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1

Convex Optimization II  

NSDL National Science Digital Library

Concentrates on recognizing and solving convex optimization problems that arise in engineering.Topics include: Convex sets, functions, and optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interiorpoint methods. Applications to signal processing, control, digital and analog circuit design, computational geometry, statistics, and mechanical engineering.Prerequisites: Good knowledge of linear algebra. Exposure to numerical computing, optimization, and application fields helpful but not required; the engineering applications will be kept basic and simple.

Boyd, Stephen

2010-12-13

2

Convex Optimization I  

NSDL National Science Digital Library

Concentrates on recognizing and solving convex optimization problems that arise in engineering.Topics include: Convex sets, functions, and optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interiorpoint methods. Applications to signal processing, control, digital and analog circuit design, computational geometry, statistics, and mechanical engineering.Prerequisites: Good knowledge of linear algebra. Exposure to numerical computing, optimization, and application fields helpful but not required; the engineering applications will be kept basic and simple.

Boyd, Stephen

2010-12-10

3

Optimal control problems with terminal functionals represented as the difference of two convex functions  

NASA Astrophysics Data System (ADS)

Two control problems for a state-linear control system are considered: the minimization of a terminal functional representable as the difference of two convex functions (d.c. functions) and the minimization of a convex terminal functional with a d.c. terminal inequality contraint. Necessary and sufficient global optimality conditions are proved for problems in which the Pontryagin and Bellman maximum principles do not distinguish between locally and globally optimal processes. The efficiency of the approach is illustrated by examples.

Strekalovsky, A. S.

2007-11-01

4

A posteriori error estimates for mixed finite element solutions of convex optimal control problems  

Microsoft Academic Search

In this paper, we present an a posteriori error analysis for mixed finite element approximation of convex optimal control problems. We derive a posteriori error estimates for the coupled state and control approximations under some assumptions which hold in many applications. Such estimates can be used to construct reliable adaptive mixed finite elements for the control problems.

Yanping Chen; Wenbin Liu

2008-01-01

5

Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm  

PubMed Central

The primal-dual optimization algorithm developed in Chambolle and Pock (CP), 2011 is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems for the purpose of designing iterative image reconstruction algorithms for CT. The primal-dual algorithm is briefly summarized in the article, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example application modeling breast CT with low-intensity X-ray illumination is presented.

Sidky, Emil Y.; J?rgensen, Jakob H.; Pan, Xiaochuan

2012-01-01

6

A posteriori error estimates for hp finite element solutions of convex optimal control problems  

Microsoft Academic Search

In this paper, we present a posteriori error analysis for hp finite element approximation of convex optimal control problems. We derive a new quasi-interpolation operator of Clément type and a new quasi-interpolation operator of Scott–Zhang type that preserves homogeneous boundary condition. The Scott–Zhang type quasi-interpolation is suitable for an application in bounding the errors in L2-norm. Then hp a posteriori

Yanping Chen; Yijie Lin

2011-01-01

7

The Optimal Solution of a Non-Convex State-Dependent LQR Problem and Its Applications  

PubMed Central

This paper studies a Non-convex State-dependent Linear Quadratic Regulator (NSLQR) problem, in which the control penalty weighting matrix in the performance index is state-dependent. A necessary and sufficient condition for the optimal solution is established with a rigorous proof by Euler-Lagrange Equation. It is found that the optimal solution of the NSLQR problem can be obtained by solving a Pseudo-Differential-Riccati-Equation (PDRE) simultaneously with the closed-loop system equation. A Comparison Theorem for the PDRE is given to facilitate solution methods for the PDRE. A linear time-variant system is employed as an example in simulation to verify the proposed optimal solution. As a non-trivial application, a goal pursuit process in psychology is modeled as a NSLQR problem and two typical goal pursuit behaviors found in human and animals are reproduced using different control weighting . It is found that these two behaviors save control energy and cause less stress over Conventional Control Behavior typified by the LQR control with a constant control weighting , in situations where only the goal discrepancy at the terminal time is of concern, such as in Marathon races and target hitting missions.

Xu, Xudan; Zhu, J. Jim; Zhang, Ping

2014-01-01

8

The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems  

Microsoft Academic Search

The DC programming and its DC algorithm (DCA) address the problem of minimizing a function f=g?h (with g,h being lower semicontinuous proper convex functions on R\\u000a \\u000a n\\u000a ) on the whole space. Based on local optimality conditions and DC duality, DCA was successfully applied to a lot of different\\u000a and various nondifferentiable nonconvex optimization problems to which it quite often

Le Thi Hoai An; Pham Dinh Tao

2005-01-01

9

Convex stochastic control problems  

Microsoft Academic Search

The solution of the infinite horizon stochastic control problem under certain criteria, the functional characterization and computation of optimal values and policies, is related to two dynamic programming-like functional equations: the discounted cost optimality equation (DCOE) and the average cost optimality equation (ACOE). The authors consider what useful properties, shared by large and important problem classes, can be used to

Emmanuel Ferndndez-Gaucherand; Aristotle Arapostathis; Steven I. Marcus

1992-01-01

10

Measuring the profile of a convex aspherical surface by solving a bi-objective optimization problem  

NASA Astrophysics Data System (ADS)

This paper describes a method based on bi-objective evolutionary algorithms to obtain the profile of a convex aspherical surface, which is defined by a set of synthetic points placed on an xyz coordinate system. The set of points to be analyzed is constructed considering the sources of measurement error in a coordinate measuring machine (CMM), such as machine, probe, and positioning errors. The proposed method is applied to solve a bi-objective optimization problem by minimizing two objective functions. By minimizing the first objective function the positioning error is removed from the coordinates of each affected point. Once the first goal is achieved, the second objective function is minimized to determine from the resulting data all parameters related to the test surface, such as paraxial radius of curvature, the conic constant and the deformation constants. Hence, this method can obtain the correct surface profile even when the positioning error tends to increase the CMM measurement error in the set of analyzed points. The bi-objective evolutionary algorithm (BEA) was tested against a single-objective evolutionary algorithm, and illustrative numerical examples demonstrate that the BEA performs better.

Jaime Sánchez Escobar, Juan

2012-07-01

11

Global search in the optimal control problem with a terminal objective functional represented as the difference of two convex functions  

NASA Astrophysics Data System (ADS)

A nonconvex optimal control problem is examined for a system that is linear with respect to state and has a terminal objective functional representable as the difference of two convex functions. A new local search method is proposed, and its convergence is proved. A strategy is also developed for the search of a globally optimal control process, because the Pontryagin and Bellman principles as applied to the above problem do not distinguish between the locally and globally optimal processes. The convergence of this strategy under appropriate conditions is proved.

Strekalovsky, A. S.; Yanulevich, M. V.

2008-07-01

12

On the connectedness of the set of weakly efficient points of a vector optimization problem in locally convex spaces  

Microsoft Academic Search

In vector optimization, topological properties of the set of efficient and weakly efficient points are of interest. In this paper, we study the connectedness of the setEw of all weakly efficient points of a subsetZ of a locally convex spaceX with respect to a continuous mappingp:X ?Y,Y locally convex and partially ordered by a closed, convex cone with nonempty interior.

S. Helbig

1990-01-01

13

An algorithm for linearizing convex extremal problems  

SciTech Connect

This paper suggests a method of approximating the solution of minimization problems for convex functions of several variables under convex constraints is suggested. The main idea of this approach is the approximation of a convex function by a piecewise linear function, which results in replacing the problem of convex programming by a linear programming problem. To carry out such an approximation, the epigraph of a convex function is approximated by the projection of a polytope of greater dimension. In the first part of the paper, the problem is considered for functions of one variable. In this case, an algorithm for approximating the epigraph of a convex function by a polygon is presented, it is shown that this algorithm is optimal with respect to the number of vertices of the polygon, and exact bounds for this number are obtained. After this, using an induction procedure, the algorithm is generalized to certain classes of functions of several variables. Applying the suggested method, polynomial algorithms for an approximate calculation of the L{sub p}-norm of a matrix and of the minimum of the entropy function on a polytope are obtained. Bibliography: 19 titles.

