on costs and appropriate cost functions however impedes general conclusions on optimal exposure measurement strategies in different epidemiologic scenarios.

Smooth Constrained Heuristic Optimization of a Combinatorial Chemical Space

DTIC Science & Technology

2015-05-01

ARL-TR-7294•MAY 2015 US Army Research Laboratory Smooth ConstrainedHeuristic Optimization of a Combinatorial Chemical Space by Berend Christopher...7294•MAY 2015 US Army Research Laboratory Smooth ConstrainedHeuristic Optimization of a Combinatorial Chemical Space by Berend Christopher...

Multi-objective optimization in quantum parameter estimation

NASA Astrophysics Data System (ADS)

Gong, BeiLi; Cui, Wei

2018-04-01

We investigate quantum parameter estimation based on linear and Kerr-type nonlinear controls in an open quantum system, and consider the dissipation rate as an unknown parameter. We show that while the precision of parameter estimation is improved, it usually introduces a significant deformation to the system state. Moreover, we propose a multi-objective model to optimize the two conflicting objectives: (1) maximizing the Fisher information, improving the parameter estimation precision, and (2) minimizing the deformation of the system state, which maintains its fidelity. Finally, simulations of a simplified ɛ-constrained model demonstrate the feasibility of the Hamiltonian control in improving the precision of the quantum parameter estimation.

Generalized Pattern Search methods for a class of nonsmooth optimization problems with structure

NASA Astrophysics Data System (ADS)

Bogani, C.; Gasparo, M. G.; Papini, A.

2009-07-01

We propose a Generalized Pattern Search (GPS) method to solve a class of nonsmooth minimization problems, where the set of nondifferentiability is included in the union of known hyperplanes and, therefore, is highly structured. Both unconstrained and linearly constrained problems are considered. At each iteration the set of poll directions is enforced to conform to the geometry of both the nondifferentiability set and the boundary of the feasible region, near the current iterate. This is the key issue to guarantee the convergence of certain subsequences of iterates to points which satisfy first-order optimality conditions. Numerical experiments on some classical problems validate the method.

A prototype upper-atmospheric data assimilation scheme based on optimal interpolation: 2. Numerical experiments

NASA Astrophysics Data System (ADS)

Akmaev, R. a.

1999-04-01

In Part 1 of this work ([Akmaev, 1999]), an overview of the theory of optimal interpolation (OI) ([Gandin, 1963]) and related techniques of data assimilation based on linear optimal estimation ([Liebelt, 1967]; [Catlin, 1989]; [Mendel, 1995]) is presented. The approach implies the use in data analysis of additional statistical information in the form of statistical moments, e.g., the mean and covariance (correlation). The a priori statistical characteristics, if available, make it possible to constrain expected errors and obtain optimal in some sense estimates of the true state from a set of observations in a given domain in space and/or time. The primary objective of OI is to provide estimates away from the observations, i.e., to fill in data voids in the domain under consideration. Additionally, OI performs smoothing suppressing the noise, i.e., the spectral components that are presumably not present in the true signal. Usually, the criterion of optimality is minimum variance of the expected errors and the whole approach may be considered constrained least squares or least squares with a priori information. Obviously, data assimilation techniques capable of incorporating any additional information are potentially superior to techniques that have no access to such information as, for example, the conventional least squares (e.g., [Liebelt, 1967]; [Weisberg, 1985]; [Press et al., 1992]; [Mendel, 1995]).

Determination of optimum values for maximizing the profit in bread production: Daily bakery Sdn Bhd

NASA Astrophysics Data System (ADS)

Muda, Nora; Sim, Raymond

2015-02-01

An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear. An ILP has many applications in industrial production, including job-shop modelling. A possible objective is to maximize the total production, without exceeding the available resources. In some cases, this can be expressed in terms of a linear program, but variables must be constrained to be integer. It concerned with the optimization of a linear function while satisfying a set of linear equality and inequality constraints and restrictions. It has been used to solve optimization problem in many industries area such as banking, nutrition, agriculture, and bakery and so on. The main purpose of this study is to formulate the best combination of all ingredients in producing different type of bread in Daily Bakery in order to gain maximum profit. This study also focuses on the sensitivity analysis due to changing of the profit and the cost of each ingredient. The optimum result obtained from QM software is RM 65,377.29 per day. This study will be benefited for Daily Bakery and also other similar industries. By formulating a combination of all ingredients make up, they can easily know their total profit in producing bread everyday.

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

Huang, Kuo -Ling; Mehrotra, Sanjay

We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadraticmore » programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).« less

Implementation and on-sky results of an optimal wavefront controller for the MMT NGS adaptive optics system

NASA Astrophysics Data System (ADS)

Powell, Keith B.; Vaitheeswaran, Vidhya

2010-07-01

The MMT observatory has recently implemented and tested an optimal wavefront controller for the NGS adaptive optics system. Open loop atmospheric data collected at the telescope is used as the input to a MATLAB based analytical model. The model uses nonlinear constrained minimization to determine controller gains and optimize the system performance. The real-time controller performing the adaptive optics close loop operation is implemented on a dedicated high performance PC based quad core server. The controller algorithm is written in C and uses the GNU scientific library for linear algebra. Tests at the MMT confirmed the optimal controller significantly reduced the residual RMS wavefront compared with the previous controller. Significant reductions in image FWHM and increased peak intensities were obtained in J, H and K-bands. The optimal PID controller is now operating as the baseline wavefront controller for the MMT NGS-AO system.

A superlinear interior points algorithm for engineering design optimization

NASA Technical Reports Server (NTRS)

Herskovits, J.; Asquier, J.

1990-01-01

We present a quasi-Newton interior points algorithm for nonlinear constrained optimization. It is based on a general approach consisting of the iterative solution in the primal and dual spaces of the equalities in Karush-Kuhn-Tucker optimality conditions. This is done in such a way to have primal and dual feasibility at each iteration, which ensures satisfaction of those optimality conditions at the limit points. This approach is very strong and efficient, since at each iteration it only requires the solution of two linear systems with the same matrix, instead of quadratic programming subproblems. It is also particularly appropriate for engineering design optimization inasmuch at each iteration a feasible design is obtained. The present algorithm uses a quasi-Newton approximation of the second derivative of the Lagrangian function in order to have superlinear asymptotic convergence. We discuss theoretical aspects of the algorithm and its computer implementation.

Inexact nonlinear improved fuzzy chance-constrained programming model for irrigation water management under uncertainty

NASA Astrophysics Data System (ADS)

Zhang, Chenglong; Zhang, Fan; Guo, Shanshan; Liu, Xiao; Guo, Ping

2018-01-01

An inexact nonlinear mλ-measure fuzzy chance-constrained programming (INMFCCP) model is developed for irrigation water allocation under uncertainty. Techniques of inexact quadratic programming (IQP), mλ-measure, and fuzzy chance-constrained programming (FCCP) are integrated into a general optimization framework. The INMFCCP model can deal with not only nonlinearities in the objective function, but also uncertainties presented as discrete intervals in the objective function, variables and left-hand side constraints and fuzziness in the right-hand side constraints. Moreover, this model improves upon the conventional fuzzy chance-constrained programming by introducing a linear combination of possibility measure and necessity measure with varying preference parameters. To demonstrate its applicability, the model is then applied to a case study in the middle reaches of Heihe River Basin, northwest China. An interval regression analysis method is used to obtain interval crop water production functions in the whole growth period under uncertainty. Therefore, more flexible solutions can be generated for optimal irrigation water allocation. The variation of results can be examined by giving different confidence levels and preference parameters. Besides, it can reflect interrelationships among system benefits, preference parameters, confidence levels and the corresponding risk levels. Comparison between interval crop water production functions and deterministic ones based on the developed INMFCCP model indicates that the former is capable of reflecting more complexities and uncertainties in practical application. These results can provide more reliable scientific basis for supporting irrigation water management in arid areas.

An interval chance-constrained fuzzy modeling approach for supporting land-use planning and eco-environment planning at a watershed level.

PubMed

Ou, Guoliang; Tan, Shukui; Zhou, Min; Lu, Shasha; Tao, Yinghui; Zhang, Zuo; Zhang, Lu; Yan, Danping; Guan, Xingliang; Wu, Gang

2017-12-15

An interval chance-constrained fuzzy land-use allocation (ICCF-LUA) model is proposed in this study to support solving land resource management problem associated with various environmental and ecological constraints at a watershed level. The ICCF-LUA model is based on the ICCF (interval chance-constrained fuzzy) model which is coupled with interval mathematical model, chance-constrained programming model and fuzzy linear programming model and can be used to deal with uncertainties expressed as intervals, probabilities and fuzzy sets. Therefore, the ICCF-LUA model can reflect the tradeoff between decision makers and land stakeholders, the tradeoff between the economical benefits and eco-environmental demands. The ICCF-LUA model has been applied to the land-use allocation of Wujiang watershed, Guizhou Province, China. The results indicate that under highly land suitable conditions, optimized area of cultivated land, forest land, grass land, construction land, water land, unused land and landfill in Wujiang watershed will be [5015, 5648] hm 2 , [7841, 7965] hm 2 , [1980, 2056] hm 2 , [914, 1423] hm 2 , [70, 90] hm 2 , [50, 70] hm 2 and [3.2, 4.3] hm 2 , the corresponding system economic benefit will be between 6831 and 7219 billion yuan. Consequently, the ICCF-LUA model can effectively support optimized land-use allocation problem in various complicated conditions which include uncertainties, risks, economic objective and eco-environmental constraints. Copyright © 2017 Elsevier Ltd. All rights reserved.

Bounding the moment deficit rate on crustal faults using geodetic data: Methods

DOE PAGES

Maurer, Jeremy; Segall, Paul; Bradley, Andrew Michael

2017-08-19

Here, the geodetically derived interseismic moment deficit rate (MDR) provides a first-order constraint on earthquake potential and can play an important role in seismic hazard assessment, but quantifying uncertainty in MDR is a challenging problem that has not been fully addressed. We establish criteria for reliable MDR estimators, evaluate existing methods for determining the probability density of MDR, and propose and evaluate new methods. Geodetic measurements moderately far from the fault provide tighter constraints on MDR than those nearby. Previously used methods can fail catastrophically under predictable circumstances. The bootstrap method works well with strong data constraints on MDR, butmore » can be strongly biased when network geometry is poor. We propose two new methods: the Constrained Optimization Bounding Estimator (COBE) assumes uniform priors on slip rate (from geologic information) and MDR, and can be shown through synthetic tests to be a useful, albeit conservative estimator; the Constrained Optimization Bounding Linear Estimator (COBLE) is the corresponding linear estimator with Gaussian priors rather than point-wise bounds on slip rates. COBE matches COBLE with strong data constraints on MDR. We compare results from COBE and COBLE to previously published results for the interseismic MDR at Parkfield, on the San Andreas Fault, and find similar results; thus, the apparent discrepancy between MDR and the total moment release (seismic and afterslip) in the 2004 Parkfield earthquake remains.« less

Bounding the moment deficit rate on crustal faults using geodetic data: Methods

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

Maurer, Jeremy; Segall, Paul; Bradley, Andrew Michael

Here, the geodetically derived interseismic moment deficit rate (MDR) provides a first-order constraint on earthquake potential and can play an important role in seismic hazard assessment, but quantifying uncertainty in MDR is a challenging problem that has not been fully addressed. We establish criteria for reliable MDR estimators, evaluate existing methods for determining the probability density of MDR, and propose and evaluate new methods. Geodetic measurements moderately far from the fault provide tighter constraints on MDR than those nearby. Previously used methods can fail catastrophically under predictable circumstances. The bootstrap method works well with strong data constraints on MDR, butmore » can be strongly biased when network geometry is poor. We propose two new methods: the Constrained Optimization Bounding Estimator (COBE) assumes uniform priors on slip rate (from geologic information) and MDR, and can be shown through synthetic tests to be a useful, albeit conservative estimator; the Constrained Optimization Bounding Linear Estimator (COBLE) is the corresponding linear estimator with Gaussian priors rather than point-wise bounds on slip rates. COBE matches COBLE with strong data constraints on MDR. We compare results from COBE and COBLE to previously published results for the interseismic MDR at Parkfield, on the San Andreas Fault, and find similar results; thus, the apparent discrepancy between MDR and the total moment release (seismic and afterslip) in the 2004 Parkfield earthquake remains.« less

Mathematical Analysis for the Optimization of Wastewater Treatment Systems in Facultative Pond Indicator Organic Matter

NASA Astrophysics Data System (ADS)

Sunarsih; Widowati; Kartono; Sutrisno

2018-02-01

Stabilization ponds are easy to operate and their maintenance is simple. Treatment is carried out naturally and they are recommended in developing countries. The main disadvantage of these systems is large land area they occupy. The aim of this study was to perform an optimization of the wastewater treatment systems in a facultative pond, considering a mathematical analysis of the methodology to determine the model constrains organic matter. Matlab optimization toolbox was used for non linear programming. A facultative pond with the method was designed and then the optimization system was applied. The analyse meet the treated water quality requirements for the discharge to the water bodies. The results show a reduction of hydraulic retention time by 4.83 days, and the efficiency of of wastewater treatment of 84.16 percent.

Optimal Power Flow for Distribution Systems under Uncertain Forecasts: Preprint

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

Dall'Anese, Emiliano; Baker, Kyri; Summers, Tyler

2016-12-01

The paper focuses on distribution systems featuring renewable energy sources and energy storage devices, and develops an optimal power flow (OPF) approach to optimize the system operation in spite of forecasting errors. The proposed method builds on a chance-constrained multi-period AC OPF formulation, where probabilistic constraints are utilized to enforce voltage regulation with a prescribed probability. To enable a computationally affordable solution approach, a convex reformulation of the OPF task is obtained by resorting to i) pertinent linear approximations of the power flow equations, and ii) convex approximations of the chance constraints. Particularly, the approximate chance constraints provide conservative boundsmore » that hold for arbitrary distributions of the forecasting errors. An adaptive optimization strategy is then obtained by embedding the proposed OPF task into a model predictive control framework.« less

Fluence map optimization (FMO) with dose-volume constraints in IMRT using the geometric distance sorting method.

PubMed

Lan, Yihua; Li, Cunhua; Ren, Haozheng; Zhang, Yong; Min, Zhifang

2012-10-21

A new heuristic algorithm based on the so-called geometric distance sorting technique is proposed for solving the fluence map optimization with dose-volume constraints which is one of the most essential tasks for inverse planning in IMRT. The framework of the proposed method is basically an iterative process which begins with a simple linear constrained quadratic optimization model without considering any dose-volume constraints, and then the dose constraints for the voxels violating the dose-volume constraints are gradually added into the quadratic optimization model step by step until all the dose-volume constraints are satisfied. In each iteration step, an interior point method is adopted to solve each new linear constrained quadratic programming. For choosing the proper candidate voxels for the current dose constraint adding, a so-called geometric distance defined in the transformed standard quadratic form of the fluence map optimization model was used to guide the selection of the voxels. The new geometric distance sorting technique can mostly reduce the unexpected increase of the objective function value caused inevitably by the constraint adding. It can be regarded as an upgrading to the traditional dose sorting technique. The geometry explanation for the proposed method is also given and a proposition is proved to support our heuristic idea. In addition, a smart constraint adding/deleting strategy is designed to ensure a stable iteration convergence. The new algorithm is tested on four cases including head-neck, a prostate, a lung and an oropharyngeal, and compared with the algorithm based on the traditional dose sorting technique. Experimental results showed that the proposed method is more suitable for guiding the selection of new constraints than the traditional dose sorting method, especially for the cases whose target regions are in non-convex shapes. It is a more efficient optimization technique to some extent for choosing constraints than the dose sorting method. By integrating a smart constraint adding/deleting scheme within the iteration framework, the new technique builds up an improved algorithm for solving the fluence map optimization with dose-volume constraints.

Optimal design of focused experiments and surveys

NASA Astrophysics Data System (ADS)

Curtis, Andrew

1999-10-01

Experiments and surveys are often performed to obtain data that constrain some previously underconstrained model. Often, constraints are most desired in a particular subspace of model space. Experiment design optimization requires that the quality of any particular design can be both quantified and then maximized. This study shows how the quality can be defined such that it depends on the amount of information that is focused in the particular subspace of interest. In addition, algorithms are presented which allow one particular focused quality measure (from the class of focused measures) to be evaluated efficiently. A subclass of focused quality measures is also related to the standard variance and resolution measures from linearized inverse theory. The theory presented here requires that the relationship between model parameters and data can be linearized around a reference model without significant loss of information. Physical and financial constraints define the space of possible experiment designs. Cross-well tomographic examples are presented, plus a strategy for survey design to maximize information about linear combinations of parameters such as bulk modulus, κ =λ+ 2μ/3.

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

Optimal HRF and smoothing parameters for fMRI time series within an autoregressive modeling framework.

PubMed

Galka, Andreas; Siniatchkin, Michael; Stephani, Ulrich; Groening, Kristina; Wolff, Stephan; Bosch-Bayard, Jorge; Ozaki, Tohru

2010-12-01

The analysis of time series obtained by functional magnetic resonance imaging (fMRI) may be approached by fitting predictive parametric models, such as nearest-neighbor autoregressive models with exogeneous input (NNARX). As a part of the modeling procedure, it is possible to apply instantaneous linear transformations to the data. Spatial smoothing, a common preprocessing step, may be interpreted as such a transformation. The autoregressive parameters may be constrained, such that they provide a response behavior that corresponds to the canonical haemodynamic response function (HRF). We present an algorithm for estimating the parameters of the linear transformations and of the HRF within a rigorous maximum-likelihood framework. Using this approach, an optimal amount of both the spatial smoothing and the HRF can be estimated simultaneously for a given fMRI data set. An example from a motor-task experiment is discussed. It is found that, for this data set, weak, but non-zero, spatial smoothing is optimal. Furthermore, it is demonstrated that activated regions can be estimated within the maximum-likelihood framework.

Closed-form solutions for linear regulator design of mechanical systems including optimal weighting matrix selection

NASA Technical Reports Server (NTRS)

Hanks, Brantley R.; Skelton, Robert E.

1991-01-01

Vibration in modern structural and mechanical systems can be reduced in amplitude by increasing stiffness, redistributing stiffness and mass, and/or adding damping if design techniques are available to do so. Linear Quadratic Regulator (LQR) theory in modern multivariable control design, attacks the general dissipative elastic system design problem in a global formulation. The optimal design, however, allows electronic connections and phase relations which are not physically practical or possible in passive structural-mechanical devices. The restriction of LQR solutions (to the Algebraic Riccati Equation) to design spaces which can be implemented as passive structural members and/or dampers is addressed. A general closed-form solution to the optimal free-decay control problem is presented which is tailored for structural-mechanical system. The solution includes, as subsets, special cases such as the Rayleigh Dissipation Function and total energy. Weighting matrix selection is a constrained choice among several parameters to obtain desired physical relationships. The closed-form solution is also applicable to active control design for systems where perfect, collocated actuator-sensor pairs exist.

Split diversity in constrained conservation prioritization using integer linear programming.

PubMed

Chernomor, Olga; Minh, Bui Quang; Forest, Félix; Klaere, Steffen; Ingram, Travis; Henzinger, Monika; von Haeseler, Arndt

2015-01-01

Phylogenetic diversity (PD) is a measure of biodiversity based on the evolutionary history of species. Here, we discuss several optimization problems related to the use of PD, and the more general measure split diversity (SD), in conservation prioritization.Depending on the conservation goal and the information available about species, one can construct optimization routines that incorporate various conservation constraints. We demonstrate how this information can be used to select sets of species for conservation action. Specifically, we discuss the use of species' geographic distributions, the choice of candidates under economic pressure, and the use of predator-prey interactions between the species in a community to define viability constraints.Despite such optimization problems falling into the area of NP hard problems, it is possible to solve them in a reasonable amount of time using integer programming. We apply integer linear programming to a variety of models for conservation prioritization that incorporate the SD measure.We exemplarily show the results for two data sets: the Cape region of South Africa and a Caribbean coral reef community. Finally, we provide user-friendly software at http://www.cibiv.at/software/pda.

Distribution-Agnostic Stochastic Optimal Power Flow for Distribution Grids: Preprint

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

Baker, Kyri; Dall'Anese, Emiliano; Summers, Tyler

2016-09-01

This paper outlines a data-driven, distributionally robust approach to solve chance-constrained AC optimal power flow problems in distribution networks. Uncertain forecasts for loads and power generated by photovoltaic (PV) systems are considered, with the goal of minimizing PV curtailment while meeting power flow and voltage regulation constraints. A data- driven approach is utilized to develop a distributionally robust conservative convex approximation of the chance-constraints; particularly, the mean and covariance matrix of the forecast errors are updated online, and leveraged to enforce voltage regulation with predetermined probability via Chebyshev-based bounds. By combining an accurate linear approximation of the AC power flowmore » equations with the distributionally robust chance constraint reformulation, the resulting optimization problem becomes convex and computationally tractable.« less

Constrained ℋ∞ control for low bandwidth active suspensions

NASA Astrophysics Data System (ADS)

Wasiwitono, Unggul; Sutantra, I. Nyoman

2017-08-01

Low Bandwidth Active Suspension (LBAS) is shown to be more competitive to High Bandwidth Active Suspension (HBAS) when energy and cost aspects are taken into account. In this paper, the constrained ℋ∞ control scheme is applied for LBAS system. The ℋ∞ performance is used to measure ride comfort while the concept of reachable set in a state-space ellipsoid defined by a quadratic storage function is used to capture the time domain constraint that representing the requirements for road holding, suspension deflection limitation and actuator saturation. Then, the control problem is derived in the framework of Linear Matrix Inequality (LMI) optimization. The simulation is conducted considering the road disturbance as a stationary random process. The achievable performance of LBAS is analyzed for different values of bandwidth and damping ratio.

MO-FG-CAMPUS-TeP2-01: A Graph Form ADMM Algorithm for Constrained Quadratic Radiation Treatment Planning

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

Liu, X; Belcher, AH; Wiersma, R

Purpose: In radiation therapy optimization the constraints can be either hard constraints which must be satisfied or soft constraints which are included but do not need to be satisfied exactly. Currently the voxel dose constraints are viewed as soft constraints and included as a part of the objective function and approximated as an unconstrained problem. However in some treatment planning cases the constraints should be specified as hard constraints and solved by constrained optimization. The goal of this work is to present a computation efficiency graph form alternating direction method of multipliers (ADMM) algorithm for constrained quadratic treatment planning optimizationmore » and compare it with several commonly used algorithms/toolbox. Method: ADMM can be viewed as an attempt to blend the benefits of dual decomposition and augmented Lagrangian methods for constrained optimization. Various proximal operators were first constructed as applicable to quadratic IMRT constrained optimization and the problem was formulated in a graph form of ADMM. A pre-iteration operation for the projection of a point to a graph was also proposed to further accelerate the computation. Result: The graph form ADMM algorithm was tested by the Common Optimization for Radiation Therapy (CORT) dataset including TG119, prostate, liver, and head & neck cases. Both unconstrained and constrained optimization problems were formulated for comparison purposes. All optimizations were solved by LBFGS, IPOPT, Matlab built-in toolbox, CVX (implementing SeDuMi) and Mosek solvers. For unconstrained optimization, it was found that LBFGS performs the best, and it was 3–5 times faster than graph form ADMM. However, for constrained optimization, graph form ADMM was 8 – 100 times faster than the other solvers. Conclusion: A graph form ADMM can be applied to constrained quadratic IMRT optimization. It is more computationally efficient than several other commercial and noncommercial optimizers and it also used significantly less computer memory.« less

The Efficiency of Split Panel Designs in an Analysis of Variance Model

PubMed Central

Wang, Wei-Guo; Liu, Hai-Jun

2016-01-01

We consider split panel design efficiency in analysis of variance models, that is, the determination of the cross-sections series optimal proportion in all samples, to minimize parametric best linear unbiased estimators of linear combination variances. An orthogonal matrix is constructed to obtain manageable expression of variances. On this basis, we derive a theorem for analyzing split panel design efficiency irrespective of interest and budget parameters. Additionally, relative estimator efficiency based on the split panel to an estimator based on a pure panel or a pure cross-section is present. The analysis shows that the gains from split panel can be quite substantial. We further consider the efficiency of split panel design, given a budget, and transform it to a constrained nonlinear integer programming. Specifically, an efficient algorithm is designed to solve the constrained nonlinear integer programming. Moreover, we combine one at time designs and factorial designs to illustrate the algorithm’s efficiency with an empirical example concerning monthly consumer expenditure on food in 1985, in the Netherlands, and the efficient ranges of the algorithm parameters are given to ensure a good solution. PMID:27163447

Optimal apodization design for medical ultrasound using constrained least squares part I: theory.

PubMed

Guenther, Drake A; Walker, William F

2007-02-01

Aperture weighting functions are critical design parameters in the development of ultrasound systems because beam characteristics affect the contrast and point resolution of the final output image. In previous work by our group, we developed a metric that quantifies a broadband imaging system's contrast resolution performance. We now use this metric to formulate a novel general ultrasound beamformer design method. In our algorithm, we use constrained least squares (CLS) techniques and a linear algebra formulation to describe the system point spread function (PSF) as a function of the aperture weightings. In one approach, we minimize the energy of the PSF outside a certain boundary and impose a linear constraint on the aperture weights. In a second approach, we minimize the energy of the PSF outside a certain boundary while imposing a quadratic constraint on the energy of the PSF inside the boundary. We present detailed analysis for an arbitrary ultrasound imaging system and discuss several possible applications of the CLS techniques, such as designing aperture weightings to maximize contrast resolution and improve the system depth of field.

Dipole and quadrupole synthesis of electric potential fields. M.S. Thesis

NASA Technical Reports Server (NTRS)

Tilley, D. G.

1979-01-01

A general technique for expanding an unknown potential field in terms of a linear summation of weighted dipole or quadrupole fields is described. Computational methods were developed for the iterative addition of dipole fields. Various solution potentials were compared inside the boundary with a more precise calculation of the potential to derive optimal schemes for locating the singularities of the dipole fields. Then, the problem of determining solutions to Laplace's equation on an unbounded domain as constrained by pertinent electron trajectory data was considered.

Mixed Integer PDE Constrained Optimization for the Control of a Wildfire Hazard

DTIC Science & Technology

2017-01-01

are nodes suitable for extinguishing the fire. We introduce a discretization of the time horizon [0, T] by the set of time T := {0, At,..., ntZ\\t = T...of the constraints and objective with a discrete counterpart. The PDE is replaced by a linear system obtained from a convergent finite difference...method [5] and the integral is replaced by a quadrature formula. The domain is discretized by replacing 17 with an equidistant grid of length Ax

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

Baker, Kyri; Dall'Anese, Emiliano; Summers, Tyler

This paper outlines a data-driven, distributionally robust approach to solve chance-constrained AC optimal power flow problems in distribution networks. Uncertain forecasts for loads and power generated by photovoltaic (PV) systems are considered, with the goal of minimizing PV curtailment while meeting power flow and voltage regulation constraints. A data- driven approach is utilized to develop a distributionally robust conservative convex approximation of the chance-constraints; particularly, the mean and covariance matrix of the forecast errors are updated online, and leveraged to enforce voltage regulation with predetermined probability via Chebyshev-based bounds. By combining an accurate linear approximation of the AC power flowmore » equations with the distributionally robust chance constraint reformulation, the resulting optimization problem becomes convex and computationally tractable.« less

Sampling with poling-based flux balance analysis: optimal versus sub-optimal flux space analysis of Actinobacillus succinogenes.

PubMed

Binns, Michael; de Atauri, Pedro; Vlysidis, Anestis; Cascante, Marta; Theodoropoulos, Constantinos

2015-02-18

Flux balance analysis is traditionally implemented to identify the maximum theoretical flux for some specified reaction and a single distribution of flux values for all the reactions present which achieve this maximum value. However it is well known that the uncertainty in reaction networks due to branches, cycles and experimental errors results in a large number of combinations of internal reaction fluxes which can achieve the same optimal flux value. In this work, we have modified the applied linear objective of flux balance analysis to include a poling penalty function, which pushes each new set of reaction fluxes away from previous solutions generated. Repeated poling-based flux balance analysis generates a sample of different solutions (a characteristic set), which represents all the possible functionality of the reaction network. Compared to existing sampling methods, for the purpose of generating a relatively "small" characteristic set, our new method is shown to obtain a higher coverage than competing methods under most conditions. The influence of the linear objective function on the sampling (the linear bias) constrains optimisation results to a subspace of optimal solutions all producing the same maximal fluxes. Visualisation of reaction fluxes plotted against each other in 2 dimensions with and without the linear bias indicates the existence of correlations between fluxes. This method of sampling is applied to the organism Actinobacillus succinogenes for the production of succinic acid from glycerol. A new method of sampling for the generation of different flux distributions (sets of individual fluxes satisfying constraints on the steady-state mass balances of intermediates) has been developed using a relatively simple modification of flux balance analysis to include a poling penalty function inside the resulting optimisation objective function. This new methodology can achieve a high coverage of the possible flux space and can be used with and without linear bias to show optimal versus sub-optimal solution spaces. Basic analysis of the Actinobacillus succinogenes system using sampling shows that in order to achieve the maximal succinic acid production CO₂ must be taken into the system. Solutions involving release of CO₂ all give sub-optimal succinic acid production.

ADS: A FORTRAN program for automated design synthesis: Version 1.10

NASA Technical Reports Server (NTRS)

Vanderplaats, G. N.

1985-01-01

A new general-purpose optimization program for engineering design is described. ADS (Automated Design Synthesis - Version 1.10) is a FORTRAN program for solution of nonlinear constrained optimization problems. The program is segmented into three levels: strategy, optimizer, and one-dimensional search. At each level, several options are available so that a total of over 100 possible combinations can be created. Examples of available strategies are sequential unconstrained minimization, the Augmented Lagrange Multiplier method, and Sequential Linear Programming. Available optimizers include variable metric methods and the Method of Feasible Directions as examples, and one-dimensional search options include polynomial interpolation and the Golden Section method as examples. Emphasis is placed on ease of use of the program. All information is transferred via a single parameter list. Default values are provided for all internal program parameters such as convergence criteria, and the user is given a simple means to over-ride these, if desired.

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.

Scheduling Aircraft Landings under Constrained Position Shifting

NASA Technical Reports Server (NTRS)

Balakrishnan, Hamsa; Chandran, Bala

2006-01-01

Optimal scheduling of airport runway operations can play an important role in improving the safety and efficiency of the National Airspace System (NAS). Methods that compute the optimal landing sequence and landing times of aircraft must accommodate practical issues that affect the implementation of the schedule. One such practical consideration, known as Constrained Position Shifting (CPS), is the restriction that each aircraft must land within a pre-specified number of positions of its place in the First-Come-First-Served (FCFS) sequence. We consider the problem of scheduling landings of aircraft in a CPS environment in order to maximize runway throughput (minimize the completion time of the landing sequence), subject to operational constraints such as FAA-specified minimum inter-arrival spacing restrictions, precedence relationships among aircraft that arise either from airline preferences or air traffic control procedures that prevent overtaking, and time windows (representing possible control actions) during which each aircraft landing can occur. We present a Dynamic Programming-based approach that scales linearly in the number of aircraft, and describe our computational experience with a prototype implementation on realistic data for Denver International Airport.

Research on optimal DEM cell size for 3D visualization of loess terraces

NASA Astrophysics Data System (ADS)

Zhao, Weidong; Tang, Guo'an; Ji, Bin; Ma, Lei

2009-10-01

In order to represent the complex artificial terrains like loess terraces in Shanxi Province in northwest China, a new 3D visual method namely Terraces Elevation Incremental Visual Method (TEIVM) is put forth by the authors. 406 elevation points and 14 enclosed constrained lines are sampled according to the TIN-based Sampling Method (TSM) and DEM Elevation Points and Lines Classification (DEPLC). The elevation points and constrained lines are used to construct Constrained Delaunay Triangulated Irregular Networks (CD-TINs) of the loess terraces. In order to visualize the loess terraces well by use of optimal combination of cell size and Elevation Increment Value (EIV), the CD-TINs is converted to Grid-based DEM (G-DEM) by use of different combination of cell size and EIV with linear interpolating method called Bilinear Interpolation Method (BIM). Our case study shows that the new visual method can visualize the loess terraces steps very well when the combination of cell size and EIV is reasonable. The optimal combination is that the cell size is 1 m and the EIV is 6 m. Results of case study also show that the cell size should be at least smaller than half of both the terraces average width and the average vertical offset of terraces steps for representing the planar shapes of the terraces surfaces and steps well, while the EIV also should be larger than 4.6 times of the terraces average height. The TEIVM and results above is of great significance to the highly refined visualization of artificial terrains like loess terraces.

The Image-Optimized Corona; Progress on Using Coronagraph Images to Constrain Coronal Magnetic Field Models

NASA Astrophysics Data System (ADS)

Jones, S. I.; Uritsky, V. M.; Davila, J. M.

2017-12-01

In absence of reliable coronal magnetic field measurements, solar physicists have worked for several decades to develop techniques for extrapolating photospheric magnetic field measurements into the solar corona and/or heliosphere. The products of these efforts tend to be very sensitive to variation in the photospheric measurements, such that the uncertainty in the photospheric measurements introduces significant uncertainty into the coronal and heliospheric models needed to predict such things as solar wind speed, IMF polarity at Earth, and CME propagation. Ultimately, the reason for the sensitivity of the model to the boundary conditions is that the model is trying to extact a great deal of information from a relatively small amout of data. We have published in recent years about a new method we are developing to use morphological information gleaned from coronagraph images to constrain models of the global coronal magnetic field. In our approach, we treat the photospheric measurements as approximations and use an optimization algorithm to iteratively find a global coronal model that best matches both the photospheric measurements and quasi-linear features observed in polarization brightness coronagraph images. Here we will summarize the approach we have developed and present recent progress in optimizing PFSS models based on GONG magnetograms and MLSO K-Cor images.

Constrained Versions of DEDICOM for Use in Unsupervised Part-Of-Speech Tagging

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

Dunlavy, Daniel; Chew, Peter A.

This reports describes extensions of DEDICOM (DEcomposition into DIrectional COMponents) data models [3] that incorporate bound and linear constraints. The main purpose of these extensions is to investigate the use of improved data models for unsupervised part-of-speech tagging, as described by Chew et al. [2]. In that work, a single domain, two-way DEDICOM model was computed on a matrix of bigram fre- quencies of tokens in a corpus and used to identify parts-of-speech as an unsupervised approach to that problem. An open problem identi ed in that work was the com- putation of a DEDICOM model that more closely resembledmore » the matrices used in a Hidden Markov Model (HMM), speci cally through post-processing of the DEDICOM factor matrices. The work reported here consists of the description of several models that aim to provide a direct solution to that problem and a way to t those models. The approach taken here is to incorporate the model requirements as bound and lin- ear constrains into the DEDICOM model directly and solve the data tting problem as a constrained optimization problem. This is in contrast to the typical approaches in the literature, where the DEDICOM model is t using unconstrained optimization approaches, and model requirements are satis ed as a post-processing step.« less

The Increased Sensitivity of Irregular Peripheral Canal and Otolith Vestibular Afferents Optimizes their Encoding of Natural Stimuli

PubMed Central

Schneider, Adam D.; Jamali, Mohsen; Carriot, Jerome; Chacron, Maurice J.

2015-01-01

Efficient processing of incoming sensory input is essential for an organism's survival. A growing body of evidence suggests that sensory systems have developed coding strategies that are constrained by the statistics of the natural environment. Consequently, it is necessary to first characterize neural responses to natural stimuli to uncover the coding strategies used by a given sensory system. Here we report for the first time the statistics of vestibular rotational and translational stimuli experienced by rhesus monkeys during natural (e.g., walking, grooming) behaviors. We find that these stimuli can reach intensities as high as 1500 deg/s and 8 G. Recordings from afferents during naturalistic rotational and linear motion further revealed strongly nonlinear responses in the form of rectification and saturation, which could not be accurately predicted by traditional linear models of vestibular processing. Accordingly, we used linear–nonlinear cascade models and found that these could accurately predict responses to naturalistic stimuli. Finally, we tested whether the statistics of natural vestibular signals constrain the neural coding strategies used by peripheral afferents. We found that both irregular otolith and semicircular canal afferents, because of their higher sensitivities, were more optimized for processing natural vestibular stimuli as compared with their regular counterparts. Our results therefore provide the first evidence supporting the hypothesis that the neural coding strategies used by the vestibular system are matched to the statistics of natural stimuli. PMID:25855169

Methods of sequential estimation for determining initial data in numerical weather prediction. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Cohn, S. E.

1982-01-01

Numerical weather prediction (NWP) is an initial-value problem for a system of nonlinear differential equations, in which initial values are known incompletely and inaccurately. Observational data available at the initial time must therefore be supplemented by data available prior to the initial time, a problem known as meteorological data assimilation. A further complication in NWP is that solutions of the governing equations evolve on two different time scales, a fast one and a slow one, whereas fast scale motions in the atmosphere are not reliably observed. This leads to the so called initialization problem: initial values must be constrained to result in a slowly evolving forecast. The theory of estimation of stochastic dynamic systems provides a natural approach to such problems. For linear stochastic dynamic models, the Kalman-Bucy (KB) sequential filter is the optimal data assimilation method, for linear models, the optimal combined data assimilation-initialization method is a modified version of the KB filter.

Optimal Model-Based Fault Estimation and Correction for Particle Accelerators and Industrial Plants Using Combined Support Vector Machines and First Principles Models

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

Sayyar-Rodsari, Bijan; Schweiger, Carl; /SLAC /Pavilion Technologies, Inc., Austin, TX

2010-08-25

Timely estimation of deviations from optimal performance in complex systems and the ability to identify corrective measures in response to the estimated parameter deviations has been the subject of extensive research over the past four decades. The implications in terms of lost revenue from costly industrial processes, operation of large-scale public works projects and the volume of the published literature on this topic clearly indicates the significance of the problem. Applications range from manufacturing industries (integrated circuits, automotive, etc.), to large-scale chemical plants, pharmaceutical production, power distribution grids, and avionics. In this project we investigated a new framework for buildingmore » parsimonious models that are suited for diagnosis and fault estimation of complex technical systems. We used Support Vector Machines (SVMs) to model potentially time-varying parameters of a First-Principles (FP) description of the process. The combined SVM & FP model was built (i.e. model parameters were trained) using constrained optimization techniques. We used the trained models to estimate faults affecting simulated beam lifetime. In the case where a large number of process inputs are required for model-based fault estimation, the proposed framework performs an optimal nonlinear principal component analysis of the large-scale input space, and creates a lower dimension feature space in which fault estimation results can be effectively presented to the operation personnel. To fulfill the main technical objectives of the Phase I research, our Phase I efforts have focused on: (1) SVM Training in a Combined Model Structure - We developed the software for the constrained training of the SVMs in a combined model structure, and successfully modeled the parameters of a first-principles model for beam lifetime with support vectors. (2) Higher-order Fidelity of the Combined Model - We used constrained training to ensure that the output of the SVM (i.e. the parameters of the beam lifetime model) are physically meaningful. (3) Numerical Efficiency of the Training - We investigated the numerical efficiency of the SVM training. More specifically, for the primal formulation of the training, we have developed a problem formulation that avoids the linear increase in the number of the constraints as a function of the number of data points. (4) Flexibility of Software Architecture - The software framework for the training of the support vector machines was designed to enable experimentation with different solvers. We experimented with two commonly used nonlinear solvers for our simulations. The primary application of interest for this project has been the sustained optimal operation of particle accelerators at the Stanford Linear Accelerator Center (SLAC). Particle storage rings are used for a variety of applications ranging from 'colliding beam' systems for high-energy physics research to highly collimated x-ray generators for synchrotron radiation science. Linear accelerators are also used for collider research such as International Linear Collider (ILC), as well as for free electron lasers, such as the Linear Coherent Light Source (LCLS) at SLAC. One common theme in the operation of storage rings and linear accelerators is the need to precisely control the particle beams over long periods of time with minimum beam loss and stable, yet challenging, beam parameters. We strongly believe that beyond applications in particle accelerators, the high fidelity and cost benefits of a combined model-based fault estimation/correction system will attract customers from a wide variety of commercial and scientific industries. Even though the acquisition of Pavilion Technologies, Inc. by Rockwell Automation Inc. in 2007 has altered the small business status of the Pavilion and it no longer qualifies for a Phase II funding, our findings in the course of the Phase I research have convinced us that further research will render a workable model-based fault estimation and correction for particle accelerators and industrial plants feasible.« less

Experimental evaluation of model predictive control and inverse dynamics control for spacecraft proximity and docking maneuvers

NASA Astrophysics Data System (ADS)

Virgili-Llop, Josep; Zagaris, Costantinos; Park, Hyeongjun; Zappulla, Richard; Romano, Marcello

2018-03-01

An experimental campaign has been conducted to evaluate the performance of two different guidance and control algorithms on a multi-constrained docking maneuver. The evaluated algorithms are model predictive control (MPC) and inverse dynamics in the virtual domain (IDVD). A linear-quadratic approach with a quadratic programming solver is used for the MPC approach. A nonconvex optimization problem results from the IDVD approach, and a nonlinear programming solver is used. The docking scenario is constrained by the presence of a keep-out zone, an entry cone, and by the chaser's maximum actuation level. The performance metrics for the experiments and numerical simulations include the required control effort and time to dock. The experiments have been conducted in a ground-based air-bearing test bed, using spacecraft simulators that float over a granite table.

Solution of monotone complementarity and general convex programming problems using a modified potential reduction interior point method

DOE PAGES

Huang, Kuo -Ling; Mehrotra, Sanjay

2016-11-08

We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadraticmore » programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).« less

Initial Assessment of a Variable-Camber Continuous Trailing-Edge Flap System on a Rigid Wing for Drag Reduction in Subsonic Cruise

NASA Technical Reports Server (NTRS)

Ippolito, Corey; Nguyen, Nhan; Totah, Joe; Trinh, Khanh; Ting, Eric

2013-01-01

In this paper, we describe an initial optimization study of a Variable-Camber Continuous Trailing-Edge Flap (VCCTEF) system. The VCCTEF provides a light-weight control system for aircraft with long flexible wings, providing efficient high-lift capability for takeoff and landing, and greater efficiency with reduced drag at cruising flight by considering the effects of aeroelastic wing deformations in the control law. The VCCTEF system is comprised of a large number of distributed and individually-actuatable control surfaces that are constrained in movement relative to neighboring surfaces, and are non-trivially coupled through structural aeroelastic dynamics. Minimzation of drag results in a constrained, coupled, non-linear optimization over a high-dimension search space. In this paper, we describe the modeling, analysis, and optimization of the VCCTEF system control inputs for minimum drag in cruise. The purpose of this initial study is to quantify the expected benefits of the system concept. The scope of this analysis is limited to consideration of a rigid wing without structural flexibility in a steady-state cruise condition at various fuel weights. For analysis, we developed an optimization engine that couples geometric synthesis with vortex-lattice analysis to automate the optimization procedure. In this paper, we present and describe the VCCTEF system concept, optimization approach and tools, run-time performance, and results of the optimization at 20%, 50%, and 80% fuel load. This initial limited-scope study finds the VCCTEF system can potentially gain nearly 10% reduction in cruise drag, provides greater drag savings at lower operating weight, and efficiency is negatively impacted by the severity of relative constraints between control surfaces.

New nonlinear control algorithms for multiple robot arms

NASA Technical Reports Server (NTRS)

Tarn, T. J.; Bejczy, A. K.; Yun, X.

1988-01-01

Multiple coordinated robot arms are modeled by considering the arms as closed kinematic chains and as a force-constrained mechanical system working on the same object simultaneously. In both formulations, a novel dynamic control method is discussed. It is based on feedback linearization and simultaneous output decoupling technique. By applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, it was found that by choosing a general output equation it became possible simultaneously to superimpose the position and velocity error feedback with the force-torque error feedback in the task space.

Maximum likelihood identification and optimal input design for identifying aircraft stability and control derivatives

NASA Technical Reports Server (NTRS)

Stepner, D. E.; Mehra, R. K.

1973-01-01

A new method of extracting aircraft stability and control derivatives from flight test data is developed based on the maximum likelihood cirterion. It is shown that this new method is capable of processing data from both linear and nonlinear models, both with and without process noise and includes output error and equation error methods as special cases. The first application of this method to flight test data is reported for lateral maneuvers of the HL-10 and M2/F3 lifting bodies, including the extraction of stability and control derivatives in the presence of wind gusts. All the problems encountered in this identification study are discussed. Several different methods (including a priori weighting, parameter fixing and constrained parameter values) for dealing with identifiability and uniqueness problems are introduced and the results given. The method for the design of optimal inputs for identifying the parameters of linear dynamic systems is also given. The criterion used for the optimization is the sensitivity of the system output to the unknown parameters. Several simple examples are first given and then the results of an extensive stability and control dervative identification simulation for a C-8 aircraft are detailed.

Optimization of Dynamic Aperture of PEP-X Baseline Design

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

Wang, Min-Huey; /SLAC; Cai, Yunhai

2010-08-23

SLAC is developing a long-range plan to transfer the evolving scientific programs at SSRL from the SPEAR3 light source to a much higher performing photon source. Storage ring design is one of the possibilities that would be housed in the 2.2-km PEP-II tunnel. The design goal of PEPX storage ring is to approach an optimal light source design with horizontal emittance less than 100 pm and vertical emittance of 8 pm to reach the diffraction limit of 1-{angstrom} x-ray. The low emittance design requires a lattice with strong focusing leading to high natural chromaticity and therefore to strong sextupoles. Themore » latter caused reduction of dynamic aperture. The dynamic aperture requirement for horizontal injection at injection point is about 10 mm. In order to achieve the desired dynamic aperture the transverse non-linearity of PEP-X is studied. The program LEGO is used to simulate the particle motion. The technique of frequency map is used to analyze the nonlinear behavior. The effect of the non-linearity is tried to minimize at the given constrains of limited space. The details and results of dynamic aperture optimization are discussed in this paper.« less

H2, fixed architecture, control design for large scale systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Mercadal, Mathieu

1990-01-01

The H2, fixed architecture, control problem is a classic linear quadratic Gaussian (LQG) problem whose solution is constrained to be a linear time invariant compensator with a decentralized processing structure. The compensator can be made of p independent subcontrollers, each of which has a fixed order and connects selected sensors to selected actuators. The H2, fixed architecture, control problem allows the design of simplified feedback systems needed to control large scale systems. Its solution becomes more complicated, however, as more constraints are introduced. This work derives the necessary conditions for optimality for the problem and studies their properties. It is found that the filter and control problems couple when the architecture constraints are introduced, and that the different subcontrollers must be coordinated in order to achieve global system performance. The problem requires the simultaneous solution of highly coupled matrix equations. The use of homotopy is investigated as a numerical tool, and its convergence properties studied. It is found that the general constrained problem may have multiple stabilizing solutions, and that these solutions may be local minima or saddle points for the quadratic cost. The nature of the solution is not invariant when the parameters of the system are changed. Bifurcations occur, and a solution may continuously transform into a nonstabilizing compensator. Using a modified homotopy procedure, fixed architecture compensators are derived for models of large flexible structures to help understand the properties of the constrained solutions and compare them to the corresponding unconstrained ones.

Publications | Grid Modernization | NREL

Science.gov Websites

Photovoltaics: Trajectories and Challenges Cover of Efficient Relaxations for Joint Chance Constrained AC Optimal Power Flow publication Efficient Relaxations for Joint Chance Constrained AC Optimal Power Flow

Power-constrained supercomputing

NASA Astrophysics Data System (ADS)

Bailey, Peter E.

As we approach exascale systems, power is turning from an optimization goal to a critical operating constraint. With power bounds imposed by both stakeholders and the limitations of existing infrastructure, achieving practical exascale computing will therefore rely on optimizing performance subject to a power constraint. However, this requirement should not add to the burden of application developers; optimizing the runtime environment given restricted power will primarily be the job of high-performance system software. In this dissertation, we explore this area and develop new techniques that extract maximum performance subject to a particular power constraint. These techniques include a method to find theoretical optimal performance, a runtime system that shifts power in real time to improve performance, and a node-level prediction model for selecting power-efficient operating points. We use a linear programming (LP) formulation to optimize application schedules under various power constraints, where a schedule consists of a DVFS state and number of OpenMP threads for each section of computation between consecutive message passing events. We also provide a more flexible mixed integer-linear (ILP) formulation and show that the resulting schedules closely match schedules from the LP formulation. Across four applications, we use our LP-derived upper bounds to show that current approaches trail optimal, power-constrained performance by up to 41%. This demonstrates limitations of current systems, and our LP formulation provides future optimization approaches with a quantitative optimization target. We also introduce Conductor, a run-time system that intelligently distributes available power to nodes and cores to improve performance. The key techniques used are configuration space exploration and adaptive power balancing. Configuration exploration dynamically selects the optimal thread concurrency level and DVFS state subject to a hardware-enforced power bound. Adaptive power balancing efficiently predicts where critical paths are likely to occur and distributes power to those paths. Greater power, in turn, allows increased thread concurrency levels, CPU frequency/voltage, or both. We describe these techniques in detail and show that, compared to the state-of-the-art technique of using statically predetermined, per-node power caps, Conductor leads to a best-case performance improvement of up to 30%, and an average improvement of 19.1%. At the node level, an accurate power/performance model will aid in selecting the right configuration from a large set of available configurations. We present a novel approach to generate such a model offline using kernel clustering and multivariate linear regression. Our model requires only two iterations to select a configuration, which provides a significant advantage over exhaustive search-based strategies. We apply our model to predict power and performance for different applications using arbitrary configurations, and show that our model, when used with hardware frequency-limiting in a runtime system, selects configurations with significantly higher performance at a given power limit than those chosen by frequency-limiting alone. When applied to a set of 36 computational kernels from a range of applications, our model accurately predicts power and performance; our runtime system based on the model maintains 91% of optimal performance while meeting power constraints 88% of the time. When the runtime system violates a power constraint, it exceeds the constraint by only 6% in the average case, while simultaneously achieving 54% more performance than an oracle. Through the combination of the above contributions, we hope to provide guidance and inspiration to research practitioners working on runtime systems for power-constrained environments. We also hope this dissertation will draw attention to the need for software and runtime-controlled power management under power constraints at various levels, from the processor level to the cluster level.