Gorskaya, Elena S [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

2010-06-09

14

Optimal Inequalities in Probability Theory: A Convex Optimization Approach  

Microsoft Academic Search

Abstract. We propose a semidefinite optimization approach to the problem of deriving tight moment inequalities for P (X ? S), for a set S defined by polynomial inequalities and a random vector X defined on ? ?R ,, we present an efficient algorithm for finding tight bounds when S is a union of convex sets, over which convex quadratic functions

Dimitris Bertsimas; Ioana Popescu

2005-01-01

15

Convex separable optimization is not much harder than linear optimization  

Microsoft Academic Search

The polynomiality of nonlinear separable convex (concave) optimization problems, on linear constraints with a matrix with “small” subdeterminants, and the polynomiality of such integer problems, provided the inteter linear version of such problems ins polynomial, is proven. This paper presents a general-purpose algorithm for converting procedures that solves linear programming problems. The conversion is polynomial for constraint matrices with polynomially

Dorit S. Hochbaum; J. George Shanthikumar

1990-01-01

16

Variable Acceleration Coefficient-based Particle Swarm Optimization for Non-Convex Economic load dispatch problem  

Microsoft Academic Search

This paper presents Variable Acceleration Coefficient-based Particle Swarm Optimization (VACPSO) method to solve the economic load dispatch for minimizing fuel cost while considering prohibited operating zones and valve point effect. The proposed VACPSO is a modified version of the conventional Particle Swarm Optimization (PSO). Three modifications are suggested in the proposed VACPSO. First, the cognitive behavior of particle is influenced

Vinay Kumar Jadoun; K. R. Niazi; Anil Swarnkar; Nikhil Gupta

2011-01-01

17

Convergent LMI relaxations for non-convex optimization over polynomials in control  

Microsoft Academic Search

Most of the analysis or design problems arising in robust or non-linear control can be formulated as global optimization problems with multivariable polynomial ob- jective and constraints. These non-convex optimization problems, which in general are dicult to solve, have motivated the development of tractable, but potentially conservative relaxation techniques relying on convex optimization and most notably semidenite programming, or optimization

Didier Henrion; Jean-Bernard Lasserre

18

New Results on Optimal Area Triangulations of Convex Polygons  

Microsoft Academic Search

We consider the problems of flnding two optimal triangulations of convex polygon: MaxMin area and MinMax area. These are the triangulations that maximize the area of the smallest area triangle in a triangulation, and respectively minimize the area of the largest area triangle in a triangulation, over all possible triangulations. The problem was originally solved by Klincsek by dynamic programming

Tigran Mirzoev; Tzvetalin S. Vassilev

19

Robust boosting via convex optimization  

NASA Astrophysics Data System (ADS)

In this work we consider statistical learning problems. A learning machine aims to extract information from a set of training examples such that it is able to predict the associated label on unseen examples. We consider the case where the resulting classification or regression rule is a combination of simple rules - also called base hypotheses. The so-called boosting algorithms iteratively find a weighted linear combination of base hypotheses that predict well on unseen data. We address the following issues: o The statistical learning theory framework for analyzing boosting methods. We study learning theoretic guarantees on the prediction performance on unseen examples. Recently, large margin classification techniques emerged as a practical result of the theory of generalization, in particular Boosting and Support Vector Machines. A large margin implies a good generalization performance. Hence, we analyze how large the margins in boosting are and find an improved algorithm that is able to generate the maximum margin solution. o How can boosting methods be related to mathematical optimization techniques? To analyze the properties of the resulting classification or regression rule, it is of high importance to understand whether and under which conditions boosting converges. We show that boosting can be used to solve large scale constrained optimization problems, whose solutions are well characterizable. To show this, we relate boosting methods to methods known from mathematical optimization, and derive convergence guarantees for a quite general family of boosting algorithms. o How to make Boosting noise robust? One of the problems of current boosting techniques is that they are sensitive to noise in the training sample. In order to make boosting robust, we transfer the soft margin idea from support vector learning to boosting. We develop theoretically motivated regularized algorithms that exhibit a high noise robustness. o How to adapt boosting to regression problems? Boosting methods are originally designed for classification problems. To extend the boosting idea to regression problems, we use the previous convergence results and relations to semi-infinite programming to design boosting-like algorithms for regression problems. We show that these leveraging algorithms have desirable theoretical and practical properties. o Can boosting techniques be useful in practice? The presented theoretical results are guided by simulation results either to illustrate properties of the proposed algorithms or to show that they work well in practice. We report on successful applications in a non-intrusive power monitoring system, chaotic time series analysis and a drug discovery process. --- Anmerkung: Der Autor ist Träger des von der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Potsdam vergebenen Michelson-Preises für die beste Promotion des Jahres 2001/2002. In dieser Arbeit werden statistische Lernprobleme betrachtet. Lernmaschinen extrahieren Informationen aus einer gegebenen Menge von Trainingsmustern, so daß sie in der Lage sind, Eigenschaften von bisher ungesehenen Mustern - z.B. eine Klassenzugehörigkeit - vorherzusagen. Wir betrachten den Fall, bei dem die resultierende Klassifikations- oder Regressionsregel aus einfachen Regeln - den Basishypothesen - zusammengesetzt ist. Die sogenannten Boosting Algorithmen erzeugen iterativ eine gewichtete Summe von Basishypothesen, die gut auf ungesehenen Mustern vorhersagen. Die Arbeit behandelt folgende Sachverhalte: o Die zur Analyse von Boosting-Methoden geeignete Statistische Lerntheorie. Wir studieren lerntheoretische Garantien zur Abschätzung der Vorhersagequalität auf ungesehenen Mustern. Kürzlich haben sich sogenannte Klassifikationstechniken mit großem Margin als ein praktisches Ergebnis dieser Theorie herausgestellt - insbesondere Boosting und Support-Vektor-Maschinen. Ein großer Margin impliziert eine hohe Vorhersagequalität der Entscheidungsregel. Deshalb wird analysiert, wie groß der Margin bei Boosting ist und ein verbesserter Algorithmus vorgeschl

Rätsch, Gunnar

2001-12-01

20

Convex Optimization-based Beamforming: From Receive to Transmit and Network Designs  

Microsoft Academic Search

In this article, an overview of advanced convex optimization approaches to multi-sensor beamforming is pre- sented, and connections are drawn between different types of optimization-based beamformers that apply to a broad class of receive, transmit, and network beamformer design problems. It is demonstrated that convex optimization provides an indispensable set of tools for beamforming, enabling rigorous formulation and effective solution

Alex B. Gershman; Nicholas D. Sidiropoulos; Shahram Shahbazpanahi; Mats Bengtsson

21

Application of convex optimization to acoustical array signal processing  

NASA Astrophysics Data System (ADS)

This paper demonstrates that optimum weighting coefficients and inverse filters for microphone arrays can be accomplished, with the aid of a systematic methodology of mathematical programming. Both far-field and near-field array problems are formulated in terms of convex optimization formalism. Three application examples, including data-independent far-field array design, nearfield array design, and pressure field interpolation, are presented. In far-field array design, array coefficients are optimized to tradeoff Directivity Index for White Noise Gain or the coefficient norm, while in nearfield array convex optimization is applied to design Equivalent Source Method-based Nearfield Acoustical Holography. Numerical examples are given for designing a far-field two-dimensional random array comprised of thirty microphones. For far-field arrays, five design approaches, including a Delay-And-Sum beamformer, a Super Directivity Array, three optimal arrays designed using ?1,?2, and ??-norms, are compared. Numerical and experimental results have shown that sufficiently high White Noise Gain was crucial to robust performance of array against sensor mismatch and noise. For nearfield arrays, inverse filters were designed in light of Equivalent Source Method and convex optimization to reconstruct the velocity field on a baffled spherical piston source. The proposed nearfield design is benchmarked by those designed using Truncated Singular Value Decomposition and Tikhonov Regularization. Compressive Sampling and convex optimization is applied to pressure field reconstruction, source separation and modal analysis with satisfactory performance in both near-field and far-field microphone arrays.

Bai, Mingsian R.; Chen, Ching-Cheng

2013-12-01

22

Sample-path optimization of convex stochastic performance functions  

Microsoft Academic Search

In this paper we propose a method for optimizing convex performance functions in stochastic systems. These functions can include\\u000a expected performance in static systems and steady-state performance in discrete-event dynamic systems; they may be nonsmooth.\\u000a The method is closely related to retrospective simulation optimization; it appears to overcome some limitations of stochastic\\u000a approximation, which is often applied to such problems.

Erica L. Plambeck; Bor-ruey Fu; Stephen M. Robinson; Rajan Suri

1996-01-01

23

Convex optimization for the design of learning machines  

Microsoft Academic Search

This paper reviews the recent surge of interest in convex optimization in a context of pattern recognition and machine learning. The main thesis of this paper is that the design of task-specific learning machines is aided substantially by using a convex optimization solver as a back-end to implement the task, liberating the designer from the concern of designing and analyzing

Kristiaan Pelckmans; Johan A. K. Suykens; Bart De Moor

2007-01-01

24

A Computational Study of the Homogeneous Algorithm for Large-scale Convex Optimization  

Microsoft Academic Search

Recently the authors have proposed a homogeneous and self-dual algorithm for solving the monotone complementarity problem (MCP) [5]. The algorithm is a single phase interior-point type method; nevertheless, it yields either an approximate optimal solution or detects a possible infeasibility of the problem. In this paper we specialize the algorithm to the solution of general smooth convex optimization problems, which

Erling D. Andersen; Yinyu Ye

1998-01-01

25

RELAXATION METHODS FOR NETWORK FLOW PROBLEMS WITH CONVEX ARC COSTS  

Microsoft Academic Search

We consider the standard single commodity network flow problem with both linear and strictly convex possibly nondifferentiable arc costs. For the case where all arc costs are strictly convex we study the convergence of a dual Gauss-Seide! type relaxation method that is well suited for parallel computation. We then extend this method to the case where some of the arc

DIMITRI P. BERTSEKASt; PATRICK A. HOSEINt; PAUL TSENGt

1987-01-01

26

AN ?-RELAXATION METHOD FOR SEPARABLE CONVEX COST NETWORK FLOW PROBLEMS1  

Microsoft Academic Search

We propose a new method for the solution of the single commodity, separable convex cost network flow problem. The method generalizes the ? -relaxation method developed for linear cost problems, and reduces to that method when applied to linear cost problems. We show that the method terminates with a near optimal solution, and we provide an associated complexity analysis. We

Dimitri P. Bertsekas; Lazaros C. Polymenakos; Paul Tseng

1997-01-01

27

Iterative Approaches to Convex Minimization Problems  

Microsoft Academic Search

The aim of this paper is to generalize the results of Yamada et al. [Yamada, I., Ogura, N., Yamashita, Y., Sakaniwa, K. (1998). Quadratic approximation of fixed points of nonexpansive mappings in Hilbert spaces. Numer. Funct. Anal. Optimiz. 19(1):165–190], and to provide complementary results to those of Deutsch and Yamada [Deutsch, F., Yamada, I. (1998). Minimizing certain convex functions over

John G. OHara; Paranjothi Pillay; Hong-Kun Xu

2004-01-01

28

The problem of convexity of Chebyshev sets  

NASA Astrophysics Data System (ADS)

Contents Introduction §1. Definitions and notation §2. Reference theorems §3. Some results Chapter I. Characterization of Banach spaces by means of the relations between approximation properties of sets §1. Existence, uniqueness §2. Prom approximate compactness to 'sun'-property §3. From 'sun'-property to approximate compactness §4. Differentiability in the direction of the gradient is sufficient for Fréchet and Gâteaux differentiability §5. Sets with convex complement Chapter II. The structure of Chebyshev and related sets §1. The isolated point method §2. Restrictions of the type \\vert\\overline{W}\\vert < \\vert X\\vert §3. The case where M is locally compact §4. The case where W lies in a hyperplane §5. Other cases Chapter III. Selected results §1. Some applications of the theory of monotone operators §2. A non-convex Chebyshev set in pre-Hilbert space §3. The example of Klee (discrete Chebyshev set) §4. A survey of some other results Conclusion Bibliography

Balaganskii, V. S.; Vlasov, L. P.

1996-12-01

29

A low-order decomposition of turbulent channel flow via resolvent analysis and convex optimization  

NASA Astrophysics Data System (ADS)

We combine resolvent-mode decomposition with techniques from convex optimization to optimally approximate velocity spectra in a turbulent channel. The velocity is expressed as a weighted sum of resolvent modes that are dynamically significant, non-empirical, and scalable with Reynolds number. To optimally represent direct numerical simulations (DNS) data at friction Reynolds number 2003, we determine the weights of resolvent modes as the solution of a convex optimization problem. Using only 12 modes per wall-parallel wavenumber pair and temporal frequency, we obtain close agreement with DNS-spectra, reducing the wall-normal and temporal resolutions used in the simulation by three orders of magnitude.

Moarref, R.; Jovanovi?, M. R.; Tropp, J. A.; Sharma, A. S.; McKeon, B. J.

2014-05-01

30

Extension of Karmarkar's algorithm onto convex quadratically constrained quadratic problems  

Microsoft Academic Search

Convex quadratically constrained quadratic problems are considered. It is shown that such problems can be transformed to aconic form. The feasible set of the conic form is the intersection of a direct product of standard quadratic cones intersected with\\u000a a hyperplane (the analogue of a simplex), and a linear subspace. For a problem of such form, the analogue of Karmarkar's

Arkadii Nemirovskii; Katya Scheinberg

1996-01-01

31

Cutting-set methods for robust convex optimization with pessimizing oracles  

Microsoft Academic Search

We consider a general worst-case robust convex optimization problem, with arbitrary dependence on the uncertain parameters, which are assumed to lie in some given set of possible values. We describe a general method for solving such a problem, which alternates between optimization and worst-case analysis. With exact worst-case analysis, the method is shown to converge to a robust optimal point.

Almir Mutapcic; Stephen Boyd

2009-01-01

32

DISTRIBUTED ASYNCHRONOUS RELAXATION METHODS FOR CONVEX NETWORK FLOW PROBLEMS  

Microsoft Academic Search

We consider the solution of the single commodity strictly convex network flow problem in a distributed asynchronous computation environment. The dual ofthis problem is unconstrained, differentiable, and well suited for solution via Gauss-Seidel relaxation. We show that the structure of the dual allows the successful application of a distributed asynchronous method whereby relaxation iterations are carried out in parallel by

DIMITRI P. BERTSEKASt; DIDIER EL BAZt

33

Performance Bounds for Optimal Control of Polynomial Systems: A Convex Optimization Approach  

NASA Astrophysics Data System (ADS)

This paper is concerned with an approach for a nonlinear optimal control of polynomial systems. The Hamilton-Jacobi-Bellman (HJB) equation is relaxed into HJB inequalities. Both an upper bound and a lower bound on the cost function, as well as a suboptimal controller, can be computed from solutions of the resulting inequalities. Solving the HJB inequalities can be cast as state-dependent matrix inequalities (SDMIs), whose derivation is based on representation of the given polynomial system in a linear-like form. The resulting SDMI for the upper-bound computation is nonconvex in the decision variables, and hence an iterative procedure is proposed to deal with the non-convexity. On the other hand, the resulting SDMI for the lower-bound computation can be written as a state-dependent linear matrix inequality, which is a convex optimization problem solvable by existing numerical tools. Numerical examples are provided to illustrate the proposed approach.

Jennawasin, Tanagorn; Kawanishi, Michihiro; Narikiyo, Tatsuo

34

Convex optimization under inequality constraints in rank-deficient systems  

NASA Astrophysics Data System (ADS)

Many geodetic applications require the minimization of a convex objective function subject to some linear equality and/or inequality constraints. If a system is singular (e.g., a geodetic network without a defined datum) this results in a manifold of solutions. Most state-of-the-art algorithms for inequality constrained optimization (e.g., the Active-Set-Method or primal-dual Interior-Point-Methods) are either not able to deal with a rank-deficient objective function or yield only one of an infinite number of particular solutions. In this contribution, we develop a framework for the rigorous computation of a general solution of a rank-deficient problem with inequality constraints. We aim for the computation of a unique particular solution which fulfills predefined optimality criteria as well as for an adequate representation of the homogeneous solution including the constraints. Our theoretical findings are applied in a case study to determine optimal repetition numbers for a geodetic network to demonstrate the potential of the proposed framework.

Roese-Koerner, Lutz; Schuh, Wolf-Dieter

2014-05-01

35

On the Relation Between Option and Stock Prices: A Convex Optimization Approach  

Microsoft Academic Search

The idea of investigating the relation of option and stock prices just based on the noarbitrageassumption, but without assuming any model for the underlying price dynamicshas a long history in the financial economics literature. We introduce convex, and in particularsemidefinite, optimization methods, duality and complexity theory to shed new lightto this relation. For the single stock problem, given moments of

Dimitris Bertsimas; Ioana Popescu

2002-01-01

36

Convex optimization and limit analysis: Application to Gurson and porous Drucker–Prager materials  

Microsoft Academic Search

First, we summarize our convex optimization method to solve the static approach of limit analysis. Then, we present the main features of a quadratic extension of a recently proposed mixed finite element method of the kinematic approach. Both methods are applied to obtain precise solutions to a forming problem with Gurson and Drucker–Prager materials. Finally, in order to analyze the

F. Pastor; Ph. Thoré; E. Loute; J. Pastor; M. Trillat

2008-01-01

37

OPTIMAL INEQUALITIES IN PROBABILITY THEORY: A CONVEX OPTIMIZATION APPROACH  

Microsoft Academic Search

We propose a semidefinite optimization approach to the problem of deriving tight moment inequalities for P (X ? S), for a set S defined by polynomial inequalities and a random vector X defined on ? ?R n that has a given collection of up to kth-order moments. In the univariate case, we provide optimal bounds on P (X ? S),

DIMITRIS BERTSIMAS; IOANA POPESCU

2000-01-01

38

Position-Patch Based Face Hallucination Using Convex Optimization  

Microsoft Academic Search

We provide a position-patch based face halluci- nation method using convex optimization. Recently, a novel position-patch based face hallucination method has been proposed to save computational time and achieve high-quality hallucinated results. This method has employed least square estimation to obtain the optimal weights for face hallucination. However, the least square estimation approach can provide biased solutions when the number

Cheolkon Jung; Licheng Jiao; Bing Liu; Maoguo Gong

2011-01-01

39

Convex Geometry of Linear Inverse Problems.  