Combining measurements to estimate properties and characterization extent of complex biochemical mixtures; applications to Heparan Sulfate

PubMed Central

Pradines, Joël R.; Beccati, Daniela; Lech, Miroslaw; Ozug, Jennifer; Farutin, Victor; Huang, Yongqing; Gunay, Nur Sibel; Capila, Ishan

2016-01-01

Complex mixtures of molecular species, such as glycoproteins and glycosaminoglycans, have important biological and therapeutic functions. Characterization of these mixtures with analytical chemistry measurements is an important step when developing generic drugs such as biosimilars. Recent developments have focused on analytical methods and statistical approaches to test similarity between mixtures. The question of how much uncertainty on mixture composition is reduced by combining several measurements still remains mostly unexplored. Mathematical frameworks to combine measurements, estimate mixture properties, and quantify remaining uncertainty, i.e. a characterization extent, are introduced here. Constrained optimization and mathematical modeling are applied to a set of twenty-three experimental measurements on heparan sulfate, a mixture of linear chains of disaccharides having different levels of sulfation. While this mixture has potentially over two million molecular species, mathematical modeling and the small set of measurements establish the existence of nonhomogeneity of sulfate level along chains and the presence of abundant sulfate repeats. Constrained optimization yields not only estimations of sulfate repeats and sulfate level at each position in the chains but also bounds on these levels, thereby estimating the extent of characterization of the sulfation pattern which is achieved by the set of measurements. PMID:27112127

Combining measurements to estimate properties and characterization extent of complex biochemical mixtures; applications to Heparan Sulfate.

PubMed

Pradines, Joël R; Beccati, Daniela; Lech, Miroslaw; Ozug, Jennifer; Farutin, Victor; Huang, Yongqing; Gunay, Nur Sibel; Capila, Ishan

2016-04-26

Complex mixtures of molecular species, such as glycoproteins and glycosaminoglycans, have important biological and therapeutic functions. Characterization of these mixtures with analytical chemistry measurements is an important step when developing generic drugs such as biosimilars. Recent developments have focused on analytical methods and statistical approaches to test similarity between mixtures. The question of how much uncertainty on mixture composition is reduced by combining several measurements still remains mostly unexplored. Mathematical frameworks to combine measurements, estimate mixture properties, and quantify remaining uncertainty, i.e. a characterization extent, are introduced here. Constrained optimization and mathematical modeling are applied to a set of twenty-three experimental measurements on heparan sulfate, a mixture of linear chains of disaccharides having different levels of sulfation. While this mixture has potentially over two million molecular species, mathematical modeling and the small set of measurements establish the existence of nonhomogeneity of sulfate level along chains and the presence of abundant sulfate repeats. Constrained optimization yields not only estimations of sulfate repeats and sulfate level at each position in the chains but also bounds on these levels, thereby estimating the extent of characterization of the sulfation pattern which is achieved by the set of measurements.

Combining measurements to estimate properties and characterization extent of complex biochemical mixtures; applications to Heparan Sulfate

NASA Astrophysics Data System (ADS)

Pradines, Joël R.; Beccati, Daniela; Lech, Miroslaw; Ozug, Jennifer; Farutin, Victor; Huang, Yongqing; Gunay, Nur Sibel; Capila, Ishan

2016-04-01

Complex mixtures of molecular species, such as glycoproteins and glycosaminoglycans, have important biological and therapeutic functions. Characterization of these mixtures with analytical chemistry measurements is an important step when developing generic drugs such as biosimilars. Recent developments have focused on analytical methods and statistical approaches to test similarity between mixtures. The question of how much uncertainty on mixture composition is reduced by combining several measurements still remains mostly unexplored. Mathematical frameworks to combine measurements, estimate mixture properties, and quantify remaining uncertainty, i.e. a characterization extent, are introduced here. Constrained optimization and mathematical modeling are applied to a set of twenty-three experimental measurements on heparan sulfate, a mixture of linear chains of disaccharides having different levels of sulfation. While this mixture has potentially over two million molecular species, mathematical modeling and the small set of measurements establish the existence of nonhomogeneity of sulfate level along chains and the presence of abundant sulfate repeats. Constrained optimization yields not only estimations of sulfate repeats and sulfate level at each position in the chains but also bounds on these levels, thereby estimating the extent of characterization of the sulfation pattern which is achieved by the set of measurements.

Optimal processor assignment for pipeline computations

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

Recovery of sparse translation-invariant signals with continuous basis pursuit

PubMed Central

Ekanadham, Chaitanya; Tranchina, Daniel; Simoncelli, Eero

2013-01-01

We consider the problem of decomposing a signal into a linear combination of features, each a continuously translated version of one of a small set of elementary features. Although these constituents are drawn from a continuous family, most current signal decomposition methods rely on a finite dictionary of discrete examples selected from this family (e.g., shifted copies of a set of basic waveforms), and apply sparse optimization methods to select and solve for the relevant coefficients. Here, we generate a dictionary that includes auxiliary interpolation functions that approximate translates of features via adjustment of their coefficients. We formulate a constrained convex optimization problem, in which the full set of dictionary coefficients represents a linear approximation of the signal, the auxiliary coefficients are constrained so as to only represent translated features, and sparsity is imposed on the primary coefficients using an L1 penalty. The basis pursuit denoising (BP) method may be seen as a special case, in which the auxiliary interpolation functions are omitted, and we thus refer to our methodology as continuous basis pursuit (CBP). We develop two implementations of CBP for a one-dimensional translation-invariant source, one using a first-order Taylor approximation, and another using a form of trigonometric spline. We examine the tradeoff between sparsity and signal reconstruction accuracy in these methods, demonstrating empirically that trigonometric CBP substantially outperforms Taylor CBP, which in turn offers substantial gains over ordinary BP. In addition, the CBP bases can generally achieve equally good or better approximations with much coarser sampling than BP, leading to a reduction in dictionary dimensionality. PMID:24352562

From diets to foods: using linear programming to formulate a nutritious, minimum-cost porridge mix for children aged 1 to 2 years.

PubMed

De Carvalho, Irene Stuart Torrié; Granfeldt, Yvonne; Dejmek, Petr; Håkansson, Andreas

2015-03-01

Linear programming has been used extensively as a tool for nutritional recommendations. Extending the methodology to food formulation presents new challenges, since not all combinations of nutritious ingredients will produce an acceptable food. Furthermore, it would help in implementation and in ensuring the feasibility of the suggested recommendations. To extend the previously used linear programming methodology from diet optimization to food formulation using consistency constraints. In addition, to exemplify usability using the case of a porridge mix formulation for emergency situations in rural Mozambique. The linear programming method was extended with a consistency constraint based on previously published empirical studies on swelling of starch in soft porridges. The new method was exemplified using the formulation of a nutritious, minimum-cost porridge mix for children aged 1 to 2 years for use as a complete relief food, based primarily on local ingredients, in rural Mozambique. A nutritious porridge fulfilling the consistency constraints was found; however, the minimum cost was unfeasible with local ingredients only. This illustrates the challenges in formulating nutritious yet economically feasible foods from local ingredients. The high cost was caused by the high cost of mineral-rich foods. A nutritious, low-cost porridge that fulfills the consistency constraints was obtained by including supplements of zinc and calcium salts as ingredients. The optimizations were successful in fulfilling all constraints and provided a feasible porridge, showing that the extended constrained linear programming methodology provides a systematic tool for designing nutritious foods.

An enhanced export coefficient based optimization model for supporting agricultural nonpoint source pollution mitigation under uncertainty.

PubMed

Rong, Qiangqiang; Cai, Yanpeng; Chen, Bing; Yue, Wencong; Yin, Xin'an; Tan, Qian

2017-02-15

In this research, an export coefficient based dual inexact two-stage stochastic credibility constrained programming (ECDITSCCP) model was developed through integrating an improved export coefficient model (ECM), interval linear programming (ILP), fuzzy credibility constrained programming (FCCP) and a fuzzy expected value equation within a general two stage programming (TSP) framework. The proposed ECDITSCCP model can effectively address multiple uncertainties expressed as random variables, fuzzy numbers, pure and dual intervals. Also, the model can provide a direct linkage between pre-regulated management policies and the associated economic implications. Moreover, the solutions under multiple credibility levels can be obtained for providing potential decision alternatives for decision makers. The proposed model was then applied to identify optimal land use structures for agricultural NPS pollution mitigation in a representative upstream subcatchment of the Miyun Reservoir watershed in north China. Optimal solutions of the model were successfully obtained, indicating desired land use patterns and nutrient discharge schemes to get a maximum agricultural system benefits under a limited discharge permit. Also, numerous results under multiple credibility levels could provide policy makers with several options, which could help get an appropriate balance between system benefits and pollution mitigation. The developed ECDITSCCP model can be effectively applied to addressing the uncertain information in agricultural systems and shows great applicability to the land use adjustment for agricultural NPS pollution mitigation. Copyright © 2016 Elsevier B.V. All rights reserved.

Effective Teaching of Economics: A Constrained Optimization Problem?

ERIC Educational Resources Information Center

Hultberg, Patrik T.; Calonge, David Santandreu

2017-01-01

One of the fundamental tenets of economics is that decisions are often the result of optimization problems subject to resource constraints. Consumers optimize utility, subject to constraints imposed by prices and income. As economics faculty, instructors attempt to maximize student learning while being constrained by their own and students'…

Variable-Metric Algorithm For Constrained Optimization

NASA Technical Reports Server (NTRS)

Frick, James D.

1989-01-01

Variable Metric Algorithm for Constrained Optimization (VMACO) is nonlinear computer program developed to calculate least value of function of n variables subject to general constraints, both equality and inequality. First set of constraints equality and remaining constraints inequalities. Program utilizes iterative method in seeking optimal solution. Written in ANSI Standard FORTRAN 77.

Chance-Constrained Guidance With Non-Convex Constraints

NASA Technical Reports Server (NTRS)

Ono, Masahiro

2011-01-01

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

Optimization of a constrained linear monochromator design for neutral atom beams.

PubMed

Kaltenbacher, Thomas

2016-04-01

A focused ground state, neutral atom beam, exploiting its de Broglie wavelength by means of atom optics, is used for neutral atom microscopy imaging. Employing Fresnel zone plates as a lens for these beams is a well established microscopy technique. To date, even for favorable beam source conditions a minimal focus spot size of slightly below 1μm was reached. This limitation is essentially given by the intrinsic spectral purity of the beam in combination with the chromatic aberration of the diffraction based zone plate. Therefore, it is important to enhance the monochromaticity of the beam, enabling a higher spatial resolution, preferably below 100nm. We propose to increase the monochromaticity of a neutral atom beam by means of a so-called linear monochromator set-up - a Fresnel zone plate in combination with a pinhole aperture - in order to gain more than one order of magnitude in spatial resolution. This configuration is known in X-ray microscopy and has proven to be useful, but has not been applied to neutral atom beams. The main result of this work is optimal design parameters based on models for this linear monochromator set-up followed by a second zone plate for focusing. The optimization was performed for minimizing the focal spot size and maximizing the centre line intensity at the detector position for an atom beam simultaneously. The results presented in this work are for, but not limited to, a neutral helium atom beam. Copyright © 2016 Elsevier B.V. All rights reserved.

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

Order-Constrained Solutions in K-Means Clustering: Even Better than Being Globally Optimal

ERIC Educational Resources Information Center

Steinley, Douglas; Hubert, Lawrence

2008-01-01

This paper proposes an order-constrained K-means cluster analysis strategy, and implements that strategy through an auxiliary quadratic assignment optimization heuristic that identifies an initial object order. A subsequent dynamic programming recursion is applied to optimally subdivide the object set subject to the order constraint. We show that…

Linear Quadratic Gaussian Controller Design Using a Graphical User Interface: Application to the Beam-Waveguide Antennas

NASA Astrophysics Data System (ADS)

Maneri, E.; Gawronski, W.

1999-10-01

The linear quadratic Gaussian (LQG) design algorithms described in [2] and [5] have been used in the controller design of JPL's beam-waveguide [5] and 70-m [6] antennas. This algorithm significantly improves tracking precision in a windy environment. This article describes the graphical user interface (GUI) software for the design LQG controllers. It consists of two parts: the basic LQG design and the fine-tuning of the basic design using a constrained optimization algorithm. The presented GUI was developed to simplify the design process, to make the design process user-friendly, and to enable design of an LQG controller for one with a limited control engineering background. The user is asked to manipulate the GUI sliders and radio buttons to watch the antenna performance. Simple rules are given at the GUI display.

Constrained growth flips the direction of optimal phenological responses among annual plants.

PubMed

Lindh, Magnus; Johansson, Jacob; Bolmgren, Kjell; Lundström, Niklas L P; Brännström, Åke; Jonzén, Niclas

2016-03-01

Phenological changes among plants due to climate change are well documented, but often hard to interpret. In order to assess the adaptive value of observed changes, we study how annual plants with and without growth constraints should optimize their flowering time when productivity and season length changes. We consider growth constraints that depend on the plant's vegetative mass: self-shading, costs for nonphotosynthetic structural tissue and sibling competition. We derive the optimal flowering time from a dynamic energy allocation model using optimal control theory. We prove that an immediate switch (bang-bang control) from vegetative to reproductive growth is optimal with constrained growth and constant mortality. Increasing mean productivity, while keeping season length constant and growth unconstrained, delayed the optimal flowering time. When growth was constrained and productivity was relatively high, the optimal flowering time advanced instead. When the growth season was extended equally at both ends, the optimal flowering time was advanced under constrained growth and delayed under unconstrained growth. Our results suggests that growth constraints are key factors to consider when interpreting phenological flowering responses. It can help to explain phenological patterns along productivity gradients, and links empirical observations made on calendar scales with life-history theory. © 2015 The Authors. New Phytologist © 2015 New Phytologist Trust.

An inexact chance-constrained programming model for water quality management in Binhai New Area of Tianjin, China.

PubMed

Xie, Y L; Li, Y P; Huang, G H; Li, Y F; Chen, L R

2011-04-15

In this study, an inexact-chance-constrained water quality management (ICC-WQM) model is developed for planning regional environmental management under uncertainty. This method is based on an integration of interval linear programming (ILP) and chance-constrained programming (CCP) techniques. ICC-WQM allows uncertainties presented as both probability distributions and interval values to be incorporated within a general optimization framework. Complexities in environmental management systems can be systematically reflected, thus applicability of the modeling process can be highly enhanced. The developed method is applied to planning chemical-industry development in Binhai New Area of Tianjin, China. Interval solutions associated with different risk levels of constraint violation have been obtained. They can be used for generating decision alternatives and thus help decision makers identify desired policies under various system-reliability constraints of water environmental capacity of pollutant. Tradeoffs between system benefits and constraint-violation risks can also be tackled. They are helpful for supporting (a) decision of wastewater discharge and government investment, (b) formulation of local policies regarding water consumption, economic development and industry structure, and (c) analysis of interactions among economic benefits, system reliability and pollutant discharges. Copyright © 2011 Elsevier B.V. All rights reserved.

A constrained robust least squares approach for contaminant release history identification

NASA Astrophysics Data System (ADS)

Sun, Alexander Y.; Painter, Scott L.; Wittmeyer, Gordon W.

2006-04-01

Contaminant source identification is an important type of inverse problem in groundwater modeling and is subject to both data and model uncertainty. Model uncertainty was rarely considered in the previous studies. In this work, a robust framework for solving contaminant source recovery problems is introduced. The contaminant source identification problem is first cast into one of solving uncertain linear equations, where the response matrix is constructed using a superposition technique. The formulation presented here is general and is applicable to any porous media flow and transport solvers. The robust least squares (RLS) estimator, which originated in the field of robust identification, directly accounts for errors arising from model uncertainty and has been shown to significantly reduce the sensitivity of the optimal solution to perturbations in model and data. In this work, a new variant of RLS, the constrained robust least squares (CRLS), is formulated for solving uncertain linear equations. CRLS allows for additional constraints, such as nonnegativity, to be imposed. The performance of CRLS is demonstrated through one- and two-dimensional test problems. When the system is ill-conditioned and uncertain, it is found that CRLS gave much better performance than its classical counterpart, the nonnegative least squares. The source identification framework developed in this work thus constitutes a reliable tool for recovering source release histories in real applications.

A constrained regularization method for inverting data represented by linear algebraic or integral equations

NASA Astrophysics Data System (ADS)

Provencher, Stephen W.

1982-09-01

CONTIN is a portable Fortran IV package for inverting noisy linear operator equations. These problems occur in the analysis of data from a wide variety experiments. They are generally ill-posed problems, which means that errors in an unregularized inversion are unbounded. Instead, CONTIN seeks the optimal solution by incorporating parsimony and any statistical prior knowledge into the regularizor and absolute prior knowledge into equallity and inequality constraints. This can be greatly increase the resolution and accuracyh of the solution. CONTIN is very flexible, consisting of a core of about 50 subprograms plus 13 small "USER" subprograms, which the user can easily modify to specify special-purpose constraints, regularizors, operator equations, simulations, statistical weighting, etc. Specjial collections of USER subprograms are available for photon correlation spectroscopy, multicomponent spectra, and Fourier-Bessel, Fourier and Laplace transforms. Numerically stable algorithms are used throughout CONTIN. A fairly precise definition of information content in terms of degrees of freedom is given. The regularization parameter can be automatically chosen on the basis of an F-test and confidence region. The interpretation of the latter and of error estimates based on the covariance matrix of the constrained regularized solution are discussed. The strategies, methods and options in CONTIN are outlined. The program itself is described in the following paper.

Derivative-free generation and interpolation of convex Pareto optimal IMRT plans

NASA Astrophysics Data System (ADS)

Hoffmann, Aswin L.; Siem, Alex Y. D.; den Hertog, Dick; Kaanders, Johannes H. A. M.; Huizenga, Henk

2006-12-01

In inverse treatment planning for intensity-modulated radiation therapy (IMRT), beamlet intensity levels in fluence maps of high-energy photon beams are optimized. Treatment plan evaluation criteria are used as objective functions to steer the optimization process. Fluence map optimization can be considered a multi-objective optimization problem, for which a set of Pareto optimal solutions exists: the Pareto efficient frontier (PEF). In this paper, a constrained optimization method is pursued to iteratively estimate the PEF up to some predefined error. We use the property that the PEF is convex for a convex optimization problem to construct piecewise-linear upper and lower bounds to approximate the PEF from a small initial set of Pareto optimal plans. A derivative-free Sandwich algorithm is presented in which these bounds are used with three strategies to determine the location of the next Pareto optimal solution such that the uncertainty in the estimated PEF is maximally reduced. We show that an intelligent initial solution for a new Pareto optimal plan can be obtained by interpolation of fluence maps from neighbouring Pareto optimal plans. The method has been applied to a simplified clinical test case using two convex objective functions to map the trade-off between tumour dose heterogeneity and critical organ sparing. All three strategies produce representative estimates of the PEF. The new algorithm is particularly suitable for dynamic generation of Pareto optimal plans in interactive treatment planning.

Big Data Challenges of High-Dimensional Continuous-Time Mean-Variance Portfolio Selection and a Remedy.

PubMed

Chiu, Mei Choi; Pun, Chi Seng; Wong, Hoi Ying

2017-08-01

Investors interested in the global financial market must analyze financial securities internationally. Making an optimal global investment decision involves processing a huge amount of data for a high-dimensional portfolio. This article investigates the big data challenges of two mean-variance optimal portfolios: continuous-time precommitment and constant-rebalancing strategies. We show that both optimized portfolios implemented with the traditional sample estimates converge to the worst performing portfolio when the portfolio size becomes large. The crux of the problem is the estimation error accumulated from the huge dimension of stock data. We then propose a linear programming optimal (LPO) portfolio framework, which applies a constrained ℓ 1 minimization to the theoretical optimal control to mitigate the risk associated with the dimensionality issue. The resulting portfolio becomes a sparse portfolio that selects stocks with a data-driven procedure and hence offers a stable mean-variance portfolio in practice. When the number of observations becomes large, the LPO portfolio converges to the oracle optimal portfolio, which is free of estimation error, even though the number of stocks grows faster than the number of observations. Our numerical and empirical studies demonstrate the superiority of the proposed approach. © 2017 Society for Risk Analysis.

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.

Multidimensional density shaping by sigmoids.

PubMed

Roth, Z; Baram, Y

1996-01-01

An estimate of the probability density function of a random vector is obtained by maximizing the output entropy of a feedforward network of sigmoidal units with respect to the input weights. Classification problems can be solved by selecting the class associated with the maximal estimated density. Newton's optimization method, applied to the estimated density, yields a recursive estimator for a random variable or a random sequence. A constrained connectivity structure yields a linear estimator, which is particularly suitable for "real time" prediction. A Gaussian nonlinearity yields a closed-form solution for the network's parameters, which may also be used for initializing the optimization algorithm when other nonlinearities are employed. A triangular connectivity between the neurons and the input, which is naturally suggested by the statistical setting, reduces the number of parameters. Applications to classification and forecasting problems are demonstrated.

Fragment approach to constrained density functional theory calculations using Daubechies wavelets

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

Ratcliff, Laura E.; Genovese, Luigi; Mohr, Stephan

2015-06-21

In a recent paper, we presented a linear scaling Kohn-Sham density functional theory (DFT) code based on Daubechies wavelets, where a minimal set of localized support functions are optimized in situ and therefore adapted to the chemical properties of the molecular system. Thanks to the systematically controllable accuracy of the underlying basis set, this approach is able to provide an optimal contracted basis for a given system: accuracies for ground state energies and atomic forces are of the same quality as an uncontracted, cubic scaling approach. This basis set offers, by construction, a natural subset where the density matrix ofmore » the system can be projected. In this paper, we demonstrate the flexibility of this minimal basis formalism in providing a basis set that can be reused as-is, i.e., without reoptimization, for charge-constrained DFT calculations within a fragment approach. Support functions, represented in the underlying wavelet grid, of the template fragments are roto-translated with high numerical precision to the required positions and used as projectors for the charge weight function. We demonstrate the interest of this approach to express highly precise and efficient calculations for preparing diabatic states and for the computational setup of systems in complex environments.« less

Optimization of natural frequencies of a slender beam shaped in a linear combination of its mode shapes

NASA Astrophysics Data System (ADS)

Silva, Guilherme Augusto Lopes da; Nicoletti, Rodrigo

2017-06-01

This work focuses on the placement of natural frequencies of beams to desired frequency regions. More specifically, we investigate the effects of combining mode shapes to shape a beam to change its natural frequencies, both numerically and experimentally. First, we present a parametric analysis of a shaped beam and we analyze the resultant effects for different boundary conditions and mode shapes. Second, we present an optimization procedure to find the optimum shape of the beam for desired natural frequencies. In this case, we adopt the Nelder-Mead simplex search method, which allows a broad search of the optimum shape in the solution domain. Finally, the obtained results are verified experimentally for a clamped-clamped beam in three different optimization runs. Results show that the method is effective in placing natural frequencies at desired values (experimental results lie within a 10% error to the expected theoretical ones). However, the beam must be axially constrained to have the natural frequencies changed.

A Piecewise Deterministic Markov Toy Model for Traffic/Maintenance and Associated Hamilton–Jacobi Integrodifferential Systems on Networks

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

Goreac, Dan, E-mail: Dan.Goreac@u-pem.fr; Kobylanski, Magdalena, E-mail: Magdalena.Kobylanski@u-pem.fr; Martinez, Miguel, E-mail: Miguel.Martinez@u-pem.fr

2016-10-15

We study optimal control problems in infinite horizon whxen the dynamics belong to a specific class of piecewise deterministic Markov processes constrained to star-shaped networks (corresponding to a toy traffic model). We adapt the results in Soner (SIAM J Control Optim 24(6):1110–1122, 1986) to prove the regularity of the value function and the dynamic programming principle. Extending the networks and Krylov’s “shaking the coefficients” method, we prove that the value function can be seen as the solution to a linearized optimization problem set on a convenient set of probability measures. The approach relies entirely on viscosity arguments. As a by-product,more » the dual formulation guarantees that the value function is the pointwise supremum over regular subsolutions of the associated Hamilton–Jacobi integrodifferential system. This ensures that the value function satisfies Perron’s preconization for the (unique) candidate to viscosity solution.« less

Contact-force distribution optimization and control for quadruped robots using both gradient and adaptive neural networks.

PubMed

Li, Zhijun; Ge, Shuzhi Sam; Liu, Sibang

2014-08-01

This paper investigates optimal feet forces' distribution and control of quadruped robots under external disturbance forces. First, we formulate a constrained dynamics of quadruped robots and derive a reduced-order dynamical model of motion/force. Consider an external wrench on quadruped robots; the distribution of required forces and moments on the supporting legs of a quadruped robot is handled as a tip-point force distribution and used to equilibrate the external wrench. Then, a gradient neural network is adopted to deal with the optimized objective function formulated as to minimize this quadratic objective function subjected to linear equality and inequality constraints. For the obtained optimized tip-point force and the motion of legs, we propose the hybrid motion/force control based on an adaptive neural network to compensate for the perturbations in the environment and approximate feedforward force and impedance of the leg joints. The proposed control can confront the uncertainties including approximation error and external perturbation. The verification of the proposed control is conducted using a simulation.

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.

Intervention in gene regulatory networks with maximal phenotype alteration.

PubMed

Yousefi, Mohammadmahdi R; Dougherty, Edward R

2013-07-15

A basic issue for translational genomics is to model gene interaction via gene regulatory networks (GRNs) and thereby provide an informatics environment to study the effects of intervention (say, via drugs) and to derive effective intervention strategies. Taking the view that the phenotype is characterized by the long-run behavior (steady-state distribution) of the network, we desire interventions to optimally move the probability mass from undesirable to desirable states Heretofore, two external control approaches have been taken to shift the steady-state mass of a GRN: (i) use a user-defined cost function for which desirable shift of the steady-state mass is a by-product and (ii) use heuristics to design a greedy algorithm. Neither approach provides an optimal control policy relative to long-run behavior. We use a linear programming approach to optimally shift the steady-state mass from undesirable to desirable states, i.e. optimization is directly based on the amount of shift and therefore must outperform previously proposed methods. Moreover, the same basic linear programming structure is used for both unconstrained and constrained optimization, where in the latter case, constraints on the optimization limit the amount of mass that may be shifted to 'ambiguous' states, these being states that are not directly undesirable relative to the pathology of interest but which bear some perceived risk. We apply the method to probabilistic Boolean networks, but the theory applies to any Markovian GRN. Supplementary materials, including the simulation results, MATLAB source code and description of suboptimal methods are available at http://gsp.tamu.edu/Publications/supplementary/yousefi13b. edward@ece.tamu.edu Supplementary data are available at Bioinformatics online.

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.

Constrained State Estimation for Individual Localization in Wireless Body Sensor Networks

PubMed Central

Feng, Xiaoxue; Snoussi, Hichem; Liang, Yan; Jiao, Lianmeng

2014-01-01

Wireless body sensor networks based on ultra-wideband radio have recently received much research attention due to its wide applications in health-care, security, sports and entertainment. Accurate localization is a fundamental problem to realize the development of effective location-aware applications above. In this paper the problem of constrained state estimation for individual localization in wireless body sensor networks is addressed. Priori knowledge about geometry among the on-body nodes as additional constraint is incorporated into the traditional filtering system. The analytical expression of state estimation with linear constraint to exploit the additional information is derived. Furthermore, for nonlinear constraint, first-order and second-order linearizations via Taylor series expansion are proposed to transform the nonlinear constraint to the linear case. Examples between the first-order and second-order nonlinear constrained filters based on interacting multiple model extended kalman filter (IMM-EKF) show that the second-order solution for higher order nonlinearity as present in this paper outperforms the first-order solution, and constrained IMM-EKF obtains superior estimation than IMM-EKF without constraint. Another brownian motion individual localization example also illustrates the effectiveness of constrained nonlinear iterative least square (NILS), which gets better filtering performance than NILS without constraint. PMID:25390408

Phase retrieval in generalized optical interferometry systems.

PubMed

Farriss, Wesley E; Fienup, James R; Malhotra, Tanya; Vamivakas, A Nick

2018-02-05

Modal analysis of an optical field via generalized interferometry (GI) is a novel technique that treats said field as a linear superposition of transverse modes and recovers the amplitudes of modal weighting coefficients. We use phase retrieval by nonlinear optimization to recover the phase of these modal weighting coefficients. Information diversity increases the robustness of the algorithm by better constraining the solution. Additionally, multiple sets of random starting phase values assist the algorithm in overcoming local minima. The algorithm was able to recover nearly all coefficient phases for simulated fields consisting of up to 21 superpositioned Hermite Gaussian modes from simulated data and proved to be resilient to shot noise.

CAD of control systems: Application of nonlinear programming to a linear quadratic formulation

NASA Technical Reports Server (NTRS)

Fleming, P.

1983-01-01

The familiar suboptimal regulator design approach is recast as a constrained optimization problem and incorporated in a Computer Aided Design (CAD) package where both design objective and constraints are quadratic cost functions. This formulation permits the separate consideration of, for example, model following errors, sensitivity measures and control energy as objectives to be minimized or limits to be observed. Efficient techniques for computing the interrelated cost functions and their gradients are utilized in conjunction with a nonlinear programming algorithm. The effectiveness of the approach and the degree of insight into the problem which it affords is illustrated in a helicopter regulation design example.

Multi-objective trajectory optimization for the space exploration vehicle

NASA Astrophysics Data System (ADS)

Qin, Xiaoli; Xiao, Zhen

2016-07-01

The research determines temperature-constrained optimal trajectory for the space exploration vehicle by developing an optimal control formulation and solving it using a variable order quadrature collocation method with a Non-linear Programming(NLP) solver. The vehicle is assumed to be the space reconnaissance aircraft that has specified takeoff/landing locations, specified no-fly zones, and specified targets for sensor data collections. A three degree of freedom aircraft model is adapted from previous work and includes flight dynamics, and thermal constraints.Vehicle control is accomplished by controlling angle of attack, roll angle, and propellant mass flow rate. This model is incorporated into an optimal control formulation that includes constraints on both the vehicle and mission parameters, such as avoidance of no-fly zones and exploration of space targets. In addition, the vehicle models include the environmental models(gravity and atmosphere). How these models are appropriately employed is key to gaining confidence in the results and conclusions of the research. Optimal trajectories are developed using several performance costs in the optimal control formation,minimum time,minimum time with control penalties,and maximum distance.The resulting analysis demonstrates that optimal trajectories that meet specified mission parameters and constraints can be quickly determined and used for large-scale space exloration.

Case studies on optimization problems in MATLAB and COMSOL multiphysics by means of the livelink

NASA Astrophysics Data System (ADS)

Ozana, Stepan; Pies, Martin; Docekal, Tomas

2016-06-01

LiveLink for COMSOL is a tool that integrates COMSOL Multiphysics with MATLAB to extend one's modeling with scripting programming in the MATLAB environment. It allows user to utilize the full power of MATLAB and its toolboxes in preprocessing, model manipulation, and post processing. At first, the head script launches COMSOL with MATLAB and defines initial value of all parameters, refers to the objective function J described in the objective function and creates and runs the defined optimization task. Once the task is launches, the COMSOL model is being called in the iteration loop (from MATLAB environment by use of API interface), changing defined optimization parameters so that the objective function is minimized, using fmincon function to find a local or global minimum of constrained linear or nonlinear multivariable function. Once the minimum is found, it returns exit flag, terminates optimization and returns the optimized values of the parameters. The cooperation with MATLAB via LiveLink enhances a powerful computational environment with complex multiphysics simulations. The paper will introduce using of the LiveLink for COMSOL for chosen case studies in the field of technical cybernetics and bioengineering.

A method for fitting regression splines with varying polynomial order in the linear mixed model.

PubMed

Edwards, Lloyd J; Stewart, Paul W; MacDougall, James E; Helms, Ronald W

2006-02-15

The linear mixed model has become a widely used tool for longitudinal analysis of continuous variables. The use of regression splines in these models offers the analyst additional flexibility in the formulation of descriptive analyses, exploratory analyses and hypothesis-driven confirmatory analyses. We propose a method for fitting piecewise polynomial regression splines with varying polynomial order in the fixed effects and/or random effects of the linear mixed model. The polynomial segments are explicitly constrained by side conditions for continuity and some smoothness at the points where they join. By using a reparameterization of this explicitly constrained linear mixed model, an implicitly constrained linear mixed model is constructed that simplifies implementation of fixed-knot regression splines. The proposed approach is relatively simple, handles splines in one variable or multiple variables, and can be easily programmed using existing commercial software such as SAS or S-plus. The method is illustrated using two examples: an analysis of longitudinal viral load data from a study of subjects with acute HIV-1 infection and an analysis of 24-hour ambulatory blood pressure profiles.

Linear and Logarithmic Speed-Accuracy Trade-Offs in Reciprocal Aiming Result from Task-Specific Parameterization of an Invariant Underlying Dynamics

ERIC Educational Resources Information Center

Bongers, Raoul M.; Fernandez, Laure; Bootsma, Reinoud J.

2009-01-01

The authors examined the origins of linear and logarithmic speed-accuracy trade-offs from a dynamic systems perspective on motor control. In each experiment, participants performed 2 reciprocal aiming tasks: (a) a velocity-constrained task in which movement time was imposed and accuracy had to be maximized, and (b) a distance-constrained task in…

Manifold Learning by Preserving Distance Orders.

PubMed

Ataer-Cansizoglu, Esra; Akcakaya, Murat; Orhan, Umut; Erdogmus, Deniz

2014-03-01

Nonlinear dimensionality reduction is essential for the analysis and the interpretation of high dimensional data sets. In this manuscript, we propose a distance order preserving manifold learning algorithm that extends the basic mean-squared error cost function used mainly in multidimensional scaling (MDS)-based methods. We develop a constrained optimization problem by assuming explicit constraints on the order of distances in the low-dimensional space. In this optimization problem, as a generalization of MDS, instead of forcing a linear relationship between the distances in the high-dimensional original and low-dimensional projection space, we learn a non-decreasing relation approximated by radial basis functions. We compare the proposed method with existing manifold learning algorithms using synthetic datasets based on the commonly used residual variance and proposed percentage of violated distance orders metrics. We also perform experiments on a retinal image dataset used in Retinopathy of Prematurity (ROP) diagnosis.

Analysis of Formation Flying in Eccentric Orbits Using Linearized Equations of Relative Motion

NASA Technical Reports Server (NTRS)

Lane, Christopher; Axelrad, Penina

2004-01-01

Geometrical methods for formation flying design based on the analytical solution to Hill's equations have been previously developed and used to specify desired relative motions in near circular orbits. By generating relationships between the vehicles that are intuitive, these approaches offer valuable insight into the relative motion and allow for the rapid design of satellite configurations to achieve mission specific requirements, such as vehicle separation at perigee or apogee, minimum separation, or a specific geometrical shape. Furthermore, the results obtained using geometrical approaches can be used to better constrain numerical optimization methods; allowing those methods to converge to optimal satellite configurations faster. This paper presents a set of geometrical relationships for formations in eccentric orbits, where Hill.s equations are not valid, and shows how these relationships can be used to investigate formation designs and how they evolve with time.

A zonal computational procedure adapted to the optimization of two-dimensional thrust augmentor inlets

NASA Technical Reports Server (NTRS)

Lund, T. S.; Tavella, D. A.; Roberts, L.

1985-01-01

A viscous-inviscid interaction methodology based on a zonal description of the flowfield is developed as a mean of predicting the performance of two-dimensional thrust augmenting ejectors. An inviscid zone comprising the irrotational flow about the device is patched together with a viscous zone containing the turbulent mixing flow. The inviscid region is computed by a higher order panel method, while an integral method is used for the description of the viscous part. A non-linear, constrained optimization study is undertaken for the design of the inlet region. In this study, the viscous-inviscid analysis is complemented with a boundary layer calculation to account for flow separation from the walls of the inlet region. The thrust-based Reynolds number as well as the free stream velocity are shown to be important parameters in the design of a thrust augmentor inlet.

Matching CT and ultrasound data of the liver by landmark constrained image registration

NASA Astrophysics Data System (ADS)

Olesch, Janine; Papenberg, Nils; Lange, Thomas; Conrad, Matthias; Fischer, Bernd

2009-02-01

In navigated liver surgery the key challenge is the registration of pre-operative planing and intra-operative navigation data. Due to the patients individual anatomy the planning is based on segmented, pre-operative CT scans whereas ultrasound captures the actual intra-operative situation. In this paper we derive a novel method based on variational image registration methods and additional given anatomic landmarks. For the first time we embed the landmark information as inequality hard constraints and thereby allowing for inaccurately placed landmarks. The yielding optimization problem allows to ensure the accuracy of the landmark fit by simultaneous intensity based image registration. Following the discretize-then-optimize approach the overall problem is solved by a generalized Gauss-Newton-method. The upcoming linear system is attacked by the MinRes solver. We demonstrate the applicability of the new approach for clinical data which lead to convincing results.

A dynamic measure of controllability and observability for the placement of actuators and sensors on large space structures

NASA Technical Reports Server (NTRS)

Vandervelde, W. E.; Carignan, C. R.

1982-01-01

The degree of controllability of a large space structure is found by a four step procedure: (1) finding the minimum control energy for driving the system from a given initial state to the origin in the prescribed time; (2) finding the region of initial state which can be driven to the origin with constrained control energy and time using optimal control strategy; (3) scaling the axes so that a unit displacement in every direction is equally important to control; and (4) finding the linear measurement of the weighted "volume" of the ellipsoid in the equicontrol space. For observability, the error covariance must be reduced toward zero using measurements optimally, and the criterion must be standardized by the magnitude of tolerable errors. The results obtained using these methods are applied to the vibration modes of a free-free beam.

Design and architecture of the Mars relay network planning and analysis framework

NASA Technical Reports Server (NTRS)

Cheung, K. M.; Lee, C. H.

2002-01-01

In this paper we describe the design and architecture of the Mars Network planning and analysis framework that supports generation and validation of efficient planning and scheduling strategy. The goals are to minimize the transmitting time, minimize the delaying time, and/or maximize the network throughputs. The proposed framework would require (1) a client-server architecture to support interactive, batch, WEB, and distributed analysis and planning applications for the relay network analysis scheme, (2) a high-fidelity modeling and simulation environment that expresses link capabilities between spacecraft to spacecraft and spacecraft to Earth stations as time-varying resources, and spacecraft activities, link priority, Solar System dynamic events, the laws of orbital mechanics, and other limiting factors as spacecraft power and thermal constraints, (3) an optimization methodology that casts the resource and constraint models into a standard linear and nonlinear constrained optimization problem that lends itself to commercial off-the-shelf (COTS)planning and scheduling algorithms.

Wind Farm Turbine Type and Placement Optimization

NASA Astrophysics Data System (ADS)

Graf, Peter; Dykes, Katherine; Scott, George; Fields, Jason; Lunacek, Monte; Quick, Julian; Rethore, Pierre-Elouan

2016-09-01

The layout of turbines in a wind farm is already a challenging nonlinear, nonconvex, nonlinearly constrained continuous global optimization problem. Here we begin to address the next generation of wind farm optimization problems by adding the complexity that there is more than one turbine type to choose from. The optimization becomes a nonlinear constrained mixed integer problem, which is a very difficult class of problems to solve. This document briefly summarizes the algorithm and code we have developed, the code validation steps we have performed, and the initial results for multi-turbine type and placement optimization (TTP_OPT) we have run.

Wind farm turbine type and placement optimization

DOE PAGES

Graf, Peter; Dykes, Katherine; Scott, George; ...

2016-10-03

The layout of turbines in a wind farm is already a challenging nonlinear, nonconvex, nonlinearly constrained continuous global optimization problem. Here we begin to address the next generation of wind farm optimization problems by adding the complexity that there is more than one turbine type to choose from. The optimization becomes a nonlinear constrained mixed integer problem, which is a very difficult class of problems to solve. Furthermore, this document briefly summarizes the algorithm and code we have developed, the code validation steps we have performed, and the initial results for multi-turbine type and placement optimization (TTP_OPT) we have run.

Use of constrained optimization in the conceptual design of a medium-range subsonic transport

NASA Technical Reports Server (NTRS)

Sliwa, S. M.

1980-01-01

Constrained parameter optimization was used to perform the optimal conceptual design of a medium range transport configuration. The impact of choosing a given performance index was studied, and the required income for a 15 percent return on investment was proposed as a figure of merit. A number of design constants and constraint functions were systematically varied to document the sensitivities of the optimal design to a variety of economic and technological assumptions. A comparison was made for each of the parameter variations between the baseline configuration and the optimally redesigned configuration.

Tomographic inversion techniques incorporating physical constraints for line integrated spectroscopy in stellarators and tokamaks

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

Pablant, N. A.; Bell, R. E.; Bitter, M.

2014-11-15

Accurate tomographic inversion is important for diagnostic systems on stellarators and tokamaks which rely on measurements of line integrated emission spectra. A tomographic inversion technique based on spline optimization with enforcement of constraints is described that can produce unique and physically relevant inversions even in situations with noisy or incomplete input data. This inversion technique is routinely used in the analysis of data from the x-ray imaging crystal spectrometer (XICS) installed at the Large Helical Device. The XICS diagnostic records a 1D image of line integrated emission spectra from impurities in the plasma. Through the use of Doppler spectroscopy andmore » tomographic inversion, XICS can provide profile measurements of the local emissivity, temperature, and plasma flow. Tomographic inversion requires the assumption that these measured quantities are flux surface functions, and that a known plasma equilibrium reconstruction is available. In the case of low signal levels or partial spatial coverage of the plasma cross-section, standard inversion techniques utilizing matrix inversion and linear-regularization often cannot produce unique and physically relevant solutions. The addition of physical constraints, such as parameter ranges, derivative directions, and boundary conditions, allow for unique solutions to be reliably found. The constrained inversion technique described here utilizes a modified Levenberg-Marquardt optimization scheme, which introduces a condition avoidance mechanism by selective reduction of search directions. The constrained inversion technique also allows for the addition of more complicated parameter dependencies, for example, geometrical dependence of the emissivity due to asymmetries in the plasma density arising from fast rotation. The accuracy of this constrained inversion technique is discussed, with an emphasis on its applicability to systems with limited plasma coverage.« less

Constrained binary classification using ensemble learning: an application to cost-efficient targeted PrEP strategies.

PubMed

Zheng, Wenjing; Balzer, Laura; van der Laan, Mark; Petersen, Maya

2018-01-30

Binary classification problems are ubiquitous in health and social sciences. In many cases, one wishes to balance two competing optimality considerations for a binary classifier. For instance, in resource-limited settings, an human immunodeficiency virus prevention program based on offering pre-exposure prophylaxis (PrEP) to select high-risk individuals must balance the sensitivity of the binary classifier in detecting future seroconverters (and hence offering them PrEP regimens) with the total number of PrEP regimens that is financially and logistically feasible for the program. In this article, we consider a general class of constrained binary classification problems wherein the objective function and the constraint are both monotonic with respect to a threshold. These include the minimization of the rate of positive predictions subject to a minimum sensitivity, the maximization of sensitivity subject to a maximum rate of positive predictions, and the Neyman-Pearson paradigm, which minimizes the type II error subject to an upper bound on the type I error. We propose an ensemble approach to these binary classification problems based on the Super Learner methodology. This approach linearly combines a user-supplied library of scoring algorithms, with combination weights and a discriminating threshold chosen to minimize the constrained optimality criterion. We then illustrate the application of the proposed classifier to develop an individualized PrEP targeting strategy in a resource-limited setting, with the goal of minimizing the number of PrEP offerings while achieving a minimum required sensitivity. This proof of concept data analysis uses baseline data from the ongoing Sustainable East Africa Research in Community Health study. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Tomographic inversion techniques incorporating physical constraints for line integrated spectroscopy in stellarators and tokamaksa)

DOE PAGES

Pablant, N. A.; Bell, R. E.; Bitter, M.; ...

2014-08-08

Accurate tomographic inversion is important for diagnostic systems on stellarators and tokamaks which rely on measurements of line integrated emission spectra. A tomographic inversion technique based on spline optimization with enforcement of constraints is described that can produce unique and physically relevant inversions even in situations with noisy or incomplete input data. This inversion technique is routinely used in the analysis of data from the x-ray imaging crystal spectrometer (XICS) installed at LHD. The XICS diagnostic records a 1D image of line integrated emission spectra from impurities in the plasma. Through the use of Doppler spectroscopy and tomographic inversion, XICSmore » can provide pro file measurements of the local emissivity, temperature and plasma flow. Tomographic inversion requires the assumption that these measured quantities are flux surface functions, and that a known plasma equilibrium reconstruction is available. In the case of low signal levels or partial spatial coverage of the plasma cross-section, standard inversion techniques utilizing matrix inversion and linear-regularization often cannot produce unique and physically relevant solutions. The addition of physical constraints, such as parameter ranges, derivative directions, and boundary conditions, allow for unique solutions to be reliably found. The constrained inversion technique described here utilizes a modifi ed Levenberg-Marquardt optimization scheme, which introduces a condition avoidance mechanism by selective reduction of search directions. The constrained inversion technique also allows for the addition of more complicated parameter dependencies, for example geometrical dependence of the emissivity due to asymmetries in the plasma density arising from fast rotation. The accuracy of this constrained inversion technique is discussed, with an emphasis on its applicability to systems with limited plasma coverage.« less

Maximum Constrained Directivity of Oversteered End-Fire Sensor Arrays

PubMed Central

Trucco, Andrea; Traverso, Federico; Crocco, Marco

2015-01-01

For linear arrays with fixed steering and an inter-element spacing smaller than one half of the wavelength, end-fire steering of a data-independent beamformer offers better directivity than broadside steering. The introduction of a lower bound on the white noise gain ensures the necessary robustness against random array errors and sensor mismatches. However, the optimum broadside performance can be obtained using a simple processing architecture, whereas the optimum end-fire performance requires a more complicated system (because complex weight coefficients are needed). In this paper, we reconsider the oversteering technique as a possible way to simplify the processing architecture of equally spaced end-fire arrays. We propose a method for computing the amount of oversteering and the related real-valued weight vector that allows the constrained directivity to be maximized for a given inter-element spacing. Moreover, we verify that the maximized oversteering performance is very close to the optimum end-fire performance. We conclude that optimized oversteering is a viable method for designing end-fire arrays that have better constrained directivity than broadside arrays but with a similar implementation complexity. A numerical simulation is used to perform a statistical analysis, which confirms that the maximized oversteering performance is robust against sensor mismatches. PMID:26066987

Time and frequency constrained sonar signal design for optimal detection of elastic objects.

PubMed

Hamschin, Brandon; Loughlin, Patrick J

2013-04-01

In this paper, the task of model-based transmit signal design for optimizing detection is considered. Building on past work that designs the spectral magnitude for optimizing detection, two methods for synthesizing minimum duration signals with this spectral magnitude are developed. The methods are applied to the design of signals that are optimal for detecting elastic objects in the presence of additive noise and self-noise. Elastic objects are modeled as linear time-invariant systems with known impulse responses, while additive noise (e.g., ocean noise or receiver noise) and acoustic self-noise (e.g., reverberation or clutter) are modeled as stationary Gaussian random processes with known power spectral densities. The first approach finds the waveform that preserves the optimal spectral magnitude while achieving the minimum temporal duration. The second approach yields a finite-length time-domain sequence by maximizing temporal energy concentration, subject to the constraint that the spectral magnitude is close (in a least-squares sense) to the optimal spectral magnitude. The two approaches are then connected analytically, showing the former is a limiting case of the latter. Simulation examples that illustrate the theory are accompanied by discussions that address practical applicability and how one might satisfy the need for target and environmental models in the real-world.

Unifying Rules for Aquatic Locomotion

NASA Astrophysics Data System (ADS)

Saadat, Mehdi; Domel, August; di Santo, Valentina; Lauder, George; Haj-Hariri, Hossein

2016-11-01

Strouhal number, St (=fA/U) , a scaling parameter that relates speed, U, to the tail-beat frequency, f, and tail-beat amplitude, A, has been used many times to describe animal locomotion. It has been observed that swimming animals cruise at 0.2 <=St <=0.4. Using simple dimensional and scaling analyses supported by new experimental evidence of a self-propelled fish-like swimmer, we show that when cruising at minimum hydrodynamic input power, St is predetermined, and is only a function of the shape, i.e. drag coefficient and area. The narrow range for St, 0.2-0.4, has been previously associated with optimal propulsive efficiency. However, St alone is insufficient for deciding optimal motion. We show that hydrodynamic input power (energy usage to propel over a unit distance) in fish locomotion is minimized at all cruising speeds when A* (= A/L), a scaling parameter that relates tail-beat amplitude, A, to the length of the swimmer, L, is constrained to a narrow range of 0.15-0.25. Our analysis proposes a constraint on A*, in addition to the previously found constraint on St, to fully describe the optimal swimming gait for fast swimmers. A survey of kinematics for dolphin, as well as new data for trout, show that the range of St and A* for fast swimmers indeed are constrained to 0.2-0.4 and 0.15-0.25, respectively. Our findings provide physical explanation as to why fast aquatic swimmers cruise with relatively constant tail-beat amplitude at approximately 20 percent of body length, while their swimming speed is linearly correlated with their tail-beat frequency.

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

Graf, Peter; Dykes, Katherine; Scott, George

The layout of turbines in a wind farm is already a challenging nonlinear, nonconvex, nonlinearly constrained continuous global optimization problem. Here we begin to address the next generation of wind farm optimization problems by adding the complexity that there is more than one turbine type to choose from. The optimization becomes a nonlinear constrained mixed integer problem, which is a very difficult class of problems to solve. Furthermore, this document briefly summarizes the algorithm and code we have developed, the code validation steps we have performed, and the initial results for multi-turbine type and placement optimization (TTP_OPT) we have run.

Time Scale Optimization and the Hunt for Astronomical Cycles in Deep Time Strata

NASA Astrophysics Data System (ADS)

Meyers, Stephen R.

2016-04-01

A valuable attribute of astrochronology is the direct link between chronometer and climate change, providing a remarkable opportunity to constrain the evolution of the surficial Earth System. Consequently, the hunt for astronomical cycles in strata has spurred the development of a rich conceptual framework for climatic/oceanographic change, and has allowed exploration of the geologic record with unprecedented temporal resolution. Accompanying these successes, however, has been a persistent skepticism about appropriate astrochronologic testing and circular reasoning: how does one reliably test for astronomical cycles in stratigraphic data, especially when time is poorly constrained? From this perspective, it would seem that the merits and promise of astrochronology (e.g., a geologic time scale measured in ≤400 kyr increments) also serves as its Achilles heel, if the confirmation of such short rhythms defies rigorous statistical testing. To address these statistical challenges in astrochronologic testing, a new approach has been developed that (1) explicitly evaluates time scale uncertainty, (2) is resilient to common problems associated with spectrum confidence level assessment and 'multiple testing', and (3) achieves high statistical power under a wide range of conditions (it can identify astronomical cycles when present in data). Designated TimeOpt (for "time scale optimization"; Meyers 2015), the method employs a probabilistic linear regression model framework to investigate amplitude modulation and frequency ratios (bundling) in stratigraphic data, while simultaneously determining the optimal time scale. This presentation will review the TimeOpt method, and demonstrate how the flexible statistical framework can be further extended to evaluate (and optimize upon) complex sedimentation rate models, enhancing the statistical power of the approach, and addressing the challenge of unsteady sedimentation. Meyers, S. R. (2015), The evaluation of eccentricity-related amplitude modulation and bundling in paleoclimate data: An inverse approach for astrochronologic testing and time scale optimization, Paleoceanography, 30, doi:10.1002/ 2015PA002850.

Learning Multirobot Hose Transportation and Deployment by Distributed Round-Robin Q-Learning.

PubMed

Fernandez-Gauna, Borja; Etxeberria-Agiriano, Ismael; Graña, Manuel

2015-01-01

Multi-Agent Reinforcement Learning (MARL) algorithms face two main difficulties: the curse of dimensionality, and environment non-stationarity due to the independent learning processes carried out by the agents concurrently. In this paper we formalize and prove the convergence of a Distributed Round Robin Q-learning (D-RR-QL) algorithm for cooperative systems. The computational complexity of this algorithm increases linearly with the number of agents. Moreover, it eliminates environment non sta tionarity by carrying a round-robin scheduling of the action selection and execution. That this learning scheme allows the implementation of Modular State-Action Vetoes (MSAV) in cooperative multi-agent systems, which speeds up learning convergence in over-constrained systems by vetoing state-action pairs which lead to undesired termination states (UTS) in the relevant state-action subspace. Each agent's local state-action value function learning is an independent process, including the MSAV policies. Coordination of locally optimal policies to obtain the global optimal joint policy is achieved by a greedy selection procedure using message passing. We show that D-RR-QL improves over state-of-the-art approaches, such as Distributed Q-Learning, Team Q-Learning and Coordinated Reinforcement Learning in a paradigmatic Linked Multi-Component Robotic System (L-MCRS) control problem: the hose transportation task. L-MCRS are over-constrained systems with many UTS induced by the interaction of the passive linking element and the active mobile robots.

Optimal group size in a highly social mammal

PubMed Central

Markham, A. Catherine; Gesquiere, Laurence R.; Alberts, Susan C.; Altmann, Jeanne

2015-01-01

Group size is an important trait of social animals, affecting how individuals allocate time and use space, and influencing both an individual’s fitness and the collective, cooperative behaviors of the group as a whole. Here we tested predictions motivated by the ecological constraints model of group size, examining the effects of group size on ranging patterns and adult female glucocorticoid (stress hormone) concentrations in five social groups of wild baboons (Papio cynocephalus) over an 11-y period. Strikingly, we found evidence that intermediate-sized groups have energetically optimal space-use strategies; both large and small groups experience ranging disadvantages, in contrast to the commonly reported positive linear relationship between group size and home range area and daily travel distance, which depict a disadvantage only in large groups. Specifically, we observed a U-shaped relationship between group size and home range area, average daily distance traveled, evenness of space use within the home range, and glucocorticoid concentrations. We propose that a likely explanation for these U-shaped patterns is that large, socially dominant groups are constrained by within-group competition, whereas small, socially subordinate groups are constrained by between-group competition and predation pressures. Overall, our results provide testable hypotheses for evaluating group-size constraints in other group-living species, in which the costs of intra- and intergroup competition vary as a function of group size. PMID:26504236

Stress-Constrained Structural Topology Optimization with Design-Dependent Loads

NASA Astrophysics Data System (ADS)

Lee, Edmund

Topology optimization is commonly used to distribute a given amount of material to obtain the stiffest structure, with predefined fixed loads. The present work investigates the result of applying stress constraints to topology optimization, for problems with design-depending loading, such as self-weight and pressure. In order to apply pressure loading, a material boundary identification scheme is proposed, iteratively connecting points of equal density. In previous research, design-dependent loading problems have been limited to compliance minimization. The present study employs a more practical approach by minimizing mass subject to failure constraints, and uses a stress relaxation technique to avoid stress constraint singularities. The results show that these design dependent loading problems may converge to a local minimum when stress constraints are enforced. Comparisons between compliance minimization solutions and stress-constrained solutions are also given. The resulting topologies of these two solutions are usually vastly different, demonstrating the need for stress-constrained topology optimization.

CONORBIT: constrained optimization by radial basis function interpolation in trust regions

DOE PAGES

Regis, Rommel G.; Wild, Stefan M.

2016-09-26

Here, this paper presents CONORBIT (CONstrained Optimization by Radial Basis function Interpolation in Trust regions), a derivative-free algorithm for constrained black-box optimization where the objective and constraint functions are computationally expensive. CONORBIT employs a trust-region framework that uses interpolating radial basis function (RBF) models for the objective and constraint functions, and is an extension of the ORBIT algorithm. It uses a small margin for the RBF constraint models to facilitate the generation of feasible iterates, and extensive numerical tests confirm that such a margin is helpful in improving performance. CONORBIT is compared with other algorithms on 27 test problems, amore » chemical process optimization problem, and an automotive application. Numerical results show that CONORBIT performs better than COBYLA, a sequential penalty derivative-free method, an augmented Lagrangian method, a direct search method, and another RBF-based algorithm on the test problems and on the automotive application.« less

Learning With Mixed Hard/Soft Pointwise Constraints.

PubMed

Gnecco, Giorgio; Gori, Marco; Melacci, Stefano; Sanguineti, Marcello

2015-09-01

A learning paradigm is proposed and investigated, in which the classical framework of learning from examples is enhanced by the introduction of hard pointwise constraints, i.e., constraints imposed on a finite set of examples that cannot be violated. Such constraints arise, e.g., when requiring coherent decisions of classifiers acting on different views of the same pattern. The classical examples of supervised learning, which can be violated at the cost of some penalization (quantified by the choice of a suitable loss function) play the role of soft pointwise constraints. Constrained variational calculus is exploited to derive a representer theorem that provides a description of the functional structure of the optimal solution to the proposed learning paradigm. It is shown that such an optimal solution can be represented in terms of a set of support constraints, which generalize the concept of support vectors and open the doors to a novel learning paradigm, called support constraint machines. The general theory is applied to derive the representation of the optimal solution to the problem of learning from hard linear pointwise constraints combined with soft pointwise constraints induced by supervised examples. In some cases, closed-form optimal solutions are obtained.

Grid generation and adaptation via Monge-Kantorovich optimization in 2D and 3D

NASA Astrophysics Data System (ADS)

Delzanno, Gian Luca; Chacon, Luis; Finn, John M.

2008-11-01

In a recent paper [1], Monge-Kantorovich (MK) optimization was proposed as a method of grid generation/adaptation in two dimensions (2D). The method is based on the minimization of the L2 norm of grid point displacement, constrained to producing a given positive-definite cell volume distribution (equidistribution constraint). The procedure gives rise to the Monge-Amp'ere (MA) equation: a single, non-linear scalar equation with no free-parameters. The MA equation was solved in Ref. [1] with the Jacobian Free Newton-Krylov technique and several challenging test cases were presented in squared domains in 2D. Here, we extend the work of Ref. [1]. We first formulate the MK approach in physical domains with curved boundary elements and in 3D. We then show the results of applying it to these more general cases. We show that MK optimization produces optimal grids in which the constraint is satisfied numerically to truncation error. [1] G.L. Delzanno, L. Chac'on, J.M. Finn, Y. Chung, G. Lapenta, A new, robust equidistribution method for two-dimensional grid generation, submitted to Journal of Computational Physics (2008).

Advanced Energy Storage Management in Distribution Network

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

Liu, Guodong; Ceylan, Oguzhan; Xiao, Bailu

2016-01-01

With increasing penetration of distributed generation (DG) in the distribution networks (DN), the secure and optimal operation of DN has become an important concern. In this paper, an iterative mixed integer quadratic constrained quadratic programming model to optimize the operation of a three phase unbalanced distribution system with high penetration of Photovoltaic (PV) panels, DG and energy storage (ES) is developed. The proposed model minimizes not only the operating cost, including fuel cost and purchasing cost, but also voltage deviations and power loss. The optimization model is based on the linearized sensitivity coefficients between state variables (e.g., node voltages) andmore » control variables (e.g., real and reactive power injections of DG and ES). To avoid slow convergence when close to the optimum, a golden search method is introduced to control the step size and accelerate the convergence. The proposed algorithm is demonstrated on modified IEEE 13 nodes test feeders with multiple PV panels, DG and ES. Numerical simulation results validate the proposed algorithm. Various scenarios of system configuration are studied and some critical findings are concluded.« less

Analysis of explicit model predictive control for path-following control

PubMed Central

2018-01-01

In this paper, explicit Model Predictive Control(MPC) is employed for automated lane-keeping systems. MPC has been regarded as the key to handle such constrained systems. However, the massive computational complexity of MPC, which employs online optimization, has been a major drawback that limits the range of its target application to relatively small and/or slow problems. Explicit MPC can reduce this computational burden using a multi-parametric quadratic programming technique(mp-QP). The control objective is to derive an optimal front steering wheel angle at each sampling time so that autonomous vehicles travel along desired paths, including straight, circular, and clothoid parts, at high entry speeds. In terms of the design of the proposed controller, a method of choosing weighting matrices in an optimization problem and the range of horizons for path-following control are described through simulations. For the verification of the proposed controller, simulation results obtained using other control methods such as MPC, Linear-Quadratic Regulator(LQR), and driver model are employed, and CarSim, which reflects the features of a vehicle more realistically than MATLAB/Simulink, is used for reliable demonstration. PMID:29534080

Analysis of explicit model predictive control for path-following control.

PubMed

Lee, Junho; Chang, Hyuk-Jun

2018-01-01

In this paper, explicit Model Predictive Control(MPC) is employed for automated lane-keeping systems. MPC has been regarded as the key to handle such constrained systems. However, the massive computational complexity of MPC, which employs online optimization, has been a major drawback that limits the range of its target application to relatively small and/or slow problems. Explicit MPC can reduce this computational burden using a multi-parametric quadratic programming technique(mp-QP). The control objective is to derive an optimal front steering wheel angle at each sampling time so that autonomous vehicles travel along desired paths, including straight, circular, and clothoid parts, at high entry speeds. In terms of the design of the proposed controller, a method of choosing weighting matrices in an optimization problem and the range of horizons for path-following control are described through simulations. For the verification of the proposed controller, simulation results obtained using other control methods such as MPC, Linear-Quadratic Regulator(LQR), and driver model are employed, and CarSim, which reflects the features of a vehicle more realistically than MATLAB/Simulink, is used for reliable demonstration.

Constraining new physics models with isotope shift spectroscopy

NASA Astrophysics Data System (ADS)

Frugiuele, Claudia; Fuchs, Elina; Perez, Gilad; Schlaffer, Matthias

2017-07-01

Isotope shifts of transition frequencies in atoms constrain generic long- and intermediate-range interactions. We focus on new physics scenarios that can be most strongly constrained by King linearity violation such as models with B -L vector bosons, the Higgs portal, and chameleon models. With the anticipated precision, King linearity violation has the potential to set the strongest laboratory bounds on these models in some regions of parameter space. Furthermore, we show that this method can probe the couplings relevant for the protophobic interpretation of the recently reported Be anomaly. We extend the formalism to include an arbitrary number of transitions and isotope pairs and fit the new physics coupling to the currently available isotope shift measurements.

High resolution near on-axis digital holography using constrained optimization approach with faster convergence

NASA Astrophysics Data System (ADS)

Pandiyan, Vimal Prabhu; Khare, Kedar; John, Renu

2017-09-01

A constrained optimization approach with faster convergence is proposed to recover the complex object field from a near on-axis digital holography (DH). We subtract the DC from the hologram after recording the object beam and reference beam intensities separately. The DC-subtracted hologram is used to recover the complex object information using a constrained optimization approach with faster convergence. The recovered complex object field is back propagated to the image plane using the Fresnel back-propagation method. The results reported in this approach provide high-resolution images compared with the conventional Fourier filtering approach and is 25% faster than the previously reported constrained optimization approach due to the subtraction of two DC terms in the cost function. We report this approach in DH and digital holographic microscopy using the U.S. Air Force resolution target as the object to retrieve the high-resolution image without DC and twin image interference. We also demonstrate the high potential of this technique in transparent microelectrode patterned on indium tin oxide-coated glass, by reconstructing a high-resolution quantitative phase microscope image. We also demonstrate this technique by imaging yeast cells.

Optimal synchronization in space

NASA Astrophysics Data System (ADS)

Brede, Markus

2010-02-01

In this Rapid Communication we investigate spatially constrained networks that realize optimal synchronization properties. After arguing that spatial constraints can be imposed by limiting the amount of “wire” available to connect nodes distributed in space, we use numerical optimization methods to construct networks that realize different trade offs between optimal synchronization and spatial constraints. Over a large range of parameters such optimal networks are found to have a link length distribution characterized by power-law tails P(l)∝l-α , with exponents α increasing as the networks become more constrained in space. It is also shown that the optimal networks, which constitute a particular type of small world network, are characterized by the presence of nodes of distinctly larger than average degree around which long-distance links are centered.

Trajectory optimization and guidance law development for national aerospace plane applications

NASA Technical Reports Server (NTRS)

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

1988-01-01

The work completed to date is comprised of the following: a simple vehicle model representative of the aerospace plane concept in the hypersonic flight regime, fuel-optimal climb profiles for the unconstrained and dynamic pressure constrained cases generated using a reduced order dynamic model, an analytic switching condition for transition to rocket powered flight as orbital velocity is approached, simple feedback guidance laws for both the unconstrained and dynamic pressure constrained cases derived via singular perturbation theory and a nonlinear transformation technique, and numerical simulation results for ascent to orbit in the dynamic pressure constrained case.

A shifted hyperbolic augmented Lagrangian-based artificial fish two-swarm algorithm with guaranteed convergence for constrained global optimization

NASA Astrophysics Data System (ADS)

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

2016-12-01

This article presents a shifted hyperbolic penalty function and proposes an augmented Lagrangian-based algorithm for non-convex constrained global optimization problems. Convergence to an ?-global minimizer is proved. At each iteration k, the algorithm requires the ?-global minimization of a bound constrained optimization subproblem, where ?. The subproblems are solved by a stochastic population-based metaheuristic that relies on the artificial fish swarm paradigm and a two-swarm strategy. To enhance the speed of convergence, the algorithm invokes the Nelder-Mead local search with a dynamically defined probability. Numerical experiments with benchmark functions and engineering design problems are presented. The results show that the proposed shifted hyperbolic augmented Lagrangian compares favorably with other deterministic and stochastic penalty-based methods.

On meeting capital requirements with a chance-constrained optimization model.

PubMed

Atta Mills, Ebenezer Fiifi Emire; Yu, Bo; Gu, Lanlan

2016-01-01

This paper deals with a capital to risk asset ratio chance-constrained optimization model in the presence of loans, treasury bill, fixed assets and non-interest earning assets. To model the dynamics of loans, we introduce a modified CreditMetrics approach. This leads to development of a deterministic convex counterpart of capital to risk asset ratio chance constraint. We pursue the scope of analyzing our model under the worst-case scenario i.e. loan default. The theoretical model is analyzed by applying numerical procedures, in order to administer valuable insights from a financial outlook. Our results suggest that, our capital to risk asset ratio chance-constrained optimization model guarantees banks of meeting capital requirements of Basel III with a likelihood of 95 % irrespective of changes in future market value of assets.

Robust Constrained Optimization Approach to Control Design for International Space Station Centrifuge Rotor Auto Balancing Control System

NASA Technical Reports Server (NTRS)

Postma, Barry Dirk

2005-01-01

This thesis discusses application of a robust constrained optimization approach to control design to develop an Auto Balancing Controller (ABC) for a centrifuge rotor to be implemented on the International Space Station. The design goal is to minimize a performance objective of the system, while guaranteeing stability and proper performance for a range of uncertain plants. The Performance objective is to minimize the translational response of the centrifuge rotor due to a fixed worst-case rotor imbalance. The robustness constraints are posed with respect to parametric uncertainty in the plant. The proposed approach to control design allows for both of these objectives to be handled within the framework of constrained optimization. The resulting controller achieves acceptable performance and robustness characteristics.

A robust, efficient equidistribution 2D grid generation method

NASA Astrophysics Data System (ADS)

Chacon, Luis; Delzanno, Gian Luca; Finn, John; Chung, Jeojin; Lapenta, Giovanni

2007-11-01

We present a new cell-area equidistribution method for two- dimensional grid adaptation [1]. The method is able to satisfy the equidistribution constraint to arbitrary precision while optimizing desired grid properties (such as isotropy and smoothness). The method is based on the minimization of the grid smoothness integral, constrained to producing a given positive-definite cell volume distribution. The procedure gives rise to a single, non-linear scalar equation with no free-parameters. We solve this equation numerically with the Newton-Krylov technique. The ellipticity property of the linearized scalar equation allows multigrid preconditioning techniques to be effectively used. We demonstrate a solution exists and is unique. Therefore, once the solution is found, the adapted grid cannot be folded due to the positivity of the constraint on the cell volumes. We present several challenging tests to show that our new method produces optimal grids in which the constraint is satisfied numerically to arbitrary precision. We also compare the new method to the deformation method [2] and show that our new method produces better quality grids. [1] G.L. Delzanno, L. Chac'on, J.M. Finn, Y. Chung, G. Lapenta, A new, robust equidistribution method for two-dimensional grid generation, in preparation. [2] G. Liao and D. Anderson, A new approach to grid generation, Appl. Anal. 44, 285--297 (1992).

Novel methods for Solving Economic Dispatch of Security-Constrained Unit Commitment Based on Linear Programming

NASA Astrophysics Data System (ADS)

Guo, Sangang

2017-09-01

There are two stages in solving security-constrained unit commitment problems (SCUC) within Lagrangian framework: one is to obtain feasible units’ states (UC), the other is power economic dispatch (ED) for each unit. The accurate solution of ED is more important for enhancing the efficiency of the solution to SCUC for the fixed feasible units’ statues. Two novel methods named after Convex Combinatorial Coefficient Method and Power Increment Method respectively based on linear programming problem for solving ED are proposed by the piecewise linear approximation to the nonlinear convex fuel cost functions. Numerical testing results show that the methods are effective and efficient.

Multi-Objective Trajectory Optimization of a Hypersonic Reconnaissance Vehicle with Temperature Constraints

NASA Astrophysics Data System (ADS)

Masternak, Tadeusz J.

This research determines temperature-constrained optimal trajectories for a scramjet-based hypersonic reconnaissance vehicle by developing an optimal control formulation and solving it using a variable order Gauss-Radau quadrature collocation method with a Non-Linear Programming (NLP) solver. The vehicle is assumed to be an air-breathing reconnaissance aircraft that has specified takeoff/landing locations, airborne refueling constraints, specified no-fly zones, and specified targets for sensor data collections. A three degree of freedom scramjet aircraft model is adapted from previous work and includes flight dynamics, aerodynamics, and thermal constraints. Vehicle control is accomplished by controlling angle of attack, roll angle, and propellant mass flow rate. This model is incorporated into an optimal control formulation that includes constraints on both the vehicle and mission parameters, such as avoidance of no-fly zones and coverage of high-value targets. To solve the optimal control formulation, a MATLAB-based package called General Pseudospectral Optimal Control Software (GPOPS-II) is used, which transcribes continuous time optimal control problems into an NLP problem. In addition, since a mission profile can have varying vehicle dynamics and en-route imposed constraints, the optimal control problem formulation can be broken up into several "phases" with differing dynamics and/or varying initial/final constraints. Optimal trajectories are developed using several different performance costs in the optimal control formulation: minimum time, minimum time with control penalties, and maximum range. The resulting analysis demonstrates that optimal trajectories that meet specified mission parameters and constraints can be quickly determined and used for larger-scale operational and campaign planning and execution.

Critical transition in the constrained traveling salesman problem.

PubMed

Andrecut, M; Ali, M K

2001-04-01

We investigate the finite size scaling of the mean optimal tour length as a function of density of obstacles in a constrained variant of the traveling salesman problem (TSP). The computational experience pointed out a critical transition (at rho(c) approximately 85%) in the dependence between the excess of the mean optimal tour length over the Held-Karp lower bound and the density of obstacles.

High-order Newton-penalty algorithms

NASA Astrophysics Data System (ADS)

Dussault, Jean-Pierre

2005-10-01

Recent efforts in differentiable non-linear programming have been focused on interior point methods, akin to penalty and barrier algorithms. In this paper, we address the classical equality constrained program solved using the simple quadratic loss penalty function/algorithm. The suggestion to use extrapolations to track the differentiable trajectory associated with penalized subproblems goes back to the classic monograph of Fiacco & McCormick. This idea was further developed by Gould who obtained a two-steps quadratically convergent algorithm using prediction steps and Newton correction. Dussault interpreted the prediction step as a combined extrapolation with respect to the penalty parameter and the residual of the first order optimality conditions. Extrapolation with respect to the residual coincides with a Newton step.We explore here higher-order extrapolations, thus higher-order Newton-like methods. We first consider high-order variants of the Newton-Raphson method applied to non-linear systems of equations. Next, we obtain improved asymptotic convergence results for the quadratic loss penalty algorithm by using high-order extrapolation steps.

Multivariate quadrature for representing cloud condensation nuclei activity of aerosol populations

DOE PAGES

Fierce, Laura; McGraw, Robert L.

2017-07-26

Here, sparse representations of atmospheric aerosols are needed for efficient regional- and global-scale chemical transport models. Here we introduce a new framework for representing aerosol distributions, based on the quadrature method of moments. Given a set of moment constraints, we show how linear programming, combined with an entropy-inspired cost function, can be used to construct optimized quadrature representations of aerosol distributions. The sparse representations derived from this approach accurately reproduce cloud condensation nuclei (CCN) activity for realistically complex distributions simulated by a particleresolved model. Additionally, the linear programming techniques described in this study can be used to bound key aerosolmore » properties, such as the number concentration of CCN. Unlike the commonly used sparse representations, such as modal and sectional schemes, the maximum-entropy approach described here is not constrained to pre-determined size bins or assumed distribution shapes. This study is a first step toward a particle-based aerosol scheme that will track multivariate aerosol distributions with sufficient computational efficiency for large-scale simulations.« less

Multivariate quadrature for representing cloud condensation nuclei activity of aerosol populations

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

Fierce, Laura; McGraw, Robert L.

Here, sparse representations of atmospheric aerosols are needed for efficient regional- and global-scale chemical transport models. Here we introduce a new framework for representing aerosol distributions, based on the quadrature method of moments. Given a set of moment constraints, we show how linear programming, combined with an entropy-inspired cost function, can be used to construct optimized quadrature representations of aerosol distributions. The sparse representations derived from this approach accurately reproduce cloud condensation nuclei (CCN) activity for realistically complex distributions simulated by a particleresolved model. Additionally, the linear programming techniques described in this study can be used to bound key aerosolmore » properties, such as the number concentration of CCN. Unlike the commonly used sparse representations, such as modal and sectional schemes, the maximum-entropy approach described here is not constrained to pre-determined size bins or assumed distribution shapes. This study is a first step toward a particle-based aerosol scheme that will track multivariate aerosol distributions with sufficient computational efficiency for large-scale simulations.« less

Tethered satellite system control using electromagnetic forces and reaction wheels

NASA Astrophysics Data System (ADS)

Alandi Hallaj, Mohammad Amin; Assadian, Nima

2015-12-01

In this paper a novel non-rotating space tethered configuration is introduced which its relative positions controlled using electromagnetic forces. The attitude dynamics is controlled by three reaction wheels in the body axes. The nonlinear coupled orbital dynamics of a dumbbell tethered satellite formation flight are derived through a constrained Lagrangian approach. These equations are presented in the leader satellite orbital frame. The tether is assumed to be mass-less and straight, and the J2 perturbation is included to the analysis. The forces and the moments of the electromagnetic coils are modeled based on the far-filed model of the magnetic dipoles. A guidance scheme for generating the desired positions as a function of time in Cartesian form is presented. The satellite tethered formation with variable length is controlled utilizing a linear controller. This approach is applied to a specified scenario and it is shown that the nonlinear guidance method and the linear controller can control the nonlinear system of the tethered formation and the results are compared with optimal control approach.

Reference governors for controlled belt restraint systems

NASA Astrophysics Data System (ADS)

van der Laan, E. P.; Heemels, W. P. M. H.; Luijten, H.; Veldpaus, F. E.; Steinbuch, M.

2010-07-01

Today's restraint systems typically include a number of airbags, and a three-point seat belt with load limiter and pretensioner. For the class of real-time controlled restraint systems, the restraint actuator settings are continuously manipulated during the crash. This paper presents a novel control strategy for these systems. The control strategy developed here is based on a combination of model predictive control and reference management, in which a non-linear device - a reference governor (RG) - is added to a primal closed-loop controlled system. This RG determines an optimal setpoint in terms of injury reduction and constraint satisfaction by solving a constrained optimisation problem. Prediction of the vehicle motion, required to predict future constraint violation, is included in the design and is based on past crash data, using linear regression techniques. Simulation results with MADYMO models show that, with ideal sensors and actuators, a significant reduction (45%) of the peak chest acceleration can be achieved, without prior knowledge of the crash. Furthermore, it is shown that the algorithms are sufficiently fast to be implemented online.

Robust model predictive control of nonlinear systems with unmodeled dynamics and bounded uncertainties based on neural networks.

PubMed

Yan, Zheng; Wang, Jun

2014-03-01

This paper presents a neural network approach to robust model predictive control (MPC) for constrained discrete-time nonlinear systems with unmodeled dynamics affected by bounded uncertainties. The exact nonlinear model of underlying process is not precisely known, but a partially known nominal model is available. This partially known nonlinear model is first decomposed to an affine term plus an unknown high-order term via Jacobian linearization. The linearization residue combined with unmodeled dynamics is then modeled using an extreme learning machine via supervised learning. The minimax methodology is exploited to deal with bounded uncertainties. The minimax optimization problem is reformulated as a convex minimization problem and is iteratively solved by a two-layer recurrent neural network. The proposed neurodynamic approach to nonlinear MPC improves the computational efficiency and sheds a light for real-time implementability of MPC technology. Simulation results are provided to substantiate the effectiveness and characteristics of the proposed approach.

Detection and Length Estimation of Linear Scratch on Solid Surfaces Using an Angle Constrained Ant Colony Technique

NASA Astrophysics Data System (ADS)

Pal, Siddharth; Basak, Aniruddha; Das, Swagatam

In many manufacturing areas the detection of surface defects is one of the most important processes in quality control. Currently in order to detect small scratches on solid surfaces most of the industries working on material manufacturing rely on visual inspection primarily. In this article we propose a hybrid computational intelligence technique to automatically detect a linear scratch from a solid surface and estimate its length (in pixel unit) simultaneously. The approach is based on a swarm intelligence algorithm called Ant Colony Optimization (ACO) and image preprocessing with Wiener and Sobel filters as well as the Canny edge detector. The ACO algorithm is mostly used to compensate for the broken parts of the scratch. Our experimental results confirm that the proposed technique can be used for detecting scratches from noisy and degraded images, even when it is very difficult for conventional image processing to distinguish the scratch area from its background.

Quadratic obstructions to small-time local controllability for scalar-input systems

NASA Astrophysics Data System (ADS)

Beauchard, Karine; Marbach, Frédéric

2018-03-01

We consider nonlinear finite-dimensional scalar-input control systems in the vicinity of an equilibrium. When the linearized system is controllable, the nonlinear system is smoothly small-time locally controllable: whatever m > 0 and T > 0, the state can reach a whole neighborhood of the equilibrium at time T with controls arbitrary small in Cm-norm. When the linearized system is not controllable, we prove that: either the state is constrained to live within a smooth strict manifold, up to a cubic residual, or the quadratic order adds a signed drift with respect to it. This drift holds along a Lie bracket of length (2 k + 1), is quantified in terms of an H-k-norm of the control, holds for controls small in W 2 k , ∞-norm and these spaces are optimal. Our proof requires only C3 regularity of the vector field. This work underlines the importance of the norm used in the smallness assumption on the control, even in finite dimension.

Investigation on a mechanical vibration absorber with tunable piecewise-linear stiffness

NASA Astrophysics Data System (ADS)

Shui, Xin; Wang, Shimin

2018-02-01

The design and characterization of a mechanical vibration absorber are addressed. A distinctive feature of the absorber is its tunable piecewise-linear stiffness, which is realized by means of a slider with two stop-blocks installed constraining the bilateral deflections of the elastic support. A new analytical approach named as the equivalent stiffness technique (EST) is introduced and then employed to obtain the analytical relations of the frequency, amplitude and phase with a view to exhibit a more comprehensive characterization of the absorber. Experiments are conducted to demonstrate the feasibility of the design. The experimental data show good agreement with the analytical results. The final results indicate that the tunable stiffness absorber (TSA) possesses a typical nonlinear characteristic at each given position of the slider, and its stiffness can be tuned in real time over a wide range by adjusting the slider position. Hence the TSA has a large optimum vibration-absorption range together with a wide suppression band around each optimal position, which contributes to its excellent capacity of vibration absorption.

Statistical model based iterative reconstruction in clinical CT systems. Part III. Task-based kV/mAs optimization for radiation dose reduction

PubMed Central

Li, Ke; Gomez-Cardona, Daniel; Hsieh, Jiang; Lubner, Meghan G.; Pickhardt, Perry J.; Chen, Guang-Hong

2015-01-01

Purpose: For a given imaging task and patient size, the optimal selection of x-ray tube potential (kV) and tube current-rotation time product (mAs) is pivotal in achieving the maximal radiation dose reduction while maintaining the needed diagnostic performance. Although contrast-to-noise (CNR)-based strategies can be used to optimize kV/mAs for computed tomography (CT) imaging systems employing the linear filtered backprojection (FBP) reconstruction method, a more general framework needs to be developed for systems using the nonlinear statistical model-based iterative reconstruction (MBIR) method. The purpose of this paper is to present such a unified framework for the optimization of kV/mAs selection for both FBP- and MBIR-based CT systems. Methods: The optimal selection of kV and mAs was formulated as a constrained optimization problem to minimize the objective function, Dose(kV,mAs), under the constraint that the achievable detectability index d′(kV,mAs) is not lower than the prescribed value of d℞′ for a given imaging task. Since it is difficult to analytically model the dependence of d′ on kV and mAs for the highly nonlinear MBIR method, this constrained optimization problem is solved with comprehensive measurements of Dose(kV,mAs) and d′(kV,mAs) at a variety of kV–mAs combinations, after which the overlay of the dose contours and d′ contours is used to graphically determine the optimal kV–mAs combination to achieve the lowest dose while maintaining the needed detectability for the given imaging task. As an example, d′ for a 17 mm hypoattenuating liver lesion detection task was experimentally measured with an anthropomorphic abdominal phantom at four tube potentials (80, 100, 120, and 140 kV) and fifteen mA levels (25 and 50–700) with a sampling interval of 50 mA at a fixed rotation time of 0.5 s, which corresponded to a dose (CTDIvol) range of [0.6, 70] mGy. Using the proposed method, the optimal kV and mA that minimized dose for the prescribed detectability level of d℞′=16 were determined. As another example, the optimal kV and mA for an 8 mm hyperattenuating liver lesion detection task were also measured using the developed framework. Both an in vivo animal and human subject study were used as demonstrations of how the developed framework can be applied to the clinical work flow. Results: For the first task, the optimal kV and mAs were measured to be 100 and 500, respectively, for FBP, which corresponded to a dose level of 24 mGy. In comparison, the optimal kV and mAs for MBIR were 80 and 150, respectively, which corresponded to a dose level of 4 mGy. The topographies of the iso-d′ map and the iso-CNR map were the same for FBP; thus, the use of d′- and CNR-based optimization methods generated the same results for FBP. However, the topographies of the iso-d′ and iso-CNR map were significantly different in MBIR; the CNR-based method overestimated the performance of MBIR, predicting an overly aggressive dose reduction factor. For the second task, the developed framework generated the following optimization results: for FBP, kV = 140, mA = 350, dose = 37.5 mGy; for MBIR, kV = 120, mA = 250, dose = 18.8 mGy. Again, the CNR-based method overestimated the performance of MBIR. Results of the preliminary in vivo studies were consistent with those of the phantom experiments. Conclusions: A unified and task-driven kV/mAs optimization framework has been developed in this work. The framework is applicable to both linear and nonlinear CT systems such as those using the MBIR method. As expected, the developed framework can be reduced to the conventional CNR-based kV/mAs optimization frameworks if the system is linear. For MBIR-based nonlinear CT systems, however, the developed task-based kV/mAs optimization framework is needed to achieve the maximal dose reduction while maintaining the desired diagnostic performance. PMID:26328971

CLFs-based optimization control for a class of constrained visual servoing systems.

PubMed

Song, Xiulan; Miaomiao, Fu

2017-03-01

In this paper, we use the control Lyapunov function (CLF) technique to present an optimized visual servo control method for constrained eye-in-hand robot visual servoing systems. With the knowledge of camera intrinsic parameters and depth of target changes, visual servo control laws (i.e. translation speed) with adjustable parameters are derived by image point features and some known CLF of the visual servoing system. The Fibonacci method is employed to online compute the optimal value of those adjustable parameters, which yields an optimized control law to satisfy constraints of the visual servoing system. The Lyapunov's theorem and the properties of CLF are used to establish stability of the constrained visual servoing system in the closed-loop with the optimized control law. One merit of the presented method is that there is no requirement of online calculating the pseudo-inverse of the image Jacobian's matrix and the homography matrix. Simulation and experimental results illustrated the effectiveness of the method proposed here. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

An optimally weighted estimator of the linear power spectrum disentangling the growth of density perturbations across galaxy surveys

NASA Astrophysics Data System (ADS)

Sorini, D.

2017-04-01

Measuring the clustering of galaxies from surveys allows us to estimate the power spectrum of matter density fluctuations, thus constraining cosmological models. This requires careful modelling of observational effects to avoid misinterpretation of data. In particular, signals coming from different distances encode information from different epochs. This is known as ``light-cone effect'' and is going to have a higher impact as upcoming galaxy surveys probe larger redshift ranges. Generalising the method by Feldman, Kaiser and Peacock (1994) [1], I define a minimum-variance estimator of the linear power spectrum at a fixed time, properly taking into account the light-cone effect. An analytic expression for the estimator is provided, and that is consistent with the findings of previous works in the literature. I test the method within the context of the Halofit model, assuming Planck 2014 cosmological parameters [2]. I show that the estimator presented recovers the fiducial linear power spectrum at present time within 5% accuracy up to k ~ 0.80 h Mpc-1 and within 10% up to k ~ 0.94 h Mpc-1, well into the non-linear regime of the growth of density perturbations. As such, the method could be useful in the analysis of the data from future large-scale surveys, like Euclid.

Constrained optimization of sequentially generated entangled multiqubit states

NASA Astrophysics Data System (ADS)

Saberi, Hamed; Weichselbaum, Andreas; Lamata, Lucas; Pérez-García, David; von Delft, Jan; Solano, Enrique

2009-08-01

We demonstrate how the matrix-product state formalism provides a flexible structure to solve the constrained optimization problem associated with the sequential generation of entangled multiqubit states under experimental restrictions. We consider a realistic scenario in which an ancillary system with a limited number of levels performs restricted sequential interactions with qubits in a row. The proposed method relies on a suitable local optimization procedure, yielding an efficient recipe for the realistic and approximate sequential generation of any entangled multiqubit state. We give paradigmatic examples that may be of interest for theoretical and experimental developments.

Solution of nonlinear multivariable constrained systems using a gradient projection digital algorithm that is insensitive to the initial state

NASA Technical Reports Server (NTRS)

Hargrove, A.

1982-01-01

Optimal digital control of nonlinear multivariable constrained systems was studied. The optimal controller in the form of an algorithm was improved and refined by reducing running time and storage requirements. A particularly difficult system of nine nonlinear state variable equations was chosen as a test problem for analyzing and improving the controller. Lengthy analysis, modeling, computing and optimization were accomplished. A remote interactive teletype terminal was installed. Analysis requiring computer usage of short duration was accomplished using Tuskegee's VAX 11/750 system.

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

PubMed Central

2013-01-01

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

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

PubMed

Ren, Shaogang; Zeng, Bo; Qian, Xiaoning

2013-01-01

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

Modified Backtracking Search Optimization Algorithm Inspired by Simulated Annealing for Constrained Engineering Optimization Problems

PubMed Central

Wang, Hailong; Sun, Yuqiu; Su, Qinghua; Xia, Xuewen

2018-01-01

The backtracking search optimization algorithm (BSA) is a population-based evolutionary algorithm for numerical optimization problems. BSA has a powerful global exploration capacity while its local exploitation capability is relatively poor. This affects the convergence speed of the algorithm. In this paper, we propose a modified BSA inspired by simulated annealing (BSAISA) to overcome the deficiency of BSA. In the BSAISA, the amplitude control factor (F) is modified based on the Metropolis criterion in simulated annealing. The redesigned F could be adaptively decreased as the number of iterations increases and it does not introduce extra parameters. A self-adaptive ε-constrained method is used to handle the strict constraints. We compared the performance of the proposed BSAISA with BSA and other well-known algorithms when solving thirteen constrained benchmarks and five engineering design problems. The simulation results demonstrated that BSAISA is more effective than BSA and more competitive with other well-known algorithms in terms of convergence speed. PMID:29666635

Management of Occupational Exposure to Engineered Nanoparticles Through a Chance-Constrained Nonlinear Programming Approach

PubMed Central

Chen, Zhi; Yuan, Yuan; Zhang, Shu-Shen; Chen, Yu; Yang, Feng-Lin

2013-01-01

Critical environmental and human health concerns are associated with the rapidly growing fields of nanotechnology and manufactured nanomaterials (MNMs). The main risk arises from occupational exposure via chronic inhalation of nanoparticles. This research presents a chance-constrained nonlinear programming (CCNLP) optimization approach, which is developed to maximize the nanaomaterial production and minimize the risks of workplace exposure to MNMs. The CCNLP method integrates nonlinear programming (NLP) and chance-constrained programming (CCP), and handles uncertainties associated with both the nanomaterial production and workplace exposure control. The CCNLP method was examined through a single-walled carbon nanotube (SWNT) manufacturing process. The study results provide optimal production strategies and alternatives. It reveal that a high control measure guarantees that environmental health and safety (EHS) standards regulations are met, while a lower control level leads to increased risk of violating EHS regulations. The CCNLP optimization approach is a decision support tool for the optimization of the increasing MNMS manufacturing with workplace safety constraints under uncertainties. PMID:23531490

Management of occupational exposure to engineered nanoparticles through a chance-constrained nonlinear programming approach.

PubMed

Chen, Zhi; Yuan, Yuan; Zhang, Shu-Shen; Chen, Yu; Yang, Feng-Lin

2013-03-26

Critical environmental and human health concerns are associated with the rapidly growing fields of nanotechnology and manufactured nanomaterials (MNMs). The main risk arises from occupational exposure via chronic inhalation of nanoparticles. This research presents a chance-constrained nonlinear programming (CCNLP) optimization approach, which is developed to maximize the nanaomaterial production and minimize the risks of workplace exposure to MNMs. The CCNLP method integrates nonlinear programming (NLP) and chance-constrained programming (CCP), and handles uncertainties associated with both the nanomaterial production and workplace exposure control. The CCNLP method was examined through a single-walled carbon nanotube (SWNT) manufacturing process. The study results provide optimal production strategies and alternatives. It reveal that a high control measure guarantees that environmental health and safety (EHS) standards regulations are met, while a lower control level leads to increased risk of violating EHS regulations. The CCNLP optimization approach is a decision support tool for the optimization of the increasing MNMS manufacturing with workplace safety constraints under uncertainties.

Thermal-economic optimisation of a CHP gas turbine system by applying a fit-problem genetic algorithm

NASA Astrophysics Data System (ADS)

Ferreira, Ana C. M.; Teixeira, Senhorinha F. C. F.; Silva, Rui G.; Silva, Ângela M.

2018-04-01

Cogeneration allows the optimal use of the primary energy sources and significant reductions in carbon emissions. Its use has great potential for applications in the residential sector. This study aims to develop a methodology for thermal-economic optimisation of small-scale micro-gas turbine for cogeneration purposes, able to fulfil domestic energy needs with a thermal power out of 125 kW. A constrained non-linear optimisation model was built. The objective function is the maximisation of the annual worth from the combined heat and power, representing the balance between the annual incomes and the expenditures subject to physical and economic constraints. A genetic algorithm coded in the java programming language was developed. An optimal micro-gas turbine able to produce 103.5 kW of electrical power with a positive annual profit (i.e. 11,925 €/year) was disclosed. The investment can be recovered in 4 years and 9 months, which is less than half of system lifetime expectancy.

Stochastic Control Synthesis of Systems with Structured Uncertainty

NASA Technical Reports Server (NTRS)

Padula, Sharon L. (Technical Monitor); Crespo, Luis G.

2003-01-01

This paper presents a study on the design of robust controllers by using random variables to model structured uncertainty for both SISO and MIMO feedback systems. Once the parameter uncertainty is prescribed with probability density functions, its effects are propagated through the analysis leading to stochastic metrics for the system's output. Control designs that aim for satisfactory performances while guaranteeing robust closed loop stability are attained by solving constrained non-linear optimization problems in the frequency domain. This approach permits not only to quantify the probability of having unstable and unfavorable responses for a particular control design but also to search for controls while favoring the values of the parameters with higher chance of occurrence. In this manner, robust optimality is achieved while the characteristic conservatism of conventional robust control methods is eliminated. Examples that admit closed form expressions for the probabilistic metrics of the output are used to elucidate the nature of the problem at hand and validate the proposed formulations.

Augmented Lagrange Hopfield network for solving economic dispatch problem in competitive environment

NASA Astrophysics Data System (ADS)

Vo, Dieu Ngoc; Ongsakul, Weerakorn; Nguyen, Khai Phuc

2012-11-01

This paper proposes an augmented Lagrange Hopfield network (ALHN) for solving economic dispatch (ED) problem in the competitive environment. The proposed ALHN is a continuous Hopfield network with its energy function based on augmented Lagrange function for efficiently dealing with constrained optimization problems. The ALHN method can overcome the drawbacks of the conventional Hopfield network such as local optimum, long computational time, and linear constraints. The proposed method is used for solving the ED problem with two revenue models of revenue based on payment for power delivered and payment for reserve allocated. The proposed ALHN has been tested on two systems of 3 units and 10 units for the two considered revenue models. The obtained results from the proposed methods are compared to those from differential evolution (DE) and particle swarm optimization (PSO) methods. The result comparison has indicated that the proposed method is very efficient for solving the problem. Therefore, the proposed ALHN could be a favorable tool for ED problem in the competitive environment.

Coordination Between the Sexes Constrains the Optimization of Reproductive Timing in Honey Bee Colonies.

PubMed

Lemanski, Natalie J; Fefferman, Nina H

2017-06-01

Honeybees are an excellent model system for examining how trade-offs shape reproductive timing in organisms with seasonal environments. Honeybee colonies reproduce two ways: producing swarms comprising a queen and thousands of workers or producing males (drones). There is an energetic trade-off between producing workers, which contribute to colony growth, and drones, which contribute only to reproduction. The timing of drone production therefore determines both the drones' likelihood of mating and when colonies reach sufficient size to swarm. Using a linear programming model, we ask when a colony should produce drones and swarms to maximize reproductive success. We find the optimal behavior for each colony is to produce all drones prior to swarming, an impossible solution on a population scale because queens and drones would never co-occur. Reproductive timing is therefore not solely determined by energetic trade-offs but by the game theoretic problem of coordinating the production of reproductives among colonies.

A closed-form trim solution yielding minimum trim drag for airplanes with multiple longitudinal-control effectors

NASA Technical Reports Server (NTRS)

Goodrich, Kenneth H.; Sliwa, Steven M.; Lallman, Frederick J.

1989-01-01

Airplane designs are currently being proposed with a multitude of lifting and control devices. Because of the redundancy in ways to generate moments and forces, there are a variety of strategies for trimming each airplane. A linear optimum trim solution (LOTS) is derived using a Lagrange formulation. LOTS enables the rapid calculation of the longitudinal load distribution resulting in the minimum trim drag in level, steady-state flight for airplanes with a mixture of three or more aerodynamic surfaces and propulsive control effectors. Comparisons of the trim drags obtained using LOTS, a direct constrained optimization method, and several ad hoc methods are presented for vortex-lattice representations of a three-surface airplane and two-surface airplane with thrust vectoring. These comparisons show that LOTS accurately predicts the results obtained from the nonlinear optimization and that the optimum methods result in trim drag reductions of up to 80 percent compared to the ad hoc methods.

Neural networks for feedback feedforward nonlinear control systems.

PubMed

Parisini, T; Zoppoli, R

1994-01-01

This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method.

Thermally-Constrained Fuel-Optimal ISS Maneuvers

NASA Technical Reports Server (NTRS)

Bhatt, Sagar; Svecz, Andrew; Alaniz, Abran; Jang, Jiann-Woei; Nguyen, Louis; Spanos, Pol

2015-01-01

Optimal Propellant Maneuvers (OPMs) are now being used to rotate the International Space Station (ISS) and have saved hundreds of kilograms of propellant over the last two years. The savings are achieved by commanding the ISS to follow a pre-planned attitude trajectory optimized to take advantage of environmental torques. The trajectory is obtained by solving an optimal control problem. Prior to use on orbit, OPM trajectories are screened to ensure a static sun vector (SSV) does not occur during the maneuver. The SSV is an indicator that the ISS hardware temperatures may exceed thermal limits, causing damage to the components. In this paper, thermally-constrained fuel-optimal trajectories are presented that avoid an SSV and can be used throughout the year while still reducing propellant consumption significantly.

Explicit reference governor for linear systems

NASA Astrophysics Data System (ADS)

Garone, Emanuele; Nicotra, Marco; Ntogramatzidis, Lorenzo

2018-06-01

The explicit reference governor is a constrained control scheme that was originally introduced for generic nonlinear systems. This paper presents two explicit reference governor strategies that are specifically tailored for the constrained control of linear time-invariant systems subject to linear constraints. Both strategies are based on the idea of maintaining the system states within an invariant set which is entirely contained in the constraints. This invariant set can be constructed by exploiting either the Lyapunov inequality or modal decomposition. To improve the performance, we show that the two strategies can be combined by choosing at each time instant the least restrictive set. Numerical simulations illustrate that the proposed scheme achieves performances that are comparable to optimisation-based reference governors.