National Technical Information Service (NTIS)

In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimension of the model to be estimated. However in many practi...

A. S. Willsky B. Recht P. A. Parrilo V. Chandrasekaran

2010-01-01

40

A Fixed Parameter Algorithm for the Minimum Number Convex Partition Problem  

Microsoft Academic Search

\\u000a Given an input consisting of an n-vertex convex polygon with k hole vertices or an n-vertex planar straight line graph (PSLG) with k holes and\\/or reflex vertices inside the convex hull, the parameterized minimum number convex partition (MNCP) problem asks\\u000a for a partition into a minimum number of convex pieces. We give a fixed-parameter tractable algorithm for this problem that\\u000a runs

Magdalene Grantson; Christos Levcopoulos

2004-01-01

41

Stable sequential convex programming in a Hilbert space and its application for solving unstable problems  

NASA Astrophysics Data System (ADS)

A parametric convex programming problem with an operator equality constraint and a finite set of functional inequality constraints is considered in a Hilbert space. The instability of this problem and, as a consequence, the instability of the classical Lagrange principle for it is closely related to its regularity and the subdifferentiability properties of the value function in the optimization problem. A sequential Lagrange principle in nondifferential form is proved for the indicated convex programming problem. The principle is stable with respect to errors in the initial data and covers the normal, regular, and abnormal cases of the problem and the case where the classical Lagrange principle does not hold. It is shown that the classical Lagrange principle in this problem can be naturally treated as a limiting variant of its stable sequential counterpart. The possibility of using the stable sequential Lagrange principle for directly solving unstable optimal control problems and inverse problems is discussed. For two illustrative problems of these kinds, the corresponding stable Lagrange principles are formulated in sequential form.

Sumin, M. I.

2014-01-01

42

A superresolution telescope that uses aberration effects suppression, deconvolution by dimensional reduction, optimal convexity and convexity normalization for image size and dark noise  

NASA Astrophysics Data System (ADS)

In this dissertation we claim to have found the solution to the problem of resolving beyond the diffraction limit (superresolution). This problem is solved by dimensional reduction, convexity optimization, and convexity normalization for image size and dark noise. By dimensional reduction we mean deconvolution on isophote ridges, which are one dimensional, thus we have reduced the dimensionality of the problem from two to one. By optimizing convexity we mean that we choose points to test for image sources for which the second derivative (convexity) of the intensity along isophote ridges is the highest. By normalization of convexity for dark noise and image size we are making sure that our optimization of convexity is not biased by dark noise at different exposures or different background convexities for images of different sizes. This biasing would create artifacts. We also invented ways to speed up our computation and overcome inverse matrix errors. For example we found a simple way to solve the illconditioned matrix problem so we could use the inverse matrix technique, and we are allowed here to replace explicit least squares with the more convenient minimum of the sum of amplitudes squared. We use methods to overcome astigmatism and spherical aberration which are not new. With a narrow field of view we don't need to use the usual iterative stochastic methods (such as MAP). This is because smoothing is effective here since the scale of the PSFs (point spread functions) is much larger than the noise scale. In this superresolution telescope we get a narrow field of view by a microscope-telescope combination. Pointing errors must be minimized to ensure that aberration effects are minimized, and astigmatism produced by air turbulence must be corrected for. Experiments have produced repeatable 1/10 Rayleigh distance resolution for SNR = 60 (with no prior knowledge of source configuration assumed). Through significant air turbulence over a 400 foot line of sight we get 1/6 Rayleigh resolution for 1.5 inch reflecting and refracting telescopes, about a factor of 12 better than you would expect.

Maker, David

43

From Nonlinear Optimization to Convex Optimization through Firefly Algorithm and Indirect Approach with Applications to CAD/CAM  

PubMed Central

Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor's method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently.

Galvez, Akemi; Iglesias, Andres

2013-01-01

44

The Convex-Hull-and-k-Line Travelling Salesman Problem  

Microsoft Academic Search

We present a polynomial time solution algorithm for the so-called Convex-hull-and-k-line TSP: This is a special case of the Euclidean TSP where n ? m of the cities lie on the convex hull and m of the cities lie on k almost parallel line segments in the interior of the hull such that the carrying lines of all these segments

Vladimir G. Deineko; Gerhard J. Woeginger

1996-01-01

45

An interior-proximal method for convex linearly constrained problems and its extension to variational inequalities  

Microsoft Academic Search

In this paper, an entropy-like proximal method for the minimization of a convex function subject to positivity constraints is extended to an interior algorithm in two directions. First, to general linearly constrained convex minimization problems and second, to variational inequalities on polyhedra. For linear programming, numerical results are presented and quadratic convergence is established.

Alfred Auslender; Mounir Haddou

1995-01-01

46

Dinkelbach NCUT: An Efficient Framework for Solving Normalized Cuts Problems with Priors and Convex Constraints (Preprint).  

National Technical Information Service (NTIS)

In this paper, we propose a novel framework, called Dinkelbach NCUT (DNCUT), which efficiently solves the normalized graph cut (NCUT) problem under general, convex constraints as well as, under given priors on the nodes of the graph. Current NCUT methods ...

B. Ghanem N. Ahuja

2010-01-01

47

The Convex-Hull-and-Line Traveling Salesman Problem: A Solvable Case  

Microsoft Academic Search

We solve the special case of the Euclidean Traveling Salesman Problem wheren \\\\Gamma m cities lie on the boundary of the convex hull of all n cities, and the otherm cities lie on a line segment inside this convex hull by an algorithm whichneeds O(mn) time and O(n) space.Keywords: Euclidean Traveling Salesman Problem, shortest path, well-solvablecase, polynomial time algorithm.12 The

Vladimir G. Deineko; René Van Dal; Günter Rote

1994-01-01

48

Implementation of a Point Algorithm for Real-Time Convex Optimization  

NASA Technical Reports Server (NTRS)

The primal-dual interior-point algorithm implemented in G-OPT is a relatively new and efficient way of solving convex optimization problems. Given a prescribed level of accuracy, the convergence to the optimal solution is guaranteed in a predetermined, finite number of iterations. G-OPT Version 1.0 is a flight software implementation written in C. Onboard application of the software enables autonomous, real-time guidance and control that explicitly incorporates mission constraints such as control authority (e.g. maximum thrust limits), hazard avoidance, and fuel limitations. This software can be used in planetary landing missions (Mars pinpoint landing and lunar landing), as well as in proximity operations around small celestial bodies (moons, asteroids, and comets). It also can be used in any spacecraft mission for thrust allocation in six-degrees-of-freedom control.

Acikmese, Behcet; Motaghedi, Shui; Carson, John

2007-01-01

49

Adaptively Constrained Convex Optimization for Accurate Fiber Orientation Estimation with High Order Spherical Harmonics  

PubMed Central

Diffusion imaging data from the Human Connectome Project (HCP) provides a great opportunity to map the whole brain white matter connectivity to unprecedented resolution in vivo. In this paper we develop a novel method for accurately reconstruct fiber orientation distribution from cutting-edge diffusion data by solving the spherical deconvolution problem as a constrained convex optimization problem. With a set of adaptively selected constraints, our method allows the use of high order spherical harmonics to reliably resolve crossing fibers with small separation angles. In our experiments, we demonstrate on simulated data that our algorithm outperforms a popular spherical deconvolution method in resolving fiber crossings. We also successfully applied our method to the multi-shell and diffusion spectrum imaging (DSI) data from HCP to demonstrate its ability in using state-of-the-art diffusion data to study complicated fiber structures.

Tran, Giang; Shi, Yonggang

2014-01-01

50

Biogeography-Based Optimization for Different Economic Load Dispatch Problems  

Microsoft Academic Search

This paper presents a biogeography-based optimization (BBO) algorithm to solve both convex and non-convex economic load dispatch (ELD) problems of thermal plants. The proposed methodology can take care of economic dispatch problems involving constraints such as transmission losses, ramp rate limits, valve point loading, multi-fuel options and prohibited operating zones. Biogeography deals with the geographical distribution of biological species. Mathematical

Aniruddha Bhattacharya; Pranab Kumar Chattopadhyay

2010-01-01

51

Applications of Fitzpatrick functions for solving optimization problems  

NASA Astrophysics Data System (ADS)

This paper presents applications of Fitzparick functions to optimization problems. The main purpose of the present work is to introduce applications of the Fitzpatrick functions, involving their specific properties as the maximal monotonicity, or the proper, convex and lower semi-continuity, for solving optimization problems.