Visual Tracking via Sparse and Local Linear Coding.

PubMed

Wang, Guofeng; Qin, Xueying; Zhong, Fan; Liu, Yue; Li, Hongbo; Peng, Qunsheng; Yang, Ming-Hsuan

2015-11-01

The state search is an important component of any object tracking algorithm. Numerous algorithms have been proposed, but stochastic sampling methods (e.g., particle filters) are arguably one of the most effective approaches. However, the discretization of the state space complicates the search for the precise object location. In this paper, we propose a novel tracking algorithm that extends the state space of particle observations from discrete to continuous. The solution is determined accurately via iterative linear coding between two convex hulls. The algorithm is modeled by an optimal function, which can be efficiently solved by either convex sparse coding or locality constrained linear coding. The algorithm is also very flexible and can be combined with many generic object representations. Thus, we first use sparse representation to achieve an efficient searching mechanism of the algorithm and demonstrate its accuracy. Next, two other object representation models, i.e., least soft-threshold squares and adaptive structural local sparse appearance, are implemented with improved accuracy to demonstrate the flexibility of our algorithm. Qualitative and quantitative experimental results demonstrate that the proposed tracking algorithm performs favorably against the state-of-the-art methods in dynamic scenes.

Flexure Based Linear and Rotary Bearings

NASA Technical Reports Server (NTRS)

Voellmer, George M. (Inventor)

2016-01-01

A flexure based linear bearing includes top and bottom parallel rigid plates; first and second flexures connecting the top and bottom plates and constraining exactly four degrees of freedom of relative motion of the plates, the four degrees of freedom being X and Y axis translation and rotation about the X and Y axes; and a strut connecting the top and bottom plates and further constraining exactly one degree of freedom of the plates, the one degree of freedom being one of Z axis translation and rotation about the Z axis.

The 2-D magnetotelluric inverse problem solved with optimization

NASA Astrophysics Data System (ADS)

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

2011-02-01

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

Optimal joint detection and estimation that maximizes ROC-type curves

PubMed Central

Wunderlich, Adam; Goossens, Bart; Abbey, Craig K.

2017-01-01

Combined detection-estimation tasks are frequently encountered in medical imaging. Optimal methods for joint detection and estimation are of interest because they provide upper bounds on observer performance, and can potentially be utilized for imaging system optimization, evaluation of observer efficiency, and development of image formation algorithms. We present a unified Bayesian framework for decision rules that maximize receiver operating characteristic (ROC)-type summary curves, including ROC, localization ROC (LROC), estimation ROC (EROC), free-response ROC (FROC), alternative free-response ROC (AFROC), and exponentially-transformed FROC (EFROC) curves, succinctly summarizing previous results. The approach relies on an interpretation of ROC-type summary curves as plots of an expected utility versus an expected disutility (or penalty) for signal-present decisions. We propose a general utility structure that is flexible enough to encompass many ROC variants and yet sufficiently constrained to allow derivation of a linear expected utility equation that is similar to that for simple binary detection. We illustrate our theory with an example comparing decision strategies for joint detection-estimation of a known signal with unknown amplitude. In addition, building on insights from our utility framework, we propose new ROC-type summary curves and associated optimal decision rules for joint detection-estimation tasks with an unknown, potentially-multiple, number of signals in each observation. PMID:27093544

Optimal Joint Detection and Estimation That Maximizes ROC-Type Curves.

PubMed

Wunderlich, Adam; Goossens, Bart; Abbey, Craig K

2016-09-01

Combined detection-estimation tasks are frequently encountered in medical imaging. Optimal methods for joint detection and estimation are of interest because they provide upper bounds on observer performance, and can potentially be utilized for imaging system optimization, evaluation of observer efficiency, and development of image formation algorithms. We present a unified Bayesian framework for decision rules that maximize receiver operating characteristic (ROC)-type summary curves, including ROC, localization ROC (LROC), estimation ROC (EROC), free-response ROC (FROC), alternative free-response ROC (AFROC), and exponentially-transformed FROC (EFROC) curves, succinctly summarizing previous results. The approach relies on an interpretation of ROC-type summary curves as plots of an expected utility versus an expected disutility (or penalty) for signal-present decisions. We propose a general utility structure that is flexible enough to encompass many ROC variants and yet sufficiently constrained to allow derivation of a linear expected utility equation that is similar to that for simple binary detection. We illustrate our theory with an example comparing decision strategies for joint detection-estimation of a known signal with unknown amplitude. In addition, building on insights from our utility framework, we propose new ROC-type summary curves and associated optimal decision rules for joint detection-estimation tasks with an unknown, potentially-multiple, number of signals in each observation.

A quasi-Newton approach to optimization problems with probability density constraints. [problem solving in mathematical programming

NASA Technical Reports Server (NTRS)

Tapia, R. A.; Vanrooy, D. L.

1976-01-01

A quasi-Newton method is presented for minimizing a nonlinear function while constraining the variables to be nonnegative and sum to one. The nonnegativity constraints were eliminated by working with the squares of the variables and the resulting problem was solved using Tapia's general theory of quasi-Newton methods for constrained optimization. A user's guide for a computer program implementing this algorithm is provided.

Necessary conditions for the optimality of variable rate residual vector quantizers

NASA Technical Reports Server (NTRS)

Kossentini, Faouzi; Smith, Mark J. T.; Barnes, Christopher F.

1993-01-01

Residual vector quantization (RVQ), or multistage VQ, as it is also called, has recently been shown to be a competitive technique for data compression. The competitive performance of RVQ reported in results from the joint optimization of variable rate encoding and RVQ direct-sum code books. In this paper, necessary conditions for the optimality of variable rate RVQ's are derived, and an iterative descent algorithm based on a Lagrangian formulation is introduced for designing RVQ's having minimum average distortion subject to an entropy constraint. Simulation results for these entropy-constrained RVQ's (EC-RVQ's) are presented for memory less Gaussian, Laplacian, and uniform sources. A Gauss-Markov source is also considered. The performance is superior to that of entropy-constrained scalar quantizers (EC-SQ's) and practical entropy-constrained vector quantizers (EC-VQ's), and is competitive with that of some of the best source coding techniques that have appeared in the literature.

Energetic Materials Optimization via Constrained Search

DTIC Science & Technology

2015-06-01

steps. 3. Optimization Methodology Our optimization problem is formulated as a constrained maximization: max x∈CCS P (x) s.t. : TED ( x )− 9.75 ≥ 0 SV (x)− 9...0 5− SA(x) ≥ 0, (1) where TED ( x ) is the total energy of detonation (TED) of compound x from the chosen chemical subspace (CCS) of chemical compound...max problem, max x∈CCS min λ∈R3+ P (x)− λTC(x), (2) where C(x) is the vector of constraint violations, i.e., η(9.75 − TED ( x )), η(9 − SV (x)), η(SA(x

A Constrained Linear Estimator for Multiple Regression

ERIC Educational Resources Information Center

Davis-Stober, Clintin P.; Dana, Jason; Budescu, David V.

2010-01-01

"Improper linear models" (see Dawes, Am. Psychol. 34:571-582, "1979"), such as equal weighting, have garnered interest as alternatives to standard regression models. We analyze the general circumstances under which these models perform well by recasting a class of "improper" linear models as "proper" statistical models with a single predictor. We…

A sequential linear optimization approach for controller design

NASA Technical Reports Server (NTRS)

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

1985-01-01

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

Application of Sequential Quadratic Programming to Minimize Smart Active Flap Rotor Hub Loads

NASA Technical Reports Server (NTRS)

Kottapalli, Sesi; Leyland, Jane

2014-01-01

In an analytical study, SMART active flap rotor hub loads have been minimized using nonlinear programming constrained optimization methodology. The recently developed NLPQLP system (Schittkowski, 2010) that employs Sequential Quadratic Programming (SQP) as its core algorithm was embedded into a driver code (NLP10x10) specifically designed to minimize active flap rotor hub loads (Leyland, 2014). Three types of practical constraints on the flap deflections have been considered. To validate the current application, two other optimization methods have been used: i) the standard, linear unconstrained method, and ii) the nonlinear Generalized Reduced Gradient (GRG) method with constraints. The new software code NLP10x10 has been systematically checked out. It has been verified that NLP10x10 is functioning as desired. The following are briefly covered in this paper: relevant optimization theory; implementation of the capability of minimizing a metric of all, or a subset, of the hub loads as well as the capability of using all, or a subset, of the flap harmonics; and finally, solutions for the SMART rotor. The eventual goal is to implement NLP10x10 in a real-time wind tunnel environment.

Reliable Adaptive Data Aggregation Route Strategy for a Trade-off between Energy and Lifetime in WSNs

PubMed Central

Guo, Wenzhong; Hong, Wei; Zhang, Bin; Chen, Yuzhong; Xiong, Naixue

2014-01-01

Mobile security is one of the most fundamental problems in Wireless Sensor Networks (WSNs). The data transmission path will be compromised for some disabled nodes. To construct a secure and reliable network, designing an adaptive route strategy which optimizes energy consumption and network lifetime of the aggregation cost is of great importance. In this paper, we address the reliable data aggregation route problem for WSNs. Firstly, to ensure nodes work properly, we propose a data aggregation route algorithm which improves the energy efficiency in the WSN. The construction process achieved through discrete particle swarm optimization (DPSO) saves node energy costs. Then, to balance the network load and establish a reliable network, an adaptive route algorithm with the minimal energy and the maximum lifetime is proposed. Since it is a non-linear constrained multi-objective optimization problem, in this paper we propose a DPSO with the multi-objective fitness function combined with the phenotype sharing function and penalty function to find available routes. Experimental results show that compared with other tree routing algorithms our algorithm can effectively reduce energy consumption and trade off energy consumption and network lifetime. PMID:25215944

JuPOETs: a constrained multiobjective optimization approach to estimate biochemical model ensembles in the Julia programming language.

PubMed

Bassen, David M; Vilkhovoy, Michael; Minot, Mason; Butcher, Jonathan T; Varner, Jeffrey D

2017-01-25

Ensemble modeling is a promising approach for obtaining robust predictions and coarse grained population behavior in deterministic mathematical models. Ensemble approaches address model uncertainty by using parameter or model families instead of single best-fit parameters or fixed model structures. Parameter ensembles can be selected based upon simulation error, along with other criteria such as diversity or steady-state performance. Simulations using parameter ensembles can estimate confidence intervals on model variables, and robustly constrain model predictions, despite having many poorly constrained parameters. In this software note, we present a multiobjective based technique to estimate parameter or models ensembles, the Pareto Optimal Ensemble Technique in the Julia programming language (JuPOETs). JuPOETs integrates simulated annealing with Pareto optimality to estimate ensembles on or near the optimal tradeoff surface between competing training objectives. We demonstrate JuPOETs on a suite of multiobjective problems, including test functions with parameter bounds and system constraints as well as for the identification of a proof-of-concept biochemical model with four conflicting training objectives. JuPOETs identified optimal or near optimal solutions approximately six-fold faster than a corresponding implementation in Octave for the suite of test functions. For the proof-of-concept biochemical model, JuPOETs produced an ensemble of parameters that gave both the mean of the training data for conflicting data sets, while simultaneously estimating parameter sets that performed well on each of the individual objective functions. JuPOETs is a promising approach for the estimation of parameter and model ensembles using multiobjective optimization. JuPOETs can be adapted to solve many problem types, including mixed binary and continuous variable types, bilevel optimization problems and constrained problems without altering the base algorithm. JuPOETs is open source, available under an MIT license, and can be installed using the Julia package manager from the JuPOETs GitHub repository.

Proportional Topology Optimization: A New Non-Sensitivity Method for Solving Stress Constrained and Minimum Compliance Problems and Its Implementation in MATLAB

PubMed Central

Biyikli, Emre; To, Albert C.

2015-01-01

A new topology optimization method called the Proportional Topology Optimization (PTO) is presented. As a non-sensitivity method, PTO is simple to understand, easy to implement, and is also efficient and accurate at the same time. It is implemented into two MATLAB programs to solve the stress constrained and minimum compliance problems. Descriptions of the algorithm and computer programs are provided in detail. The method is applied to solve three numerical examples for both types of problems. The method shows comparable efficiency and accuracy with an existing optimality criteria method which computes sensitivities. Also, the PTO stress constrained algorithm and minimum compliance algorithm are compared by feeding output from one algorithm to the other in an alternative manner, where the former yields lower maximum stress and volume fraction but higher compliance compared to the latter. Advantages and disadvantages of the proposed method and future works are discussed. The computer programs are self-contained and publicly shared in the website www.ptomethod.org. PMID:26678849

Firefly algorithm for cardinality constrained mean-variance portfolio optimization problem with entropy diversity constraint.

PubMed

Bacanin, Nebojsa; Tuba, Milan

2014-01-01

Portfolio optimization (selection) problem is an important and hard optimization problem that, with the addition of necessary realistic constraints, becomes computationally intractable. Nature-inspired metaheuristics are appropriate for solving such problems; however, literature review shows that there are very few applications of nature-inspired metaheuristics to portfolio optimization problem. This is especially true for swarm intelligence algorithms which represent the newer branch of nature-inspired algorithms. No application of any swarm intelligence metaheuristics to cardinality constrained mean-variance (CCMV) portfolio problem with entropy constraint was found in the literature. This paper introduces modified firefly algorithm (FA) for the CCMV portfolio model with entropy constraint. Firefly algorithm is one of the latest, very successful swarm intelligence algorithm; however, it exhibits some deficiencies when applied to constrained problems. To overcome lack of exploration power during early iterations, we modified the algorithm and tested it on standard portfolio benchmark data sets used in the literature. Our proposed modified firefly algorithm proved to be better than other state-of-the-art algorithms, while introduction of entropy diversity constraint further improved results.

Firefly Algorithm for Cardinality Constrained Mean-Variance Portfolio Optimization Problem with Entropy Diversity Constraint

PubMed Central

2014-01-01

Portfolio optimization (selection) problem is an important and hard optimization problem that, with the addition of necessary realistic constraints, becomes computationally intractable. Nature-inspired metaheuristics are appropriate for solving such problems; however, literature review shows that there are very few applications of nature-inspired metaheuristics to portfolio optimization problem. This is especially true for swarm intelligence algorithms which represent the newer branch of nature-inspired algorithms. No application of any swarm intelligence metaheuristics to cardinality constrained mean-variance (CCMV) portfolio problem with entropy constraint was found in the literature. This paper introduces modified firefly algorithm (FA) for the CCMV portfolio model with entropy constraint. Firefly algorithm is one of the latest, very successful swarm intelligence algorithm; however, it exhibits some deficiencies when applied to constrained problems. To overcome lack of exploration power during early iterations, we modified the algorithm and tested it on standard portfolio benchmark data sets used in the literature. Our proposed modified firefly algorithm proved to be better than other state-of-the-art algorithms, while introduction of entropy diversity constraint further improved results. PMID:24991645

Study of Interpolated Timing Recovery Phase-Locked Loop with Linearly Constrained Adaptive Prefilter for Higher-Density Optical Disc

NASA Astrophysics Data System (ADS)

Kajiwara, Yoshiyuki; Shiraishi, Junya; Kobayashi, Shoei; Yamagami, Tamotsu

2009-03-01

A digital phase-locked loop (PLL) with a linearly constrained adaptive filter (LCAF) has been studied for higher-linear-density optical discs. LCAF has been implemented before an interpolated timing recovery (ITR) PLL unit in order to improve the quality of phase error calculation by using an adaptively equalized partial response (PR) signal. Coefficient update of an asynchronous sampled adaptive FIR filter with a least-mean-square (LMS) algorithm has been constrained by a projection matrix in order to suppress the phase shift of the tap coefficients of the adaptive filter. We have developed projection matrices that are suitable for Blu-ray disc (BD) drive systems by numerical simulation. Results have shown the properties of the projection matrices. Then, we have designed the read channel system of the ITR PLL with an LCAF model on the FPGA board for experiments. Results have shown that the LCAF improves the tilt margins of 30 gigabytes (GB) recordable BD (BD-R) and 33 GB BD read-only memory (BD-ROM) with a sufficient LMS adaptation stability.

[Retrieval of crown closure of moso bamboo forest using unmanned aerial vehicle (UAV) remotely sensed imagery based on geometric-optical model].

PubMed

Wang, Cong; Du, Hua-qiang; Zhou, Guo-mo; Xu, Xiao-jun; Sun, Shao-bo; Gao, Guo-long

2015-05-01

This research focused on the application of remotely sensed imagery from unmanned aerial vehicle (UAV) with high spatial resolution for the estimation of crown closure of moso bamboo forest based on the geometric-optical model, and analyzed the influence of unconstrained and fully constrained linear spectral mixture analysis (SMA) on the accuracy of the estimated results. The results demonstrated that the combination of UAV remotely sensed imagery and geometric-optical model could, to some degrees, achieve the estimation of crown closure. However, the different SMA methods led to significant differentiation in the estimation accuracy. Compared with unconstrained SMA, the fully constrained linear SMA method resulted in higher accuracy of the estimated values, with the coefficient of determination (R2) of 0.63 at 0.01 level, against the measured values acquired during the field survey. Root mean square error (RMSE) of approximate 0.04 was low, indicating that the usage of fully constrained linear SMA could bring about better results in crown closure estimation, which was closer to the actual condition in moso bamboo forest.

Optimal Guaranteed Cost Sliding Mode Control for Constrained-Input Nonlinear Systems With Matched and Unmatched Disturbances.

PubMed

Zhang, Huaguang; Qu, Qiuxia; Xiao, Geyang; Cui, Yang

2018-06-01

Based on integral sliding mode and approximate dynamic programming (ADP) theory, a novel optimal guaranteed cost sliding mode control is designed for constrained-input nonlinear systems with matched and unmatched disturbances. When the system moves on the sliding surface, the optimal guaranteed cost control problem of sliding mode dynamics is transformed into the optimal control problem of a reformulated auxiliary system with a modified cost function. The ADP algorithm based on single critic neural network (NN) is applied to obtain the approximate optimal control law for the auxiliary system. Lyapunov techniques are used to demonstrate the convergence of the NN weight errors. In addition, the derived approximate optimal control is verified to guarantee the sliding mode dynamics system to be stable in the sense of uniform ultimate boundedness. Some simulation results are presented to verify the feasibility of the proposed control scheme.

Linear model correction: A method for transferring a near-infrared multivariate calibration model without standard samples.

PubMed

Liu, Yan; Cai, Wensheng; Shao, Xueguang

2016-12-05

Calibration transfer is essential for practical applications of near infrared (NIR) spectroscopy because the measurements of the spectra may be performed on different instruments and the difference between the instruments must be corrected. For most of calibration transfer methods, standard samples are necessary to construct the transfer model using the spectra of the samples measured on two instruments, named as master and slave instrument, respectively. In this work, a method named as linear model correction (LMC) is proposed for calibration transfer without standard samples. The method is based on the fact that, for the samples with similar physical and chemical properties, the spectra measured on different instruments are linearly correlated. The fact makes the coefficients of the linear models constructed by the spectra measured on different instruments are similar in profile. Therefore, by using the constrained optimization method, the coefficients of the master model can be transferred into that of the slave model with a few spectra measured on slave instrument. Two NIR datasets of corn and plant leaf samples measured with different instruments are used to test the performance of the method. The results show that, for both the datasets, the spectra can be correctly predicted using the transferred partial least squares (PLS) models. Because standard samples are not necessary in the method, it may be more useful in practical uses. Copyright © 2016 Elsevier B.V. All rights reserved.

An optimally weighted estimator of the linear power spectrum disentangling the growth of density perturbations across galaxy surveys

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

Sorini, D., E-mail: sorini@mpia-hd.mpg.de

2017-04-01

Measuring the clustering of galaxies from surveys allows us to estimate the power spectrum of matter density fluctuations, thus constraining cosmological models. This requires careful modelling of observational effects to avoid misinterpretation of data. In particular, signals coming from different distances encode information from different epochs. This is known as ''light-cone effect'' and is going to have a higher impact as upcoming galaxy surveys probe larger redshift ranges. Generalising the method by Feldman, Kaiser and Peacock (1994) [1], I define a minimum-variance estimator of the linear power spectrum at a fixed time, properly taking into account the light-cone effect. Anmore » analytic expression for the estimator is provided, and that is consistent with the findings of previous works in the literature. I test the method within the context of the Halofit model, assuming Planck 2014 cosmological parameters [2]. I show that the estimator presented recovers the fiducial linear power spectrum at present time within 5% accuracy up to k ∼ 0.80 h Mpc{sup −1} and within 10% up to k ∼ 0.94 h Mpc{sup −1}, well into the non-linear regime of the growth of density perturbations. As such, the method could be useful in the analysis of the data from future large-scale surveys, like Euclid.« less

Toward Overcoming the Local Minimum Trap in MFBD

DTIC Science & Technology

2015-07-14

the first two years of this grant: • A. Cornelio, E. Loli -Piccolomini, and J. G. Nagy. Constrained Variable Projection Method for Blind Deconvolution...Cornelio, E. Loli -Piccolomini, and J. G. Nagy. Constrained Numerical Optimization Meth- ods for Blind Deconvolution, Numerical Algorithms, volume 65, issue 1...Publications (published) during reporting period: A. Cornelio, E. Loli Piccolomini, and J. G. Nagy. Constrained Variable Projection Method for Blind

Pump-dump iterative squeezing of vibrational wave packets.

PubMed

Chang, Bo Y; Sola, Ignacio R

2005-12-22

The free motion of a nonstationary vibrational wave packet in an electronic potential is a source of interesting quantum properties. In this work we propose an iterative scheme that allows continuous stretching and squeezing of a wave packet in the ground or in an excited electronic state, by switching the wave function between both potentials with pi pulses at certain times. Using a simple model of displaced harmonic oscillators and delta pulses, we derive the analytical solution and the conditions for its possible implementation and optimization in different molecules and electronic states. We show that the main constraining parameter is the pulse bandwidth. Although in principle the degree of squeezing (or stretching) is not bounded, the physical resources increase quadratically with the number of iterations, while the achieved squeezing only increases linearly.

Use of system identification techniques for improving airframe finite element models using test data

NASA Technical Reports Server (NTRS)

Hanagud, Sathya V.; Zhou, Weiyu; Craig, James I.; Weston, Neil J.

1991-01-01

A method for using system identification techniques to improve airframe finite element models was developed and demonstrated. The method uses linear sensitivity matrices to relate changes in selected physical parameters to changes in total system matrices. The values for these physical parameters were determined using constrained optimization with singular value decomposition. The method was confirmed using both simple and complex finite element models for which pseudo-experimental data was synthesized directly from the finite element model. The method was then applied to a real airframe model which incorporated all the complexities and details of a large finite element model and for which extensive test data was available. The method was shown to work, and the differences between the identified model and the measured results were considered satisfactory.

Sound reproduction in personal audio systems using the least-squares approach with acoustic contrast control constraint.

PubMed

Cai, Yefeng; Wu, Ming; Yang, Jun

2014-02-01

This paper describes a method for focusing the reproduced sound in the bright zone without disturbing other people in the dark zone in personal audio systems. The proposed method combines the least-squares and acoustic contrast criteria. A constrained parameter is introduced to tune the balance between two performance indices, namely, the acoustic contrast and the spatial average error. An efficient implementation of this method using convex optimization is presented. Offline simulations and real-time experiments using a linear loudspeaker array are conducted to evaluate the performance of the presented method. Results show that compared with the traditional acoustic contrast control method, the proposed method can improve the flatness of response in the bright zone by sacrificing the level of acoustic contrast.

A greedy algorithm for species selection in dimension reduction of combustion chemistry

NASA Astrophysics Data System (ADS)

Hiremath, Varun; Ren, Zhuyin; Pope, Stephen B.

2010-09-01

Computational calculations of combustion problems involving large numbers of species and reactions with a detailed description of the chemistry can be very expensive. Numerous dimension reduction techniques have been developed in the past to reduce the computational cost. In this paper, we consider the rate controlled constrained-equilibrium (RCCE) dimension reduction method, in which a set of constrained species is specified. For a given number of constrained species, the 'optimal' set of constrained species is that which minimizes the dimension reduction error. The direct determination of the optimal set is computationally infeasible, and instead we present a greedy algorithm which aims at determining a 'good' set of constrained species; that is, one leading to near-minimal dimension reduction error. The partially-stirred reactor (PaSR) involving methane premixed combustion with chemistry described by the GRI-Mech 1.2 mechanism containing 31 species is used to test the algorithm. Results on dimension reduction errors for different sets of constrained species are presented to assess the effectiveness of the greedy algorithm. It is shown that the first four constrained species selected using the proposed greedy algorithm produce lower dimension reduction error than constraints on the major species: CH4, O2, CO2 and H2O. It is also shown that the first ten constrained species selected using the proposed greedy algorithm produce a non-increasing dimension reduction error with every additional constrained species; and produce the lowest dimension reduction error in many cases tested over a wide range of equivalence ratios, pressures and initial temperatures.

Comments on "The multisynapse neural network and its application to fuzzy clustering".

PubMed

Yu, Jian; Hao, Pengwei

2005-05-01

In the above-mentioned paper, Wei and Fahn proposed a neural architecture, the multisynapse neural network, to solve constrained optimization problems including high-order, logarithmic, and sinusoidal forms, etc. As one of its main applications, a fuzzy bidirectional associative clustering network (FBACN) was proposed for fuzzy-partition clustering according to the objective-functional method. The connection between the objective-functional-based fuzzy c-partition algorithms and FBACN is the Lagrange multiplier approach. Unfortunately, the Lagrange multiplier approach was incorrectly applied so that FBACN does not equivalently minimize its corresponding constrained objective-function. Additionally, Wei and Fahn adopted traditional definition of fuzzy c-partition, which is not satisfied by FBACN. Therefore, FBACN can not solve constrained optimization problems, either.

Investigation on Constrained Matrix Factorization for Hyperspectral Image Analysis

DTIC Science & Technology

2005-07-25

analysis. Keywords: matrix factorization; nonnegative matrix factorization; linear mixture model ; unsupervised linear unmixing; hyperspectral imagery...spatial resolution permits different materials present in the area covered by a single pixel. The linear mixture model says that a pixel reflectance in...in r. In the linear mixture model , r is considered as the linear mixture of m1, m2, …, mP as nMαr += (1) where n is included to account for

NEWSUMT: A FORTRAN program for inequality constrained function minimization, users guide

NASA Technical Reports Server (NTRS)

Miura, H.; Schmit, L. A., Jr.

1979-01-01

A computer program written in FORTRAN subroutine form for the solution of linear and nonlinear constrained and unconstrained function minimization problems is presented. The algorithm is the sequence of unconstrained minimizations using the Newton's method for unconstrained function minimizations. The use of NEWSUMT and the definition of all parameters are described.

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.

A novel approach based on preference-based index for interval bilevel linear programming problem.

PubMed

Ren, Aihong; Wang, Yuping; Xue, Xingsi

2017-01-01

This paper proposes a new methodology for solving the interval bilevel linear programming problem in which all coefficients of both objective functions and constraints are considered as interval numbers. In order to keep as much uncertainty of the original constraint region as possible, the original problem is first converted into an interval bilevel programming problem with interval coefficients in both objective functions only through normal variation of interval number and chance-constrained programming. With the consideration of different preferences of different decision makers, the concept of the preference level that the interval objective function is preferred to a target interval is defined based on the preference-based index. Then a preference-based deterministic bilevel programming problem is constructed in terms of the preference level and the order relation [Formula: see text]. Furthermore, the concept of a preference δ -optimal solution is given. Subsequently, the constructed deterministic nonlinear bilevel problem is solved with the help of estimation of distribution algorithm. Finally, several numerical examples are provided to demonstrate the effectiveness of the proposed approach.

Constrained non-linear multi-objective optimisation of preventive maintenance scheduling for offshore wind farms

NASA Astrophysics Data System (ADS)

Zhong, Shuya; Pantelous, Athanasios A.; Beer, Michael; Zhou, Jian

2018-05-01

Offshore wind farm is an emerging source of renewable energy, which has been shown to have tremendous potential in recent years. In this blooming area, a key challenge is that the preventive maintenance of offshore turbines should be scheduled reasonably to satisfy the power supply without failure. In this direction, two significant goals should be considered simultaneously as a trade-off. One is to maximise the system reliability and the other is to minimise the maintenance related cost. Thus, a non-linear multi-objective programming model is proposed including two newly defined objectives with thirteen families of constraints suitable for the preventive maintenance of offshore wind farms. In order to solve our model effectively, the nondominated sorting genetic algorithm II, especially for the multi-objective optimisation is utilised and Pareto-optimal solutions of schedules can be obtained to offer adequate support to decision-makers. Finally, an example is given to illustrate the performances of the devised model and algorithm, and explore the relationships of the two targets with the help of a contrast model.

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.

Coordinated trajectory planning of dual-arm space robot using constrained particle swarm optimization

NASA Astrophysics Data System (ADS)

Wang, Mingming; Luo, Jianjun; Yuan, Jianping; Walter, Ulrich

2018-05-01

Application of the multi-arm space robot will be more effective than single arm especially when the target is tumbling. This paper investigates the application of particle swarm optimization (PSO) strategy to coordinated trajectory planning of the dual-arm space robot in free-floating mode. In order to overcome the dynamics singularities issue, the direct kinematics equations in conjunction with constrained PSO are employed for coordinated trajectory planning of dual-arm space robot. The joint trajectories are parametrized with Bézier curve to simplify the calculation. Constrained PSO scheme with adaptive inertia weight is implemented to find the optimal solution of joint trajectories while specific objectives and imposed constraints are satisfied. The proposed method is not sensitive to the singularity issue due to the application of forward kinematic equations. Simulation results are presented for coordinated trajectory planning of two kinematically redundant manipulators mounted on a free-floating spacecraft and demonstrate the effectiveness of the proposed method.

Deterministic Reconfigurable Control Design for the X-33 Vehicle

NASA Technical Reports Server (NTRS)

Wagner, Elaine A.; Burken, John J.; Hanson, Curtis E.; Wohletz, Jerry M.

1998-01-01

In the event of a control surface failure, the purpose of a reconfigurable control system is to redistribute the control effort among the remaining working surfaces such that satisfactory stability and performance are retained. Four reconfigurable control design methods were investigated for the X-33 vehicle: Redistributed Pseudo-Inverse, General Constrained Optimization, Automated Failure Dependent Gain Schedule, and an Off-line Nonlinear General Constrained Optimization. The Off-line Nonlinear General Constrained Optimization approach was chosen for implementation on the X-33. Two example failures are shown, a right outboard elevon jam at 25 deg. at a Mach 3 entry condition, and a left rudder jam at 30 degrees. Note however, that reconfigurable control laws have been designed for the entire flight envelope. Comparisons between responses with the nominal controller and reconfigurable controllers show the benefits of reconfiguration. Single jam aerosurface failures were considered, and failure detection and identification is considered accomplished in the actuator controller. The X-33 flight control system will incorporate reconfigurable flight control in the baseline system.

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.

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

Constrained minimization of smooth functions using a genetic algorithm

NASA Technical Reports Server (NTRS)

Moerder, Daniel D.; Pamadi, Bandu N.

1994-01-01

The use of genetic algorithms for minimization of differentiable functions that are subject to differentiable constraints is considered. A technique is demonstrated for converting the solution of the necessary conditions for a constrained minimum into an unconstrained function minimization. This technique is extended as a global constrained optimization algorithm. The theory is applied to calculating minimum-fuel ascent control settings for an energy state model of an aerospace plane.

Incorporating a Constrained Optimization Algorithm into Remote- Sensing/Precision Agriculture Methodology

NASA Astrophysics Data System (ADS)

Morgenthaler, George; Khatib, Nader; Kim, Byoungsoo

with information to improve their crop's vigor has been a major topic of interest. With world population growing exponentially, arable land being consumed by urbanization, and an unfavorable farm economy, the efficiency of farming must increase to meet future food requirements and to make farming a sustainable occupation for the farmer. "Precision Agriculture" refers to a farming methodology that applies nutrients and moisture only where and when they are needed in the field. The goal is to increase farm revenue by increasing crop yield and decreasing applications of costly chemical and water treatments. In addition, this methodology will decrease the environmental costs of farming, i.e., reduce air, soil, and water pollution. Sensing/Precision Agriculture has not grown as rapidly as early advocates envisioned. Technology for a successful Remote Sensing/Precision Agriculture system is now available. Commercial satellite systems can image (multi-spectral) the Earth with a resolution of approximately 2.5 m. Variable precision dispensing systems using GPS are available and affordable. Crop models that predict yield as a function of soil, chemical, and irrigation parameter levels have been formulated. Personal computers and internet access are in place in most farm homes and can provide a mechanism to periodically disseminate, e.g. bi-weekly, advice on what quantities of water and chemicals are needed in individual regions of the field. What is missing is a model that fuses the disparate sources of information on the current states of the crop and soil, and the remaining resource levels available with the decisions farmers are required to make. This must be a product that is easy for the farmer to understand and to implement. A "Constrained Optimization Feed-back Control Model" to fill this void will be presented. The objective function of the model will be used to maximize the farmer's profit by increasing yields while decreasing environmental costs and decreasing application of costly treatments. This model will incorporate information from remote sensing, in-situ weather sources, soil measurements, crop models, and tacit farmer knowledge of the relative productivity of the selected control regions of the farm to provide incremental advice throughout the growing season on water and chemical treatments. Genetic and meta-heuristic algorithms will be used to solve the constrained optimization problem that possesses complex constraints and a non-linear objective function. *

Testing the Einstein's equivalence principle with polarized gamma-ray bursts

NASA Astrophysics Data System (ADS)

Yang, Chao; Zou, Yuan-Chuan; Zhang, Yue-Yang; Liao, Bin; Lei, Wei-Hua

2017-07-01

The Einstein's equivalence principle can be tested by using parametrized post-Newtonian parameters, of which the parameter γ has been constrained by comparing the arrival times of photons with different energies. It has been constrained by a variety of astronomical transient events, such as gamma-ray bursts (GRBs), fast radio bursts as well as pulses of pulsars, with the most stringent constraint of Δγ ≲ 10-15. In this Letter, we consider the arrival times of lights with different circular polarization. For a linearly polarized light, it is the combination of two circularly polarized lights. If the arrival time difference between the two circularly polarized lights is too large, their combination may lose the linear polarization. We constrain the value of Δγp < 1.6 × 10-27 by the measurement of the polarization of GRB 110721A, which is the most stringent constraint ever achieved.

Existence and Optimality Conditions for Risk-Averse PDE-Constrained Optimization

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

Kouri, Drew Philip; Surowiec, Thomas M.

Uncertainty is ubiquitous in virtually all engineering applications, and, for such problems, it is inadequate to simulate the underlying physics without quantifying the uncertainty in unknown or random inputs, boundary and initial conditions, and modeling assumptions. Here in this paper, we introduce a general framework for analyzing risk-averse optimization problems constrained by partial differential equations (PDEs). In particular, we postulate conditions on the random variable objective function as well as the PDE solution that guarantee existence of minimizers. Furthermore, we derive optimality conditions and apply our results to the control of an environmental contaminant. Lastly, we introduce a new riskmore » measure, called the conditional entropic risk, that fuses desirable properties from both the conditional value-at-risk and the entropic risk measures.« less

Existence and Optimality Conditions for Risk-Averse PDE-Constrained Optimization

DOE PAGES

Kouri, Drew Philip; Surowiec, Thomas M.

2018-06-05

Uncertainty is ubiquitous in virtually all engineering applications, and, for such problems, it is inadequate to simulate the underlying physics without quantifying the uncertainty in unknown or random inputs, boundary and initial conditions, and modeling assumptions. Here in this paper, we introduce a general framework for analyzing risk-averse optimization problems constrained by partial differential equations (PDEs). In particular, we postulate conditions on the random variable objective function as well as the PDE solution that guarantee existence of minimizers. Furthermore, we derive optimality conditions and apply our results to the control of an environmental contaminant. Lastly, we introduce a new riskmore » measure, called the conditional entropic risk, that fuses desirable properties from both the conditional value-at-risk and the entropic risk measures.« less

Memory and Energy Optimization Strategies for Multithreaded Operating System on the Resource-Constrained Wireless Sensor Node

PubMed Central

Liu, Xing; Hou, Kun Mean; de Vaulx, Christophe; Xu, Jun; Yang, Jianfeng; Zhou, Haiying; Shi, Hongling; Zhou, Peng

2015-01-01

Memory and energy optimization strategies are essential for the resource-constrained wireless sensor network (WSN) nodes. In this article, a new memory-optimized and energy-optimized multithreaded WSN operating system (OS) LiveOS is designed and implemented. Memory cost of LiveOS is optimized by using the stack-shifting hybrid scheduling approach. Different from the traditional multithreaded OS in which thread stacks are allocated statically by the pre-reservation, thread stacks in LiveOS are allocated dynamically by using the stack-shifting technique. As a result, memory waste problems caused by the static pre-reservation can be avoided. In addition to the stack-shifting dynamic allocation approach, the hybrid scheduling mechanism which can decrease both the thread scheduling overhead and the thread stack number is also implemented in LiveOS. With these mechanisms, the stack memory cost of LiveOS can be reduced more than 50% if compared to that of a traditional multithreaded OS. Not is memory cost optimized, but also the energy cost is optimized in LiveOS, and this is achieved by using the multi-core “context aware” and multi-core “power-off/wakeup” energy conservation approaches. By using these approaches, energy cost of LiveOS can be reduced more than 30% when compared to the single-core WSN system. Memory and energy optimization strategies in LiveOS not only prolong the lifetime of WSN nodes, but also make the multithreaded OS feasible to run on the memory-constrained WSN nodes. PMID:25545264

Linear quadratic optimization for positive LTI system

NASA Astrophysics Data System (ADS)

Muhafzan, Yenti, Syafrida Wirma; Zulakmal

2017-05-01

Nowaday the linear quadratic optimization subject to positive linear time invariant (LTI) system constitute an interesting study considering it can become a mathematical model of variety of real problem whose variables have to nonnegative and trajectories generated by these variables must be nonnegative. In this paper we propose a method to generate an optimal control of linear quadratic optimization subject to positive linear time invariant (LTI) system. A sufficient condition that guarantee the existence of such optimal control is discussed.

Mixed-Strategy Chance Constrained Optimal Control

NASA Technical Reports Server (NTRS)

Ono, Masahiro; Kuwata, Yoshiaki; Balaram, J.

2013-01-01

This paper presents a novel chance constrained optimal control (CCOC) algorithm that chooses a control action probabilistically. A CCOC problem is to find a control input that minimizes the expected cost while guaranteeing that the probability of violating a set of constraints is below a user-specified threshold. We show that a probabilistic control approach, which we refer to as a mixed control strategy, enables us to obtain a cost that is better than what deterministic control strategies can achieve when the CCOC problem is nonconvex. The resulting mixed-strategy CCOC problem turns out to be a convexification of the original nonconvex CCOC problem. Furthermore, we also show that a mixed control strategy only needs to "mix" up to two deterministic control actions in order to achieve optimality. Building upon an iterative dual optimization, the proposed algorithm quickly converges to the optimal mixed control strategy with a user-specified tolerance.

Kalman Filter Constraint Tuning for Turbofan Engine Health Estimation

NASA Technical Reports Server (NTRS)

Simon, Dan; Simon, Donald L.

2005-01-01

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints are often neglected because they do not fit easily into the structure of the Kalman filter. Recently published work has shown a new method for incorporating state variable inequality constraints in the Kalman filter, which has been shown to generally improve the filter s estimation accuracy. However, the incorporation of inequality constraints poses some risk to the estimation accuracy as the Kalman filter is theoretically optimal. This paper proposes a way to tune the filter constraints so that the state estimates follow the unconstrained (theoretically optimal) filter when the confidence in the unconstrained filter is high. When confidence in the unconstrained filter is not so high, then we use our heuristic knowledge to constrain the state estimates. The confidence measure is based on the agreement of measurement residuals with their theoretical values. The algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate engine health.

Application of multivariable search techniques to structural design optimization

NASA Technical Reports Server (NTRS)

Jones, R. T.; Hague, D. S.

1972-01-01

Multivariable optimization techniques are applied to a particular class of minimum weight structural design problems: the design of an axially loaded, pressurized, stiffened cylinder. Minimum weight designs are obtained by a variety of search algorithms: first- and second-order, elemental perturbation, and randomized techniques. An exterior penalty function approach to constrained minimization is employed. Some comparisons are made with solutions obtained by an interior penalty function procedure. In general, it would appear that an interior penalty function approach may not be as well suited to the class of design problems considered as the exterior penalty function approach. It is also shown that a combination of search algorithms will tend to arrive at an extremal design in a more reliable manner than a single algorithm. The effect of incorporating realistic geometrical constraints on stiffener cross-sections is investigated. A limited comparison is made between minimum weight cylinders designed on the basis of a linear stability analysis and cylinders designed on the basis of empirical buckling data. Finally, a technique for locating more than one extremal is demonstrated.

Sparseness- and continuity-constrained seismic imaging

NASA Astrophysics Data System (ADS)

Herrmann, Felix J.

2005-04-01

Non-linear solution strategies to the least-squares seismic inverse-scattering problem with sparseness and continuity constraints are proposed. Our approach is designed to (i) deal with substantial amounts of additive noise (SNR < 0 dB); (ii) use the sparseness and locality (both in position and angle) of directional basis functions (such as curvelets and contourlets) on the model: the reflectivity; and (iii) exploit the near invariance of these basis functions under the normal operator, i.e., the scattering-followed-by-imaging operator. Signal-to-noise ratio and the continuity along the imaged reflectors are significantly enhanced by formulating the solution of the seismic inverse problem in terms of an optimization problem. During the optimization, sparseness on the basis and continuity along the reflectors are imposed by jointly minimizing the l1- and anisotropic diffusion/total-variation norms on the coefficients and reflectivity, respectively. [Joint work with Peyman P. Moghaddam was carried out as part of the SINBAD project, with financial support secured through ITF (the Industry Technology Facilitator) from the following organizations: BG Group, BP, ExxonMobil, and SHELL. Additional funding came from the NSERC Discovery Grants 22R81254.

A real-time approximate optimal guidance law for flight in a plane

NASA Technical Reports Server (NTRS)

Feeley, Timothy S.; Speyer, Jason L.

1990-01-01

A real-time guidance scheme is presented for the problem of maximizing the payload into orbit subject to the equations of motion of a rocket over a nonrotating spherical earth. The flight is constrained to a path in the equatorial plane while reaching an orbital altitude at orbital injection speeds. The dynamics of the problem can be separated into primary and perturbation effects by a small parameter, epsilon, which is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in an asymptotic series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The neglected perturbation terms are included in the higher-order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only integrations which are quadratures. The quadratures can be performed rapidly with emerging computer capability, so that real-time approximate optimization can be used to construct the launch guidance law. The application of this technique to flight in three-dimensions is made apparent from the solution presented.

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.

Solution of a Complex Least Squares Problem with Constrained Phase.

PubMed

Bydder, Mark

2010-12-30

The least squares solution of a complex linear equation is in general a complex vector with independent real and imaginary parts. In certain applications in magnetic resonance imaging, a solution is desired such that each element has the same phase. A direct method for obtaining the least squares solution to the phase constrained problem is described.

Constrained Multi-Level Algorithm for Trajectory Optimization

NASA Astrophysics Data System (ADS)

Adimurthy, V.; Tandon, S. R.; Jessy, Antony; Kumar, C. Ravi

The emphasis on low cost access to space inspired many recent developments in the methodology of trajectory optimization. Ref.1 uses a spectral patching method for optimization, where global orthogonal polynomials are used to describe the dynamical constraints. A two-tier approach of optimization is used in Ref.2 for a missile mid-course trajectory optimization. A hybrid analytical/numerical approach is described in Ref.3, where an initial analytical vacuum solution is taken and gradually atmospheric effects are introduced. Ref.4 emphasizes the fact that the nonlinear constraints which occur in the initial and middle portions of the trajectory behave very nonlinearly with respect the variables making the optimization very difficult to solve in the direct and indirect shooting methods. The problem is further made complex when different phases of the trajectory have different objectives of optimization and also have different path constraints. Such problems can be effectively addressed by multi-level optimization. In the multi-level methods reported so far, optimization is first done in identified sub-level problems, where some coordination variables are kept fixed for global iteration. After all the sub optimizations are completed, higher-level optimization iteration with all the coordination and main variables is done. This is followed by further sub system optimizations with new coordination variables. This process is continued until convergence. In this paper we use a multi-level constrained optimization algorithm which avoids the repeated local sub system optimizations and which also removes the problem of non-linear sensitivity inherent in the single step approaches. Fall-zone constraints, structural load constraints and thermal constraints are considered. In this algorithm, there is only a single multi-level sequence of state and multiplier updates in a framework of an augmented Lagrangian. Han Tapia multiplier updates are used in view of their special role in diagonalised methods, being the only single update with quadratic convergence. For a single level, the diagonalised multiplier method (DMM) is described in Ref.5. The main advantage of the two-level analogue of the DMM approach is that it avoids the inner loop optimizations required in the other methods. The scheme also introduces a gradient change measure to reduce the computational time needed to calculate the gradients. It is demonstrated that the new multi-level scheme leads to a robust procedure to handle the sensitivity of the constraints, and the multiple objectives of different trajectory phases. Ref. 1. Fahroo, F and Ross, M., " A Spectral Patching Method for Direct Trajectory Optimization" The Journal of the Astronautical Sciences, Vol.48, 2000, pp.269-286 Ref. 2. Phililps, C.A. and Drake, J.C., "Trajectory Optimization for a Missile using a Multitier Approach" Journal of Spacecraft and Rockets, Vol.37, 2000, pp.663-669 Ref. 3. Gath, P.F., and Calise, A.J., " Optimization of Launch Vehicle Ascent Trajectories with Path Constraints and Coast Arcs", Journal of Guidance, Control, and Dynamics, Vol. 24, 2001, pp.296-304 Ref. 4. Betts, J.T., " Survey of Numerical Methods for Trajectory Optimization", Journal of Guidance, Control, and Dynamics, Vol.21, 1998, pp. 193-207 Ref. 5. Adimurthy, V., " Launch Vehicle Trajectory Optimization", Acta Astronautica, Vol.15, 1987, pp.845-850.

A quantitative method for evaluating inferior glenohumeral joint stiffness using ultrasonography.

PubMed

Tsai, Wen-Wei; Lee, Ming-Yih; Yeh, Wen-Lin; Cheng, Shih-Chung; Soon, Kok-Soon; Lei, Kin Fong; Lin, Wen-Yen

2013-02-01

Subluxation of the affected shoulder in post-stroke patients is associated with nerve disorders and muscle fatigue. Clinicians must be able to accurately and reliably measure inferior glenohumeral subluxation in patients to provide appropriate treatment. However, quantitative methods for evaluating the laxity and stiffness of the glenohumeral joint (GHJ) are still being developed. The aim of this study was to develop a new protocol for evaluating the laxity and stiffness of the inferior GHJ using ultrasonography under optimal testing conditions and to investigate changes in the GHJ from a commercially available humerus brace and shoulder brace. Multistage inferior displacement forces were applied to create a glide between the most cephalad point on the visible anterosuperior surface of the humeral head and coracoid process in seven healthy volunteers. GHJ stiffness was defined as the slope of the linear regression line between the glides and different testing loads. The testing conditions were defined by different test loading mechanisms (n=2), shoulder constraining conditions (n=2), and loading modes (n=4). The optimal testing condition was defined as the condition with the least residual variance of measured laxity to the calculated stiffness under different testing loads. A paired t-test was used to compare the laxity and stiffness of the inferior GHJ using different braces. No significant difference was identified between the two test loading mechanisms (t=0.218, p=0.831) and two shoulder constraining conditions (t=-0.235, p=0.818). We concluded that ultrasonographic laxity measurements performed using a pulley set loading mechanism was as reliable as direct loading. Additionally, constraining the unloaded shoulder was proposed due to the lower mean residual variance value. Moreover, pulling the elbow downward with loading on the upper arm was suggested, as pulling the elbow downward with the elbow flexed and loading on the forearm may overestimate stiffness and pain in the inferior GHJ at the loading point due to friction between the wide belt and skin. Furthermore, subjects wearing a humerus brace with a belt, which creates the effect of lifting the humerus toward the acromion, had greater GHJ stiffness compared to subjects wearing a shoulder brace without a belt to lift the humerus under the proposed testing conditions. This study provides experimental evidence that shoulder braces may reduce GHJ laxity under an external load, implying that the use of a humeral brace can prevent subluxation in post-stroke patients. The resulting optimal testing conditions for measuring the laxity and stiffness of the GHJ is to constrain the unloaded shoulder and bend the loaded arm at the elbow with loading on the upper arm using a pulley system. Copyright © 2011 IPEM. Published by Elsevier Ltd. All rights reserved.

Developments in Stochastic Fuel Efficient Cruise Control and Constrained Control with Applications to Aircraft

NASA Astrophysics Data System (ADS)

McDonough, Kevin K.

The dissertation presents contributions to fuel-efficient control of vehicle speed and constrained control with applications to aircraft. In the first part of this dissertation a stochastic approach to fuel-efficient vehicle speed control is developed. This approach encompasses stochastic modeling of road grade and traffic speed, modeling of fuel consumption through the use of a neural network, and the application of stochastic dynamic programming to generate vehicle speed control policies that are optimized for the trade-off between fuel consumption and travel time. The fuel economy improvements with the proposed policies are quantified through simulations and vehicle experiments. It is shown that the policies lead to the emergence of time-varying vehicle speed patterns that are referred to as time-varying cruise. Through simulations and experiments it is confirmed that these time-varying vehicle speed profiles are more fuel-efficient than driving at a comparable constant speed. Motivated by these results, a simpler implementation strategy that is more appealing for practical implementation is also developed. This strategy relies on a finite state machine and state transition threshold optimization, and its benefits are quantified through model-based simulations and vehicle experiments. Several additional contributions are made to approaches for stochastic modeling of road grade and vehicle speed that include the use of Kullback-Liebler divergence and divergence rate and a stochastic jump-like model for the behavior of the road grade. In the second part of the dissertation, contributions to constrained control with applications to aircraft are described. Recoverable sets and integral safe sets of initial states of constrained closed-loop systems are introduced first and computational procedures of such sets based on linear discrete-time models are given. The use of linear discrete-time models is emphasized as they lead to fast computational procedures. Examples of these sets for aircraft longitudinal and lateral aircraft dynamics are reported, and it is shown that these sets can be larger in size compared to the more commonly used safe sets. An approach to constrained maneuver planning based on chaining recoverable sets or integral safe sets is described and illustrated with a simulation example. To facilitate the application of this maneuver planning approach in aircraft loss of control (LOC) situations when the model is only identified at the current trim condition but when these sets need to be predicted at other flight conditions, the dependence trends of the safe and recoverable sets on aircraft flight conditions are characterized. The scaling procedure to estimate subsets of safe and recoverable sets at one trim condition based on their knowledge at another trim condition is defined. Finally, two control schemes that exploit integral safe sets are proposed. The first scheme, referred to as the controller state governor (CSG), resets the controller state (typically an integrator) to enforce the constraints and enlarge the set of plant states that can be recovered without constraint violation. The second scheme, referred to as the controller state and reference governor (CSRG), combines the controller state governor with the reference governor control architecture and provides the capability of simultaneously modifying the reference command and the controller state to enforce the constraints. Theoretical results that characterize the response properties of both schemes are presented. Examples are reported that illustrate the operation of these schemes on aircraft flight dynamics models and gas turbine engine dynamic models.

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.

Solution techniques for transient stability-constrained optimal power flow – Part II

DOE PAGES

Geng, Guangchao; Abhyankar, Shrirang; Wang, Xiaoyu; ...

2017-06-28

Transient stability-constrained optimal power flow is an important emerging problem with power systems pushed to the limits for economic benefits, dense and larger interconnected systems, and reduced inertia due to expected proliferation of renewable energy resources. In this study, two more approaches: single machine equivalent and computational intelligence are presented. Also discussed are various application areas, and future directions in this research area. In conclusion, a comprehensive resource for the available literature, publicly available test systems, and relevant numerical libraries is also provided.

Solution techniques for transient stability-constrained optimal power flow – Part II

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

Geng, Guangchao; Abhyankar, Shrirang; Wang, Xiaoyu

Transient stability-constrained optimal power flow is an important emerging problem with power systems pushed to the limits for economic benefits, dense and larger interconnected systems, and reduced inertia due to expected proliferation of renewable energy resources. In this study, two more approaches: single machine equivalent and computational intelligence are presented. Also discussed are various application areas, and future directions in this research area. In conclusion, a comprehensive resource for the available literature, publicly available test systems, and relevant numerical libraries is also provided.

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.

Spacecraft Constrained Maneuver Planning Using Positively Invariant Constraint Admissible Sets (Postprint)

DTIC Science & Technology

2013-08-14

Connectivity Graph; Graph Search; Bounded Disturbances; Linear Time-Varying (LTV); Clohessy - Wiltshire -Hill (CWH) 16. SECURITY CLASSIFICATION OF: 17...the linearization of the relative motion model given by the Hill- Clohessy - Wiltshire (CWH) equations is used [14]. A. Nonlinear equations of motion...equations can be used to describe the motion of the debris. B. Linearized HCW equations in discrete-time For δr << R, the linearized Hill- Clohessy

The scope of the LeChatelier Principle

NASA Astrophysics Data System (ADS)

George M., Lady; Quirk, James P.

2007-07-01

LeChatelier [Comptes Rendus 99 (1884) 786; Ann. Mines 13 (2) (1888) 157] showed that a physical system's “adjustment” to a disturbance to its equilibrium tended to be smaller as constraints were added to the adjustment process. Samuelson [Foundations of Economic Analysis, Harvard University Press, Cambridge, 1947] applied this result to economics in the context of the comparative statics of the actions of individual agents characterized as the solutions to optimization problems; and later (1960), extended the application of the Principle to a stable, multi-market equilibrium and the case of all commodities gross substitutes [e.g., L. Metzler, Stability of multiple markets: the hicks conditions. Econometrica 13 (1945) 277-292]. Refinements and alternative routes of derivation have appeared in the literature since then, e.g., Silberberg [The LeChatelier Principle as a corollary to a generalized envelope theorem, J. Econ. Theory 3 (1971) 146-155; A revision of comparative statics methodology in economics, or, how to do comparative statics on the back of an envelope, J. Econ. Theory 7 (1974) 159-172], Milgrom and Roberts [The LeChatelier Principle, Am. Econ. Rev. 86 (1996) 173-179], W. Suen, E. Silberberg, P. Tseng [The LeChatelier Principle: the long and the short of it, Econ. Theory 16 (2000) 471-476], and Chavas [A global analysis of constrained behavior: the LeChatelier Principle ‘in the large’, South. Econ. J. 72 (3) (2006) 627-644]. In this paper, we expand the scope of the Principle in various ways keyed to Samuelson's proposed means of testing comparative statics results (optimization, stability, and qualitative analysis). In the optimization framework, we show that the converse LeChatelier Principle also can be found in constrained optimization problems and for not initially “conjugate” sensitivities. We then show how the Principle and its converse can be found through the qualitative analysis of any linear system. In these terms, the Principle and its converse also may be found in the same system at the same time with respect to the imposition of the same constraint. Based upon this, we expand the cases for which the Principle can be found based upon the stability hypothesis.

Optimization-based channel constrained data aggregation routing algorithms in multi-radio wireless sensor networks.

PubMed

Yen, Hong-Hsu

2009-01-01

In wireless sensor networks, data aggregation routing could reduce the number of data transmissions so as to achieve energy efficient transmission. However, data aggregation introduces data retransmission that is caused by co-channel interference from neighboring sensor nodes. This kind of co-channel interference could result in extra energy consumption and significant latency from retransmission. This will jeopardize the benefits of data aggregation. One possible solution to circumvent data retransmission caused by co-channel interference is to assign different channels to every sensor node that is within each other's interference range on the data aggregation tree. By associating each radio with a different channel, a sensor node could receive data from all the children nodes on the data aggregation tree simultaneously. This could reduce the latency from the data source nodes back to the sink so as to meet the user's delay QoS. Since the number of radios on each sensor node and the number of non-overlapping channels are all limited resources in wireless sensor networks, a challenging question here is to minimize the total transmission cost under limited number of non-overlapping channels in multi-radio wireless sensor networks. This channel constrained data aggregation routing problem in multi-radio wireless sensor networks is an NP-hard problem. I first model this problem as a mixed integer and linear programming problem where the objective is to minimize the total transmission subject to the data aggregation routing, channel and radio resources constraints. The solution approach is based on the Lagrangean relaxation technique to relax some constraints into the objective function and then to derive a set of independent subproblems. By optimally solving these subproblems, it can not only calculate the lower bound of the original primal problem but also provide useful information to get the primal feasible solutions. By incorporating these Lagrangean multipliers as the link arc weight, the optimization-based heuristics are proposed to get energy-efficient data aggregation tree with better resource (channel and radio) utilization. From the computational experiments, the proposed optimization-based approach is superior to existing heuristics under all tested cases.

Competitive learning with pairwise constraints.

PubMed

Covões, Thiago F; Hruschka, Eduardo R; Ghosh, Joydeep

2013-01-01

Constrained clustering has been an active research topic since the last decade. Most studies focus on batch-mode algorithms. This brief introduces two algorithms for on-line constrained learning, named on-line linear constrained vector quantization error (O-LCVQE) and constrained rival penalized competitive learning (C-RPCL). The former is a variant of the LCVQE algorithm for on-line settings, whereas the latter is an adaptation of the (on-line) RPCL algorithm to deal with constrained clustering. The accuracy results--in terms of the normalized mutual information (NMI)--from experiments with nine datasets show that the partitions induced by O-LCVQE are competitive with those found by the (batch-mode) LCVQE. Compared with this formidable baseline algorithm, it is surprising that C-RPCL can provide better partitions (in terms of the NMI) for most of the datasets. Also, experiments on a large dataset show that on-line algorithms for constrained clustering can significantly reduce the computational time.

Spacecraft Mission Design for the Mitigation of the 2017 PDC Hypothetical Asteroid Threat

NASA Technical Reports Server (NTRS)

Barbee, Brent W.; Sarli, Bruno V.; Lyzhoft, Josh; Chodas, Paul W.; Englander, Jacob A.

2017-01-01

This paper presents a detailed mission design analysis results for the 2017 Planetary Defense Conference (PDC) Hypothetical Asteroid Impact Scenario, documented at https:cneos.jpl.nasa.govpdcspdc17. The mission design includes campaigns for both reconnaissance (flyby or rendezvous) of the asteroid (to characterize it and the nature of the threat it poses to Earth) and mitigation of the asteroid, via kinetic impactor deflection, nuclear explosive device (NED) deflection, or NED disruption. Relevant scenario parameters are varied to assess the sensitivity of the design outcome, such as asteroid bulk density, asteroid diameter, momentum enhancement factor, spacecraft launch vehicle, and mitigation system type. Different trajectory types are evaluated in the mission design process from purely ballistic to those involving optimal midcourse maneuvers, planetary gravity assists, and/or low-thrust solar electric propulsion. The trajectory optimization is targeted around peak deflection points that were found through a novel linear numerical technique method. The optimization process includes constrain parameters, such as Earth departure date, launch declination, spacecraft, asteroid relative velocity and solar phase angle, spacecraft dry mass, minimum/maximum spacecraft distances from Sun and Earth, and Earth-spacecraft communications line of sight. Results show that one of the best options for the 2017 PDC deflection is solar electric propelled rendezvous mission with a single spacecraft using NED for the deflection.

Spatial and Spin Symmetry Breaking in Semidefinite-Programming-Based Hartree-Fock Theory.

PubMed

Nascimento, Daniel R; DePrince, A Eugene

2018-05-08

The Hartree-Fock problem was recently recast as a semidefinite optimization over the space of rank-constrained two-body reduced-density matrices (RDMs) [ Phys. Rev. A 2014 , 89 , 010502(R) ]. This formulation of the problem transfers the nonconvexity of the Hartree-Fock energy functional to the rank constraint on the two-body RDM. We consider an equivalent optimization over the space of positive semidefinite one-electron RDMs (1-RDMs) that retains the nonconvexity of the Hartree-Fock energy expression. The optimized 1-RDM satisfies ensemble N-representability conditions, and ensemble spin-state conditions may be imposed as well. The spin-state conditions place additional linear and nonlinear constraints on the 1-RDM. We apply this RDM-based approach to several molecular systems and explore its spatial (point group) and spin ( Ŝ 2 and Ŝ 3 ) symmetry breaking properties. When imposing Ŝ 2 and Ŝ 3 symmetry but relaxing point group symmetry, the procedure often locates spatial-symmetry-broken solutions that are difficult to identify using standard algorithms. For example, the RDM-based approach yields a smooth, spatial-symmetry-broken potential energy curve for the well-known Be-H 2 insertion pathway. We also demonstrate numerically that, upon relaxation of Ŝ 2 and Ŝ 3 symmetry constraints, the RDM-based approach is equivalent to real-valued generalized Hartree-Fock theory.

MODOPTIM: A general optimization program for ground-water flow model calibration and ground-water management with MODFLOW

USGS Publications Warehouse

Halford, Keith J.

2006-01-01

MODOPTIM is a non-linear ground-water model calibration and management tool that simulates flow with MODFLOW-96 as a subroutine. A weighted sum-of-squares objective function defines optimal solutions for calibration and management problems. Water levels, discharges, water quality, subsidence, and pumping-lift costs are the five direct observation types that can be compared in MODOPTIM. Differences between direct observations of the same type can be compared to fit temporal changes and spatial gradients. Water levels in pumping wells, wellbore storage in the observation wells, and rotational translation of observation wells also can be compared. Negative and positive residuals can be weighted unequally so inequality constraints such as maximum chloride concentrations or minimum water levels can be incorporated in the objective function. Optimization parameters are defined with zones and parameter-weight matrices. Parameter change is estimated iteratively with a quasi-Newton algorithm and is constrained to a user-defined maximum parameter change per iteration. Parameters that are less sensitive than a user-defined threshold are not estimated. MODOPTIM facilitates testing more conceptual models by expediting calibration of each conceptual model. Examples of applying MODOPTIM to aquifer-test analysis, ground-water management, and parameter estimation problems are presented.

Use of system identification techniques for improving airframe finite element models using test data

NASA Technical Reports Server (NTRS)

Hanagud, Sathya V.; Zhou, Weiyu; Craig, James I.; Weston, Neil J.

1993-01-01

A method for using system identification techniques to improve airframe finite element models using test data was developed and demonstrated. The method uses linear sensitivity matrices to relate changes in selected physical parameters to changes in the total system matrices. The values for these physical parameters were determined using constrained optimization with singular value decomposition. The method was confirmed using both simple and complex finite element models for which pseudo-experimental data was synthesized directly from the finite element model. The method was then applied to a real airframe model which incorporated all of the complexities and details of a large finite element model and for which extensive test data was available. The method was shown to work, and the differences between the identified model and the measured results were considered satisfactory.

Joint sparse representation for robust multimodal biometrics recognition.

PubMed

Shekhar, Sumit; Patel, Vishal M; Nasrabadi, Nasser M; Chellappa, Rama

2014-01-01

Traditional biometric recognition systems rely on a single biometric signature for authentication. While the advantage of using multiple sources of information for establishing the identity has been widely recognized, computational models for multimodal biometrics recognition have only recently received attention. We propose a multimodal sparse representation method, which represents the test data by a sparse linear combination of training data, while constraining the observations from different modalities of the test subject to share their sparse representations. Thus, we simultaneously take into account correlations as well as coupling information among biometric modalities. A multimodal quality measure is also proposed to weigh each modality as it gets fused. Furthermore, we also kernelize the algorithm to handle nonlinearity in data. The optimization problem is solved using an efficient alternative direction method. Various experiments show that the proposed method compares favorably with competing fusion-based methods.

The generalized quadratic knapsack problem. A neuronal network approach.

PubMed

Talaván, Pedro M; Yáñez, Javier

2006-05-01

The solution of an optimization problem through the continuous Hopfield network (CHN) is based on some energy or Lyapunov function, which decreases as the system evolves until a local minimum value is attained. A new energy function is proposed in this paper so that any 0-1 linear constrains programming with quadratic objective function can be solved. This problem, denoted as the generalized quadratic knapsack problem (GQKP), includes as particular cases well-known problems such as the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). This new energy function generalizes those proposed by other authors. Through this energy function, any GQKP can be solved with an appropriate parameter setting procedure, which is detailed in this paper. As a particular case, and in order to test this generalized energy function, some computational experiments solving the traveling salesman problem are also included.

High Order Entropy-Constrained Residual VQ for Lossless Compression of Images

NASA Technical Reports Server (NTRS)

Kossentini, Faouzi; Smith, Mark J. T.; Scales, Allen

1995-01-01

High order entropy coding is a powerful technique for exploiting high order statistical dependencies. However, the exponentially high complexity associated with such a method often discourages its use. In this paper, an entropy-constrained residual vector quantization method is proposed for lossless compression of images. The method consists of first quantizing the input image using a high order entropy-constrained residual vector quantizer and then coding the residual image using a first order entropy coder. The distortion measure used in the entropy-constrained optimization is essentially the first order entropy of the residual image. Experimental results show very competitive performance.

Inexact fuzzy-stochastic mixed-integer programming approach for long-term planning of waste management--Part A: methodology.

PubMed

Guo, P; Huang, G H

2009-01-01

In this study, an inexact fuzzy chance-constrained two-stage mixed-integer linear programming (IFCTIP) approach is proposed for supporting long-term planning of waste-management systems under multiple uncertainties in the City of Regina, Canada. The method improves upon the existing inexact two-stage programming and mixed-integer linear programming techniques by incorporating uncertainties expressed as multiple uncertainties of intervals and dual probability distributions within a general optimization framework. The developed method can provide an effective linkage between the predefined environmental policies and the associated economic implications. Four special characteristics of the proposed method make it unique compared with other optimization techniques that deal with uncertainties. Firstly, it provides a linkage to predefined policies that have to be respected when a modeling effort is undertaken; secondly, it is useful for tackling uncertainties presented as intervals, probabilities, fuzzy sets and their incorporation; thirdly, it facilitates dynamic analysis for decisions of facility-expansion planning and waste-flow allocation within a multi-facility, multi-period, multi-level, and multi-option context; fourthly, the penalties are exercised with recourse against any infeasibility, which permits in-depth analyses of various policy scenarios that are associated with different levels of economic consequences when the promised solid waste-generation rates are violated. In a companion paper, the developed method is applied to a real case for the long-term planning of waste management in the City of Regina, Canada.

Constrained variational calculus for higher order classical field theories

NASA Astrophysics Data System (ADS)

Campos, Cédric M.; de León, Manuel; Martín de Diego, David

2010-11-01

We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.

Design optimization of axial flow hydraulic turbine runner: Part II - multi-objective constrained optimization method

NASA Astrophysics Data System (ADS)

Peng, Guoyi; Cao, Shuliang; Ishizuka, Masaru; Hayama, Shinji

2002-06-01

This paper is concerned with the design optimization of axial flow hydraulic turbine runner blade geometry. In order to obtain a better design plan with good performance, a new comprehensive performance optimization procedure has been presented by combining a multi-variable multi-objective constrained optimization model with a Q3D inverse computation and a performance prediction procedure. With careful analysis of the inverse design of axial hydraulic turbine runner, the total hydraulic loss and the cavitation coefficient are taken as optimization objectives and a comprehensive objective function is defined using the weight factors. Parameters of a newly proposed blade bound circulation distribution function and parameters describing positions of blade leading and training edges in the meridional flow passage are taken as optimization variables.The optimization procedure has been applied to the design optimization of a Kaplan runner with specific speed of 440 kW. Numerical results show that the performance of designed runner is successfully improved through optimization computation. The optimization model is found to be validated and it has the feature of good convergence. With the multi-objective optimization model, it is possible to control the performance of designed runner by adjusting the value of weight factors defining the comprehensive objective function. Copyright

Robust Path Planning and Feedback Design Under Stochastic Uncertainty

NASA Technical Reports Server (NTRS)

Blackmore, Lars

2008-01-01

Autonomous vehicles require optimal path planning algorithms to achieve mission goals while avoiding obstacles and being robust to uncertainties. The uncertainties arise from exogenous disturbances, modeling errors, and sensor noise, which can be characterized via stochastic models. Previous work defined a notion of robustness in a stochastic setting by using the concept of chance constraints. This requires that mission constraint violation can occur with a probability less than a prescribed value.In this paper we describe a novel method for optimal chance constrained path planning with feedback design. The approach optimizes both the reference trajectory to be followed and the feedback controller used to reject uncertainty. Our method extends recent results in constrained control synthesis based on convex optimization to solve control problems with nonconvex constraints. This extension is essential for path planning problems, which inherently have nonconvex obstacle avoidance constraints. Unlike previous approaches to chance constrained path planning, the new approach optimizes the feedback gain as wellas the reference trajectory.The key idea is to couple a fast, nonconvex solver that does not take into account uncertainty, with existing robust approaches that apply only to convex feasible regions. By alternating between robust and nonrobust solutions, the new algorithm guarantees convergence to a global optimum. We apply the new method to an unmanned aircraft and show simulation results that demonstrate the efficacy of the approach.

The Linearized Bregman Method for Frugal Full-waveform Inversion with Compressive Sensing and Sparsity-promoting

NASA Astrophysics Data System (ADS)

Chai, Xintao; Tang, Genyang; Peng, Ronghua; Liu, Shaoyong

2018-03-01

Full-waveform inversion (FWI) reconstructs the subsurface properties from acquired seismic data via minimization of the misfit between observed and simulated data. However, FWI suffers from considerable computational costs resulting from the numerical solution of the wave equation for each source at each iteration. To reduce the computational burden, constructing supershots by combining several sources (aka source encoding) allows mitigation of the number of simulations at each iteration, but it gives rise to crosstalk artifacts because of interference between the individual sources of the supershot. A modified Gauss-Newton FWI (MGNFWI) approach showed that as long as the difference between the initial and true models permits a sparse representation, the ℓ _1-norm constrained model updates suppress subsampling-related artifacts. However, the spectral-projected gradient ℓ _1 (SPGℓ _1) algorithm employed by MGNFWI is rather complicated that makes its implementation difficult. To facilitate realistic applications, we adapt a linearized Bregman (LB) method to sparsity-promoting FWI (SPFWI) because of the efficiency and simplicity of LB in the framework of ℓ _1-norm constrained optimization problem and compressive sensing. Numerical experiments performed with the BP Salt model, the Marmousi model and the BG Compass model verify the following points. The FWI result with LB solving ℓ _1-norm sparsity-promoting problem for the model update outperforms that generated by solving ℓ _2-norm problem in terms of crosstalk elimination and high-fidelity results. The simpler LB method performs comparably and even superiorly to the complicated SPGℓ _1 method in terms of computational efficiency and model quality, making the LB method a viable alternative for realistic implementations of SPFWI.

Can re-regulation reservoirs and batteries cost-effectively mitigate sub-daily hydropeaking?

NASA Astrophysics Data System (ADS)

Haas, J.; Nowak, W.; Anindito, Y.; Olivares, M. A.

2017-12-01

To compensate for mismatches between generation and load, hydropower plants frequently operate in strong hydropeaking schemes, which is harmful to the downstream ecosystem. Furthermore, new power market structures and variable renewable systems may exacerbate this behavior. Ecological constraints (minimum flows, maximum ramps) are frequently used to mitigate hydropeaking, but these stand in direct tradeoff with the operational flexibility required for integrating renewable technologies. Fortunately, there are also physical methods (i.e. re-regulation reservoirs and batteries) but to date, there are no studies about their cost-effectiveness for hydropeaking mitigation. This study aims to fill that gap. For this, we formulate an hourly mixed-integer linear optimization model to plan the weekly operation of a hydro-thermal-renewable power system from southern Chile. The opportunity cost of water (needed for this weekly scheduling) is obtained from a mid-term programming solved with dynamic programming. We compare the current (unconstrained) hydropower operation with an ecologically constrained operation. The resulting cost increase is then contrasted with the annual payments necessary for the physical hydropeaking mitigation options. For highly constrained operations, both re-regulation reservoirs and batteries show to be economically attractive for hydropeaking mitigation. For intermediate constrained scenarios, re-regulation reservoirs are still economic, whereas batteries can be a viable solution only if they become cheaper in future. Given current cost projections, their break-even point (for hydropeaking mitigation) is expected within the next ten years. Finally, less stringent hydropeaking constraints do not justify physical mitigation measures, as the necessary flexibility can be provided by other power plants of the system.

A Bayesian approach to earthquake source studies

NASA Astrophysics Data System (ADS)

Minson, Sarah

Bayesian sampling has several advantages over conventional optimization approaches to solving inverse problems. It produces the distribution of all possible models sampled proportionally to how much each model is consistent with the data and the specified prior information, and thus images the entire solution space, revealing the uncertainties and trade-offs in the model. Bayesian sampling is applicable to both linear and non-linear modeling, and the values of the model parameters being sampled can be constrained based on the physics of the process being studied and do not have to be regularized. However, these methods are computationally challenging for high-dimensional problems. Until now the computational expense of Bayesian sampling has been too great for it to be practicable for most geophysical problems. I present a new parallel sampling algorithm called CATMIP for Cascading Adaptive Tempered Metropolis In Parallel. This technique, based on Transitional Markov chain Monte Carlo, makes it possible to sample distributions in many hundreds of dimensions, if the forward model is fast, or to sample computationally expensive forward models in smaller numbers of dimensions. The design of the algorithm is independent of the model being sampled, so CATMIP can be applied to many areas of research. I use CATMIP to produce a finite fault source model for the 2007 Mw 7.7 Tocopilla, Chile earthquake. Surface displacements from the earthquake were recorded by six interferograms and twelve local high-rate GPS stations. Because of the wealth of near-fault data, the source process is well-constrained. I find that the near-field high-rate GPS data have significant resolving power above and beyond the slip distribution determined from static displacements. The location and magnitude of the maximum displacement are resolved. The rupture almost certainly propagated at sub-shear velocities. The full posterior distribution can be used not only to calculate source parameters but also to determine their uncertainties. So while kinematic source modeling and the estimation of source parameters is not new, with CATMIP I am able to use Bayesian sampling to determine which parts of the source process are well-constrained and which are not.

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.

A Near-Optimal Distributed QoS Constrained Routing Algorithm for Multichannel Wireless Sensor Networks

PubMed Central

Lin, Frank Yeong-Sung; Hsiao, Chiu-Han; Yen, Hong-Hsu; Hsieh, Yu-Jen

2013-01-01

One of the important applications in Wireless Sensor Networks (WSNs) is video surveillance that includes the tasks of video data processing and transmission. Processing and transmission of image and video data in WSNs has attracted a lot of attention in recent years. This is known as Wireless Visual Sensor Networks (WVSNs). WVSNs are distributed intelligent systems for collecting image or video data with unique performance, complexity, and quality of service challenges. WVSNs consist of a large number of battery-powered and resource constrained camera nodes. End-to-end delay is a very important Quality of Service (QoS) metric for video surveillance application in WVSNs. How to meet the stringent delay QoS in resource constrained WVSNs is a challenging issue that requires novel distributed and collaborative routing strategies. This paper proposes a Near-Optimal Distributed QoS Constrained (NODQC) routing algorithm to achieve an end-to-end route with lower delay and higher throughput. A Lagrangian Relaxation (LR)-based routing metric that considers the “system perspective” and “user perspective” is proposed to determine the near-optimal routing paths that satisfy end-to-end delay constraints with high system throughput. The empirical results show that the NODQC routing algorithm outperforms others in terms of higher system throughput with lower average end-to-end delay and delay jitter. In this paper, for the first time, the algorithm shows how to meet the delay QoS and at the same time how to achieve higher system throughput in stringently resource constrained WVSNs.

Control of the constrained planar simple inverted pendulum

NASA Technical Reports Server (NTRS)

Bavarian, B.; Wyman, B. F.; Hemami, H.

1983-01-01

Control of a constrained planar inverted pendulum by eigenstructure assignment is considered. Linear feedback is used to stabilize and decouple the system in such a way that specified subspaces of the state space are invariant for the closed-loop system. The effectiveness of the feedback law is tested by digital computer simulation. Pre-compensation by an inverse plant is used to improve performance.

How to Test the SME with Space Missions?

NASA Technical Reports Server (NTRS)

Hees, A.; Lamine, B.; Le Poncin-Lafitte, C.; Wolf, P.

2013-01-01

In this communication, we focus on possibilities to constrain SME coefficients using Cassini and Messenger data. We present simulations of radio science observables within the framework of the SME, identify the linear combinations of SME coefficients the observations depend on and determine the sensitivity of these measurements to the SME coefficients. We show that these datasets are very powerful for constraining SME coefficients.

Automated mapping of linear dunefield morphometric parameters from remotely-sensed data

NASA Astrophysics Data System (ADS)

Telfer, M. W.; Fyfe, R. M.; Lewin, S.

2015-12-01

Linear dunes are among the world's most common desert dune types, and typically occur in dunefields arranged in remarkably organized patterns extending over hundreds of kilometers. The causes of the patterns, formed by dunes merging, bifurcating and terminating, are still poorly understood, although it is widely accepted that they are emergent properties of the complex system of interactions between the boundary layer and an often-vegetated erodible substrate. Where such dunefields are vegetated, they are typically used as extensive rangeland, yet it is evident that many currently stabilized dunefields have been reactivated repeatedly during the late Quaternary. It has been suggested that dunefield patterning and the temporal evolution of dunefields are related, and thus there is considerable interest in better understanding the boundary conditions controlling dune patterning, especially given the possibility of reactivation of currently-stabilized dunefields under 21st century climate change. However, the time-consuming process of manual dune mapping has hampered attempts at quantitative description of dunefield patterning. This study aims to develop and test methods for delineating linear dune trendlines automatically from freely-available remotely sensed datasets. The highest resolution free global topographic data presently available (Aster GDEM v2) proved to be of marginal use, as the topographic expression of the dunes is of the same order as the vertical precision of the dataset (∼10 m), but in regions with relatively simple patterning it defined dune trends adequately. Analysis of spectral data (panchromatic Landsat 8 data) proved more promising in five of the six test sites, and despite poor panchromatic signal/noise ratios for the sixth site, the reflectance in the deep blue/violet (Landsat 8 Band 1) offers an alternative method of delineating dune pattern. A new edge detection algorithm (LInear Dune Optimized edge detection; LIDO) is proposed, based on Sobel operators with directional filtering and topologically-constrained recursion to optimize the inclusion of marginal zones. The method offers the potential for rapid quantitative mapping of linear dunefield patterning, providing validation data for modeling studies, and offering for the first time the ability to readily remap dunefields to assess dune reorganization at the dunefield scale.

Trade-offs and efficiencies in optimal budget-constrained multispecies corridor networks

Treesearch

Bistra Dilkina; Rachel Houtman; Carla P. Gomes; Claire A. Montgomery; Kevin S. McKelvey; Katherine Kendall; Tabitha A. Graves; Richard Bernstein; Michael K. Schwartz

2016-01-01

Conservation biologists recognize that a system of isolated protected areas will be necessary but insufficient to meet biodiversity objectives. Current approaches to connecting core conservation areas through corridors consider optimal corridor placement based on a single optimization goal: commonly, maximizing the movement for a target species across a...

A method of minimum volume simplex analysis constrained unmixing for hyperspectral image

NASA Astrophysics Data System (ADS)

Zou, Jinlin; Lan, Jinhui; Zeng, Yiliang; Wu, Hongtao

2017-07-01

The signal recorded by a low resolution hyperspectral remote sensor from a given pixel, letting alone the effects of the complex terrain, is a mixture of substances. To improve the accuracy of classification and sub-pixel object detection, hyperspectral unmixing(HU) is a frontier-line in remote sensing area. Unmixing algorithm based on geometric has become popular since the hyperspectral image possesses abundant spectral information and the mixed model is easy to understand. However, most of the algorithms are based on pure pixel assumption, and since the non-linear mixed model is complex, it is hard to obtain the optimal endmembers especially under a highly mixed spectral data. To provide a simple but accurate method, we propose a minimum volume simplex analysis constrained (MVSAC) unmixing algorithm. The proposed approach combines the algebraic constraints that are inherent to the convex minimum volume with abundance soft constraint. While considering abundance fraction, we can obtain the pure endmember set and abundance fraction correspondingly, and the final unmixing result is closer to reality and has better accuracy. We illustrate the performance of the proposed algorithm in unmixing simulated data and real hyperspectral data, and the result indicates that the proposed method can obtain the distinct signatures correctly without redundant endmember and yields much better performance than the pure pixel based algorithm.

Portfolio optimization by using linear programing models based on genetic algorithm

NASA Astrophysics Data System (ADS)

Sukono; Hidayat, Y.; Lesmana, E.; Putra, A. S.; Napitupulu, H.; Supian, S.

2018-01-01

In this paper, we discussed the investment portfolio optimization using linear programming model based on genetic algorithms. It is assumed that the portfolio risk is measured by absolute standard deviation, and each investor has a risk tolerance on the investment portfolio. To complete the investment portfolio optimization problem, the issue is arranged into a linear programming model. Furthermore, determination of the optimum solution for linear programming is done by using a genetic algorithm. As a numerical illustration, we analyze some of the stocks traded on the capital market in Indonesia. Based on the analysis, it is shown that the portfolio optimization performed by genetic algorithm approach produces more optimal efficient portfolio, compared to the portfolio optimization performed by a linear programming algorithm approach. Therefore, genetic algorithms can be considered as an alternative on determining the investment portfolio optimization, particularly using linear programming models.

Comparing Multiple-Group Multinomial Log-Linear Models for Multidimensional Skill Distributions in the General Diagnostic Model. Research Report. ETS RR-08-35

ERIC Educational Resources Information Center

Xu, Xueli; von Davier, Matthias

2008-01-01

The general diagnostic model (GDM) utilizes located latent classes for modeling a multidimensional proficiency variable. In this paper, the GDM is extended by employing a log-linear model for multiple populations that assumes constraints on parameters across multiple groups. This constrained model is compared to log-linear models that assume…

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 TV-constrained decomposition method for spectral CT

NASA Astrophysics Data System (ADS)

Guo, Xiaoyue; Zhang, Li; Xing, Yuxiang

2017-03-01

Spectral CT is attracting more and more attention in medicine, industrial nondestructive testing and security inspection field. Material decomposition is an important issue to a spectral CT to discriminate materials. Because of the spectrum overlap of energy channels, as well as the correlation of basis functions, it is well acknowledged that decomposition step in spectral CT imaging causes noise amplification and artifacts in component coefficient images. In this work, we propose materials decomposition via an optimization method to improve the quality of decomposed coefficient images. On the basis of general optimization problem, total variance minimization is constrained on coefficient images in our overall objective function with adjustable weights. We solve this constrained optimization problem under the framework of ADMM. Validation on both a numerical dental phantom in simulation and a real phantom of pig leg on a practical CT system using dual-energy imaging is executed. Both numerical and physical experiments give visually obvious better reconstructions than a general direct inverse method. SNR and SSIM are adopted to quantitatively evaluate the image quality of decomposed component coefficients. All results demonstrate that the TV-constrained decomposition method performs well in reducing noise without losing spatial resolution so that improving the image quality. The method can be easily incorporated into different types of spectral imaging modalities, as well as for cases with energy channels more than two.

PAPR-Constrained Pareto-Optimal Waveform Design for OFDM-STAP Radar

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

Sen, Satyabrata

We propose a peak-to-average power ratio (PAPR) constrained Pareto-optimal waveform design approach for an orthogonal frequency division multiplexing (OFDM) radar signal to detect a target using the space-time adaptive processing (STAP) technique. The use of an OFDM signal does not only increase the frequency diversity of our system, but also enables us to adaptively design the OFDM coefficients in order to further improve the system performance. First, we develop a parametric OFDM-STAP measurement model by considering the effects of signaldependent clutter and colored noise. Then, we observe that the resulting STAP-performance can be improved by maximizing the output signal-to-interference-plus-noise ratiomore » (SINR) with respect to the signal parameters. However, in practical scenarios, the computation of output SINR depends on the estimated values of the spatial and temporal frequencies and target scattering responses. Therefore, we formulate a PAPR-constrained multi-objective optimization (MOO) problem to design the OFDM spectral parameters by simultaneously optimizing four objective functions: maximizing the output SINR, minimizing two separate Cramer-Rao bounds (CRBs) on the normalized spatial and temporal frequencies, and minimizing the trace of CRB matrix on the target scattering coefficients estimations. We present several numerical examples to demonstrate the achieved performance improvement due to the adaptive waveform design.« less

Weighted SGD for ℓ p Regression with Randomized Preconditioning.

PubMed

Yang, Jiyan; Chow, Yin-Lam; Ré, Christopher; Mahoney, Michael W

2016-01-01

In recent years, stochastic gradient descent (SGD) methods and randomized linear algebra (RLA) algorithms have been applied to many large-scale problems in machine learning and data analysis. SGD methods are easy to implement and applicable to a wide range of convex optimization problems. In contrast, RLA algorithms provide much stronger performance guarantees but are applicable to a narrower class of problems. We aim to bridge the gap between these two methods in solving constrained overdetermined linear regression problems-e.g., ℓ 2 and ℓ 1 regression problems. We propose a hybrid algorithm named pwSGD that uses RLA techniques for preconditioning and constructing an importance sampling distribution, and then performs an SGD-like iterative process with weighted sampling on the preconditioned system.By rewriting a deterministic ℓ p regression problem as a stochastic optimization problem, we connect pwSGD to several existing ℓ p solvers including RLA methods with algorithmic leveraging (RLA for short).We prove that pwSGD inherits faster convergence rates that only depend on the lower dimension of the linear system, while maintaining low computation complexity. Such SGD convergence rates are superior to other related SGD algorithm such as the weighted randomized Kaczmarz algorithm.Particularly, when solving ℓ 1 regression with size n by d , pwSGD returns an approximate solution with ε relative error in the objective value in (log n ·nnz( A )+poly( d )/ ε 2 ) time. This complexity is uniformly better than that of RLA methods in terms of both ε and d when the problem is unconstrained. In the presence of constraints, pwSGD only has to solve a sequence of much simpler and smaller optimization problem over the same constraints. In general this is more efficient than solving the constrained subproblem required in RLA.For ℓ 2 regression, pwSGD returns an approximate solution with ε relative error in the objective value and the solution vector measured in prediction norm in (log n ·nnz( A )+poly( d ) log(1/ ε )/ ε ) time. We show that for unconstrained ℓ 2 regression, this complexity is comparable to that of RLA and is asymptotically better over several state-of-the-art solvers in the regime where the desired accuracy ε , high dimension n and low dimension d satisfy d ≥ 1/ ε and n ≥ d 2 / ε . We also provide lower bounds on the coreset complexity for more general regression problems, indicating that still new ideas will be needed to extend similar RLA preconditioning ideas to weighted SGD algorithms for more general regression problems. Finally, the effectiveness of such algorithms is illustrated numerically on both synthetic and real datasets, and the results are consistent with our theoretical findings and demonstrate that pwSGD converges to a medium-precision solution, e.g., ε = 10 -3 , more quickly.

Weighted SGD for ℓp Regression with Randomized Preconditioning*

PubMed Central

Yang, Jiyan; Chow, Yin-Lam; Ré, Christopher; Mahoney, Michael W.

2018-01-01

In recent years, stochastic gradient descent (SGD) methods and randomized linear algebra (RLA) algorithms have been applied to many large-scale problems in machine learning and data analysis. SGD methods are easy to implement and applicable to a wide range of convex optimization problems. In contrast, RLA algorithms provide much stronger performance guarantees but are applicable to a narrower class of problems. We aim to bridge the gap between these two methods in solving constrained overdetermined linear regression problems—e.g., ℓ2 and ℓ1 regression problems. We propose a hybrid algorithm named pwSGD that uses RLA techniques for preconditioning and constructing an importance sampling distribution, and then performs an SGD-like iterative process with weighted sampling on the preconditioned system.By rewriting a deterministic ℓp regression problem as a stochastic optimization problem, we connect pwSGD to several existing ℓp solvers including RLA methods with algorithmic leveraging (RLA for short).We prove that pwSGD inherits faster convergence rates that only depend on the lower dimension of the linear system, while maintaining low computation complexity. Such SGD convergence rates are superior to other related SGD algorithm such as the weighted randomized Kaczmarz algorithm.Particularly, when solving ℓ1 regression with size n by d, pwSGD returns an approximate solution with ε relative error in the objective value in 𝒪(log n·nnz(A)+poly(d)/ε2) time. This complexity is uniformly better than that of RLA methods in terms of both ε and d when the problem is unconstrained. In the presence of constraints, pwSGD only has to solve a sequence of much simpler and smaller optimization problem over the same constraints. In general this is more efficient than solving the constrained subproblem required in RLA.For ℓ2 regression, pwSGD returns an approximate solution with ε relative error in the objective value and the solution vector measured in prediction norm in 𝒪(log n·nnz(A)+poly(d) log(1/ε)/ε) time. We show that for unconstrained ℓ2 regression, this complexity is comparable to that of RLA and is asymptotically better over several state-of-the-art solvers in the regime where the desired accuracy ε, high dimension n and low dimension d satisfy d ≥ 1/ε and n ≥ d2/ε. We also provide lower bounds on the coreset complexity for more general regression problems, indicating that still new ideas will be needed to extend similar RLA preconditioning ideas to weighted SGD algorithms for more general regression problems. Finally, the effectiveness of such algorithms is illustrated numerically on both synthetic and real datasets, and the results are consistent with our theoretical findings and demonstrate that pwSGD converges to a medium-precision solution, e.g., ε = 10−3, more quickly. PMID:29782626

Megaplumes on Venus

NASA Technical Reports Server (NTRS)

Kaula, W. M.

1993-01-01

The geoid and topography heights of Atla Regio and Beta Regio, both peaks and slopes, appear explicable as steady-state plumes, if non-linear viscosity eta(Tau, epsilon) is taken into account. Strongly constrained by the data are an effective plume depth of about 700 km, with a temperature anomaly thereat of about 30 degrees, leading to more than 400 degrees at the plume head. Also well constrained is the combination Q(eta)/s(sup 4)(sub 0) = (volume flow rate)(viscosity)/(plume radius): about 11 Pa/m/sec. The topographic slopes dh/ds constrain the combination Q/A, where A is the thickness of the spreading layer, since the slope varies inversely with velocity. The geoid slopes dN/ds require enhancement of the deeper flow, as expected from non-linear viscosity. The Beta data are best fit by Q = 500 m(sup 3)/sec and A equals 140 km; the Atla, by Q equals 440 m(exp 3)/sec and A equals 260 km. The dynamic contribution to the topographic slope is minor.

An indirect method for numerical optimization using the Kreisselmeir-Steinhauser function

NASA Technical Reports Server (NTRS)

Wrenn, Gregory A.

1989-01-01

A technique is described for converting a constrained optimization problem into an unconstrained problem. The technique transforms one of more objective functions into reduced objective functions, which are analogous to goal constraints used in the goal programming method. These reduced objective functions are appended to the set of constraints and an envelope of the entire function set is computed using the Kreisselmeir-Steinhauser function. This envelope function is then searched for an unconstrained minimum. The technique may be categorized as a SUMT algorithm. Advantages of this approach are the use of unconstrained optimization methods to find a constrained minimum without the draw down factor typical of penalty function methods, and that the technique may be started from the feasible or infeasible design space. In multiobjective applications, the approach has the advantage of locating a compromise minimum design without the need to optimize for each individual objective function separately.

Optimization of Stability Constrained Geometrically Nonlinear Shallow Trusses Using an Arc Length Sparse Method with a Strain Energy Density Approach

NASA Technical Reports Server (NTRS)

Hrinda, Glenn A.; Nguyen, Duc T.

2008-01-01

A technique for the optimization of stability constrained geometrically nonlinear shallow trusses with snap through behavior is demonstrated using the arc length method and a strain energy density approach within a discrete finite element formulation. The optimization method uses an iterative scheme that evaluates the design variables' performance and then updates them according to a recursive formula controlled by the arc length method. A minimum weight design is achieved when a uniform nonlinear strain energy density is found in all members. This minimal condition places the design load just below the critical limit load causing snap through of the structure. The optimization scheme is programmed into a nonlinear finite element algorithm to find the large strain energy at critical limit loads. Examples of highly nonlinear trusses found in literature are presented to verify the method.

OpenMDAO: Framework for Flexible Multidisciplinary Design, Analysis and Optimization Methods

NASA Technical Reports Server (NTRS)

Heath, Christopher M.; Gray, Justin S.

2012-01-01

The OpenMDAO project is underway at NASA to develop a framework which simplifies the implementation of state-of-the-art tools and methods for multidisciplinary design, analysis and optimization. Foremost, OpenMDAO has been designed to handle variable problem formulations, encourage reconfigurability, and promote model reuse. This work demonstrates the concept of iteration hierarchies in OpenMDAO to achieve a flexible environment for supporting advanced optimization methods which include adaptive sampling and surrogate modeling techniques. In this effort, two efficient global optimization methods were applied to solve a constrained, single-objective and constrained, multiobjective version of a joint aircraft/engine sizing problem. The aircraft model, NASA's nextgeneration advanced single-aisle civil transport, is being studied as part of the Subsonic Fixed Wing project to help meet simultaneous program goals for reduced fuel burn, emissions, and noise. This analysis serves as a realistic test problem to demonstrate the flexibility and reconfigurability offered by OpenMDAO.

Optimal lifting ascent trajectories for the space shuttle

NASA Technical Reports Server (NTRS)

Rau, T. R.; Elliott, J. R.

1972-01-01

The performance gains which are possible through the use of optimal trajectories for a particular space shuttle configuration are discussed. The spacecraft configurations and aerodynamic characteristics are described. Shuttle mission payload capability is examined with respect to the optimal orbit inclination for unconstrained, constrained, and nonlifting conditions. The effects of velocity loss and heating rate on the optimal ascent trajectory are investigated.

Artifact reduction in short-scan CBCT by use of optimization-based reconstruction

PubMed Central

Zhang, Zheng; Han, Xiao; Pearson, Erik; Pelizzari, Charles; Sidky, Emil Y; Pan, Xiaochuan

2017-01-01

Increasing interest in optimization-based reconstruction in research on, and applications of, cone-beam computed tomography (CBCT) exists because it has been shown to have to potential to reduce artifacts observed in reconstructions obtained with the Feldkamp–Davis–Kress (FDK) algorithm (or its variants), which is used extensively for image reconstruction in current CBCT applications. In this work, we carried out a study on optimization-based reconstruction for possible reduction of artifacts in FDK reconstruction specifically from short-scan CBCT data. The investigation includes a set of optimization programs such as the image-total-variation (TV)-constrained data-divergency minimization, data-weighting matrices such as the Parker weighting matrix, and objects of practical interest for demonstrating and assessing the degree of artifact reduction. Results of investigative work reveal that appropriately designed optimization-based reconstruction, including the image-TV-constrained reconstruction, can reduce significant artifacts observed in FDK reconstruction in CBCT with a short-scan configuration. PMID:27046218

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

PubMed

Xu, Jiuping; Feng, Cuiying

2014-01-01

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

Mixed Integer Programming and Heuristic Scheduling for Space Communication Networks

NASA Technical Reports Server (NTRS)

Cheung, Kar-Ming; Lee, Charles H.

2012-01-01

We developed framework and the mathematical formulation for optimizing communication network using mixed integer programming. The design yields a system that is much smaller, in search space size, when compared to the earlier approach. Our constrained network optimization takes into account the dynamics of link performance within the network along with mission and operation requirements. A unique penalty function is introduced to transform the mixed integer programming into the more manageable problem of searching in a continuous space. The constrained optimization problem was proposed to solve in two stages: first using the heuristic Particle Swarming Optimization algorithm to get a good initial starting point, and then feeding the result into the Sequential Quadratic Programming algorithm to achieve the final optimal schedule. We demonstrate the above planning and scheduling methodology with a scenario of 20 spacecraft and 3 ground stations of a Deep Space Network site. Our approach and framework have been simple and flexible so that problems with larger number of constraints and network can be easily adapted and solved.

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

PubMed Central

Xu, Jiuping

2014-01-01

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

Program Aids Analysis And Optimization Of Design

NASA Technical Reports Server (NTRS)

Rogers, James L., Jr.; Lamarsh, William J., II

1994-01-01

NETS/ PROSSS (NETS Coupled With Programming System for Structural Synthesis) computer program developed to provide system for combining NETS (MSC-21588), neural-network application program and CONMIN (Constrained Function Minimization, ARC-10836), optimization program. Enables user to reach nearly optimal design. Design then used as starting point in normal optimization process, possibly enabling user to converge to optimal solution in significantly fewer iterations. NEWT/PROSSS written in C language and FORTRAN 77.

Comparisons of a Constrained Least Squares Model versus Human-in-the-Loop for Spectral Unmixing to Determine Material Type of GEO Debris

NASA Technical Reports Server (NTRS)

Abercromby, Kira J.; Rapp, Jason; Bedard, Donald; Seitzer, Patrick; Cardona, Tommaso; Cowardin, Heather; Barker, Ed; Lederer, Susan

2013-01-01

Constrained Linear Least Squares model is generally more accurate than the "human-in-the-loop". However, "human-in-the-loop" can remove materials that make no sense. The speed of the model in determining a "first cut" at the material ID makes it a viable option for spectral unmixing of debris objects.

Highly Constrained Bicyclic Scaffolds for the Discovery of Protease-Stable Peptides via mRNA Display.

PubMed

Hacker, David E; Hoinka, Jan; Iqbal, Emil S; Przytycka, Teresa M; Hartman, Matthew C T

2017-03-17

Highly constrained peptides such as the knotted peptide natural products are promising medicinal agents because of their impressive biostability and potent activity. Yet, libraries of highly constrained peptides are challenging to prepare. Here, we present a method which utilizes two robust, orthogonal chemical steps to create highly constrained bicyclic peptide libraries. This technology was optimized to be compatible with in vitro selections by mRNA display. We performed side-by-side monocyclic and bicyclic selections against a model protein (streptavidin). Both selections resulted in peptides with mid-nanomolar affinity, and the bicyclic selection yielded a peptide with remarkable protease resistance.