Nashed, Z.; Raykov, I.

2012-10-01

52

Block Coordinate Descent Method for Multi-Convex Optimization with Applications to Nonnegative Tensor Factorization and Completion.  

National Technical Information Service (NTIS)

This paper considers block multi-convex optimization, where the feasible set and objective function are generally non-convex but convex in each block of variables. We review some of its interesting examples and propose a generalized block coordinate desce...

W. Yin Y. Xu

2012-01-01

53

Note on the Aspect Angle Formed between the Convex Hull and its Interior Points, in the Context of the Euclidean Traveling Salesman Problem.  

National Technical Information Service (NTIS)

For the Euclidean traveling salesman problem (ETSP), it has long been known that the relative order of the cities comprising the convex hull is preserved within an optimal tour. It is thus during ETSP problem solving to utilize the hull as an initial tour...

T. M. Cronin

1992-01-01

54

Higher order sensitivity of solutions to convex programming problems without strict complementarity  

NASA Technical Reports Server (NTRS)

Consideration is given to a family of convex programming problems which depend on a vector parameter. It is shown that the solutions of the problems and the associated Lagrange multipliers are arbitrarily many times directionally differentiable functions of the parameter, provided that the data of the problems are sufficiently regular. The characterizations of the respective derivatives are given.

Malanowski, Kazimierz

1988-01-01

55

Simulation of stochastic systems via polynomial chaos expansions and convex optimization  

NASA Astrophysics Data System (ADS)

Polynomial chaos expansions represent a powerful tool to simulate stochastic models of dynamical systems. Yet, deriving the expansion's coefficients for complex systems might require a significant and nontrivial manipulation of the model, or the computation of large numbers of simulation runs, rendering the approach too time consuming and impracticable for applications with more than a handful of random variables. We introduce a computationally tractable technique for computing the coefficients of polynomial chaos expansions. The approach exploits a regularization technique with a particular choice of weighting matrices, which allows to take into account the specific features of polynomial chaos expansions. The method, completely based on convex optimization, can be applied to problems with a large number of random variables and uses a modest number of Monte Carlo simulations, while avoiding model manipulations. Additional information on the stochastic process, when available, can be also incorporated in the approach by means of convex constraints. We show the effectiveness of the proposed technique in three applications in diverse fields, including the analysis of a nonlinear electric circuit, a chaotic model of organizational behavior, and finally a chemical oscillator.

Fagiano, Lorenzo; Khammash, Mustafa

2012-09-01

56

Algorithms for optimal area triangulations of a convex polygon  

Microsoft Academic Search

Given a convex polygon with n vertices in the plane, we are interested in triangulations of its interior, i.e., maximal sets of non-intersecting diagonals that subdivide the interior of the polygon into triangles. The MaxMin area triangulation is the triangulation of the polygon that maximizes the area of the smallest triangle in the triangulation. Similarly, the MinMax area triangulation is

J. Mark Keil; Tzvetalin S. Vassilev

2006-01-01

57

DEMOS for OPTIMIZATION Problems  

NSDL National Science Digital Library

This demo provides a gallery of visual aids that illustrate fundamental concepts for understanding and developing equations that model optimization problems, commonly referred to as max-min problems. Animations, MATLAB routines and Java applets are included.

Roberts, Lila F.; Hill, David R.

2002-09-16

58

Coordination and Control of Multiple Spacecraft using Convex Optimization Techniques  

NASA Astrophysics Data System (ADS)

Formation flying of multiple spacecraft is an enabling technology for many future space science missions. These future missions will, for example, use the highly coordinated, distributed array of vehicles for earth mapping interferometers and synthetic aperture radar. This thesis presents coordination and control algorithms designed for a fleet of spacecraft. These algorithms are embedded in a hierarchical fleet archi- tecture that includes a high-level coordinator for the fleet maneuvers used to form, re-size, or re-target the formation configuration and low-level controllers to generate and implement the individual control inputs for each vehicle. The trajectory and control problems are posed as linear programming (LP) optimizations to solve for the minimum fuel maneuvers. The combined result of the high-level coordination and low-level controllers is a very flexible optimization framework that can be used off-line to analyze aspects of a mission design and in real-time as part of an on-board autonomous formation flying control system. This thesis also investigates several crit- ical issues associated with the implementation of this formation flying approach. In particular, modifications to the LP algorithms are presented to: include robustness to sensor noise, include actuator constraints, ensure that the optimization solutions are always feasible, and reduce the LP solution times. Furthermore, the dynamics for the control problem are analyzed in terms of two key issues: 1) what dynamics model should be used to specify the desired state to maintain a passive aperture; and 2) what dynamics model should be used in the LP to represent the motion about this state. Several linearized models of the relative dynamics are considered in this analysis, including Hill's equations for circular orbits, modified linear dynamics that partially account for the J2 effects, and Lawden's equations for eccentric orbits.

How, Jonathan P.

2002-06-01

59

Exact boundary conditions for the initial value problem of convex conservation laws  

Microsoft Academic Search

The initial value problem of convex conservation laws, which includes the famous Burgers’ (inviscid) equation, plays an important rule not only in theoretical analysis for conservation laws, but also in numerical computations for various numerical methods. For example, the initial value problem of the Burgers’ equation is one of the most popular benchmarks in testing various numerical methods. But in

Zhen-Huan Teng

2010-01-01

60

AN ?-RELAXATION METHOD FOR SEPARABLE CONVEX COST GENERALIZED NETWORK FLOW PROBLEMS1  

Microsoft Academic Search

We generalize the ? -relaxation method of (BPT97a) for the single commodity, linear or separable convex cost network flow problem to network flow problems with positive gains. The method maintains ? -complementary slackness at all iterations and adjusts the arc flows and the node prices so as to satisfy flow conservation upon termination. Each iteration of the method involves either

Paul Tseng; Dimitri P. Bertsekas

61

Convex Optimization of Coincidence Time Resolution for a High-Resolution PET System  

PubMed Central

We are developing a dual panel breast-dedicated positron emission tomography (PET) system using LSO scintillators coupled to position sensitive avalanche photodiodes (PSAPD). The charge output is amplified and read using NOVA RENA-3 ASICs. This paper shows that the coincidence timing resolution of the RENA-3 ASIC can be improved using certain list-mode calibrations. We treat the calibration problem as a convex optimization problem and use the RENA-3’s analog-based timing system to correct the measured data for time dispersion effects from correlated noise, PSAPD signal delays and varying signal amplitudes. The direct solution to the optimization problem involves a matrix inversion that grows order (n3) with the number of parameters. An iterative method using single-coordinate descent to approximate the inversion grows order (n). The inversion does not need to run to convergence, since any gains at high iteration number will be low compared to noise amplification. The system calibration method is demonstrated with measured pulser data as well as with two LSO-PSAPD detectors in electronic coincidence. After applying the algorithm, the 511 keV photopeak paired coincidence time resolution from the LSO-PSAPD detectors under study improved by 57%, from the raw value of 16.3 ± 0.07 ns full-width at half-maximum (FWHM) to 6.92 ± 0.02 ns FWHM (11.52 ± 0.05 ns to 4.89 ± 0.02 ns for unpaired photons).

Reynolds, Paul D.; Olcott, Peter D.; Pratx, Guillem; Lau, Frances W. Y.

2013-01-01

62

Convex optimization of coincidence time resolution for a high-resolution PET system.  

PubMed

We are developing a dual panel breast-dedicated positron emission tomography (PET) system using LSO scintillators coupled to position sensitive avalanche photodiodes (PSAPD). The charge output is amplified and read using NOVA RENA-3 ASICs. This paper shows that the coincidence timing resolution of the RENA-3 ASIC can be improved using certain list-mode calibrations. We treat the calibration problem as a convex optimization problem and use the RENA-3's analog-based timing system to correct the measured data for time dispersion effects from correlated noise, PSAPD signal delays and varying signal amplitudes. The direct solution to the optimization problem involves a matrix inversion that grows order (n(3)) with the number of parameters. An iterative method using single-coordinate descent to approximate the inversion grows order (n). The inversion does not need to run to convergence, since any gains at high iteration number will be low compared to noise amplification. The system calibration method is demonstrated with measured pulser data as well as with two LSO-PSAPD detectors in electronic coincidence. After applying the algorithm, the 511 keV photopeak paired coincidence time resolution from the LSO-PSAPD detectors under study improved by 57%, from the raw value of 16.3 ±0.07 ns full-width at half-maximum (FWHM) to 6.92 ±0.02 ns FWHM ( 11.52 ±0.05 ns to 4.89 ±0.02 ns for unpaired photons). PMID:20876008

Reynolds, Paul D; Olcott, Peter D; Pratx, Guillem; Lau, Frances W Y; Levin, Craig S

2011-02-01

63

Smoothers for Optimization Problems  

NASA Technical Reports Server (NTRS)

We present a multigrid one-shot algorithm, and a smoothing analysis, for the numerical solution of optimal control problems which are governed by an elliptic PDE. The analysis provides a simple tool to determine a smoothing minimization process which is essential for multigrid application. Numerical results include optimal control of boundary data using different discretization schemes and an optimal shape design problem in 2D with Dirichlet boundary conditions.

Arian, Eyal; Ta'asan, Shlomo

1996-01-01

64

Solving complex economic load dispatch problems using biogeography-based optimization  

Microsoft Academic Search

This paper presents an algorithm, biogeography-based optimization (BBO) to solve both convex and non-convex economic load dispatch (ELD) problems of thermal generators of a power system. The Proposed methodology easily takes care of solving non-convex economic dispatch problems considering different constraints such as transmission losses, ramp rate limits, multi-fuel options and prohibited operating zones. Biogeography deals with the geographical distribution

Aniruddha Bhattacharya; P. K. Chattopadhyay

2010-01-01

65

On the optimal two-block H? problem  

Microsoft Academic Search

This paper provides the duality structure of the optimal two-block H? problem. The dual description leads naturally to a numerical solution based on convex programming for LTI (including infinite dimensional) systems. Alignment conditions are obtained and show that the optimal solution is flat in general, and unique in the SISO case. It is also proved that under specific conditions, a

Seddik M. Djouadi; J. Douglas Birdwell

2005-01-01

66

The convex hull of two core capacitated network design problems  

Microsoft Academic Search

The network loading problem (NLP) is a specialized capacitated network design problem in which prescribed point-to-point demand between various pairs of nodes of a network must be met by installing (loading) a capacitated facility. We can load any number of units of the facility on each of the arcs at a specified arc dependent cost. The problem is to determine

Thomas L. Magnanti; Prakash Mirchandani; Rita Vachani

1993-01-01

67

Efficient recurrent neural network model for the solution of general nonlinear optimization problems  

Microsoft Academic Search

In this paper, we propose a projection neural network model for solving nonlinear convex optimization problems with general linear constraints. Compared with the existing neural network models for solving nonlinear optimization problems, the proposed neural network can be applied to solve a broad class of constrained optimization problems such as degenerate, saddle point, and quadratic problems. It is shown that

A. Malek; N. Hosseinipour-Mahani; S. Ezazipour

2010-01-01

68

An ?-relaxation method for separable convex cost generalized network flow problems  

Microsoft Academic Search

.   We generalize the ?-relaxation method of [14] for the single commodity, linear or separable convex cost network flow problem\\u000a to network flow problems with positive gains. The method maintains ?-complementary slackness at all iterations and adjusts\\u000a the arc flows and the node prices so as to satisfy flow conservation upon termination. Each iteration of the method involves\\u000a either a

Paul Tseng; Dimitri P. Bertsekas

2000-01-01

69

Co-clustering of image segments using convex optimization applied to EM neuronal reconstruction  

Microsoft Academic Search

This paper addresses the problem of jointly clustering two segmentations of closely correlated images. We focus in particular on the application of reconstructing neuronal structures in over-segmented electron microscopy images. We formulate the problem of co-clustering as a quadratic semi-assignment problem and investigate convex relaxations using semidefinite and linear programming. We further introduce a linear programming method with manageable number

Shiv Naga Prasad Vitaladevuni; Ronen Basri

2010-01-01

70

Compensation of modal dispersion in multimode fiber systems using adaptive optics via convex optimization  

NASA Astrophysics Data System (ADS)

Multimode fibers (MMF) are widely deployed in local-, campus-, and storage-area-networks. Achievable data rates and transmission distances are, however, limited by the phenomenon of modal dispersion. We propose a system to compensate for modal dispersion using adaptive optics. This leads to a 10- to 100-fold improvement in performance over current standards. We propose a provably optimal technique for minimizing inter-symbol interference (ISI) in MMF systems using adaptive optics via convex optimization. We use a spatial light modulator (SLM) to shape the spatial profile of light launched into an MMF. We derive an expression for the system impulse response in terms of the SLM reflectance and the field patterns of the MMF principal modes. Finding optimal SLM settings to minimize ISI, subject to physical constraints, is posed as an optimization problem. We observe that our problem can be cast as a second-order cone program, which is a convex optimization problem. Its global solution can, therefore, be found with minimal computational complexity. Simulations show that this technique opens up an eye pattern originally closed due to ISI. We then propose fast, low-complexity adaptive algorithms for optimizing the SLM settings. We show that some of these converge to the global optimum in the absence of noise. We also propose modified versions of these algorithms to improve resilience to noise and speed of convergence. Next, we experimentally compare the proposed adaptive algorithms in 50-mum graded-index (GRIN) MMFs using a liquid-crystal SLM. We show that continuous-phase sequential coordinate ascent (CPSCA) gives better bit-error-ratio performance than 2- or 4-phase sequential coordinate ascent, in concordance with simulations. We evaluate the bandwidth characteristics of CPSCA, and show that a single SLM is able to simultaneously compensate over up to 9 wavelength-division-multiplexed (WDM) 10-Gb/s channels, spaced by 50 GHz, over a total bandwidth of 450 GHz. We also show that CPSCA is able to compensate for modal dispersion over up to 2.2 km, even in the presence of mid-span connector offsets up to 4 mum (simulated in experiment by offset splices). A known non-adaptive launching technique using a fusion-spliced single-mode-to-multimode patchcord is shown to fail under these conditions. Finally, we demonstrate 10 x 10 Gb/s dense WDM transmission over 2.2 km of 50-mum GRIN MMF. We combine transmitter-based adaptive optics and receiver-based single-mode filtering, and control the launched field pattern for ten 10-Gb/s non-return-to-zero channels, wavelength-division multiplexed on a 200-GHz grid in the C band. We achieve error-free transmission through 2.2 km of 50-mum GRIN MMF for launch offsets up to 10 mum and for worst-case launched polarization. We employ a ten-channel transceiver based on parallel integration of electronics and photonics.

Panicker, Rahul Alex

71

A difference of convex formulation of value-at-risk constrained optimization  

Microsoft Academic Search

In this article, we present a representation of value-at-risk (VaR) as a difference of convex (D.C.) functions in the case where the distribution of the underlying random variable is discrete and has finitely many atoms. The D.C. representation is used to study a financial risk-return portfolio selection problem with a VaR constraint. A branch-and-bound algorithm that numerically solves the problem

David Wozabal; Ronald Hochreiter; Georg Ch. Pflug

2010-01-01

72

Heuristic solutions to polynomial moment problems with some convex entropic objectives  

NASA Astrophysics Data System (ADS)

We are asking to estimate a nonnegative density on Rm, given some of its algebraic or trigonometric moments. The maximum entropy method is to introduce an entropy-like objective function and then solve a convex minimization programming with some linear constraints. In the existing literature, Newton's method or some other iteration methods are used to solve its dual problem. In this paper, special structures of the problem have been discovered when we use some particular entropies, which include Boltzmann-Shannon entropy and Burg's entropy. Useful linear relationships among the moments help us to set up very fast and effective algorithms. Numerical computations and comparison are also presented.

Huang, Wanzhen

1996-09-01

73

EUROPT Workshop on Advances in Continuous Optimization (8th) Held in Aveiro, Portugal, on July 9-10, 2010.  

National Technical Information Service (NTIS)

Applications of Continuous Optimization to Combinatorial Problems; Complexity and Efficiency of Optimization Algorithms; Convex and Nonsmooth Optimization; Complementarity and Variational Problems; Derivative-free Optimization; Global Optimization; Linear...

D. Cardoso T. Tchemisova

2010-01-01

74

Optimality conditions and duality for constrained measurable subset selection problems with minmax objective functions  

Microsoft Academic Search

Necessary conditions and sufficient conditions of optimality and several duality results are established under generalized ?-convexity assumptions for constrained measurable subset selection problems with discrete minmax fractional objective functions. As byproducts of these results, one also obtains similar optimality and duality criteria for three additional classes of problems with discrete minmax, fractional, and ordinary objective functions, which are special cases

G. J. Zaimai

1989-01-01

75

A Problem on Optimal Transportation  

ERIC Educational Resources Information Center

Mathematical optimization problems are not typical in the classical curriculum of mathematics. In this paper we show how several generalizations of an easy problem on optimal transportation were solved by gifted secondary school pupils in a correspondence mathematical seminar, how they can be used in university courses of linear programming and…

Cechlarova, Katarina

2005-01-01

76

A fast nonstationary iterative method with convex penalty for inverse problems in Hilbert spaces  

NASA Astrophysics Data System (ADS)

In this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex functions are introduced as penalty terms. By exploiting the Hilbert space structure of the underlying problems, we propose a fast iterative regularization method which reduces to the classical nonstationary iterated Tikhonov regularization when the penalty term is chosen to be the square of norm. Each iteration of the method consists of two steps: the first step involves only the operator from the problem while the second step involves only the penalty term. This splitting character has the advantage of making the computation efficient. In case the data is corrupted by noise, a stopping rule is proposed to terminate the method and the corresponding regularization property is established. Finally, we test the performance of the method by reporting various numerical simulations, including the image deblurring, the determination of source term in Poisson equation, and the de-autoconvolution problem.