Multidisciplinary Optimization Approach for Design and Operation of Constrained and Complex-shaped Space Systems

NASA Astrophysics Data System (ADS)

Lee, Dae Young

The design of a small satellite is challenging since they are constrained by mass, volume, and power. To mitigate these constraint effects, designers adopt deployable configurations on the spacecraft that result in an interesting and difficult optimization problem. The resulting optimization problem is challenging due to the computational complexity caused by the large number of design variables and the model complexity created by the deployables. Adding to these complexities, there is a lack of integration of the design optimization systems into operational optimization, and the utility maximization of spacecraft in orbit. The developed methodology enables satellite Multidisciplinary Design Optimization (MDO) that is extendable to on-orbit operation. Optimization of on-orbit operations is possible with MDO since the model predictive controller developed in this dissertation guarantees the achievement of the on-ground design behavior in orbit. To enable the design optimization of highly constrained and complex-shaped space systems, the spherical coordinate analysis technique, called the "Attitude Sphere", is extended and merged with an additional engineering tools like OpenGL. OpenGL's graphic acceleration facilitates the accurate estimation of the shadow-degraded photovoltaic cell area. This technique is applied to the design optimization of the satellite Electric Power System (EPS) and the design result shows that the amount of photovoltaic power generation can be increased more than 9%. Based on this initial methodology, the goal of this effort is extended from Single Discipline Optimization to Multidisciplinary Optimization, which includes the design and also operation of the EPS, Attitude Determination and Control System (ADCS), and communication system. The geometry optimization satisfies the conditions of the ground development phase; however, the operation optimization may not be as successful as expected in orbit due to disturbances. To address this issue, for the ADCS operations, controllers based on Model Predictive Control that are effective for constraint handling were developed and implemented. All the suggested design and operation methodologies are applied to a mission "CADRE", which is space weather mission scheduled for operation in 2016. This application demonstrates the usefulness and capability of the methodology to enhance CADRE's capabilities, and its ability to be applied to a variety of missions.

Do Vascular Networks Branch Optimally or Randomly across Spatial Scales?

PubMed Central

Newberry, Mitchell G.; Savage, Van M.

2016-01-01

Modern models that derive allometric relationships between metabolic rate and body mass are based on the architectural design of the cardiovascular system and presume sibling vessels are symmetric in terms of radius, length, flow rate, and pressure. Here, we study the cardiovascular structure of the human head and torso and of a mouse lung based on three-dimensional images processed via our software Angicart. In contrast to modern allometric theories, we find systematic patterns of asymmetry in vascular branching, potentially explaining previously documented mismatches between predictions (power-law or concave curvature) and observed empirical data (convex curvature) for the allometric scaling of metabolic rate. To examine why these systematic asymmetries in vascular branching might arise, we construct a mathematical framework to derive predictions based on local, junction-level optimality principles that have been proposed to be favored in the course of natural selection and development. The two most commonly used principles are material-cost optimizations (construction materials or blood volume) and optimization of efficient flow via minimization of power loss. We show that material-cost optimization solutions match with distributions for asymmetric branching across the whole network but do not match well for individual junctions. Consequently, we also explore random branching that is constrained at scales that range from local (junction-level) to global (whole network). We find that material-cost optimizations are the strongest predictor of vascular branching in the human head and torso, whereas locally or intermediately constrained random branching is comparable to material-cost optimizations for the mouse lung. These differences could be attributable to developmentally-programmed local branching for larger vessels and constrained random branching for smaller vessels. PMID:27902691

Time and Memory Efficient Online Piecewise Linear Approximation of Sensor Signals.

PubMed

Grützmacher, Florian; Beichler, Benjamin; Hein, Albert; Kirste, Thomas; Haubelt, Christian

2018-05-23

Piecewise linear approximation of sensor signals is a well-known technique in the fields of Data Mining and Activity Recognition. In this context, several algorithms have been developed, some of them with the purpose to be performed on resource constrained microcontroller architectures of wireless sensor nodes. While microcontrollers are usually constrained in computational power and memory resources, all state-of-the-art piecewise linear approximation techniques either need to buffer sensor data or have an execution time depending on the segment’s length. In the paper at hand, we propose a novel piecewise linear approximation algorithm, with a constant computational complexity as well as a constant memory complexity. Our proposed algorithm’s worst-case execution time is one to three orders of magnitude smaller and its average execution time is three to seventy times smaller compared to the state-of-the-art Piecewise Linear Approximation (PLA) algorithms in our experiments. In our evaluations, we show that our algorithm is time and memory efficient without sacrificing the approximation quality compared to other state-of-the-art piecewise linear approximation techniques, while providing a maximum error guarantee per segment, a small parameter space of only one parameter, and a maximum latency of one sample period plus its worst-case execution time.

Constraining the braneworld with gravitational wave observations.

PubMed

McWilliams, Sean T

2010-04-09

Some braneworld models may have observable consequences that, if detected, would validate a requisite element of string theory. In the infinite Randall-Sundrum model (RS2), the AdS radius of curvature, l, of the extra dimension supports a single bound state of the massless graviton on the brane, thereby reproducing Newtonian gravity in the weak-field limit. However, using the AdS/CFT correspondence, it has been suggested that one possible consequence of RS2 is an enormous increase in Hawking radiation emitted by black holes. We utilize this possibility to derive two novel methods for constraining l via gravitational wave measurements. We show that the EMRI event rate detected by LISA can constrain l at the approximately 1 microm level for optimal cases, while the observation of a single galactic black hole binary with LISA results in an optimal constraint of l < or = 5 microm.

Constraining the Braneworld with Gravitational Wave Observations

NASA Technical Reports Server (NTRS)

McWilliams, Sean T.

2011-01-01

Some braneworld models may have observable consequences that, if detected, would validate a requisite element of string theory. In the infinite Randall-Sundrum model (RS2), the AdS radius of curvature, L, of the extra dimension supports a single bound state of the massless graviton on the brane, thereby reproducing Newtonian gravity in the weak-field limit. However, using the AdS/CFT correspondence, it has been suggested that one possible consequence of RS2 is an enormous increase in Hawking radiation emitted by black holes. We utilize this possibility to derive two novel methods for constraining L via gravitational wave measurements. We show that the EMRI event rate detected by LISA can constrain L at the approximately 1 micron level for optimal cases, while the observation of a single galactic black hole binary with LISA results in an optimal constraint of L less than or equal to 5 microns.

A hierarchical transition state search algorithm

NASA Astrophysics Data System (ADS)

del Campo, Jorge M.; Köster, Andreas M.

2008-07-01

A hierarchical transition state search algorithm is developed and its implementation in the density functional theory program deMon2k is described. This search algorithm combines the double ended saddle interpolation method with local uphill trust region optimization. A new formalism for the incorporation of the distance constrain in the saddle interpolation method is derived. The similarities between the constrained optimizations in the local trust region method and the saddle interpolation are highlighted. The saddle interpolation and local uphill trust region optimizations are validated on a test set of 28 representative reactions. The hierarchical transition state search algorithm is applied to an intramolecular Diels-Alder reaction with several internal rotors, which makes automatic transition state search rather challenging. The obtained reaction mechanism is discussed in the context of the experimentally observed product distribution.

Flux-corrected transport algorithms for continuous Galerkin methods based on high order Bernstein finite elements

NASA Astrophysics Data System (ADS)

Lohmann, Christoph; Kuzmin, Dmitri; Shadid, John N.; Mabuza, Sibusiso

2017-09-01

This work extends the flux-corrected transport (FCT) methodology to arbitrary order continuous finite element discretizations of scalar conservation laws on simplex meshes. Using Bernstein polynomials as local basis functions, we constrain the total variation of the numerical solution by imposing local discrete maximum principles on the Bézier net. The design of accuracy-preserving FCT schemes for high order Bernstein-Bézier finite elements requires the development of new algorithms and/or generalization of limiting techniques tailored for linear and multilinear Lagrange elements. In this paper, we propose (i) a new discrete upwinding strategy leading to local extremum bounded low order approximations with compact stencils, (ii) high order variational stabilization based on the difference between two gradient approximations, and (iii) new localized limiting techniques for antidiffusive element contributions. The optional use of a smoothness indicator, based on a second derivative test, makes it possible to potentially avoid unnecessary limiting at smooth extrema and achieve optimal convergence rates for problems with smooth solutions. The accuracy of the proposed schemes is assessed in numerical studies for the linear transport equation in 1D and 2D.

Computing Generalized Matrix Inverse on Spiking Neural Substrate.

PubMed

Shukla, Rohit; Khoram, Soroosh; Jorgensen, Erik; Li, Jing; Lipasti, Mikko; Wright, Stephen

2018-01-01

Emerging neural hardware substrates, such as IBM's TrueNorth Neurosynaptic System, can provide an appealing platform for deploying numerical algorithms. For example, a recurrent Hopfield neural network can be used to find the Moore-Penrose generalized inverse of a matrix, thus enabling a broad class of linear optimizations to be solved efficiently, at low energy cost. However, deploying numerical algorithms on hardware platforms that severely limit the range and precision of representation for numeric quantities can be quite challenging. This paper discusses these challenges and proposes a rigorous mathematical framework for reasoning about range and precision on such substrates. The paper derives techniques for normalizing inputs and properly quantizing synaptic weights originating from arbitrary systems of linear equations, so that solvers for those systems can be implemented in a provably correct manner on hardware-constrained neural substrates. The analytical model is empirically validated on the IBM TrueNorth platform, and results show that the guarantees provided by the framework for range and precision hold under experimental conditions. Experiments with optical flow demonstrate the energy benefits of deploying a reduced-precision and energy-efficient generalized matrix inverse engine on the IBM TrueNorth platform, reflecting 10× to 100× improvement over FPGA and ARM core baselines.

Reusable Launch Vehicle Control In Multiple Time Scale Sliding Modes

NASA Technical Reports Server (NTRS)

Shtessel, Yuri; Hall, Charles; Jackson, Mark

2000-01-01

A reusable launch vehicle control problem during ascent is addressed via multiple-time scaled continuous sliding mode control. The proposed sliding mode controller utilizes a two-loop structure and provides robust, de-coupled tracking of both orientation angle command profiles and angular rate command profiles in the presence of bounded external disturbances and plant uncertainties. Sliding mode control causes the angular rate and orientation angle tracking error dynamics to be constrained to linear, de-coupled, homogeneous, and vector valued differential equations with desired eigenvalues placement. Overall stability of a two-loop control system is addressed. An optimal control allocation algorithm is designed that allocates torque commands into end-effector deflection commands, which are executed by the actuators. The dual-time scale sliding mode controller was designed for the X-33 technology demonstration sub-orbital launch vehicle in the launch mode. Simulation results show that the designed controller provides robust, accurate, de-coupled tracking of the orientation angle command profiles in presence of external disturbances and vehicle inertia uncertainties. This is a significant advancement in performance over that achieved with linear, gain scheduled control systems currently being used for launch vehicles.

Reflections of the social environment in chimpanzee memory: applying rational analysis beyond humans.

PubMed

Stevens, Jeffrey R; Marewski, Julian N; Schooler, Lael J; Gilby, Ian C

2016-08-01

In cognitive science, the rational analysis framework allows modelling of how physical and social environments impose information-processing demands onto cognitive systems. In humans, for example, past social contact among individuals predicts their future contact with linear and power functions. These features of the human environment constrain the optimal way to remember information and probably shape how memory records are retained and retrieved. We offer a primer on how biologists can apply rational analysis to study animal behaviour. Using chimpanzees ( Pan troglodytes ) as a case study, we modelled 19 years of observational data on their social contact patterns. Much like humans, the frequency of past encounters in chimpanzees linearly predicted future encounters, and the recency of past encounters predicted future encounters with a power function. Consistent with the rational analyses carried out for human memory, these findings suggest that chimpanzee memory performance should reflect those environmental regularities. In re-analysing existing chimpanzee memory data, we found that chimpanzee memory patterns mirrored their social contact patterns. Our findings hint that human and chimpanzee memory systems may have evolved to solve similar information-processing problems. Overall, rational analysis offers novel theoretical and methodological avenues for the comparative study of cognition.

Reflections of the social environment in chimpanzee memory: applying rational analysis beyond humans

PubMed Central

Marewski, Julian N.; Schooler, Lael J.; Gilby, Ian C.

2016-01-01

In cognitive science, the rational analysis framework allows modelling of how physical and social environments impose information-processing demands onto cognitive systems. In humans, for example, past social contact among individuals predicts their future contact with linear and power functions. These features of the human environment constrain the optimal way to remember information and probably shape how memory records are retained and retrieved. We offer a primer on how biologists can apply rational analysis to study animal behaviour. Using chimpanzees (Pan troglodytes) as a case study, we modelled 19 years of observational data on their social contact patterns. Much like humans, the frequency of past encounters in chimpanzees linearly predicted future encounters, and the recency of past encounters predicted future encounters with a power function. Consistent with the rational analyses carried out for human memory, these findings suggest that chimpanzee memory performance should reflect those environmental regularities. In re-analysing existing chimpanzee memory data, we found that chimpanzee memory patterns mirrored their social contact patterns. Our findings hint that human and chimpanzee memory systems may have evolved to solve similar information-processing problems. Overall, rational analysis offers novel theoretical and methodological avenues for the comparative study of cognition. PMID:27853606

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

Unkelbach, Jan, E-mail: junkelbach@mgh.harvard.edu; Botas, Pablo; Faculty of Physics, Ruprecht-Karls-Universität Heidelberg, Heidelberg

Purpose: We describe a treatment plan optimization method for intensity modulated proton therapy (IMPT) that avoids high values of linear energy transfer (LET) in critical structures located within or near the target volume while limiting degradation of the best possible physical dose distribution. Methods and Materials: To allow fast optimization based on dose and LET, a GPU-based Monte Carlo code was extended to provide dose-averaged LET in addition to dose for all pencil beams. After optimizing an initial IMPT plan based on physical dose, a prioritized optimization scheme is used to modify the LET distribution while constraining the physical dosemore » objectives to values close to the initial plan. The LET optimization step is performed based on objective functions evaluated for the product of LET and physical dose (LET×D). To first approximation, LET×D represents a measure of the additional biological dose that is caused by high LET. Results: The method is effective for treatments where serial critical structures with maximum dose constraints are located within or near the target. We report on 5 patients with intracranial tumors (high-grade meningiomas, base-of-skull chordomas, ependymomas) in whom the target volume overlaps with the brainstem and optic structures. In all cases, high LET×D in critical structures could be avoided while minimally compromising physical dose planning objectives. Conclusion: LET-based reoptimization of IMPT plans represents a pragmatic approach to bridge the gap between purely physical dose-based and relative biological effectiveness (RBE)-based planning. The method makes IMPT treatments safer by mitigating a potentially increased risk of side effects resulting from elevated RBE of proton beams near the end of range.« less

Transcranial Electrical Neuromodulation Based on the Reciprocity Principle

PubMed Central

Fernández-Corazza, Mariano; Turovets, Sergei; Luu, Phan; Anderson, Erik; Tucker, Don

2016-01-01

A key challenge in multi-electrode transcranial electrical stimulation (TES) or transcranial direct current stimulation (tDCS) is to find a current injection pattern that delivers the necessary current density at a target and minimizes it in the rest of the head, which is mathematically modeled as an optimization problem. Such an optimization with the Least Squares (LS) or Linearly Constrained Minimum Variance (LCMV) algorithms is generally computationally expensive and requires multiple independent current sources. Based on the reciprocity principle in electroencephalography (EEG) and TES, it could be possible to find the optimal TES patterns quickly whenever the solution of the forward EEG problem is available for a brain region of interest. Here, we investigate the reciprocity principle as a guideline for finding optimal current injection patterns in TES that comply with safety constraints. We define four different trial cortical targets in a detailed seven-tissue finite element head model, and analyze the performance of the reciprocity family of TES methods in terms of electrode density, targeting error, focality, intensity, and directionality using the LS and LCMV solutions as the reference standards. It is found that the reciprocity algorithms show good performance comparable to the LCMV and LS solutions. Comparing the 128 and 256 electrode cases, we found that use of greater electrode density improves focality, directionality, and intensity parameters. The results show that reciprocity principle can be used to quickly determine optimal current injection patterns in TES and help to simplify TES protocols that are consistent with hardware and software availability and with safety constraints. PMID:27303311

Transcranial Electrical Neuromodulation Based on the Reciprocity Principle.

PubMed

Fernández-Corazza, Mariano; Turovets, Sergei; Luu, Phan; Anderson, Erik; Tucker, Don

2016-01-01

A key challenge in multi-electrode transcranial electrical stimulation (TES) or transcranial direct current stimulation (tDCS) is to find a current injection pattern that delivers the necessary current density at a target and minimizes it in the rest of the head, which is mathematically modeled as an optimization problem. Such an optimization with the Least Squares (LS) or Linearly Constrained Minimum Variance (LCMV) algorithms is generally computationally expensive and requires multiple independent current sources. Based on the reciprocity principle in electroencephalography (EEG) and TES, it could be possible to find the optimal TES patterns quickly whenever the solution of the forward EEG problem is available for a brain region of interest. Here, we investigate the reciprocity principle as a guideline for finding optimal current injection patterns in TES that comply with safety constraints. We define four different trial cortical targets in a detailed seven-tissue finite element head model, and analyze the performance of the reciprocity family of TES methods in terms of electrode density, targeting error, focality, intensity, and directionality using the LS and LCMV solutions as the reference standards. It is found that the reciprocity algorithms show good performance comparable to the LCMV and LS solutions. Comparing the 128 and 256 electrode cases, we found that use of greater electrode density improves focality, directionality, and intensity parameters. The results show that reciprocity principle can be used to quickly determine optimal current injection patterns in TES and help to simplify TES protocols that are consistent with hardware and software availability and with safety constraints.

Utilization of Optimization for Design of Morphing Wing Structures for Enhanced Flight

NASA Astrophysics Data System (ADS)

Detrick, Matthew Scott

Conventional aircraft control surfaces constrain maneuverability. This work is a comprehensive study that looks at both smart material and conventional actuation methods to achieve wing twist to potentially improve flight capability using minimal actuation energy while allowing minimal wing deformation under aerodynamic loading. A continuous wing is used in order to reduce drag while allowing the aircraft to more closely approximate the wing deformation used by birds while loitering. The morphing wing for this work consists of a skin supported by an underlying truss structure whose goal is to achieve a given roll moment using less actuation energy than conventional control surfaces. A structural optimization code has been written in order to achieve minimal wing deformation under aerodynamic loading while allowing wing twist under actuation. The multi-objective cost function for the optimization consists of terms that ensure small deformation under aerodynamic loading, small change in airfoil shape during wing twist, a linear variation of wing twist along the length of the wing, small deviation from the desired wing twist, minimal number of truss members, minimal wing weight, and minimal actuation energy. Hydraulic cylinders and a two member linkage driven by a DC motor are tested separately to provide actuation. Since the goal of the current work is simply to provide a roll moment, only one actuator is implemented along the wing span. Optimization is also used to find the best location within the truss structure for the actuator. The active structure produced by optimization is then compared to simulated and experimental results from other researchers as well as characteristics of conventional aircraft.

Incorporating deliverable monitor unit constraints into spot intensity optimization in intensity modulated proton therapy treatment planning

PubMed Central

Cao, Wenhua; Lim, Gino; Li, Xiaoqiang; Li, Yupeng; Zhu, X. Ronald; Zhang, Xiaodong

2014-01-01

The purpose of this study is to investigate the feasibility and impact of incorporating deliverable monitor unit (MU) constraints into spot intensity optimization in intensity modulated proton therapy (IMPT) treatment planning. The current treatment planning system (TPS) for IMPT disregards deliverable MU constraints in the spot intensity optimization (SIO) routine. It performs a post-processing procedure on an optimized plan to enforce deliverable MU values that are required by the spot scanning proton delivery system. This procedure can create a significant dose distribution deviation between the optimized and post-processed deliverable plans, especially when small spot spacings are used. In this study, we introduce a two-stage linear programming (LP) approach to optimize spot intensities and constrain deliverable MU values simultaneously, i.e., a deliverable spot intensity optimization (DSIO) model. Thus, the post-processing procedure is eliminated and the associated optimized plan deterioration can be avoided. Four prostate cancer cases at our institution were selected for study and two parallel opposed beam angles were planned for all cases. A quadratic programming (QP) based model without MU constraints, i.e., a conventional spot intensity optimization (CSIO) model, was also implemented to emulate the commercial TPS. Plans optimized by both the DSIO and CSIO models were evaluated for five different settings of spot spacing from 3 mm to 7 mm. For all spot spacings, the DSIO-optimized plans yielded better uniformity for the target dose coverage and critical structure sparing than did the CSIO-optimized plans. With reduced spot spacings, more significant improvements in target dose uniformity and critical structure sparing were observed in the DSIO- than in the CSIO-optimized plans. Additionally, better sparing of the rectum and bladder was achieved when reduced spacings were used for the DSIO-optimized plans. The proposed DSIO approach ensures the deliverability of optimized IMPT plans that take into account MU constraints. This eliminates the post-processing procedure required by the TPS as well as the resultant deteriorating effect on ultimate dose distributions. This approach therefore allows IMPT plans to adopt all possible spot spacings optimally. Moreover, dosimetric benefits can be achieved using smaller spot spacings. PMID:23835656

Fast alternating projection methods for constrained tomographic reconstruction

PubMed Central

Liu, Li; Han, Yongxin

2017-01-01

The alternating projection algorithms are easy to implement and effective for large-scale complex optimization problems, such as constrained reconstruction of X-ray computed tomography (CT). A typical method is to use projection onto convex sets (POCS) for data fidelity, nonnegative constraints combined with total variation (TV) minimization (so called TV-POCS) for sparse-view CT reconstruction. However, this type of method relies on empirically selected parameters for satisfactory reconstruction and is generally slow and lack of convergence analysis. In this work, we use a convex feasibility set approach to address the problems associated with TV-POCS and propose a framework using full sequential alternating projections or POCS (FS-POCS) to find the solution in the intersection of convex constraints of bounded TV function, bounded data fidelity error and non-negativity. The rationale behind FS-POCS is that the mathematically optimal solution of the constrained objective function may not be the physically optimal solution. The breakdown of constrained reconstruction into an intersection of several feasible sets can lead to faster convergence and better quantification of reconstruction parameters in a physical meaningful way than that in an empirical way of trial-and-error. In addition, for large-scale optimization problems, first order methods are usually used. Not only is the condition for convergence of gradient-based methods derived, but also a primal-dual hybrid gradient (PDHG) method is used for fast convergence of bounded TV. The newly proposed FS-POCS is evaluated and compared with TV-POCS and another convex feasibility projection method (CPTV) using both digital phantom and pseudo-real CT data to show its superior performance on reconstruction speed, image quality and quantification. PMID:28253298

String theory origin of constrained multiplets

NASA Astrophysics Data System (ADS)

Kallosh, Renata; Vercnocke, Bert; Wrase, Timm

2016-09-01

We study the non-linearly realized spontaneously broken supersymmetry of the (anti-)D3-brane action in type IIB string theory. The worldvolume fields are one vector A μ , three complex scalars ϕ i and four 4d fermions λ 0, λ i. These transform, in addition to the more familiar {N}=4 linear supersymmetry, also under 16 spontaneously broken, non-linearly realized supersymmetries. We argue that the worldvolume fields can be packaged into the following constrained 4d non-linear {N}=1 multiplets: four chiral multiplets S, Y i that satisfy S 2 = SY i =0 and contain the worldvolume fermions λ 0 and λ i ; and four chiral multiplets W α , H i that satisfy S{W}_{α }=S{overline{D}}_{overset{\\cdotp }{α }}{overline{H}}^{overline{imath}}=0 and contain the vector A μ and the scalars ϕ i . We also discuss how placing an anti-D3-brane on top of intersecting O7-planes can lead to an orthogonal multiplet Φ that satisfies S(Φ -overline{Φ})=0 , which is particularly interesting for inflationary cosmology.

Robust Neighboring Optimal Guidance for the Advanced Launch System

NASA Technical Reports Server (NTRS)

Hull, David G.

1993-01-01

In recent years, optimization has become an engineering tool through the availability of numerous successful nonlinear programming codes. Optimal control problems are converted into parameter optimization (nonlinear programming) problems by assuming the control to be piecewise linear, making the unknowns the nodes or junction points of the linear control segments. Once the optimal piecewise linear control (suboptimal) control is known, a guidance law for operating near the suboptimal path is the neighboring optimal piecewise linear control (neighboring suboptimal control). Research conducted under this grant has been directed toward the investigation of neighboring suboptimal control as a guidance scheme for an advanced launch system.

Conformationally constrained farnesoid X receptor (FXR) agonists: alternative replacements of the stilbene.

PubMed

Akwabi-Ameyaw, Adwoa; Caravella, Justin A; Chen, Lihong; Creech, Katrina L; Deaton, David N; Madauss, Kevin P; Marr, Harry B; Miller, Aaron B; Navas, Frank; Parks, Derek J; Spearing, Paul K; Todd, Dan; Williams, Shawn P; Wisely, G Bruce

2011-10-15

To further explore the optimum placement of the acid moiety in conformationally constrained analogs of GW 4064 1a, a series of stilbene replacements were prepared. The benzothiophene 1f and the indole 1g display the optimal orientation of the carboxylate for enhanced FXR agonist potency. Copyright © 2011 Elsevier Ltd. All rights reserved.

Longitudinal train dynamics model for a rail transit simulation system

DOE PAGES

Wang, Jinghui; Rakha, Hesham A.

2018-01-01

The paper develops a longitudinal train dynamics model in support of microscopic railway transportation simulation. The model can be calibrated without any mechanical data making it ideal for implementation in transportation simulators. The calibration and validation work is based on data collected from the Portland light rail train fleet. The calibration procedure is mathematically formulated as a constrained non-linear optimization problem. The validity of the model is assessed by comparing instantaneous model predictions against field observations, and also evaluated in the domains of acceleration/deceleration versus speed and acceleration/deceleration versus distance. A test is conducted to investigate the adequacy of themore » model in simulation implementation. The results demonstrate that the proposed model can adequately capture instantaneous train dynamics, and provides good performance in the simulation test. Thus, the model provides a simple theoretical foundation for microscopic simulators and will significantly support the planning, management and control of railway transportation systems.« less

Form of prior for constrained thermodynamic processes with uncertainty

NASA Astrophysics Data System (ADS)

Aneja, Preety; Johal, Ramandeep S.

2015-05-01

We consider the quasi-static thermodynamic processes with constraints, but with additional uncertainty about the control parameters. Motivated by inductive reasoning, we assign prior distribution that provides a rational guess about likely values of the uncertain parameters. The priors are derived explicitly for both the entropy-conserving and the energy-conserving processes. The proposed form is useful when the constraint equation cannot be treated analytically. The inference is performed using spin-1/2 systems as models for heat reservoirs. Analytical results are derived in the high-temperatures limit. An agreement beyond linear response is found between the estimates of thermal quantities and their optimal values obtained from extremum principles. We also seek an intuitive interpretation for the prior and the estimated value of temperature obtained therefrom. We find that the prior over temperature becomes uniform over the quantity kept conserved in the process.

Longitudinal train dynamics model for a rail transit simulation system

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

Wang, Jinghui; Rakha, Hesham A.

The paper develops a longitudinal train dynamics model in support of microscopic railway transportation simulation. The model can be calibrated without any mechanical data making it ideal for implementation in transportation simulators. The calibration and validation work is based on data collected from the Portland light rail train fleet. The calibration procedure is mathematically formulated as a constrained non-linear optimization problem. The validity of the model is assessed by comparing instantaneous model predictions against field observations, and also evaluated in the domains of acceleration/deceleration versus speed and acceleration/deceleration versus distance. A test is conducted to investigate the adequacy of themore » model in simulation implementation. The results demonstrate that the proposed model can adequately capture instantaneous train dynamics, and provides good performance in the simulation test. Thus, the model provides a simple theoretical foundation for microscopic simulators and will significantly support the planning, management and control of railway transportation systems.« less

MM Algorithms for Geometric and Signomial Programming

PubMed Central

Lange, Kenneth; Zhou, Hua

2013-01-01

This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates. PMID:24634545

[Research on the measurement of flue-dust concentration in Vis, IR spectral region].

PubMed

Sun, Xiao-gang; Tang, Hong; Yuan, Gui-bin

2008-10-01

In the measurement of flue-dust concentration based on the transmission method, the dependent model algorithm was used to invert the flue-dust concentration in the visible, infrared and visible-infrared spectral regions respectively. By the analysis and comparison of the accuracy, linearity and sensitivity of the inversion flue-dust concentration, the optimal spectral region was determined. Meanwhile, the influence of the water droplet with different size distribution and volume concentration was simulated, and a method was proposed which has advantages of simplicity, rapidity, and suitability for on line measurement. Simulation experiments illustrate that the flue-dust concentration can be inverted very well in the visible-infrared spectral region, and it is feasible to use the ratio of the constrained light extinction method to overcome the influence of water droplet. The inverse results all remain satisfactory when 2% stochastic noise is added to the value of the light extinction.

MM Algorithms for Geometric and Signomial Programming.

PubMed

Lange, Kenneth; Zhou, Hua

2014-02-01

This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates.

Thin film module electrical configuration versus electrical performance

NASA Technical Reports Server (NTRS)

Morel, D. L.

1985-01-01

The as made and degraded states of thin film silicon (TFS) based modules have been modelled in terms of series resistance losses. The origins of these losses lie in interface and bulk regions of the devices. When modules degrade under light exposure, increases occur in both the interface and bulk components of the loss based on series resistance. Actual module performance can thus be simulated by use of only one unknown parameter, shunt losses. Use of the simulation to optimize module design indicates that the current design of 25 cells per linear foot is near optimum. Degradation performance suggests a shift to approx. 35 cells to effect maximum output for applications not constrained to 12 volts. Earlier studies of energy based performance and tandem structures should be updated to include stability factors, not only the initial loss factor tested here, but also appropriate annealing factors.

Application of precomputed control laws in a reconfigurable aircraft flight control system

NASA Technical Reports Server (NTRS)

Moerder, Daniel D.; Halyo, Nesim; Broussard, John R.; Caglayan, Alper K.

1989-01-01

A self-repairing flight control system concept in which the control law is reconfigured after actuator and/or control surface damage to preserve stability and pilot command tracking is described. A key feature of the controller is reconfigurable multivariable feedback. The feedback gains are designed off-line and scheduled as a function of the aircraft control impairment status so that reconfiguration is performed simply by updating the gain schedule after detection of an impairment. A novel aspect of the gain schedule design procedure is that the schedule is calculated using a linear quadratic optimization-based simultaneous stabilization algorithm in which the scheduled gain is constrained to stabilize a collection of plant models representing the aircraft in various control failure modes. A description and numerical evaluation of a controller design for a model of a statically unstable high-performance aircraft are given.

On optimal strategies in event-constrained differential games

NASA Technical Reports Server (NTRS)

Heymann, M.; Rajan, N.; Ardema, M.

1985-01-01

Combat games are formulated as zero-sum differential games with unilateral event constraints. An interior penalty function approach is employed to approximate optimal strategies for the players. The method is very attractive computationally and possesses suitable approximation and convergence properties.

A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: I. Robust Linear Optimization and Robust Mixed Integer Linear Optimization

PubMed Central

Li, Zukui; Ding, Ran; Floudas, Christodoulos A.

2011-01-01

Robust counterpart optimization techniques for linear optimization and mixed integer linear optimization problems are studied in this paper. Different uncertainty sets, including those studied in literature (i.e., interval set; combined interval and ellipsoidal set; combined interval and polyhedral set) and new ones (i.e., adjustable box; pure ellipsoidal; pure polyhedral; combined interval, ellipsoidal, and polyhedral set) are studied in this work and their geometric relationship is discussed. For uncertainty in the left hand side, right hand side, and objective function of the optimization problems, robust counterpart optimization formulations induced by those different uncertainty sets are derived. Numerical studies are performed to compare the solutions of the robust counterpart optimization models and applications in refinery production planning and batch process scheduling problem are presented. PMID:21935263

Constraining gross primary production and ecosystem respiration estimates for North America using atmospheric observations of carbonyl sulfide (OCS) and CO2

NASA Astrophysics Data System (ADS)

He, W.; Ju, W.; Chen, H.; Peters, W.; van der Velde, I.; Baker, I. T.; Andrews, A. E.; Zhang, Y.; Launois, T.; Campbell, J. E.; Suntharalingam, P.; Montzka, S. A.

2016-12-01

Carbonyl sulfide (OCS) is a promising novel atmospheric tracer for studying carbon cycle processes. OCS shares a similar pathway as CO2 during photosynthesis but not released through a respiration-like process, thus could be used to partition Gross Primary Production (GPP) from Net Ecosystem-atmosphere CO2 Exchange (NEE). This study uses joint atmospheric observations of OCS and CO2 to constrain GPP and ecosystem respiration (Re). Flask data from tower and aircraft sites over North America are collected. We employ our recently developed CarbonTracker (CT)-Lagrange carbon assimilation system, which is based on the CT framework and the Weather Research and Forecasting - Stochastic Time-Inverted Lagrangian Transport (WRF-STILT) model, and the Simple Biosphere model with simulated OCS (SiB3-OCS) that provides prior GPP, Re and plant uptake fluxes of OCS. Derived plant OCS fluxes from both process model and GPP-scaled model are tested in our inversion. To investigate the ability of OCS to constrain GPP and understand the uncertainty propagated from OCS modeling errors to constrained fluxes in a dual-tracer system including OCS and CO2, two inversion schemes are implemented and compared: (1) a two-step scheme, which firstly optimizes GPP using OCS observations, and then simultaneously optimizes GPP and Re using CO2 observations with OCS-constrained GPP in the first step as prior; (2) a joint scheme, which simultaneously optimizes GPP and Re using OCS and CO2 observations. We will evaluate the result using an estimated GPP from space-borne solar-induced fluorescence observations and a data-driven GPP upscaled from FLUXNET data with a statistical model (Jung et al., 2011). Preliminary result for the year 2010 shows the joint inversion makes simulated mole fractions more consistent with observations for both OCS and CO2. However, the uncertainty of OCS simulation is larger than that of CO2. The two-step and joint schemes perform similarly in improving the consistence with observations for OCS, implicating that OCS could provide independent constraint in joint inversion. Optimization makes less total GPP and Re but more NEE, when testing with prior CO2 fluxes from two biosphere models. This study gives an in-depth insight into the role of joint atmospheric OCS and CO2 observations in constraining CO2 fluxes.

How wet should be the reaction coordinate for ligand unbinding?

PubMed

Tiwary, Pratyush; Berne, B J

2016-08-07

We use a recently proposed method called Spectral Gap Optimization of Order Parameters (SGOOP) [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. U. S. A. 113, 2839 (2016)], to determine an optimal 1-dimensional reaction coordinate (RC) for the unbinding of a bucky-ball from a pocket in explicit water. This RC is estimated as a linear combination of the multiple available order parameters that collectively can be used to distinguish the various stable states relevant for unbinding. We pay special attention to determining and quantifying the degree to which water molecules should be included in the RC. Using SGOOP with under-sampled biased simulations, we predict that water plays a distinct role in the reaction coordinate for unbinding in the case when the ligand is sterically constrained to move along an axis of symmetry. This prediction is validated through extensive calculations of the unbinding times through metadynamics and by comparison through detailed balance with unbiased molecular dynamics estimate of the binding time. However when the steric constraint is removed, we find that the role of water in the reaction coordinate diminishes. Here instead SGOOP identifies a good one-dimensional RC involving various motional degrees of freedom.

How wet should be the reaction coordinate for ligand unbinding?

NASA Astrophysics Data System (ADS)

Tiwary, Pratyush; Berne, B. J.

2016-08-01

We use a recently proposed method called Spectral Gap Optimization of Order Parameters (SGOOP) [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. U. S. A. 113, 2839 (2016)], to determine an optimal 1-dimensional reaction coordinate (RC) for the unbinding of a bucky-ball from a pocket in explicit water. This RC is estimated as a linear combination of the multiple available order parameters that collectively can be used to distinguish the various stable states relevant for unbinding. We pay special attention to determining and quantifying the degree to which water molecules should be included in the RC. Using SGOOP with under-sampled biased simulations, we predict that water plays a distinct role in the reaction coordinate for unbinding in the case when the ligand is sterically constrained to move along an axis of symmetry. This prediction is validated through extensive calculations of the unbinding times through metadynamics and by comparison through detailed balance with unbiased molecular dynamics estimate of the binding time. However when the steric constraint is removed, we find that the role of water in the reaction coordinate diminishes. Here instead SGOOP identifies a good one-dimensional RC involving various motional degrees of freedom.

How wet should be the reaction coordinate for ligand unbinding?

PubMed Central

Tiwary, Pratyush; Berne, B. J.

2016-01-01

We use a recently proposed method called Spectral Gap Optimization of Order Parameters (SGOOP) [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. U. S. A. 113, 2839 (2016)], to determine an optimal 1-dimensional reaction coordinate (RC) for the unbinding of a bucky-ball from a pocket in explicit water. This RC is estimated as a linear combination of the multiple available order parameters that collectively can be used to distinguish the various stable states relevant for unbinding. We pay special attention to determining and quantifying the degree to which water molecules should be included in the RC. Using SGOOP with under-sampled biased simulations, we predict that water plays a distinct role in the reaction coordinate for unbinding in the case when the ligand is sterically constrained to move along an axis of symmetry. This prediction is validated through extensive calculations of the unbinding times through metadynamics and by comparison through detailed balance with unbiased molecular dynamics estimate of the binding time. However when the steric constraint is removed, we find that the role of water in the reaction coordinate diminishes. Here instead SGOOP identifies a good one-dimensional RC involving various motional degrees of freedom. PMID:27497545

Directional constraint of endpoint force emerges from hindlimb anatomy.

PubMed

Bunderson, Nathan E; McKay, J Lucas; Ting, Lena H; Burkholder, Thomas J

2010-06-15

Postural control requires the coordination of force production at the limb endpoints to apply an appropriate force to the body. Subjected to horizontal plane perturbations, quadruped limbs stereotypically produce force constrained along a line that passes near the center of mass. This phenomenon, referred to as the force constraint strategy, may reflect mechanical constraints on the limb or body, a specific neural control strategy or an interaction among neural controls and mechanical constraints. We used a neuromuscular model of the cat hindlimb to test the hypothesis that the anatomical constraints restrict the mechanical action of individual muscles during stance and constrain the response to perturbations to a line independent of perturbation direction. In a linearized neuromuscular model of the cat hindlimb, muscle lengthening directions were highly conserved across 10,000 different muscle activation patterns, each of which produced an identical, stance-like endpoint force. These lengthening directions were closely aligned with the sagittal plane and reveal an anatomical structure for directionally constrained force responses. Each of the 10,000 activation patterns was predicted to produce stable stance based on Lyapunov stability analysis. In forward simulations of the nonlinear, seven degree of freedom model under the action of 200 random muscle activation patterns, displacement of the endpoint from its equilibrium position produced restoring forces, which were also biased toward the sagittal plane. The single exception was an activation pattern based on minimum muscle stress optimization, which produced destabilizing force responses in some perturbation directions. The sagittal force constraint increased during simulations as the system shifted from an inertial response during the acceleration phase to a viscoelastic response as peak velocity was obtained. These results qualitatively match similar experimental observations and suggest that the force constraint phenomenon may result from the anatomical arrangement of the limb.

A SEARCH FOR STELLAR-MASS BLACK HOLES VIA ASTROMETRIC MICROLENSING

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

Lu, J. R.; Sinukoff, E.; Ofek, E. O.

While dozens of stellar-mass black holes (BHs) have been discovered in binary systems, isolated BHs have eluded detection. Their presence can be inferred when they lens light from a background star. We attempt to detect the astrometric lensing signatures of three photometrically identified microlensing events, OGLE-2011-BLG-0022, OGLE-2011-BLG-0125, and OGLE-2012-BLG-0169 (OB110022, OB110125, and OB120169), located toward the Galactic Bulge. These events were selected because of their long durations, which statistically favors more massive lenses. Astrometric measurements were made over one to two years using laser-guided adaptive optics observations from the W. M. Keck Observatory. Lens model parameters were first constrained bymore » the photometric light curves. The OB120169 light curve is well fit by a single-lens model, while both OB110022 and OB110125 light curves favor binary lens models. Using the photometric fits as prior information, no significant astrometric lensing signal was detected and all targets were consistent with linear motion. The significant lack of astrometric signal constrains the lens mass of OB110022 to 0.05–1.79 M {sub ⊙} in a 99.7% confidence interval, which disfavors a BH lens. Fits to OB110125 yielded a reduced Einstein crossing time and insufficient observations during the peak, so no mass limits were obtained. Two degenerate solutions exist for OB120169, which have a lens mass between 0.2–38.8 M {sub ⊙} and 0.4–39.8 M {sub ⊙} for a 99.7% confidence interval. Follow-up observations of OB120169 will further constrain the lens mass. Based on our experience, we use simulations to design optimal astrometric observing strategies and show that with more typical observing conditions the detection of BHs is feasible.« less

Directional constraint of endpoint force emerges from hindlimb anatomy

PubMed Central

Bunderson, Nathan E.; McKay, J. Lucas; Ting, Lena H.; Burkholder, Thomas J.

2010-01-01

Postural control requires the coordination of force production at the limb endpoints to apply an appropriate force to the body. Subjected to horizontal plane perturbations, quadruped limbs stereotypically produce force constrained along a line that passes near the center of mass. This phenomenon, referred to as the force constraint strategy, may reflect mechanical constraints on the limb or body, a specific neural control strategy or an interaction among neural controls and mechanical constraints. We used a neuromuscular model of the cat hindlimb to test the hypothesis that the anatomical constraints restrict the mechanical action of individual muscles during stance and constrain the response to perturbations to a line independent of perturbation direction. In a linearized neuromuscular model of the cat hindlimb, muscle lengthening directions were highly conserved across 10,000 different muscle activation patterns, each of which produced an identical, stance-like endpoint force. These lengthening directions were closely aligned with the sagittal plane and reveal an anatomical structure for directionally constrained force responses. Each of the 10,000 activation patterns was predicted to produce stable stance based on Lyapunov stability analysis. In forward simulations of the nonlinear, seven degree of freedom model under the action of 200 random muscle activation patterns, displacement of the endpoint from its equilibrium position produced restoring forces, which were also biased toward the sagittal plane. The single exception was an activation pattern based on minimum muscle stress optimization, which produced destabilizing force responses in some perturbation directions. The sagittal force constraint increased during simulations as the system shifted from an inertial response during the acceleration phase to a viscoelastic response as peak velocity was obtained. These results qualitatively match similar experimental observations and suggest that the force constraint phenomenon may result from the anatomical arrangement of the limb. PMID:20511528

Fat water decomposition using globally optimal surface estimation (GOOSE) algorithm.

PubMed

Cui, Chen; Wu, Xiaodong; Newell, John D; Jacob, Mathews

2015-03-01

This article focuses on developing a novel noniterative fat water decomposition algorithm more robust to fat water swaps and related ambiguities. Field map estimation is reformulated as a constrained surface estimation problem to exploit the spatial smoothness of the field, thus minimizing the ambiguities in the recovery. Specifically, the differences in the field map-induced frequency shift between adjacent voxels are constrained to be in a finite range. The discretization of the above problem yields a graph optimization scheme, where each node of the graph is only connected with few other nodes. Thanks to the low graph connectivity, the problem is solved efficiently using a noniterative graph cut algorithm. The global minimum of the constrained optimization problem is guaranteed. The performance of the algorithm is compared with that of state-of-the-art schemes. Quantitative comparisons are also made against reference data. The proposed algorithm is observed to yield more robust fat water estimates with fewer fat water swaps and better quantitative results than other state-of-the-art algorithms in a range of challenging applications. The proposed algorithm is capable of considerably reducing the swaps in challenging fat water decomposition problems. The experiments demonstrate the benefit of using explicit smoothness constraints in field map estimation and solving the problem using a globally convergent graph-cut optimization algorithm. © 2014 Wiley Periodicals, Inc.

Robust Constrained Blackbox Optimization with Surrogates

DTIC Science & Technology

2015-05-21

algorithms with OPAL . Mathematical Programming Computation, 6(3):233–254, 2014. 6. M.S. Ouali, H. Aoudjit, and C. Audet. Replacement scheduling of a fleet of...Orban. Optimization of Algorithms with OPAL . Mathematical Programming Computation, 6(3), 233-254, September 2014. DISTRIBUTION A: Distribution

Hierarchical Bayesian Model Averaging for Chance Constrained Remediation Designs

NASA Astrophysics Data System (ADS)

Chitsazan, N.; Tsai, F. T.

2012-12-01

Groundwater remediation designs are heavily relying on simulation models which are subjected to various sources of uncertainty in their predictions. To develop a robust remediation design, it is crucial to understand the effect of uncertainty sources. In this research, we introduce a hierarchical Bayesian model averaging (HBMA) framework to segregate and prioritize sources of uncertainty in a multi-layer frame, where each layer targets a source of uncertainty. The HBMA framework provides an insight to uncertainty priorities and propagation. In addition, HBMA allows evaluating model weights in different hierarchy levels and assessing the relative importance of models in each level. To account for uncertainty, we employ a chance constrained (CC) programming for stochastic remediation design. Chance constrained programming was implemented traditionally to account for parameter uncertainty. Recently, many studies suggested that model structure uncertainty is not negligible compared to parameter uncertainty. Using chance constrained programming along with HBMA can provide a rigorous tool for groundwater remediation designs under uncertainty. In this research, the HBMA-CC was applied to a remediation design in a synthetic aquifer. The design was to develop a scavenger well approach to mitigate saltwater intrusion toward production wells. HBMA was employed to assess uncertainties from model structure, parameter estimation and kriging interpolation. An improved harmony search optimization method was used to find the optimal location of the scavenger well. We evaluated prediction variances of chloride concentration at the production wells through the HBMA framework. The results showed that choosing the single best model may lead to a significant error in evaluating prediction variances for two reasons. First, considering the single best model, variances that stem from uncertainty in the model structure will be ignored. Second, considering the best model with non-dominant model weight may underestimate or overestimate prediction variances by ignoring other plausible propositions. Chance constraints allow developing a remediation design with a desirable reliability. However, considering the single best model, the calculated reliability will be different from the desirable reliability. We calculated the reliability of the design for the models at different levels of HBMA. The results showed that by moving toward the top layers of HBMA, the calculated reliability converges to the chosen reliability. We employed the chance constrained optimization along with the HBMA framework to find the optimal location and pumpage for the scavenger well. The results showed that using models at different levels in the HBMA framework, the optimal location of the scavenger well remained the same, but the optimal extraction rate was altered. Thus, we concluded that the optimal pumping rate was sensitive to the prediction variance. Also, the prediction variance was changed by using different extraction rate. Using very high extraction rate will cause prediction variances of chloride concentration at the production wells to approach zero regardless of which HBMA models used.

Optimal Control of Evolution Mixed Variational Inclusions

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

Alduncin, Gonzalo, E-mail: alduncin@geofisica.unam.mx

2013-12-15

Optimal control problems of primal and dual evolution mixed variational inclusions, in reflexive Banach spaces, are studied. The solvability analysis of the mixed state systems is established via duality principles. The optimality analysis is performed in terms of perturbation conjugate duality methods, and proximation penalty-duality algorithms to mixed optimality conditions are further presented. Applications to nonlinear diffusion constrained problems as well as quasistatic elastoviscoplastic bilateral contact problems exemplify the theory.

Continuous Shape Estimation of Continuum Robots Using X-ray Images

PubMed Central

Lobaton, Edgar J.; Fu, Jinghua; Torres, Luis G.; Alterovitz, Ron

2015-01-01

We present a new method for continuously and accurately estimating the shape of a continuum robot during a medical procedure using a small number of X-ray projection images (e.g., radiographs or fluoroscopy images). Continuum robots have curvilinear structure, enabling them to maneuver through constrained spaces by bending around obstacles. Accurately estimating the robot’s shape continuously over time is crucial for the success of procedures that require avoidance of anatomical obstacles and sensitive tissues. Online shape estimation of a continuum robot is complicated by uncertainty in its kinematic model, movement of the robot during the procedure, noise in X-ray images, and the clinical need to minimize the number of X-ray images acquired. Our new method integrates kinematics models of the robot with data extracted from an optimally selected set of X-ray projection images. Our method represents the shape of the continuum robot over time as a deformable surface which can be described as a linear combination of time and space basis functions. We take advantage of probabilistic priors and numeric optimization to select optimal camera configurations, thus minimizing the expected shape estimation error. We evaluate our method using simulated concentric tube robot procedures and demonstrate that obtaining between 3 and 10 images from viewpoints selected by our method enables online shape estimation with errors significantly lower than using the kinematic model alone or using randomly spaced viewpoints. PMID:26279960

Continuous Shape Estimation of Continuum Robots Using X-ray Images.