Jin, Qinian; Lu, Xiliang

2014-04-01

77

Fast and optimal solution for the generalized attitude determination problem  

NASA Astrophysics Data System (ADS)

This thesis provides a fast and optimal approach to solve Wahba's general weighted problem. Applications of Wahba's general weighted problem involve attitude determination using wide field-of-view sensors or GPS sensor observations. The first approach developed applies a homotopy continuation based solver to find the global minimizer of the minimization problem. This approach first finds all the stationary points of the minimization problem by solving the polynomial equations satisfied by the stationary points and then chooses the global minimizer from them. Next, a second approach is discussed, based on solving an unconstrained optimization problem using an iterative Newton solution. The parameter space includes the attitude and lagrange multipliers. The initial guess for Newton's method is calculated by approximating the Wahba's general weighted cost and constraints to a convex form and applying semidefinite programming to have global optimum attitude. Monte Carlo-based simulation results indicate that convergence is given quickly to the optimal solution.

Ghosh, Arnab

78

Benchmark Problems in Structural Optimization  

Microsoft Academic Search

\\u000a Structural optimization is an important area related to both optimization and structural engineering. Structural optimization\\u000a problems are often used as benchmarks to validate new optimization algorithms or to test the suitability of a chosen algorithm.\\u000a In almost all structural engineering applications, it is very important to find the best possible parameters for given design\\u000a objectives and constraints which are highly

Amir Hossein Gandomi; Xin-She Yang

79

Lossless Convexification of Control Constraints for a Class of Nonlinear Optimal Control Problems  

NASA Technical Reports Server (NTRS)

In this paper we consider a class of optimal control problems that have continuous-time nonlinear dynamics and nonconvex control constraints. We propose a convex relaxation of the nonconvex control constraints, and prove that the optimal solution to the relaxed problem is the globally optimal solution to the original problem with nonconvex control constraints. This lossless convexification enables a computationally simpler problem to be solved instead of the original problem. We demonstrate the approach in simulation with a planetary soft landing problem involving a nonlinear gravity field.

Blackmore, Lars; Acikmese, Behcet; Carson, John M.,III

2012-01-01

80

Convex piecewise-linear fitting  

Microsoft Academic Search

We consider the problem of fitting a convex piecewise-linear function, with some specified form, to given multi-dimensional\\u000a data. Except for a few special cases, this problem is hard to solve exactly, so we focus on heuristic methods that find locally\\u000a optimal fits. The method we describe, which is a variation on the K-means algorithm for clustering, seems to work well

Alessandro Magnani; Stephen P. Boyd

2009-01-01

81

Automatic Segmentation of Neonatal Images Using Convex Optimization and Coupled Level Sets  

PubMed Central

Accurate segmentation of neonatal brain MR images remains challenging mainly due to their poor spatial resolution, inverted contrast between white matter and gray matter, and high intensity inhomogeneity. Most existing methods for neonatal brain segmentation are atlas-based and voxel-wise. Although active contour/surface models with geometric information constraint have been successfully applied to adult brain segmentation, they are not fully explored in the neonatal image segmentation. In this paper, we propose a novel neonatal image segmentation method by combining local intensity information, atlas spatial prior, and cortical thickness constraint in a single level-set framework. Besides, we also provide a robust and reliable tissue surface initialization for the proposed method by using a convex optimization technique. Thus, tissue segmentation, as well as inner and outer cortical surface reconstruction, can be obtained simultaneously. The proposed method has been tested on a large neonatal dataset, and the validation on 10 neonatal brain images (with manual segmentations) shows very promising results.

Wang, Li; Shi, Feng; Lin, Weili; Gilmore, John H.; Shen, Dinggang

2011-01-01

82

EXISTENCE OF SOLUTIONS FOR A MULTIVALUED BOUNDARY VALUE PROBLEM WITH NON-CONVEX AND UNBOUNDED RIGHT-HAND SIDE  

Microsoft Academic Search

Let F : (a;b) £ IRn £ IRn ! 2IR n be a multifunction with possibly non-convex and unbounded values. The main re- sult of this paper (Theorem 1) asserts that, given the multivalued boundary value problem ‰ u00 2 F(t;u;u0) u(a) = u(b) = #IRn; (PF) if an appropriate restriction of the multifunction F has non-empty and closed values

DIEGO AVERNA; GABRIELE BONANNO

83

Automatic Treatment Planning with Convex Imputing  

NASA Astrophysics Data System (ADS)

Current inverse optimization-based treatment planning for radiotherapy requires a set of complex DVH objectives to be simultaneously minimized. This process, known as multi-objective optimization, is challenging due to non-convexity in individual objectives and insufficient knowledge in the tradeoffs among the objective set. As such, clinical practice involves numerous iterations of human intervention that is costly and often inconsistent. In this work, we propose to address treatment planning with convex imputing, a new-data mining technique that explores the existence of a latent convex objective whose optimizer reflects the DVH and dose-shaping properties of previously optimized cases. Using ten clinical prostate cases as the basis for comparison, we imputed a simple least-squares problem from the optimized solutions of the prostate cases, and show that the imputed plans are more consistent than their clinical counterparts in achieving planning goals.

Sayre, G. A.; Ruan, D.

2014-03-01

84

Optimization and geophysical inverse problems  

SciTech Connect

A fundamental part of geophysics is to make inferences about the interior of the earth on the basis of data collected at or near the surface of the earth. In almost all cases these measured data are only indirectly related to the properties of the earth that are of interest, so an inverse problem must be solved in order to obtain estimates of the physical properties within the earth. In February of 1999 the U.S. Department of Energy sponsored a workshop that was intended to examine the methods currently being used to solve geophysical inverse problems and to consider what new approaches should be explored in the future. The interdisciplinary area between inverse problems in geophysics and optimization methods in mathematics was specifically targeted as one where an interchange of ideas was likely to be fruitful. Thus about half of the participants were actively involved in solving geophysical inverse problems and about half were actively involved in research on general optimization methods. This report presents some of the topics that were explored at the workshop and the conclusions that were reached. In general, the objective of a geophysical inverse problem is to find an earth model, described by a set of physical parameters, that is consistent with the observational data. It is usually assumed that the forward problem, that of calculating simulated data for an earth model, is well enough understood so that reasonably accurate synthetic data can be generated for an arbitrary model. The inverse problem is then posed as an optimization problem, where the function to be optimized is variously called the objective function, misfit function, or fitness function. The objective function is typically some measure of the difference between observational data and synthetic data calculated for a trial model. However, because of incomplete and inaccurate data, the objective function often incorporates some additional form of regularization, such as a measure of smoothness or distance from a prior model. Various other constraints may also be imposed upon the process. Inverse problems are not restricted to geophysics, but can be found in a wide variety of disciplines where inferences must be made on the basis of indirect measurements. For instance, most imaging problems, whether in the field of medicine or non-destructive evaluation, require the solution of an inverse problem. In this report, however, the examples used for illustration are taken exclusively from the field of geophysics. The generalization of these examples to other disciplines should be straightforward, as all are based on standard second-order partial differential equations of physics. In fact, sometimes the non-geophysical inverse problems are significantly easier to treat (as in medical imaging) because the limitations on data collection, and in particular on multiple views, are not so severe as they generally are in geophysics. This report begins with an introduction to geophysical inverse problems by briefly describing four canonical problems that are typical of those commonly encountered in geophysics. Next the connection with optimization methods is made by presenting a general formulation of geophysical inverse problems. This leads into the main subject of this report, a discussion of methods for solving such problems with an emphasis upon newer approaches that have not yet become prominent in geophysics. A separate section is devoted to a subject that is not encountered in all optimization problems but is particularly important in geophysics, the need for a careful appraisal of the results in terms of their resolution and uncertainty. The impact on geophysical inverse problems of continuously improving computational resources is then discussed. The main results are then brought together in a final summary and conclusions section.

Barhen, J.; Berryman, J.G.; Borcea, L.; Dennis, J.; de Groot-Hedlin, C.; Gilbert, F.; Gill, P.; Heinkenschloss, M.; Johnson, L.; McEvilly, T.; More, J.; Newman, G.; Oldenburg, D.; Parker, P.; Porto, B.; Sen, M.; Torczon, V.; Vasco, D.; Woodward, N.B.