PubMed

Lobaton, Edgar J; Fu, Jinghua; Torres, Luis G; Alterovitz, Ron

2013-05-06

We present a new method for continuously and accurately estimating the shape of a continuum robot during a medical procedure using a small number of X-ray projection images (e.g., radiographs or fluoroscopy images). Continuum robots have curvilinear structure, enabling them to maneuver through constrained spaces by bending around obstacles. Accurately estimating the robot's shape continuously over time is crucial for the success of procedures that require avoidance of anatomical obstacles and sensitive tissues. Online shape estimation of a continuum robot is complicated by uncertainty in its kinematic model, movement of the robot during the procedure, noise in X-ray images, and the clinical need to minimize the number of X-ray images acquired. Our new method integrates kinematics models of the robot with data extracted from an optimally selected set of X-ray projection images. Our method represents the shape of the continuum robot over time as a deformable surface which can be described as a linear combination of time and space basis functions. We take advantage of probabilistic priors and numeric optimization to select optimal camera configurations, thus minimizing the expected shape estimation error. We evaluate our method using simulated concentric tube robot procedures and demonstrate that obtaining between 3 and 10 images from viewpoints selected by our method enables online shape estimation with errors significantly lower than using the kinematic model alone or using randomly spaced viewpoints.

Microgrid optimal scheduling considering impact of high penetration wind generation

NASA Astrophysics Data System (ADS)

Alanazi, Abdulaziz

The objective of this thesis is to study the impact of high penetration wind energy in economic and reliable operation of microgrids. Wind power is variable, i.e., constantly changing, and nondispatchable, i.e., cannot be controlled by the microgrid controller. Thus an accurate forecasting of wind power is an essential task in order to study its impacts in microgrid operation. Two commonly used forecasting methods including Autoregressive Integrated Moving Average (ARIMA) and Artificial Neural Network (ANN) have been used in this thesis to improve the wind power forecasting. The forecasting error is calculated using a Mean Absolute Percentage Error (MAPE) and is improved using the ANN. The wind forecast is further used in the microgrid optimal scheduling problem. The microgrid optimal scheduling is performed by developing a viable model for security-constrained unit commitment (SCUC) based on mixed-integer linear programing (MILP) method. The proposed SCUC is solved for various wind penetration levels and the relationship between the total cost and the wind power penetration is found. In order to reduce microgrid power transfer fluctuations, an additional constraint is proposed and added to the SCUC formulation. The new constraint would control the time-based fluctuations. The impact of the constraint on microgrid SCUC results is tested and validated with numerical analysis. Finally, the applicability of proposed models is demonstrated through numerical simulations.

Spacecraft Mission Design for the Mitigation of the 2017 PDC Hypothetical Asteroid Threat

NASA Technical Reports Server (NTRS)

Barbee, Brent W.; Sarli, Bruno V.; Lyzhoft, Joshua; Chodas, Paul W.; Englander, Jacob A.

2017-01-01

This paper presents a detailed mission design analysis results for the 2017 Planetary Defense Conference (PDC) Hypothetical Asteroid Impact Scenario, documented at https://cneos.jpl.nasa.gov/ pd/cs/pdc17/. The mission design includes campaigns for both reconnaissance (flyby or rendezvous) of the asteroid (to characterize it and the nature of the threat it poses to Earth) and mitigation of the asteroid, via kinetic impactor deflection, nuclear explosive device (NED) deflection, or NED disruption. Relevant scenario parameters are varied to assess the sensitivity of the design outcome, such as asteroid bulk density, asteroid diameter, momentum enhancement factor, spacecraft launch vehicle, and mitigation system type. Different trajectory types are evaluated in the mission design process from purely ballistic to those involving optimal midcourse maneuvers, planetary gravity assists, and/or lowthrust solar electric propulsion. The trajectory optimization is targeted around peak deflection points that were found through a novel linear numerical technique method. The optimization process includes constrain parameters, such as Earth departure date, launch declination, spacecraft/asteroid relative velocity and solar phase angle, spacecraft dry mass, minimum/maximum spacecraft distances from Sun and Earth, and Earth/spacecraft communications line of sight. Results show that one of the best options for the 2017 PDC deflection is solar electric propelled rendezvous mission with a single spacecraft using NED for the deflection

What linear programming contributes: world food programme experience with the "cost of the diet" tool.

PubMed

Frega, Romeo; Lanfranco, Jose Guerra; De Greve, Sam; Bernardini, Sara; Geniez, Perrine; Grede, Nils; Bloem, Martin; de Pee, Saskia

2012-09-01

Linear programming has been used for analyzing children's complementary feeding diets, for optimizing nutrient adequacy of dietary recommendations for a population, and for estimating the economic value of fortified foods. To describe and apply a linear programming tool ("Cost of the Diet") with data from Mozambique to determine what could be cost-effective fortification strategies. Based on locally assessed average household dietary needs, seasonal market prices of available food products, and food composition data, the tool estimates the lowest-cost diet that meets almost all nutrient needs. The results were compared with expenditure data from Mozambique to establish the affordability of this diet by quintiles of the population. Three different applications were illustrated: identifying likely "limiting nutrients," comparing cost effectiveness of different fortification interventions at the household level, and assessing economic access to nutritious foods. The analysis identified iron, vitamin B2, and pantothenic acid as "limiting nutrients." Under the Mozambique conditions, vegetable oil was estimated as a more cost-efficient vehicle for vitamin A fortification than sugar; maize flour may also be an effective vehicle to provide other constraining micronutrients. Multiple micronutrient fortification of maize flour could reduce the cost of the "lowest-cost nutritious diet" by 18%, but even this diet can be afforded by only 20% of the Mozambican population. Within the context of fortification, linear programming can be a useful tool for identifying likely nutrient inadequacies, for comparing fortification options in terms of cost effectiveness, and for illustrating the potential benefit of fortification for improving household access to a nutritious diet.

Number-unconstrained quantum sensing

NASA Astrophysics Data System (ADS)

Mitchell, Morgan W.

2017-12-01

Quantum sensing is commonly described as a constrained optimization problem: maximize the information gained about an unknown quantity using a limited number of particles. Important sensors including gravitational wave interferometers and some atomic sensors do not appear to fit this description, because there is no external constraint on particle number. Here, we develop the theory of particle-number-unconstrained quantum sensing, and describe how optimal particle numbers emerge from the competition of particle-environment and particle-particle interactions. We apply the theory to optical probing of an atomic medium modeled as a resonant, saturable absorber, and observe the emergence of well-defined finite optima without external constraints. The results contradict some expectations from number-constrained quantum sensing and show that probing with squeezed beams can give a large sensitivity advantage over classical strategies when each is optimized for particle number.

Women in Transition: Experiences of Health and Health Care for Recently Incarcerated Women Living in Community Corrections Facilities.

PubMed

Colbert, Alison M; Goshin, Lorie S; Durand, Vanessa; Zoucha, Rick; Sekula, L Kathleen

2016-12-01

Health priorities of women after incarceration remain poorly understood, constraining development of interventions targeted at their health during that time. We explored the experience of health and health care after incarceration in a focused ethnography of 28 women who had been released from prison or jail within the past year and were living in community corrections facilities. The women's outlook on health was rooted in a newfound core optimism, but this was constrained by their pressing health-related issues; stress and uncertainty; and the pressures of the criminal justice system. These external forces threatened to cause collapse of women's core optimism. Findings support interventions that capitalize on women's optimism and address barriers specific to criminal justice contexts. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

SU-E-T-574: Novel Chance-Constrained Optimization in Intensity-Modulated Proton Therapy Planning to Account for Range and Patient Setup Uncertainties

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

An, Y; Liang, J; Liu, W

2015-06-15

Purpose: We propose to apply a probabilistic framework, namely chanceconstrained optimization, in the intensity-modulated proton therapy (IMPT) planning subject to range and patient setup uncertainties. The purpose is to hedge against the influence of uncertainties and improve robustness of treatment plans. Methods: IMPT plans were generated for a typical prostate patient. Nine dose distributions are computed — the nominal one and one each for ±5mm setup uncertainties along three cardinal axes and for ±3.5% range uncertainty. These nine dose distributions are supplied to the solver CPLEX as chance constraints to explicitly control plan robustness under these representative uncertainty scenarios withmore » certain probability. This probability is determined by the tolerance level. We make the chance-constrained model tractable by converting it to a mixed integer optimization problem. The quality of plans derived from this method is evaluated using dose-volume histogram (DVH) indices such as tumor dose homogeneity (D5% – D95%) and coverage (D95%) and normal tissue sparing like V70 of rectum, V65, and V40 of bladder. We also compare the results from this novel method with the conventional PTV-based method to further demonstrate its effectiveness Results: Our model can yield clinically acceptable plans within 50 seconds. The chance-constrained optimization produces IMPT plans with comparable target coverage, better target dose homogeneity, and better normal tissue sparing compared to the PTV-based optimization [D95% CTV: 67.9 vs 68.7 (Gy), D5% – D95% CTV: 11.9 vs 18 (Gy), V70 rectum: 0.0 % vs 0.33%, V65 bladder: 2.17% vs 9.33%, V40 bladder: 8.83% vs 21.83%]. It also simultaneously makes the plan more robust [Width of DVH band at D50%: 2.0 vs 10.0 (Gy)]. The tolerance level may be varied to control the tradeoff between plan robustness and quality. Conclusion: The chance-constrained optimization generates superior IMPT plan compared to the PTV-based optimization with explicit control of plan robustness. NIH/NCI K25CA168984, Eagles Cancer Research Career Development, The Lawrence W. and Marilyn W. Matteson Fund for Cancer Research, Mayo ASU Seed Grant, and The Kemper Marley Foundation.« less

Maximum entropy production: Can it be used to constrain conceptual hydrological models?

Treesearch

M.C. Westhoff; E. Zehe

2013-01-01

In recent years, optimality principles have been proposed to constrain hydrological models. The principle of maximum entropy production (MEP) is one of the proposed principles and is subject of this study. It states that a steady state system is organized in such a way that entropy production is maximized. Although successful applications have been reported in...

(R-X-R)4 -Motif Peptides Containing Conformationally Constrained Cyclohexane-Derived Spacers: Effect on Cellular Uptake.

PubMed

Bhosle, Govind S; Fernandes, Moneesha

2017-11-08

Arginine-rich peptides having the (R-X-R) n motif are among the most effective cell-penetrating peptides (CPPs). Herein we report a several-fold increase in the efficacy of such CPPs if the linear flexible spacer (-X-) in the (R-X-R) motif is replaced by constrained cyclic 1,4-substituted-cyclohexane-derived spacers. Internalization of these oligomers in mammalian cell lines was found to be an energy-dependent process. Incorporation of these constrained, non-proteinogenic amino acid spacers in the CPPs is shown to enhance their proteolytic stability. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Finite-horizon control-constrained nonlinear optimal control using single network adaptive critics.

PubMed

Heydari, Ali; Balakrishnan, Sivasubramanya N

2013-01-01

To synthesize fixed-final-time control-constrained optimal controllers for discrete-time nonlinear control-affine systems, a single neural network (NN)-based controller called the Finite-horizon Single Network Adaptive Critic is developed in this paper. Inputs to the NN are the current system states and the time-to-go, and the network outputs are the costates that are used to compute optimal feedback control. Control constraints are handled through a nonquadratic cost function. Convergence proofs of: 1) the reinforcement learning-based training method to the optimal solution; 2) the training error; and 3) the network weights are provided. The resulting controller is shown to solve the associated time-varying Hamilton-Jacobi-Bellman equation and provide the fixed-final-time optimal solution. Performance of the new synthesis technique is demonstrated through different examples including an attitude control problem wherein a rigid spacecraft performs a finite-time attitude maneuver subject to control bounds. The new formulation has great potential for implementation since it consists of only one NN with single set of weights and it provides comprehensive feedback solutions online, though it is trained offline.

Experimental design approach to the process parameter optimization for laser welding of martensitic stainless steels in a constrained overlap configuration

NASA Astrophysics Data System (ADS)

Khan, M. M. A.; Romoli, L.; Fiaschi, M.; Dini, G.; Sarri, F.

2011-02-01

This paper presents an experimental design approach to process parameter optimization for the laser welding of martensitic AISI 416 and AISI 440FSe stainless steels in a constrained overlap configuration in which outer shell was 0.55 mm thick. To determine the optimal laser-welding parameters, a set of mathematical models were developed relating welding parameters to each of the weld characteristics. These were validated both statistically and experimentally. The quality criteria set for the weld to determine optimal parameters were the minimization of weld width and the maximization of weld penetration depth, resistance length and shearing force. Laser power and welding speed in the range 855-930 W and 4.50-4.65 m/min, respectively, with a fiber diameter of 300 μm were identified as the optimal set of process parameters. However, the laser power and welding speed can be reduced to 800-840 W and increased to 4.75-5.37 m/min, respectively, to obtain stronger and better welds.

Constraining DALECv2 using multiple data streams and ecological constraints: analysis and application

DOE PAGES

Delahaies, Sylvain; Roulstone, Ian; Nichols, Nancy

2017-07-10

We use a variational method to assimilate multiple data streams into the terrestrial ecosystem carbon cycle model DALECv2 (Data Assimilation Linked Ecosystem Carbon). Ecological and dynamical constraints have recently been introduced to constrain unresolved components of this otherwise ill-posed problem. We recast these constraints as a multivariate Gaussian distribution to incorporate them into the variational framework and we demonstrate their advantage through a linear analysis. By using an adjoint method we study a linear approximation of the inverse problem: firstly we perform a sensitivity analysis of the different outputs under consideration, and secondly we use the concept of resolution matricesmore » to diagnose the nature of the ill-posedness and evaluate regularisation strategies. We then study the non-linear problem with an application to real data. Finally, we propose a modification to the model: introducing a spin-up period provides us with a built-in formulation of some ecological constraints which facilitates the variational approach.« less

Constraining DALECv2 using multiple data streams and ecological constraints: analysis and application

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

Delahaies, Sylvain; Roulstone, Ian; Nichols, Nancy

We use a variational method to assimilate multiple data streams into the terrestrial ecosystem carbon cycle model DALECv2 (Data Assimilation Linked Ecosystem Carbon). Ecological and dynamical constraints have recently been introduced to constrain unresolved components of this otherwise ill-posed problem. We recast these constraints as a multivariate Gaussian distribution to incorporate them into the variational framework and we demonstrate their advantage through a linear analysis. By using an adjoint method we study a linear approximation of the inverse problem: firstly we perform a sensitivity analysis of the different outputs under consideration, and secondly we use the concept of resolution matricesmore » to diagnose the nature of the ill-posedness and evaluate regularisation strategies. We then study the non-linear problem with an application to real data. Finally, we propose a modification to the model: introducing a spin-up period provides us with a built-in formulation of some ecological constraints which facilitates the variational approach.« less

Large deformation image classification using generalized locality-constrained linear coding.

PubMed

Zhang, Pei; Wee, Chong-Yaw; Niethammer, Marc; Shen, Dinggang; Yap, Pew-Thian

2013-01-01

Magnetic resonance (MR) imaging has been demonstrated to be very useful for clinical diagnosis of Alzheimer's disease (AD). A common approach to using MR images for AD detection is to spatially normalize the images by non-rigid image registration, and then perform statistical analysis on the resulting deformation fields. Due to the high nonlinearity of the deformation field, recent studies suggest to use initial momentum instead as it lies in a linear space and fully encodes the deformation field. In this paper we explore the use of initial momentum for image classification by focusing on the problem of AD detection. Experiments on the public ADNI dataset show that the initial momentum, together with a simple sparse coding technique-locality-constrained linear coding (LLC)--can achieve a classification accuracy that is comparable to or even better than the state of the art. We also show that the performance of LLC can be greatly improved by introducing proper weights to the codebook.

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.

An all-at-once reduced Hessian SQP scheme for aerodynamic design optimization

NASA Technical Reports Server (NTRS)

Feng, Dan; Pulliam, Thomas H.

1995-01-01

This paper introduces a computational scheme for solving a class of aerodynamic design problems that can be posed as nonlinear equality constrained optimizations. The scheme treats the flow and design variables as independent variables, and solves the constrained optimization problem via reduced Hessian successive quadratic programming. It updates the design and flow variables simultaneously at each iteration and allows flow variables to be infeasible before convergence. The solution of an adjoint flow equation is never needed. In addition, a range space basis is chosen so that in a certain sense the 'cross term' ignored in reduced Hessian SQP methods is minimized. Numerical results for a nozzle design using the quasi-one-dimensional Euler equations show that this scheme is computationally efficient and robust. The computational cost of a typical nozzle design is only a fraction more than that of the corresponding analysis flow calculation. Superlinear convergence is also observed, which agrees with the theoretical properties of this scheme. All optimal solutions are obtained by starting far away from the final solution.

Climate change in fish: effects of respiratory constraints on optimal life history and behaviour.

PubMed

Holt, Rebecca E; Jørgensen, Christian

2015-02-01

The difference between maximum metabolic rate and standard metabolic rate is referred to as aerobic scope, and because it constrains performance it is suggested to constitute a key limiting process prescribing how fish may cope with or adapt to climate warming. We use an evolutionary bioenergetics model for Atlantic cod (Gadus morhua) to predict optimal life histories and behaviours at different temperatures. The model assumes common trade-offs and predicts that optimal temperatures for growth and fitness lie below that for aerobic scope; aerobic scope is thus a poor predictor of fitness at high temperatures. Initially, warming expands aerobic scope, allowing for faster growth and increased reproduction. Beyond the optimal temperature for fitness, increased metabolic requirements intensify foraging and reduce survival; oxygen budgeting conflicts thus constrain successful completion of the life cycle. The model illustrates how physiological adaptations are part of a suite of traits that have coevolved. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

A formulation and analysis of combat games

NASA Technical Reports Server (NTRS)

Heymann, M.; Ardema, M. D.; Rajan, N.

1984-01-01

Combat which is formulated as a dynamical encounter between two opponents, each of whom has offensive capabilities and objectives is outlined. A target set is associated with each opponent in the event space in which he endeavors to terminate the combat, thereby winning. If the combat terminates in both target sets simultaneously, or in neither, a joint capture or a draw, respectively, occurs. Resolution of the encounter is formulated as a combat game; as a pair of competing event constrained differential games. If exactly one of the players can win, the optimal strategies are determined from a resulting constrained zero sum differential game. Otherwise the optimal strategies are computed from a resulting nonzero sum game. Since optimal combat strategies may frequently not exist, approximate or delta combat games are also formulated leading to approximate or delta optimal strategies. The turret game is used to illustrate combat games. This game is sufficiently complex to exhibit a rich variety of combat behavior, much of which is not found in pursuit evasion games.

Optimization Research of Generation Investment Based on Linear Programming Model

NASA Astrophysics Data System (ADS)

Wu, Juan; Ge, Xueqian

Linear programming is an important branch of operational research and it is a mathematical method to assist the people to carry out scientific management. GAMS is an advanced simulation and optimization modeling language and it will combine a large number of complex mathematical programming, such as linear programming LP, nonlinear programming NLP, MIP and other mixed-integer programming with the system simulation. In this paper, based on the linear programming model, the optimized investment decision-making of generation is simulated and analyzed. At last, the optimal installed capacity of power plants and the final total cost are got, which provides the rational decision-making basis for optimized investments.

Calculation of Pareto-optimal solutions to multiple-objective problems using threshold-of-acceptability constraints

NASA Technical Reports Server (NTRS)

Giesy, D. P.

1978-01-01

A technique is presented for the calculation of Pareto-optimal solutions to a multiple-objective constrained optimization problem by solving a series of single-objective problems. Threshold-of-acceptability constraints are placed on the objective functions at each stage to both limit the area of search and to mathematically guarantee convergence to a Pareto optimum.

Fusion of Hard and Soft Information in Nonparametric Density Estimation

DTIC Science & Technology

2015-06-10

and stochastic optimization models, in analysis of simulation output, and when instantiating probability models. We adopt a constrained maximum...particular, density estimation is needed for generation of input densities to simulation and stochastic optimization models, in analysis of simulation output...an essential step in simulation analysis and stochastic optimization is the generation of probability densities for input random variables; see for

Distributed Constrained Optimization with Semicoordinate Transformations

NASA Technical Reports Server (NTRS)

Macready, William; Wolpert, David

2006-01-01

Recent work has shown how information theory extends conventional full-rationality game theory to allow bounded rational agents. The associated mathematical framework can be used to solve constrained optimization problems. This is done by translating the problem into an iterated game, where each agent controls a different variable of the problem, so that the joint probability distribution across the agents moves gives an expected value of the objective function. The dynamics of the agents is designed to minimize a Lagrangian function of that joint distribution. Here we illustrate how the updating of the Lagrange parameters in the Lagrangian is a form of automated annealing, which focuses the joint distribution more and more tightly about the joint moves that optimize the objective function. We then investigate the use of "semicoordinate" variable transformations. These separate the joint state of the agents from the variables of the optimization problem, with the two connected by an onto mapping. We present experiments illustrating the ability of such transformations to facilitate optimization. We focus on the special kind of transformation in which the statistically independent states of the agents induces a mixture distribution over the optimization variables. Computer experiment illustrate this for &sat constraint satisfaction problems and for unconstrained minimization of NK functions.

Risk-Constrained Dynamic Programming for Optimal Mars Entry, Descent, and Landing

NASA Technical Reports Server (NTRS)

Ono, Masahiro; Kuwata, Yoshiaki

2013-01-01

A chance-constrained dynamic programming algorithm was developed that is capable of making optimal sequential decisions within a user-specified risk bound. This work handles stochastic uncertainties over multiple stages in the CEMAT (Combined EDL-Mobility Analyses Tool) framework. It was demonstrated by a simulation of Mars entry, descent, and landing (EDL) using real landscape data obtained from the Mars Reconnaissance Orbiter. Although standard dynamic programming (DP) provides a general framework for optimal sequential decisionmaking under uncertainty, it typically achieves risk aversion by imposing an arbitrary penalty on failure states. Such a penalty-based approach cannot explicitly bound the probability of mission failure. A key idea behind the new approach is called risk allocation, which decomposes a joint chance constraint into a set of individual chance constraints and distributes risk over them. The joint chance constraint was reformulated into a constraint on an expectation over a sum of an indicator function, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the chance-constraint optimization problem can be turned into an unconstrained optimization over a Lagrangian, which can be solved efficiently using a standard DP approach.

SU-E-I-23: A General KV Constrained Optimization of CNR for CT Abdominal Imaging

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

Weir, V; Zhang, J

Purpose: While Tube current modulation has been well accepted for CT dose reduction, kV adjusting in clinical settings is still at its early stage. This is mainly due to the limited kV options of most current CT scanners. kV adjusting can potentially reduce radiation dose and optimize image quality. This study is to optimize CT abdomen imaging acquisition based on the assumption of a continuous kV, with the goal to provide the best contrast to noise ratio (CNR). Methods: For a given dose (CTDIvol) level, the CNRs at different kV and pitches were measured with an ACR GAMMEX phantom. Themore » phantom was scanned in a Siemens Sensation 64 scanner and a GE VCT 64 scanner. A constrained mathematical optimization was used to find the kV which led to the highest CNR for the anatomy and pitch setting. Parametric equations were obtained from polynomial fitting of plots of kVs vs CNRs. A suitable constraint region for optimization was chosen. Subsequent optimization yielded a peak CNR at a particular kV for different collimations and pitch setting. Results: The constrained mathematical optimization approach yields kV of 114.83 and 113.46, with CNRs of 1.27 and 1.11 at the pitch of 1.2 and 1.4, respectively, for the Siemens Sensation 64 scanner with the collimation of 32 x 0.625mm. An optimized kV of 134.25 and 1.51 CNR is obtained for a GE VCT 64 slice scanner with a collimation of 32 x 0.625mm and a pitch of 0.969. At 0.516 pitch and 32 x 0.625 mm an optimized kV of 133.75 and a CNR of 1.14 was found for the GE VCT 64 slice scanner. Conclusion: CNR in CT image acquisition can be further optimized with a continuous kV option instead of current discrete or fixed kV settings. A continuous kV option is a key for individualized CT protocols.« less

Enhanced Fuel-Optimal Trajectory-Generation Algorithm for Planetary Pinpoint Landing

NASA Technical Reports Server (NTRS)

Acikmese, Behcet; Blackmore, James C.; Scharf, Daniel P.

2011-01-01

An enhanced algorithm is developed that builds on a previous innovation of fuel-optimal powered-descent guidance (PDG) for planetary pinpoint landing. The PDG problem is to compute constrained, fuel-optimal trajectories to land a craft at a prescribed target on a planetary surface, starting from a parachute cut-off point and using a throttleable descent engine. The previous innovation showed the minimal-fuel PDG problem can be posed as a convex optimization problem, in particular, as a Second-Order Cone Program, which can be solved to global optimality with deterministic convergence properties, and hence is a candidate for onboard implementation. To increase the speed and robustness of this convex PDG algorithm for possible onboard implementation, the following enhancements are incorporated: 1) Fast detection of infeasibility (i.e., control authority is not sufficient for soft-landing) for subsequent fault response. 2) The use of a piecewise-linear control parameterization, providing smooth solution trajectories and increasing computational efficiency. 3) An enhanced line-search algorithm for optimal time-of-flight, providing quicker convergence and bounding the number of path-planning iterations needed. 4) An additional constraint that analytically guarantees inter-sample satisfaction of glide-slope and non-sub-surface flight constraints, allowing larger discretizations and, hence, faster optimization. 5) Explicit incorporation of Mars rotation rate into the trajectory computation for improved targeting accuracy. These enhancements allow faster convergence to the fuel-optimal solution and, more importantly, remove the need for a "human-in-the-loop," as constraints will be satisfied over the entire path-planning interval independent of step-size (as opposed to just at the discrete time points) and infeasible initial conditions are immediately detected. Finally, while the PDG stage is typically only a few minutes, ignoring the rotation rate of Mars can introduce 10s of meters of error. By incorporating it, the enhanced PDG algorithm becomes capable of pinpoint targeting.

A Computational Framework for Quantifying and Optimizing the Performance of Observational Networks in 4D-Var Data Assimilation

NASA Astrophysics Data System (ADS)

Cioaca, Alexandru

A deep scientific understanding of complex physical systems, such as the atmosphere, can be achieved neither by direct measurements nor by numerical simulations alone. Data assimila- tion is a rigorous procedure to fuse information from a priori knowledge of the system state, the physical laws governing the evolution of the system, and real measurements, all with associated error statistics. Data assimilation produces best (a posteriori) estimates of model states and parameter values, and results in considerably improved computer simulations. The acquisition and use of observations in data assimilation raises several important scientific questions related to optimal sensor network design, quantification of data impact, pruning redundant data, and identifying the most beneficial additional observations. These questions originate in operational data assimilation practice, and have started to attract considerable interest in the recent past. This dissertation advances the state of knowledge in four dimensional variational (4D-Var) data assimilation by developing, implementing, and validating a novel computational framework for estimating observation impact and for optimizing sensor networks. The framework builds on the powerful methodologies of second-order adjoint modeling and the 4D-Var sensitivity equations. Efficient computational approaches for quantifying the observation impact include matrix free linear algebra algorithms and low-rank approximations of the sensitivities to observations. The sensor network configuration problem is formulated as a meta-optimization problem. Best values for parameters such as sensor location are obtained by optimizing a performance criterion, subject to the constraint posed by the 4D-Var optimization. Tractable computational solutions to this "optimization-constrained" optimization problem are provided. The results of this work can be directly applied to the deployment of intelligent sensors and adaptive observations, as well as to reducing the operating costs of measuring networks, while preserving their ability to capture the essential features of the system under consideration.

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

Birge, J. R.; Qi, L.; Wei, Z.

In this paper we give a variant of the Topkis-Veinott method for solving inequality constrained optimization problems. This method uses a linearly constrained positive semidefinite quadratic problem to generate a feasible descent direction at each iteration. Under mild assumptions, the algorithm is shown to be globally convergent in the sense that every accumulation point of the sequence generated by the algorithm is a Fritz-John point of the problem. We introduce a Fritz-John (FJ) function, an FJ1 strong second-order sufficiency condition (FJ1-SSOSC), and an FJ2 strong second-order sufficiency condition (FJ2-SSOSC), and then show, without any constraint qualification (CQ), that (i) ifmore » an FJ point z satisfies the FJ1-SSOSC, then there exists a neighborhood N(z) of z such that, for any FJ point y element of N(z) {l_brace}z {r_brace} , f{sub 0}(y) {ne} f{sub 0}(z) , where f{sub 0} is the objective function of the problem; (ii) if an FJ point z satisfies the FJ2-SSOSC, then z is a strict local minimum of the problem. The result (i) implies that the entire iteration point sequence generated by the method converges to an FJ point. We also show that if the parameters are chosen large enough, a unit step length can be accepted by the proposed algorithm.« less

Computation of maximum gust loads in nonlinear aircraft using a new method based on the matched filter approach and numerical optimization

NASA Technical Reports Server (NTRS)

Pototzky, Anthony S.; Heeg, Jennifer; Perry, Boyd, III

1990-01-01

Time-correlated gust loads are time histories of two or more load quantities due to the same disturbance time history. Time correlation provides knowledge of the value (magnitude and sign) of one load when another is maximum. At least two analysis methods have been identified that are capable of computing maximized time-correlated gust loads for linear aircraft. Both methods solve for the unit-energy gust profile (gust velocity as a function of time) that produces the maximum load at a given location on a linear airplane. Time-correlated gust loads are obtained by re-applying this gust profile to the airplane and computing multiple simultaneous load responses. Such time histories are physically realizable and may be applied to aircraft structures. Within the past several years there has been much interest in obtaining a practical analysis method which is capable of solving the analogous problem for nonlinear aircraft. Such an analysis method has been the focus of an international committee of gust loads specialists formed by the U.S. Federal Aviation Administration and was the topic of a panel discussion at the Gust and Buffet Loads session at the 1989 SDM Conference in Mobile, Alabama. The kinds of nonlinearities common on modern transport aircraft are indicated. The Statical Discrete Gust method is capable of being, but so far has not been, applied to nonlinear aircraft. To make the method practical for nonlinear applications, a search procedure is essential. Another method is based on Matched Filter Theory and, in its current form, is applicable to linear systems only. The purpose here is to present the status of an attempt to extend the matched filter approach to nonlinear systems. The extension uses Matched Filter Theory as a starting point and then employs a constrained optimization algorithm to attack the nonlinear problem.

Linear antenna array optimization using flower pollination algorithm.

PubMed

Saxena, Prerna; Kothari, Ashwin

2016-01-01

Flower pollination algorithm (FPA) is a new nature-inspired evolutionary algorithm used to solve multi-objective optimization problems. The aim of this paper is to introduce FPA to the electromagnetics and antenna community for the optimization of linear antenna arrays. FPA is applied for the first time to linear array so as to obtain optimized antenna positions in order to achieve an array pattern with minimum side lobe level along with placement of deep nulls in desired directions. Various design examples are presented that illustrate the use of FPA for linear antenna array optimization, and subsequently the results are validated by benchmarking along with results obtained using other state-of-the-art, nature-inspired evolutionary algorithms such as particle swarm optimization, ant colony optimization and cat swarm optimization. The results suggest that in most cases, FPA outperforms the other evolutionary algorithms and at times it yields a similar performance.

Constrained Optimization Methods in Health Services Research-An Introduction: Report 1 of the ISPOR Optimization Methods Emerging Good Practices Task Force.

PubMed

Crown, William; Buyukkaramikli, Nasuh; Thokala, Praveen; Morton, Alec; Sir, Mustafa Y; Marshall, Deborah A; Tosh, Jon; Padula, William V; Ijzerman, Maarten J; Wong, Peter K; Pasupathy, Kalyan S

2017-03-01

Providing health services with the greatest possible value to patients and society given the constraints imposed by patient characteristics, health care system characteristics, budgets, and so forth relies heavily on the design of structures and processes. Such problems are complex and require a rigorous and systematic approach to identify the best solution. Constrained optimization is a set of methods designed to identify efficiently and systematically the best solution (the optimal solution) to a problem characterized by a number of potential solutions in the presence of identified constraints. This report identifies 1) key concepts and the main steps in building an optimization model; 2) the types of problems for which optimal solutions can be determined in real-world health applications; and 3) the appropriate optimization methods for these problems. We first present a simple graphical model based on the treatment of "regular" and "severe" patients, which maximizes the overall health benefit subject to time and budget constraints. We then relate it back to how optimization is relevant in health services research for addressing present day challenges. We also explain how these mathematical optimization methods relate to simulation methods, to standard health economic analysis techniques, and to the emergent fields of analytics and machine learning. Copyright © 2017 International Society for Pharmacoeconomics and Outcomes Research (ISPOR). Published by Elsevier Inc. All rights reserved.

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.

Multidimensional indexing structure for use with linear optimization queries

NASA Technical Reports Server (NTRS)

Bergman, Lawrence David (Inventor); Castelli, Vittorio (Inventor); Chang, Yuan-Chi (Inventor); Li, Chung-Sheng (Inventor); Smith, John Richard (Inventor)

2002-01-01

Linear optimization queries, which usually arise in various decision support and resource planning applications, are queries that retrieve top N data records (where N is an integer greater than zero) which satisfy a specific optimization criterion. The optimization criterion is to either maximize or minimize a linear equation. The coefficients of the linear equation are given at query time. Methods and apparatus are disclosed for constructing, maintaining and utilizing a multidimensional indexing structure of database records to improve the execution speed of linear optimization queries. Database records with numerical attributes are organized into a number of layers and each layer represents a geometric structure called convex hull. Such linear optimization queries are processed by searching from the outer-most layer of this multi-layer indexing structure inwards. At least one record per layer will satisfy the query criterion and the number of layers needed to be searched depends on the spatial distribution of records, the query-issued linear coefficients, and N, the number of records to be returned. When N is small compared to the total size of the database, answering the query typically requires searching only a small fraction of all relevant records, resulting in a tremendous speedup as compared to linearly scanning the entire dataset.

Cosmicflows Constrained Local UniversE Simulations

NASA Astrophysics Data System (ADS)

Sorce, Jenny G.; Gottlöber, Stefan; Yepes, Gustavo; Hoffman, Yehuda; Courtois, Helene M.; Steinmetz, Matthias; Tully, R. Brent; Pomarède, Daniel; Carlesi, Edoardo

2016-01-01

This paper combines observational data sets and cosmological simulations to generate realistic numerical replicas of the nearby Universe. The latter are excellent laboratories for studies of the non-linear process of structure formation in our neighbourhood. With measurements of radial peculiar velocities in the local Universe (cosmicflows-2) and a newly developed technique, we produce Constrained Local UniversE Simulations (CLUES). To assess the quality of these constrained simulations, we compare them with random simulations as well as with local observations. The cosmic variance, defined as the mean one-sigma scatter of cell-to-cell comparison between two fields, is significantly smaller for the constrained simulations than for the random simulations. Within the inner part of the box where most of the constraints are, the scatter is smaller by a factor of 2 to 3 on a 5 h-1 Mpc scale with respect to that found for random simulations. This one-sigma scatter obtained when comparing the simulated and the observation-reconstructed velocity fields is only 104 ± 4 km s-1, I.e. the linear theory threshold. These two results demonstrate that these simulations are in agreement with each other and with the observations of our neighbourhood. For the first time, simulations constrained with observational radial peculiar velocities resemble the local Universe up to a distance of 150 h-1 Mpc on a scale of a few tens of megaparsecs. When focusing on the inner part of the box, the resemblance with our cosmic neighbourhood extends to a few megaparsecs (<5 h-1 Mpc). The simulations provide a proper large-scale environment for studies of the formation of nearby objects.

Benchmarking optimization software with COPS 3.0.

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

Dolan, E. D.; More, J. J.; Munson, T. S.

2004-05-24

The authors describe version 3.0 of the COPS set of nonlinearly constrained optimization problems. They have added new problems, as well as streamlined and improved most of the problems. They also provide a comparison of the FILTER, KNITRO, LOQO, MINOS, and SNOPT solvers on these problems.

Evaluating data worth for ground-water management under uncertainty

USGS Publications Warehouse

Wagner, B.J.

1999-01-01

A decision framework is presented for assessing the value of ground-water sampling within the context of ground-water management under uncertainty. The framework couples two optimization models-a chance-constrained ground-water management model and an integer-programing sampling network design model-to identify optimal pumping and sampling strategies. The methodology consists of four steps: (1) The optimal ground-water management strategy for the present level of model uncertainty is determined using the chance-constrained management model; (2) for a specified data collection budget, the monitoring network design model identifies, prior to data collection, the sampling strategy that will minimize model uncertainty; (3) the optimal ground-water management strategy is recalculated on the basis of the projected model uncertainty after sampling; and (4) the worth of the monitoring strategy is assessed by comparing the value of the sample information-i.e., the projected reduction in management costs-with the cost of data collection. Steps 2-4 are repeated for a series of data collection budgets, producing a suite of management/monitoring alternatives, from which the best alternative can be selected. A hypothetical example demonstrates the methodology's ability to identify the ground-water sampling strategy with greatest net economic benefit for ground-water management.A decision framework is presented for assessing the value of ground-water sampling within the context of ground-water management under uncertainty. The framework couples two optimization models - a chance-constrained ground-water management model and an integer-programming sampling network design model - to identify optimal pumping and sampling strategies. The methodology consists of four steps: (1) The optimal ground-water management strategy for the present level of model uncertainty is determined using the chance-constrained management model; (2) for a specified data collection budget, the monitoring network design model identifies, prior to data collection, the sampling strategy that will minimize model uncertainty; (3) the optimal ground-water management strategy is recalculated on the basis of the projected model uncertainty after sampling; and (4) the worth of the monitoring strategy is assessed by comparing the value of the sample information - i.e., the projected reduction in management costs - with the cost of data collection. Steps 2-4 are repeated for a series of data collection budgets, producing a suite of management/monitoring alternatives, from which the best alternative can be selected. A hypothetical example demonstrates the methodology's ability to identify the ground-water sampling strategy with greatest net economic benefit for ground-water management.

Experimental and simulation studies of multivariable adaptive optimization of continuous bioreactors using bilevel forgetting factors.

PubMed

Chang, Y K; Lim, H C

1989-08-20

A multivariable on-line adaptive optimization algorithm using a bilevel forgetting factor method was developed and applied to a continuous baker's yeast culture in simulation and experimental studies to maximize the cellular productivity by manipulating the dilution rate and the temperature. The algorithm showed a good optimization speed and a good adaptability and reoptimization capability. The algorithm was able to stably maintain the process around the optimum point for an extended period of time. Two cases were investigated: an unconstrained and a constrained optimization. In the constrained optimization the ethanol concentration was used as an index for the baking quality of yeast cells. An equality constraint with a quadratic penalty was imposed on the ethanol concentration to keep its level close to a hypothetical "optimum" value. The developed algorithm was experimentally applied to a baker's yeast culture to demonstrate its validity. Only unconstrained optimization was carried out experimentally. A set of tuning parameter values was suggested after evaluating the results from several experimental runs. With those tuning parameter values the optimization took 50-90 h. At the attained steady state the dilution rate was 0.310 h(-1) the temperature 32.8 degrees C, and the cellular productivity 1.50 g/L/h.

A subgradient approach for constrained binary optimization via quantum adiabatic evolution

NASA Astrophysics Data System (ADS)

Karimi, Sahar; Ronagh, Pooya

2017-08-01

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

Rapid Slewing of Flexible Space Structures

DTIC Science & Technology

2015-09-01

axis gimbal with elastic joints. The performance of the system can be enhanced by designing antenna maneuvers in which the flexible effects are...the effects of the nonlinearities so the vibrational motion can be constrained for a time-optimal slew. It is shown that by constructing an...joints. The performance of the system can be enhanced by designing antenna maneuvers in which the flexible effects are properly constrained, thus

Development of WRF-CO2 4DVAR Data Assimilation System

NASA Astrophysics Data System (ADS)

Zheng, T.; French, N. H. F.

2016-12-01

Four dimensional variational (4DVar) assimilation systems have been widely used for CO2 inverse modeling at global scale. At regional scale, however, 4DVar assimilation systems have been lacking. At present, most regional CO2 inverse models use Lagrangian particle backward trajectory tools to compute influence function in an analytical/synthesis framework. To provide a 4DVar based alternative, we developed WRF-CO2 4DVAR based on Weather Research and Forecasting (WRF), its chemistry extension (WRF-Chem), and its data assimilation system (WRFDA/WRFPLUS). Different from WRFDA, WRF-CO2 4DVAR does not optimize meteorology initial condition, instead it solves for the optimized CO2 surface fluxes (sources/sink) constrained by atmospheric CO2 observations. Based on WRFPLUS, we developed tangent linear and adjoint code for CO2 emission, advection, vertical mixing in boundary layer, and convective transport. Furthermore, we implemented an incremental algorithm to solve for optimized CO2 emission scaling factors by iteratively minimizing the cost function in a Bayes framework. The model sensitivity (of atmospheric CO2 with respect to emission scaling factor) calculated by tangent linear and adjoint model agrees well with that calculated by finite difference, indicating the validity of the newly developed code. The effectiveness of WRF-CO2 4DVar for inverse modeling is tested using forward-model generated pseudo-observation data in two experiments: first-guess CO2 fluxes has a 50% overestimation in the first case and 50% underestimation in the second. In both cases, WRF-CO2 4DVar reduces cost function to less than 10-4 of its initial values in less than 20 iterations and successfully recovers the true values of emission scaling factors. We expect future applications of WRF-CO2 4DVar with satellite observations will provide insights for CO2 regional inverse modeling, including the impacts of model transport error in vertical mixing.

Pyrrolidine-constrained phenethylamines: The design of potent, selective, and pharmacologically efficacious dipeptidyl peptidase IV (DPP4) inhibitors from a lead-like screening hit.

PubMed

Backes, Bradley J; Longenecker, Kenton; Hamilton, Gregory L; Stewart, Kent; Lai, Chunqiu; Kopecka, Hana; von Geldern, Thomas W; Madar, David J; Pei, Zhonghua; Lubben, Thomas H; Zinker, Bradley A; Tian, Zhenping; Ballaron, Stephen J; Stashko, Michael A; Mika, Amanda K; Beno, David W A; Kempf-Grote, Anita J; Black-Schaefer, Candace; Sham, Hing L; Trevillyan, James M

2007-04-01

A novel series of pyrrolidine-constrained phenethylamines were developed as dipeptidyl peptidase IV (DPP4) inhibitors for the treatment of type 2 diabetes. The cyclohexene ring of lead-like screening hit 5 was replaced with a pyrrolidine to enable parallel chemistry, and protein co-crystal structural data guided the optimization of N-substituents. Employing this strategy, a >400x improvement in potency over the initial hit was realized in rapid fashion. Optimized compounds are potent and selective inhibitors with excellent pharmacokinetic profiles. Compound 30 was efficacious in vivo, lowering blood glucose in ZDF rats that were allowed to feed freely on a mixed meal.

Statistical mechanics of budget-constrained auctions

NASA Astrophysics Data System (ADS)

Altarelli, F.; Braunstein, A.; Realpe-Gomez, J.; Zecchina, R.

2009-07-01

Finding the optimal assignment in budget-constrained auctions is a combinatorial optimization problem with many important applications, a notable example being in the sale of advertisement space by search engines (in this context the problem is often referred to as the off-line AdWords problem). On the basis of the cavity method of statistical mechanics, we introduce a message-passing algorithm that is capable of solving efficiently random instances of the problem extracted from a natural distribution, and we derive from its properties the phase diagram of the problem. As the control parameter (average value of the budgets) is varied, we find two phase transitions delimiting a region in which long-range correlations arise.

Two tradeoffs between economy and reliability in loss of load probability constrained unit commitment

NASA Astrophysics Data System (ADS)

Liu, Yuan; Wang, Mingqiang; Ning, Xingyao

2018-02-01

Spinning reserve (SR) should be scheduled considering the balance between economy and reliability. To address the computational intractability cursed by the computation of loss of load probability (LOLP), many probabilistic methods use simplified formulations of LOLP to improve the computational efficiency. Two tradeoffs embedded in the SR optimization model are not explicitly analyzed in these methods. In this paper, two tradeoffs including primary tradeoff and secondary tradeoff between economy and reliability in the maximum LOLP constrained unit commitment (UC) model are explored and analyzed in a small system and in IEEE-RTS System. The analysis on the two tradeoffs can help in establishing new efficient simplified LOLP formulations and new SR optimization models.

Angular velocity discrimination

NASA Technical Reports Server (NTRS)

Kaiser, Mary K.

1990-01-01

Three experiments designed to investigate the ability of naive observers to discriminate rotational velocities of two simultaneously viewed objects are described. Rotations are constrained to occur about the x and y axes, resulting in linear two-dimensional image trajectories. The results indicate that observers can discriminate angular velocities with a competence near that for linear velocities. However, perceived angular rate is influenced by structural aspects of the stimuli.

Analysis of the faster-than-Nyquist optimal linear multicarrier system

NASA Astrophysics Data System (ADS)

Marquet, Alexandre; Siclet, Cyrille; Roque, Damien

2017-02-01

Faster-than-Nyquist signalization enables a better spectral efficiency at the expense of an increased computational complexity. Regarding multicarrier communications, previous work mainly relied on the study of non-linear systems exploiting coding and/or equalization techniques, with no particular optimization of the linear part of the system. In this article, we analyze the performance of the optimal linear multicarrier system when used together with non-linear receiving structures (iterative decoding and direct feedback equalization), or in a standalone fashion. We also investigate the limits of the normality assumption of the interference, used for implementing such non-linear systems. The use of this optimal linear system leads to a closed-form expression of the bit-error probability that can be used to predict the performance and help the design of coded systems. Our work also highlights the great performance/complexity trade-off offered by decision feedback equalization in a faster-than-Nyquist context. xml:lang="fr"

Designing optimal cell factories: integer programming couples elementary mode analysis with regulation

PubMed Central

2012-01-01

Background Elementary mode (EM) analysis is ideally suited for metabolic engineering as it allows for an unbiased decomposition of metabolic networks in biologically meaningful pathways. Recently, constrained minimal cut sets (cMCS) have been introduced to derive optimal design strategies for strain improvement by using the full potential of EM analysis. However, this approach does not allow for the inclusion of regulatory information. Results Here we present an alternative, novel and simple method for the prediction of cMCS, which allows to account for boolean transcriptional regulation. We use binary linear programming and show that the design of a regulated, optimal metabolic network of minimal functionality can be formulated as a standard optimization problem, where EM and regulation show up as constraints. We validated our tool by optimizing ethanol production in E. coli. Our study showed that up to 70% of the predicted cMCS contained non-enzymatic, non-annotated reactions, which are difficult to engineer. These cMCS are automatically excluded by our approach utilizing simple weight functions. Finally, due to efficient preprocessing, the binary program remains computationally feasible. Conclusions We used integer programming to predict efficient deletion strategies to metabolically engineer a production organism. Our formulation utilizes the full potential of cMCS but adds additional flexibility to the design process. In particular our method allows to integrate regulatory information into the metabolic design process and explicitly favors experimentally feasible deletions. Our method remains manageable even if millions or potentially billions of EM enter the analysis. We demonstrated that our approach is able to correctly predict the most efficient designs for ethanol production in E. coli. PMID:22898474

Constraining the atmosphere of GJ 1214b using an optimal estimation technique

NASA Astrophysics Data System (ADS)

Barstow, J. K.; Aigrain, S.; Irwin, P. G. J.; Fletcher, L. N.; Lee, J.-M.

2013-09-01

We explore cloudy, extended H2-He atmosphere scenarios for the warm super-Earth GJ 1214b using an optimal estimation retrieval technique. This planet, orbiting an M4.5 star only 13 pc from the Earth, is of particular interest because it lies between the Earth and Neptune in size and may be a member of a new class of planet that is neither terrestrial nor gas giant. Its relatively flat transmission spectrum has so far made atmospheric characterization difficult. The Non-linear optimal Estimator for MultivariateE spectral analySIS (NEMESIS) algorithm is used to explore the degenerate model parameter space for a cloudy, H2-He-dominated atmosphere scenario. Optimal estimation is a data-led approach that allows solutions beyond the range permitted by ab initio equilibrium model atmosphere calculations, and as such prevents restriction from prior expectations. We show that optimal estimation retrieval is a powerful tool for this kind of study, and present an exploration of the degenerate atmospheric scenarios for GJ 1214b. Whilst we find a family of solutions that provide a very good fit to the data, the quality and coverage of these data are insufficient for us to more precisely determine the abundances of cloud and trace gases given an H2-He atmosphere, and we also cannot rule out the possibility of a high molecular weight atmosphere. Future ground- and space-based observations will provide the opportunity to confirm or rule out an extended H2-He atmosphere, but more precise constraints will be limited by intrinsic degeneracies in the retrieval problem, such as variations in cloud top pressure and temperature.

Near-optimal alternative generation using modified hit-and-run sampling for non-linear, non-convex problems

NASA Astrophysics Data System (ADS)

Rosenberg, D. E.; Alafifi, A.

2016-12-01

Water resources systems analysis often focuses on finding optimal solutions. Yet an optimal solution is optimal only for the modelled issues and managers often seek near-optimal alternatives that address un-modelled objectives, preferences, limits, uncertainties, and other issues. Early on, Modelling to Generate Alternatives (MGA) formalized near-optimal as the region comprising the original problem constraints plus a new constraint that allowed performance within a specified tolerance of the optimal objective function value. MGA identified a few maximally-different alternatives from the near-optimal region. Subsequent work applied Markov Chain Monte Carlo (MCMC) sampling to generate a larger number of alternatives that span the near-optimal region of linear problems or select portions for non-linear problems. We extend the MCMC Hit-And-Run method to generate alternatives that span the full extent of the near-optimal region for non-linear, non-convex problems. First, start at a feasible hit point within the near-optimal region, then run a random distance in a random direction to a new hit point. Next, repeat until generating the desired number of alternatives. The key step at each iterate is to run a random distance along the line in the specified direction to a new hit point. If linear equity constraints exist, we construct an orthogonal basis and use a null space transformation to confine hits and runs to a lower-dimensional space. Linear inequity constraints define the convex bounds on the line that runs through the current hit point in the specified direction. We then use slice sampling to identify a new hit point along the line within bounds defined by the non-linear inequity constraints. This technique is computationally efficient compared to prior near-optimal alternative generation techniques such MGA, MCMC Metropolis-Hastings, evolutionary, or firefly algorithms because search at each iteration is confined to the hit line, the algorithm can move in one step to any point in the near-optimal region, and each iterate generates a new, feasible alternative. We use the method to generate alternatives that span the near-optimal regions of simple and more complicated water management problems and may be preferred to optimal solutions. We also discuss extensions to handle non-linear equity constraints.

A mathematical framework for yield (vs. rate) optimization in constraint-based modeling and applications in metabolic engineering.

PubMed

Klamt, Steffen; Müller, Stefan; Regensburger, Georg; Zanghellini, Jürgen

2018-05-01

The optimization of metabolic rates (as linear objective functions) represents the methodical core of flux-balance analysis techniques which have become a standard tool for the study of genome-scale metabolic models. Besides (growth and synthesis) rates, metabolic yields are key parameters for the characterization of biochemical transformation processes, especially in the context of biotechnological applications. However, yields are ratios of rates, and hence the optimization of yields (as nonlinear objective functions) under arbitrary linear constraints is not possible with current flux-balance analysis techniques. Despite the fundamental importance of yields in constraint-based modeling, a comprehensive mathematical framework for yield optimization is still missing. We present a mathematical theory that allows one to systematically compute and analyze yield-optimal solutions of metabolic models under arbitrary linear constraints. In particular, we formulate yield optimization as a linear-fractional program. For practical computations, we transform the linear-fractional yield optimization problem to a (higher-dimensional) linear problem. Its solutions determine the solutions of the original problem and can be used to predict yield-optimal flux distributions in genome-scale metabolic models. For the theoretical analysis, we consider the linear-fractional problem directly. Most importantly, we show that the yield-optimal solution set (like the rate-optimal solution set) is determined by (yield-optimal) elementary flux vectors of the underlying metabolic model. However, yield- and rate-optimal solutions may differ from each other, and hence optimal (biomass or product) yields are not necessarily obtained at solutions with optimal (growth or synthesis) rates. Moreover, we discuss phase planes/production envelopes and yield spaces, in particular, we prove that yield spaces are convex and provide algorithms for their computation. We illustrate our findings by a small example and demonstrate their relevance for metabolic engineering with realistic models of E. coli. We develop a comprehensive mathematical framework for yield optimization in metabolic models. Our theory is particularly useful for the study and rational modification of cell factories designed under given yield and/or rate requirements. Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.

Application’s Method of Quadratic Programming for Optimization of Portfolio Selection

NASA Astrophysics Data System (ADS)

Kawamoto, Shigeru; Takamoto, Masanori; Kobayashi, Yasuhiro

Investors or fund-managers face with optimization of portfolio selection, which means that determine the kind and the quantity of investment among several brands. We have developed a method to obtain optimal stock’s portfolio more rapidly from twice to three times than conventional method with efficient universal optimization. The method is characterized by quadratic matrix of utility function and constrained matrices divided into several sub-matrices by focusing on structure of these matrices.

Robust fuel- and time-optimal control of uncertain flexible space structures

NASA Technical Reports Server (NTRS)

Wie, Bong; Sinha, Ravi; Sunkel, John; Cox, Ken

1993-01-01

The problem of computing open-loop, fuel- and time-optimal control inputs for flexible space structures in the face of modeling uncertainty is investigated. Robustified, fuel- and time-optimal pulse sequences are obtained by solving a constrained optimization problem subject to robustness constraints. It is shown that 'bang-off-bang' pulse sequences with a finite number of switchings provide a practical tradeoff among the maneuvering time, fuel consumption, and performance robustness of uncertain flexible space structures.

Fitting Prony Series To Data On Viscoelastic Materials

NASA Technical Reports Server (NTRS)

Hill, S. A.

1995-01-01

Improved method of fitting Prony series to data on viscoelastic materials involves use of least-squares optimization techniques. Based on optimization techniques yields closer correlation with data than traditional method. Involves no assumptions regarding the gamma'(sub i)s and higher-order terms, and provides for as many Prony terms as needed to represent higher-order subtleties in data. Curve-fitting problem treated as design-optimization problem and solved by use of partially-constrained-optimization techniques.

SU-E-T-551: Monitor Unit Optimization in Stereotactic Body Radiation Therapy for Stage I Lung Cancer

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

Huang, B-T; Lu, J-Y

2015-06-15

Purpose: The study aims to reduce the monitor units (MUs) in the stereotactic body radiation therapy (SBRT) treatment for lung cancer by adjusting the optimizing parameters. Methods: Fourteen patients suffered from stage I Non-Small Cell Lung Cancer (NSCLC) were enrolled. Three groups of parameters were adjusted to investigate their effects on MU numbers and organs at risk (OARs) sparing: (1) the upper objective of planning target volume (UOPTV); (2) strength setting in the MU constraining objective; (3) max MU setting in the MU constraining objective. Results: We found that the parameters in the optimizer influenced the MU numbers in amore » priority, strength and max MU dependent manner. MU numbers showed a decreasing trend with the UOPTV increasing. MU numbers with low, medium and high priority for the UOPTV were 428±54, 312±48 and 258±31 MU/Gy, respectively. High priority for UOPTV also spared the heart, cord and lung while maintaining comparable PTV coverage than the low and medium priority group. It was observed that MU numbers tended to decrease with the strength increasing and max MU setting decreasing. With maximum strength, the MU numbers reached its minimum while maintaining comparable or improved dose to the normal tissues. It was also found that the MU numbers continued to decline at 85% and 75% max MU setting but no longer to decrease at 50% and 25%. Combined with high priority for UOPTV and MU constraining objectives, the MU numbers can be decreased as low as 223±26 MU/Gy. Conclusion:: The priority of UOPTV, MU constraining objective in the optimizer impact on the MU numbers in SBRT treatment for lung cancer. Giving high priority to the UOPTV, setting the strength to maximum value and the max MU to 50% in the MU objective achieves the lowest MU numbers while maintaining comparable or improved OAR sparing.« less

Molecularly imprinted cavities template the macrocyclization of tetrapeptides.

PubMed

Tai, Dar-Fu; Lin, Yee-Fung

2008-11-21

Cavities formed using cyclic tetrapeptides (CTPs) or heat-induced conformers act as templates for cyclization; the cavities bind to linear tetrapeptides and enforce turn conformations to enhance cyclization to constrained CTPs.

APPLICATION OF A BIP CONSTRAINED OPTIMIZATION MODEL COMBINED WITH NASA's ATLAS MODEL TO OPTIMIZE THE SOCIETAL BENEFITS OF THE USA's INTERNATIONAL SPACE EXPLORATION AND UTILIZATION INITIATIVE OF 1/14/04

NASA Technical Reports Server (NTRS)

Morgenthaler, George W.; Glover, Fred W.; Woodcock, Gordon R.; Laguna, Manuel

2005-01-01

The 1/14/04 USA Space Exploratiofltilization Initiative invites all Space-faring Nations, all Space User Groups in Science, Space Entrepreneuring, Advocates of Robotic and Human Space Exploration, Space Tourism and Colonization Promoters, etc., to join an International Space Partnership. With more Space-faring Nations and Space User Groups each year, such a Partnership would require Multi-year (35 yr.-45 yr.) Space Mission Planning. With each Nation and Space User Group demanding priority for its missions, one needs a methodology for obiectively selecting the best mission sequences to be added annually to this 45 yr. Moving Space Mission Plan. How can this be done? Planners have suggested building a Reusable, Sustainable, Space Transportation Infrastructure (RSSn) to increase Mission synergism, reduce cost, and increase scientific and societal returns from this Space Initiative. Morgenthaler and Woodcock presented a Paper at the 55th IAC, Vancouver B.C., Canada, entitled Constrained Optimization Models For Optimizing Multi - Year Space Programs. This Paper showed that a Binary Integer Programming (BIP) Constrained Optimization Model combined with the NASA ATLAS Cost and Space System Operational Parameter Estimating Model has the theoretical capability to solve such problems. IAA Commission III, Space Technology and Space System Development, in its ACADEMY DAY meeting at Vancouver, requested that the Authors and NASA experts find several Space Exploration Architectures (SEAS), apply the combined BIP/ATLAS Models, and report the results at the 56th Fukuoka IAC. While the mathematical Model is in Ref.[2] this Paper presents the Application saga of that effort.

Recursive Hierarchical Image Segmentation by Region Growing and Constrained Spectral Clustering

NASA Technical Reports Server (NTRS)

Tilton, James C.

2002-01-01

This paper describes an algorithm for hierarchical image segmentation (referred to as HSEG) and its recursive formulation (referred to as RHSEG). The HSEG algorithm is a hybrid of region growing and constrained spectral clustering that produces a hierarchical set of image segmentations based on detected convergence points. In the main, HSEG employs the hierarchical stepwise optimization (HS WO) approach to region growing, which seeks to produce segmentations that are more optimized than those produced by more classic approaches to region growing. In addition, HSEG optionally interjects between HSWO region growing iterations merges between spatially non-adjacent regions (i.e., spectrally based merging or clustering) constrained by a threshold derived from the previous HSWO region growing iteration. While the addition of constrained spectral clustering improves the segmentation results, especially for larger images, it also significantly increases HSEG's computational requirements. To counteract this, a computationally efficient recursive, divide-and-conquer, implementation of HSEG (RHSEG) has been devised and is described herein. Included in this description is special code that is required to avoid processing artifacts caused by RHSEG s recursive subdivision of the image data. Implementations for single processor and for multiple processor computer systems are described. Results with Landsat TM data are included comparing HSEG with classic region growing. Finally, an application to image information mining and knowledge discovery is discussed.

Exponential Arithmetic Based Self-Healing Group Key Distribution Scheme with Backward Secrecy under the Resource-Constrained Wireless Networks

PubMed Central

Guo, Hua; Zheng, Yandong; Zhang, Xiyong; Li, Zhoujun

2016-01-01

In resource-constrained wireless networks, resources such as storage space and communication bandwidth are limited. To guarantee secure communication in resource-constrained wireless networks, group keys should be distributed to users. The self-healing group key distribution (SGKD) scheme is a promising cryptographic tool, which can be used to distribute and update the group key for the secure group communication over unreliable wireless networks. Among all known SGKD schemes, exponential arithmetic based SGKD (E-SGKD) schemes reduce the storage overhead to constant, thus is suitable for the the resource-constrained wireless networks. In this paper, we provide a new mechanism to achieve E-SGKD schemes with backward secrecy. We first propose a basic E-SGKD scheme based on a known polynomial-based SGKD, where it has optimal storage overhead while having no backward secrecy. To obtain the backward secrecy and reduce the communication overhead, we introduce a novel approach for message broadcasting and self-healing. Compared with other E-SGKD schemes, our new E-SGKD scheme has the optimal storage overhead, high communication efficiency and satisfactory security. The simulation results in Zigbee-based networks show that the proposed scheme is suitable for the resource-restrained wireless networks. Finally, we show the application of our proposed scheme. PMID:27136550

Computing Generalized Matrix Inverse on Spiking Neural Substrate

PubMed Central

Shukla, Rohit; Khoram, Soroosh; Jorgensen, Erik; Li, Jing; Lipasti, Mikko; Wright, Stephen

2018-01-01

Emerging neural hardware substrates, such as IBM's TrueNorth Neurosynaptic System, can provide an appealing platform for deploying numerical algorithms. For example, a recurrent Hopfield neural network can be used to find the Moore-Penrose generalized inverse of a matrix, thus enabling a broad class of linear optimizations to be solved efficiently, at low energy cost. However, deploying numerical algorithms on hardware platforms that severely limit the range and precision of representation for numeric quantities can be quite challenging. This paper discusses these challenges and proposes a rigorous mathematical framework for reasoning about range and precision on such substrates. The paper derives techniques for normalizing inputs and properly quantizing synaptic weights originating from arbitrary systems of linear equations, so that solvers for those systems can be implemented in a provably correct manner on hardware-constrained neural substrates. The analytical model is empirically validated on the IBM TrueNorth platform, and results show that the guarantees provided by the framework for range and precision hold under experimental conditions. Experiments with optical flow demonstrate the energy benefits of deploying a reduced-precision and energy-efficient generalized matrix inverse engine on the IBM TrueNorth platform, reflecting 10× to 100× improvement over FPGA and ARM core baselines. PMID:29593483

An Approximation Solution to Refinery Crude Oil Scheduling Problem with Demand Uncertainty Using Joint Constrained Programming

PubMed Central

Duan, Qianqian; Yang, Genke; Xu, Guanglin; Pan, Changchun

2014-01-01

This paper is devoted to develop an approximation method for scheduling refinery crude oil operations by taking into consideration the demand uncertainty. In the stochastic model the demand uncertainty is modeled as random variables which follow a joint multivariate distribution with a specific correlation structure. Compared to deterministic models in existing works, the stochastic model can be more practical for optimizing crude oil operations. Using joint chance constraints, the demand uncertainty is treated by specifying proximity level on the satisfaction of product demands. However, the joint chance constraints usually hold strong nonlinearity and consequently, it is still hard to handle it directly. In this paper, an approximation method combines a relax-and-tight technique to approximately transform the joint chance constraints to a serial of parameterized linear constraints so that the complicated problem can be attacked iteratively. The basic idea behind this approach is to approximate, as much as possible, nonlinear constraints by a lot of easily handled linear constraints which will lead to a well balance between the problem complexity and tractability. Case studies are conducted to demonstrate the proposed methods. Results show that the operation cost can be reduced effectively compared with the case without considering the demand correlation. PMID:24757433

An approximation solution to refinery crude oil scheduling problem with demand uncertainty using joint constrained programming.

PubMed

Duan, Qianqian; Yang, Genke; Xu, Guanglin; Pan, Changchun

2014-01-01

This paper is devoted to develop an approximation method for scheduling refinery crude oil operations by taking into consideration the demand uncertainty. In the stochastic model the demand uncertainty is modeled as random variables which follow a joint multivariate distribution with a specific correlation structure. Compared to deterministic models in existing works, the stochastic model can be more practical for optimizing crude oil operations. Using joint chance constraints, the demand uncertainty is treated by specifying proximity level on the satisfaction of product demands. However, the joint chance constraints usually hold strong nonlinearity and consequently, it is still hard to handle it directly. In this paper, an approximation method combines a relax-and-tight technique to approximately transform the joint chance constraints to a serial of parameterized linear constraints so that the complicated problem can be attacked iteratively. The basic idea behind this approach is to approximate, as much as possible, nonlinear constraints by a lot of easily handled linear constraints which will lead to a well balance between the problem complexity and tractability. Case studies are conducted to demonstrate the proposed methods. Results show that the operation cost can be reduced effectively compared with the case without considering the demand correlation.

Fast Combinatorial Algorithm for the Solution of Linearly Constrained Least Squares Problems

DOEpatents

Van Benthem, Mark H.; Keenan, Michael R.

2008-11-11

A fast combinatorial algorithm can significantly reduce the computational burden when solving general equality and inequality constrained least squares problems with large numbers of observation vectors. The combinatorial algorithm provides a mathematically rigorous solution and operates at great speed by reorganizing the calculations to take advantage of the combinatorial nature of the problems to be solved. The combinatorial algorithm exploits the structure that exists in large-scale problems in order to minimize the number of arithmetic operations required to obtain a solution.

Linear diffusion model dating of cinder cones in Central Anatolia, Turkey

NASA Astrophysics Data System (ADS)

O'Sadnick, L. G.; Reid, M. R.; Cline, M. L.; Cosca, M. A.; Kuscu, G.

2013-12-01

The progressive decrease in slope angle, cone height and cone height/width ratio over time provides the basis for geomorphic dating of cinder cones using linear diffusion models. Previous research using diffusion models to date cinder cones has focused on the cone height/width ratio as the basis for dating cones of unknown age [1,2]. Here we apply linear diffusion models to dating cinder cones. A suite of 16 cinder cones from the Hasandağ volcano area of the Neogene-Quaternary Central Anatolian Volcanic Zone, for which samples are available, were selected for morphologic dating analysis. New 40Ar/39Ar dates for five of these cones range from 62 × 4 to 517 × 9 ka. Linear diffusion models were used to model the erosional degradation of each cone. Diffusion coefficients (κ) for the 5 cinder cones with known ages were constrained by comparing various modeled slope profiles to the current slope profile. The resulting κ is 7.5×0.5 m2kyr-1. Using this κ value, eruption ages were modeled for the remaining 11 cinder cones and range from 53×3 to 455×30 ka. These ages are within the range of ages previously reported for cinder cones in the Hasandağ region. The linear diffusion model-derived ages are being compared to additional new 40Ar/39Ar dates in order to further assess the applicability of morphological dating to constrain the ages of cinder cones. The relatively well-constrained κ value we obtained by applying the linear diffusion model to cinder cones that range in age by nearly 500 ka suggests that this model can be used to date cinder cones. This κ value is higher than the well-established value of κ =3.9 for a cinder cone in a similar climate [3]. Therefore our work confirms the importance of determining appropriate κ values from nearby cones with known ages. References 1. C.A. Wood, J. Volcanol. Geotherm. Res. 8, 137 (1980) 2. D.M. Wood, M.F. Sheridan, J. Volcanol. Geotherm. Res. 83, 241 (1998) 3. J.D. Pelletier, M.L. Cline, Geology 35, 1067 (2007)

Linear-constraint wavefront control for exoplanet coronagraphic imaging systems

NASA Astrophysics Data System (ADS)

Sun, He; Eldorado Riggs, A. J.; Kasdin, N. Jeremy; Vanderbei, Robert J.; Groff, Tyler Dean

2017-01-01

A coronagraph is a leading technology for achieving high-contrast imaging of exoplanets in a space telescope. It uses a system of several masks to modify the diffraction and achieve extremely high contrast in the image plane around target stars. However, coronagraphic imaging systems are very sensitive to optical aberrations, so wavefront correction using deformable mirrors (DMs) is necessary to avoid contrast degradation in the image plane. Electric field conjugation (EFC) and Stroke minimization (SM) are two primary high-contrast wavefront controllers explored in the past decade. EFC minimizes the average contrast in the search areas while regularizing the strength of the control inputs. Stroke minimization calculates the minimum DM commands under the constraint that a target average contrast is achieved. Recently in the High Contrast Imaging Lab at Princeton University (HCIL), a new linear-constraint wavefront controller based on stroke minimization was developed and demonstrated using numerical simulation. Instead of only constraining the average contrast over the entire search area, the new controller constrains the electric field of each single pixel using linear programming, which could led to significant increases in speed of the wavefront correction and also create more uniform dark holes. As a follow-up of this work, another linear-constraint controller modified from EFC is demonstrated theoretically and numerically and the lab verification of the linear-constraint controllers is reported. Based on the simulation and lab results, the pros and cons of linear-constraint controllers are carefully compared with EFC and stroke minimization.

Fitting and forecasting coupled dark energy in the non-linear regime

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

Casas, Santiago; Amendola, Luca; Pettorino, Valeria

2016-01-01

We consider cosmological models in which dark matter feels a fifth force mediated by the dark energy scalar field, also known as coupled dark energy. Our interest resides in estimating forecasts for future surveys like Euclid when we take into account non-linear effects, relying on new fitting functions that reproduce the non-linear matter power spectrum obtained from N-body simulations. We obtain fitting functions for models in which the dark matter-dark energy coupling is constant. Their validity is demonstrated for all available simulations in the redshift range 0z=–1.6 and wave modes below 0k=1 h/Mpc. These fitting formulas can be used tomore » test the predictions of the model in the non-linear regime without the need for additional computing-intensive N-body simulations. We then use these fitting functions to perform forecasts on the constraining power that future galaxy-redshift surveys like Euclid will have on the coupling parameter, using the Fisher matrix method for galaxy clustering (GC) and weak lensing (WL). We find that by using information in the non-linear power spectrum, and combining the GC and WL probes, we can constrain the dark matter-dark energy coupling constant squared, β{sup 2}, with precision smaller than 4% and all other cosmological parameters better than 1%, which is a considerable improvement of more than an order of magnitude compared to corresponding linear power spectrum forecasts with the same survey specifications.« less

Energy-Efficient Cognitive Radio Sensor Networks: Parametric and Convex Transformations

PubMed Central

Naeem, Muhammad; Illanko, Kandasamy; Karmokar, Ashok; Anpalagan, Alagan; Jaseemuddin, Muhammad

2013-01-01

Designing energy-efficient cognitive radio sensor networks is important to intelligently use battery energy and to maximize the sensor network life. In this paper, the problem of determining the power allocation that maximizes the energy-efficiency of cognitive radio-based wireless sensor networks is formed as a constrained optimization problem, where the objective function is the ratio of network throughput and the network power. The proposed constrained optimization problem belongs to a class of nonlinear fractional programming problems. Charnes-Cooper Transformation is used to transform the nonlinear fractional problem into an equivalent concave optimization problem. The structure of the power allocation policy for the transformed concave problem is found to be of a water-filling type. The problem is also transformed into a parametric form for which a ε-optimal iterative solution exists. The convergence of the iterative algorithms is proven, and numerical solutions are presented. The iterative solutions are compared with the optimal solution obtained from the transformed concave problem, and the effects of different system parameters (interference threshold level, the number of primary users and secondary sensor nodes) on the performance of the proposed algorithms are investigated. PMID:23966194

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

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

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

2015-09-01

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

Adaptive nearly optimal control for a class of continuous-time nonaffine nonlinear systems with inequality constraints.

PubMed

Fan, Quan-Yong; Yang, Guang-Hong

2017-01-01

The state inequality constraints have been hardly considered in the literature on solving the nonlinear optimal control problem based the adaptive dynamic programming (ADP) method. In this paper, an actor-critic (AC) algorithm is developed to solve the optimal control problem with a discounted cost function for a class of state-constrained nonaffine nonlinear systems. To overcome the difficulties resulting from the inequality constraints and the nonaffine nonlinearities of the controlled systems, a novel transformation technique with redesigned slack functions and a pre-compensator method are introduced to convert the constrained optimal control problem into an unconstrained one for affine nonlinear systems. Then, based on the policy iteration (PI) algorithm, an online AC scheme is proposed to learn the nearly optimal control policy for the obtained affine nonlinear dynamics. Using the information of the nonlinear model, novel adaptive update laws are designed to guarantee the convergence of the neural network (NN) weights and the stability of the affine nonlinear dynamics without the requirement for the probing signal. Finally, the effectiveness of the proposed method is validated by simulation studies. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

A tutorial description of an interior point method and its applications to security-constrained economic dispatch

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

Vargas, L.S.; Quintana, V.H.; Vannelli, A.

This paper deals with the use of Successive Linear Programming (SLP) for the solution of the Security-Constrained Economic Dispatch (SCED) problem. The authors tutorially describe an Interior Point Method (IPM) for the solution of Linear Programming (LP) problems, discussing important implementation issues that really make this method far superior to the simplex method. A study of the convergence of the SLP technique and a practical criterion to avoid oscillatory behavior in the iteration process are also proposed. A comparison of the proposed method with an efficient simplex code (MINOS) is carried out by solving SCED problems on two standard IEEEmore » systems. The results show that the interior point technique is reliable, accurate and more than two times faster than the simplex algorithm.« less

Optimal non-linear health insurance.

PubMed

Blomqvist, A

1997-06-01

Most theoretical and empirical work on efficient health insurance has been based on models with linear insurance schedules (a constant co-insurance parameter). In this paper, dynamic optimization techniques are used to analyse the properties of optimal non-linear insurance schedules in a model similar to one originally considered by Spence and Zeckhauser (American Economic Review, 1971, 61, 380-387) and reminiscent of those that have been used in the literature on optimal income taxation. The results of a preliminary numerical example suggest that the welfare losses from the implicit subsidy to employer-financed health insurance under US tax law may be a good deal smaller than previously estimated using linear models.

Improving Free-Piston Stirling Engine Specific Power

NASA Technical Reports Server (NTRS)

Briggs, Maxwell Henry

2014-01-01

This work uses analytical methods to demonstrate the potential benefits of optimizing piston and/or displacer motion in a Stirling Engine. Isothermal analysis was used to show the potential benefits of ideal motion in ideal Stirling engines. Nodal analysis is used to show that ideal piston and displacer waveforms are not optimal in real Stirling engines. Constrained optimization was used to identify piston and displacer waveforms that increase Stirling engine specific power.

Improving Free-Piston Stirling Engine Specific Power

NASA Technical Reports Server (NTRS)

Briggs, Maxwell H.

2015-01-01

This work uses analytical methods to demonstrate the potential benefits of optimizing piston and/or displacer motion in a Stirling engine. Isothermal analysis was used to show the potential benefits of ideal motion in ideal Stirling engines. Nodal analysis is used to show that ideal piston and displacer waveforms are not optimal in real Stirling engines. Constrained optimization was used to identify piston and displacer waveforms that increase Stirling engine specific power.

Adaptive sparsest narrow-band decomposition method and its applications to rolling element bearing fault diagnosis

NASA Astrophysics Data System (ADS)

Cheng, Junsheng; Peng, Yanfeng; Yang, Yu; Wu, Zhantao

2017-02-01

Enlightened by ASTFA method, adaptive sparsest narrow-band decomposition (ASNBD) method is proposed in this paper. In ASNBD method, an optimized filter must be established at first. The parameters of the filter are determined by solving a nonlinear optimization problem. A regulated differential operator is used as the objective function so that each component is constrained to be a local narrow-band signal. Afterwards, the signal is filtered by the optimized filter to generate an intrinsic narrow-band component (INBC). ASNBD is proposed aiming at solving the problems existed in ASTFA. Gauss-Newton type method, which is applied to solve the optimization problem in ASTFA, is irreplaceable and very sensitive to initial values. However, more appropriate optimization method such as genetic algorithm (GA) can be utilized to solve the optimization problem in ASNBD. Meanwhile, compared with ASTFA, the decomposition results generated by ASNBD have better physical meaning by constraining the components to be local narrow-band signals. Comparisons are made between ASNBD, ASTFA and EMD by analyzing simulation and experimental signals. The results indicate that ASNBD method is superior to the other two methods in generating more accurate components from noise signal, restraining the boundary effect, possessing better orthogonality and diagnosing rolling element bearing fault.

Optimized Hyper Beamforming of Linear Antenna Arrays Using Collective Animal Behaviour

PubMed Central

Ram, Gopi; Mandal, Durbadal; Kar, Rajib; Ghoshal, Sakti Prasad

2013-01-01

A novel optimization technique which is developed on mimicking the collective animal behaviour (CAB) is applied for the optimal design of hyper beamforming of linear antenna arrays. Hyper beamforming is based on sum and difference beam patterns of the array, each raised to the power of a hyperbeam exponent parameter. The optimized hyperbeam is achieved by optimization of current excitation weights and uniform interelement spacing. As compared to conventional hyper beamforming of linear antenna array, real coded genetic algorithm (RGA), particle swarm optimization (PSO), and differential evolution (DE) applied to the hyper beam of the same array can achieve reduction in sidelobe level (SLL) and same or less first null beam width (FNBW), keeping the same value of hyperbeam exponent. Again, further reductions of sidelobe level (SLL) and first null beam width (FNBW) have been achieved by the proposed collective animal behaviour (CAB) algorithm. CAB finds near global optimal solution unlike RGA, PSO, and DE in the present problem. The above comparative optimization is illustrated through 10-, 14-, and 20-element linear antenna arrays to establish the optimization efficacy of CAB. PMID:23970843

A general-purpose optimization program for engineering design

NASA Technical Reports Server (NTRS)

Vanderplaats, G. N.; Sugimoto, H.

1986-01-01

A new general-purpose optimization program for engineering design is described. ADS (Automated Design Synthesis) is a FORTRAN program for nonlinear constrained (or unconstrained) function minimization. The optimization process is segmented into three levels: Strategy, Optimizer, and One-dimensional search. At each level, several options are available so that a total of nearly 100 possible combinations can be created. An example of available combinations is the Augmented Lagrange Multiplier method, using the BFGS variable metric unconstrained minimization together with polynomial interpolation for the one-dimensional search.

Subpixel Mapping of Hyperspectral Image Based on Linear Subpixel Feature Detection and Object Optimization

NASA Astrophysics Data System (ADS)

Liu, Zhaoxin; Zhao, Liaoying; Li, Xiaorun; Chen, Shuhan

2018-04-01

Owing to the limitation of spatial resolution of the imaging sensor and the variability of ground surfaces, mixed pixels are widesperead in hyperspectral imagery. The traditional subpixel mapping algorithms treat all mixed pixels as boundary-mixed pixels while ignoring the existence of linear subpixels. To solve this question, this paper proposed a new subpixel mapping method based on linear subpixel feature detection and object optimization. Firstly, the fraction value of each class is obtained by spectral unmixing. Secondly, the linear subpixel features are pre-determined based on the hyperspectral characteristics and the linear subpixel feature; the remaining mixed pixels are detected based on maximum linearization index analysis. The classes of linear subpixels are determined by using template matching method. Finally, the whole subpixel mapping results are iteratively optimized by binary particle swarm optimization algorithm. The performance of the proposed subpixel mapping method is evaluated via experiments based on simulated and real hyperspectral data sets. The experimental results demonstrate that the proposed method can improve the accuracy of subpixel mapping.

Determination of the Conservation Time of Periodicals for Optimal Shelf Maintenance of a Library.

ERIC Educational Resources Information Center

Miyamoto, Sadaaki; Nakayama, Kazuhiko

1981-01-01

Presents a method based on a constrained optimization technique that determines the time of removal of scientific periodicals from the shelf of a library. A geometrical interpretation of the theoretical result is given, and a numerical example illustrates how the technique is applicable to real bibliographic data. (FM)

A chance constraint estimation approach to optimizing resource management under uncertainty

Treesearch

Michael Bevers

2007-01-01

Chance-constrained optimization is an important method for managing risk arising from random variations in natural resource systems, but the probabilistic formulations often pose mathematical programming problems that cannot be solved with exact methods. A heuristic estimation method for these problems is presented that combines a formulation for order statistic...

Optimal Chebyshev polynomials on ellipses in the complex plane

NASA Technical Reports Server (NTRS)

Fischer, Bernd; Freund, Roland

1989-01-01

The design of iterative schemes for sparse matrix computations often leads to constrained polynomial approximation problems on sets in the complex plane. For the case of ellipses, we introduce a new class of complex polynomials which are in general very good approximations to the best polynomials and even optimal in most cases.

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

PubMed Central

Jiang, Yuyi; Shao, Zhiqing; Guo, Yi

2014-01-01

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

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

PubMed

Jiang, Yuyi; Shao, Zhiqing; Guo, Yi

2014-01-01

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

Multivariate constrained shape optimization: Application to extrusion bell shape for pasta production

NASA Astrophysics Data System (ADS)

Sarghini, Fabrizio; De Vivo, Angela; Marra, Francesco

2017-10-01

Computational science and engineering methods have allowed a major change in the way products and processes are designed, as validated virtual models - capable to simulate physical, chemical and bio changes occurring during production processes - can be realized and used in place of real prototypes and performing experiments, often time and money consuming. Among such techniques, Optimal Shape Design (OSD) (Mohammadi & Pironneau, 2004) represents an interesting approach. While most classical numerical simulations consider fixed geometrical configurations, in OSD a certain number of geometrical degrees of freedom is considered as a part of the unknowns: this implies that the geometry is not completely defined, but part of it is allowed to move dynamically in order to minimize or maximize the objective function. The applications of optimal shape design (OSD) are uncountable. For systems governed by partial differential equations, they range from structure mechanics to electromagnetism and fluid mechanics or to a combination of the three. This paper presents one of possible applications of OSD, particularly how extrusion bell shape, for past production, can be designed by applying a multivariate constrained shape optimization.

Trajectory optimization for the National aerospace plane

NASA Technical Reports Server (NTRS)

Lu, Ping

1993-01-01

While continuing the application of the inverse dynamics approach in obtaining the optimal numerical solutions, the research during the past six months has been focused on the formulation and derivation of closed-form solutions for constrained hypersonic flight trajectories. Since it was found in the research of the first year that a dominant portion of the optimal ascent trajectory of the aerospace plane is constrained by dynamic pressure and heating constraints, the application of the analytical solutions significantly enhances the efficiency in trajectory optimization, provides a better insight to understanding of the trajectory and conceivably has great potential in guidance of the vehicle. Work of this period has been reported in four technical papers. Two of the papers were presented in the AIAA Guidance, Navigation, and Control Conference (Hilton Head, SC, August, 1992) and Fourth International Aerospace Planes Conference (Orlando, FL, December, 1992). The other two papers have been accepted for publication by Journal of Guidance, Control, and Dynamics, and will appear in 1993. This report briefly summarizes the work done in the past six months and work currently underway.

Joint Chance-Constrained Dynamic Programming

NASA Technical Reports Server (NTRS)

Ono, Masahiro; Kuwata, Yoshiaki; Balaram, J. Bob

2012-01-01

This paper presents a novel dynamic programming algorithm with a joint chance constraint, which explicitly bounds the risk of failure in order to maintain the state within a specified feasible region. A joint chance constraint cannot be handled by existing constrained dynamic programming approaches since their application is limited to constraints in the same form as the cost function, that is, an expectation over a sum of one-stage costs. We overcome this challenge by reformulating the joint chance constraint into a constraint on an expectation over a sum of indicator functions, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the primal variables can be optimized by a standard dynamic programming, while the dual variable is optimized by a root-finding algorithm that converges exponentially. Error bounds on the primal and dual objective values are rigorously derived. We demonstrate the algorithm on a path planning problem, as well as an optimal control problem for Mars entry, descent and landing. The simulations are conducted using a real terrain data of Mars, with four million discrete states at each time step.

A formulation and analysis of combat games

NASA Technical Reports Server (NTRS)

Heymann, M.; Ardema, M. D.; Rajan, N.

1985-01-01

Combat is formulated as a dynamical encounter between two opponents, each of whom has offensive capabilities and objectives. With each opponent is associated a target in the event space in which he endeavors to terminate the combat, thereby winning. If the combat terminates in both target sets simultaneously or in neither, a joint capture or a draw, respectively, is said to occur. Resolution of the encounter is formulated as a combat game; namely, as a pair of competing event-constrained differential games. If exactly one of the players can win, the optimal strategies are determined from a resulting constrained zero-sum differential game. Otherwise the optimal strategies are computed from a resulting non-zero-sum game. Since optimal combat strategies frequencies may not exist, approximate of delta-combat games are also formulated leading to approximate or delta-optimal strategies. To illustrate combat games, an example, called the turret game, is considered. This game may be thought of as a highly simplified model of air combat, yet it is sufficiently complex to exhibit a rich variety of combat behavior, much of which is not found in pursuit-evasion games.

Role of slack variables in quasi-Newton methods for constrained optimization

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

Tapia, R.A.

In constrained optimization the technique of converting an inequality constraint into an equality constraint by the addition of a squared slack variable is well known but rarely used. In choosing an active constraint philosophy over the slack variable approach, researchers quickly justify their choice with the standard criticisms: the slack variable approach increases the dimension of the problem, is numerically unstable, and gives rise to singular systems. It is shown that these criticisms of the slack variable approach need not apply and the two seemingly distinct approaches are actually very closely related. In fact, the squared slack variable formulation canmore » be used to develop a superior and more comprehensive active constraint philosophy.« less

Nonlinear model predictive control of a wave energy converter based on differential flatness parameterisation

NASA Astrophysics Data System (ADS)

Li, Guang

2017-01-01

This paper presents a fast constrained optimization approach, which is tailored for nonlinear model predictive control of wave energy converters (WEC). The advantage of this approach relies on its exploitation of the differential flatness of the WEC model. This can reduce the dimension of the resulting nonlinear programming problem (NLP) derived from the continuous constrained optimal control of WEC using pseudospectral method. The alleviation of computational burden using this approach helps to promote an economic implementation of nonlinear model predictive control strategy for WEC control problems. The method is applicable to nonlinear WEC models, nonconvex objective functions and nonlinear constraints, which are commonly encountered in WEC control problems. Numerical simulations demonstrate the efficacy of this approach.

A Stationary North-Finding Scheme for an Azimuth Rotational IMU Utilizing a Linear State Equality Constraint

PubMed Central

Yu, Huapeng; Zhu, Hai; Gao, Dayuan; Yu, Meng; Wu, Wenqi

2015-01-01

The Kalman filter (KF) has always been used to improve north-finding performance under practical conditions. By analyzing the characteristics of the azimuth rotational inertial measurement unit (ARIMU) on a stationary base, a linear state equality constraint for the conventional KF used in the fine north-finding filtering phase is derived. Then, a constrained KF using the state equality constraint is proposed and studied in depth. Estimation behaviors of the concerned navigation errors when implementing the conventional KF scheme and the constrained KF scheme during stationary north-finding are investigated analytically by the stochastic observability approach, which can provide explicit formulations of the navigation errors with influencing variables. Finally, multiple practical experimental tests at a fixed position are done on a postulate system to compare the stationary north-finding performance of the two filtering schemes. In conclusion, this study has successfully extended the utilization of the stochastic observability approach for analytic descriptions of estimation behaviors of the concerned navigation errors, and the constrained KF scheme has demonstrated its superiority over the conventional KF scheme for ARIMU stationary north-finding both theoretically and practically. PMID:25688588

Immersed Boundary Methods for Optimization of Strongly Coupled Fluid-Structure Systems

NASA Astrophysics Data System (ADS)

Jenkins, Nicholas J.

Conventional methods for design of tightly coupled multidisciplinary systems, such as fluid-structure interaction (FSI) problems, traditionally rely on manual revisions informed by a loosely coupled linearized analysis. These approaches are both inaccurate for a multitude of applications, and they require an intimate understanding of the assumptions and limitations of the procedure in order to soundly optimize the design. Computational optimization, in particular topology optimization, has been shown to yield remarkable results for problems in solid mechanics using density interpolations schemes. In the context of FSI, however, well defined boundaries play a key role in both the design problem and the mechanical model. Density methods neither accurately represent the material boundary, nor provide a suitable platform to apply appropriate interface conditions. This thesis presents a new framework for shape and topology optimization of FSI problems that uses for the design problem the Level Set method (LSM) to describe the geometry evolution in the optimization process. The Extended Finite Element method (XFEM) is combined with a fictitiously deforming fluid domain (stationary arbitrary Lagrangian-Eulerian method) to predict the FSI response. The novelty of the proposed approach lies in the fact that the XFEM explicitly captures the material boundary defined by the level set iso-surface. Moreover, the XFEM provides a means to discretize the governing equations, and weak immersed boundary conditions are applied with Nitsche's Method to couple the fields. The flow is predicted by the incompressible Navier-Stokes equations, and a finite-deformation solid model is developed and tested for both hyperelastic and linear elastic problems. Transient and stationary numerical examples are presented to validate the FSI model and numerical solver approach. Pertaining to the optimization of FSI problems, the parameters of the discretized level set function are defined as explicit functions of the optimization variables, and the parameteric optimization problem is solved by nonlinear programming methods. The gradients of the objective and constrains are computed by the adjoint method for the global monolithic fluid-solid system. Two types of design problems are explored for optimization of the fluid-structure response: 1) the internal structural topology is varied, preserving the fluid-solid interface geometry, and 2) the fluid-solid interface is manipulated directly, which leads to simultaneously configuring both internal structural topology and outer mold shape. The numerical results show that the LSM-XFEM approach is well suited for designing practical applications, while at the same time reducing the requirement on highly refined mesh resolution compared to traditional density methods. However, these results also emphasize the need for a more robust embedded boundary condition framework. Further, the LSM can exhibit greater dependence on initial design seeding, and can impede design convergence. In particular for the strongly coupled FSI analysis developed here, the thinning and eventual removal of structural members can cause jumps in the evolution of the optimization functions.

Finite-horizon differential games for missile-target interception system using adaptive dynamic programming with input constraints

NASA Astrophysics Data System (ADS)

Sun, Jingliang; Liu, Chunsheng

2018-01-01

In this paper, the problem of intercepting a manoeuvring target within a fixed final time is posed in a non-linear constrained zero-sum differential game framework. The Nash equilibrium solution is found by solving the finite-horizon constrained differential game problem via adaptive dynamic programming technique. Besides, a suitable non-quadratic functional is utilised to encode the control constraints into a differential game problem. The single critic network with constant weights and time-varying activation functions is constructed to approximate the solution of associated time-varying Hamilton-Jacobi-Isaacs equation online. To properly satisfy the terminal constraint, an additional error term is incorporated in a novel weight-updating law such that the terminal constraint error is also minimised over time. By utilising Lyapunov's direct method, the closed-loop differential game system and the estimation weight error of the critic network are proved to be uniformly ultimately bounded. Finally, the effectiveness of the proposed method is demonstrated by using a simple non-linear system and a non-linear missile-target interception system, assuming first-order dynamics for the interceptor and target.

ORACLS: A system for linear-quadratic-Gaussian control law design

NASA Technical Reports Server (NTRS)

Armstrong, E. S.

1978-01-01

A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

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

NASA Astrophysics Data System (ADS)

Heinkenschloss, Matthias

2005-01-01

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

Linearization methods for optimizing the low thrust spacecraft trajectory: Theoretical aspects

NASA Astrophysics Data System (ADS)

Kazmerchuk, P. V.

2016-12-01

The theoretical aspects of the modified linearization method, which makes it possible to solve a wide class of nonlinear problems on optimizing low-thrust spacecraft trajectories (V. V. Efanov et al., 2009; V. V. Khartov et al., 2010) are examined. The main modifications of the linearization method are connected with its refinement for optimizing the main dynamic systems and design parameters of the spacecraft.

WE-FG-207B-05: Iterative Reconstruction Via Prior Image Constrained Total Generalized Variation for Spectral CT

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

Niu, S; Zhang, Y; Ma, J

Purpose: To investigate iterative reconstruction via prior image constrained total generalized variation (PICTGV) for spectral computed tomography (CT) using fewer projections while achieving greater image quality. Methods: The proposed PICTGV method is formulated as an optimization problem, which balances the data fidelity and prior image constrained total generalized variation of reconstructed images in one framework. The PICTGV method is based on structure correlations among images in the energy domain and high-quality images to guide the reconstruction of energy-specific images. In PICTGV method, the high-quality image is reconstructed from all detector-collected X-ray signals and is referred as the broad-spectrum image. Distinctmore » from the existing reconstruction methods applied on the images with first order derivative, the higher order derivative of the images is incorporated into the PICTGV method. An alternating optimization algorithm is used to minimize the PICTGV objective function. We evaluate the performance of PICTGV on noise and artifacts suppressing using phantom studies and compare the method with the conventional filtered back-projection method as well as TGV based method without prior image. Results: On the digital phantom, the proposed method outperforms the existing TGV method in terms of the noise reduction, artifacts suppression, and edge detail preservation. Compared to that obtained by the TGV based method without prior image, the relative root mean square error in the images reconstructed by the proposed method is reduced by over 20%. Conclusion: The authors propose an iterative reconstruction via prior image constrained total generalize variation for spectral CT. Also, we have developed an alternating optimization algorithm and numerically demonstrated the merits of our approach. Results show that the proposed PICTGV method outperforms the TGV method for spectral CT.« less

A hybrid approach to generating search subspaces in dynamically constrained 4-dimensional data assimilation

NASA Astrophysics Data System (ADS)

Yaremchuk, Max; Martin, Paul; Beattie, Christopher

2017-09-01

Development and maintenance of the linearized and adjoint code for advanced circulation models is a challenging issue, requiring a significant proportion of total effort in operational data assimilation (DA). The ensemble-based DA techniques provide a derivative-free alternative, which appears to be competitive with variational methods in many practical applications. This article proposes a hybrid scheme for generating the search subspaces in the adjoint-free 4-dimensional DA method (a4dVar) that does not use a predefined ensemble. The method resembles 4dVar in that the optimal solution is strongly constrained by model dynamics and search directions are supplied iteratively using information from the current and previous model trajectories generated in the process of optimization. In contrast to 4dVar, which produces a single search direction from exact gradient information, a4dVar employs an ensemble of directions to form a subspace in order to proceed. In the earlier versions of a4dVar, search subspaces were built using the leading EOFs of either the model trajectory or the projections of the model-data misfits onto the range of the background error covariance (BEC) matrix at the current iteration. In the present study, we blend both approaches and explore a hybrid scheme of ensemble generation in order to improve the performance and flexibility of the algorithm. In addition, we introduce balance constraints into the BEC structure and periodically augment the search ensemble with BEC eigenvectors to avoid repeating minimization over already explored subspaces. Performance of the proposed hybrid a4dVar (ha4dVar) method is compared with that of standard 4dVar in a realistic regional configuration assimilating real data into the Navy Coastal Ocean Model (NCOM). It is shown that the ha4dVar converges faster than a4dVar and can be potentially competitive with 4dvar both in terms of the required computational time and the forecast skill.

Hydrology, description of computer models, and evaluation of selected water-management alternatives in the San Bernardino area, California

USGS Publications Warehouse

Danskin, Wesley R.; McPherson, Kelly R.; Woolfenden, Linda R.

2006-01-01

The San Bernardino area of southern California has complex water-management issues. As an aid to local water managers, this report provides an integrated analysis of the surface-water and ground-water systems, documents ground-water flow and constrained optimization models, and provides seven examples using the models to better understand and manage water resources of the area. As an aid to investigators and water managers in other areas, this report provides an expanded description of constrained optimization techniques and how to use them to better understand the local hydrogeology and to evaluate inter-related water-management problems. In this report, the hydrology of the San Bernardino area, defined as the Bunker Hill and Lytle Creek basins, is described and quantified for calendar years 1945-98. The major components of the surface-water system are identified, and a routing diagram of flow through these components is provided. Annual surface-water inflow and outflow for the area are tabulated using gaged measurements and estimated values derived from linear-regression equations. Average inflow for the 54-year period (1945-98) was 146,452 acre-feet per year; average outflow was 67,931 acre-feet per year. The probability of exceedance for annual surface-water inflow is calculated using a Log Pearson Type III analysis. Cumulative surface-water inflow and outflow and ground-water-level measurements indicate that the relation between the surface-water system and the ground-water system changed in about 1951, in about 1979, and again in about 1992. Higher ground-water levels prior to 1951 and between 1979 and 1992 induced ground-water discharge to Warm Creek. This discharge was quantified using streamflow measurements and can be estimated for other time periods using ground-water levels from a monitoring well (1S/4W-3Q1) and a logarithmic-regression equation. Annual wastewater discharge from the area is tabulated for the major sewage and power-plant facilities. More...

An augmented Lagrangian trust region method for inclusion boundary reconstruction using ultrasound/electrical dual-modality tomography

NASA Astrophysics Data System (ADS)

Liang, Guanghui; Ren, Shangjie; Dong, Feng

2018-07-01

The ultrasound/electrical dual-modality tomography utilizes the complementarity of ultrasound reflection tomography (URT) and electrical impedance tomography (EIT) to improve the speed and accuracy of image reconstruction. Due to its advantages of no-invasive, no-radiation and low-cost, ultrasound/electrical dual-modality tomography has attracted much attention in the field of dual-modality imaging and has many potential applications in industrial and biomedical imaging. However, the data fusion of URT and EIT is difficult due to their different theoretical foundations and measurement principles. The most commonly used data fusion strategy in ultrasound/electrical dual-modality tomography is incorporating the structured information extracted from the URT into the EIT image reconstruction process through a pixel-based constraint. Due to the inherent non-linearity and ill-posedness of EIT, the reconstructed images from the strategy suffer from the low resolution, especially at the boundary of the observed inclusions. To improve this condition, an augmented Lagrangian trust region method is proposed to directly reconstruct the shapes of the inclusions from the ultrasound/electrical dual-modality measurements. In the proposed method, the shape of the target inclusion is parameterized by a radial shape model whose coefficients are used as the shape parameters. Then, the dual-modality shape inversion problem is formulated by an energy minimization problem in which the energy function derived from EIT is constrained by an ultrasound measurements model through an equality constraint equation. Finally, the optimal shape parameters associated with the optimal inclusion shape guesses are determined by minimizing the constrained cost function using the augmented Lagrangian trust region method. To evaluate the proposed method, numerical tests are carried out. Compared with single modality EIT, the proposed dual-modality inclusion boundary reconstruction method has a higher accuracy and is more robust to the measurement noise.

An Efficient Augmented Lagrangian Method with Applications to Total Variation Minimization

DTIC Science & Technology

2012-08-17

the classic augmented Lagrangian multiplier method, we propose, analyze and test an algorithm for solving a class of equality-constrained non-smooth...method, we propose, analyze and test an algorithm for solving a class of equality-constrained non-smooth optimization problems (chie y but not...significantly outperforming several state-of-the-art solvers on most tested problems. The resulting MATLAB solver, called TVAL3, has been posted online [23]. 2