2000-10-01

85

Billiards and Two-Dimensional Problems of Optimal Resistance  

NASA Astrophysics Data System (ADS)

A body moves in a medium composed of noninteracting point particles; the interaction of the particles with the body is completely elastic. The problem is: find the body’s shape that minimizes or maximizes resistance of the medium to its motion. This is the general setting of the optimal resistance problem going back to Newton. Here, we restrict ourselves to the two-dimensional problems for rotating (generally non-convex) bodies. The main results of the paper are the following. First, to any compact connected set with piecewise smooth boundary {B subset mathbb{R}^2} we assign a measure ? B on ?(conv B)×[ - ?/2, ?/2] generated by the billiard in {mathbb{R}^2 setminus B} and characterize the set of measures { ? B }. Second, using this characterization, we solve various problems of minimal and maximal resistance of rotating bodies by reducing them to special Monge-Kantorovich problems.

Plakhov, Alexander

2009-11-01

86

A posteriori error estimates for mixed finite element approximation of nonlinear quadratic optimal control problems  

Microsoft Academic Search

In this paper, we obtain an a posteriori error analysis for mixed finite element approximation of convex optimal control problems governed by a nonlinear second-order elliptic equation. Our results are based on the approximation for both the coupled state variables and the control variable. We propose to improve the error estimates, which can be used to construct an adaptive finite

Yanping Chen; Zuliang Lu; Min Fu

2012-01-01

87

Interval-Valued Optimization Problems Involving (?, ?)-Right Upper-Dini-Derivative Functions  

PubMed Central

We consider an interval-valued multiobjective problem. Some necessary and sufficient optimality conditions for weak efficient solutions are established under new generalized convexities with the tool-right upper-Dini-derivative, which is an extension of directional derivative. Also some duality results are proved for Wolfe and Mond-Weir duals.

2014-01-01

88

Optimization and Openmp Parallelization of a Discrete Element Code for Convex Polyhedra on Multi-Core Machines  

NASA Astrophysics Data System (ADS)

We report our experiences with the optimization and parallelization of a discrete element code for convex polyhedra on multi-core machines and introduce a novel variant of the sort-and-sweep neighborhood algorithm. While in theory the whole code in itself parallelizes ideally, in practice the results on different architectures with different compilers and performance measurement tools depend very much on the particle number and optimization of the code. After difficulties with the interpretation of the data for speedup and efficiency are overcome, respectable parallelization speedups could be obtained.

Chen, Jian; Matuttis, Hans-Georg

2013-02-01

89

A numerical approach to the non-convex dynamic problem of pipeline-soil interaction under environmental effects  

NASA Astrophysics Data System (ADS)

A numerical approach for a problem arising in Civil and Environmental Engineering is presented. This problem concerns the dynamic soil-pipeline interaction, when unilateral contact conditions due to tensionless and elastoplastic softening/fracturing behaviour of the soil as well as due to gapping caused by earthquake excitations are taken into account. Moreover, soil-capacity degradation due to environmental effects are taken into account. The mathematical formulation of this dynamic elastoplasticity problem leads to a system of partial differential equations with equality domain and inequality boundary conditions. The proposed numerical approach is based on a double discretization, in space and time, and on mathematical programming methods. First, in space the finite element method (FEM) is used for the simulation of the pipeline and the unilateral contact interface, in combination with the boundary element method (BEM) for the soil simulation. Concepts of the non-convex analysis are used. Next, with the aid of Laplace transform, the equality problem conditions are transformed to convolutional ones involving as unknowns the unilateral quantities only. So the number of unknowns is significantly reduced. Then a marching-time approach is applied and a non-convex linear complementarity problem is solved in each time-step.

Liolios, K.; Georgiev, I.; Liolios, A.

2012-10-01

90

Fixed, low-order controller design with time response specifications using non-convex optimization.  

PubMed

In this paper, we present a new algorithm for designing a fixed, low-order controller with time response specifications for a linear time invariant (LTI), single input single output (SISO) plant. For a two-parameter feedback configuration, the problem of finding a fixed or low-order controller to meet the desired time response specification is reduced to the least square estimation (LSE) in the sense of partial model matching (PMM), which minimizes a quadratic cost function. The closed-loop stability condition imposed on the controller parameters is formulated by the polynomial matrix inequality (PMI) constraint associated with the cost function. When the cascade feedback structure is considered, the zeros of the controller may be a substantial obstacle when designing a controller that has a good time response. This problem can also be formulated using polynomial constraints. Consequently, it is shown that the total problem here can be formulated as an optimization problem with a quadratic objective function and several polynomial constraints in the controller parameter space. We show that the SeDuMi with YALMIP interface [Löfberg J. YALMIP: A toolbox for modeling and optimization in MATLAB, in: Proceedings of the IEEE symposium on computer aided control systems design 2004. p. 284-9. http://control.ee.ethz.ch/~joloef/yalmip.php] can be used for solving this problem. Finally, several illustrative examples are given. PMID:18606409

Jin, Lihua; Kim, Young Chol

2008-10-01

91

Models for optimal harvest with convex function of growth rate of a population  

SciTech Connect

Two models for growth of a population, which are described by a Cauchy problem for an ordinary differential equation with right-hand side depending on the population size and time, are investigated. The first model is time-discrete, i.e., the moments of harvest are fixed and discrete. The second model is time-continuous, i.e., a crop is harvested continuously in time. For autonomous systems, the second model is a particular case of the variational model for optimal control with constraints investigated in. However, the prerequisites and the method of investigation are somewhat different, for they are based on Lemma 1 presented below. In this paper, the existence and uniqueness theorem for the solution of the discrete and continuous problems of optimal harvest is proved, and the corresponding algorithms are presented. The results obtained are illustrated by a model for growth of the light-requiring green alga Chlorella.

Lyashenko, O.I.

1995-12-10

92

Convex Drawings of Graphs with Non-convex Boundary  

Microsoft Academic Search

In this paper, we study a new problem of flnding a convex drawing of graphs with a non-convex boundary. It is proved that every triconnected plane graph whose boundary is flxed with a star-shaped polygon admits a drawing in which every inner facial cycle is drawn as a convex polygon. Such a drawing, called an inner-convex drawing, can be obtained

Seok-hee Hong; Hiroshi Nagamochi

2006-01-01

93

Morrey regularity results for asymptotically convex variational problems with (p,q) growth  

NASA Astrophysics Data System (ADS)

We prove some global Morrey regularity results for almost minimizers of functionals of the form u??? f(x,?u) dx. This regularity is valid up to the boundary, provided the boundary data is sufficiently regular. The main assumption on f is that for each x, the function f(x,?) behaves asymptotically like a convex function with (p,q) growth. Some discontinuous behavior in the first argument is allowed. As a main application, we establish analogous regularity results for a broad class of systems of nonhomogeneous partial differential equations.

Fey, Kyle; Foss, Mikil

94

An Optimal Method for Stochastic Composite Optimization  

Microsoft Academic Search

This paper considers an important class of convex programming problems, namely, the stochastic composite optimization (SCO), whose objective function is given by the summation of general nonsmooth and smooth stochastic components. Since SCO covers non-smooth, smooth and stochastic convex optimization as certain special cases, a valid lower bound on the rate of convergence for solving these problems is known from

Guanghui Lan

2009-01-01

95

Applying optimization software libraries to engineering problems  

NASA Technical Reports Server (NTRS)

Nonlinear programming, preliminary design problems, performance simulation problems trajectory optimization, flight computer optimization, and linear least squares problems are among the topics covered. The nonlinear programming applications encountered in a large aerospace company are a real challenge to those who provide mathematical software libraries and consultation services. Typical applications include preliminary design studies, data fitting and filtering, jet engine simulations, control system analysis, and trajectory optimization and optimal control. Problem sizes range from single-variable unconstrained minimization to constrained problems with highly nonlinear functions and hundreds of variables. Most of the applications can be posed as nonlinearly constrained minimization problems. Highly complex optimization problems with many variables were formulated in the early days of computing. At the time, many problems had to be reformulated or bypassed entirely, and solution methods often relied on problem-specific strategies. Problems with more than ten variables usually went unsolved.

Healy, M. J.

1984-01-01

96

Optimization Problems in Multisensor and Multitarget Tracking.  

National Technical Information Service (NTIS)

The objective of this research program is to develop optimization algorithms that solve key problems in multiple target tracking and sensor data fusion. The central problem in multiple target tracking is the data association problem of partitioning sensor...

A. B. Poore

2008-01-01

97

On the optimizing-adaptive control problem  

Microsoft Academic Search

The optimizing-adaptive control problem arises in applications where the desired behavior is not specified explicitly, but instead, an objective function of the plant behavior and the unknown plant itself is to be optimized. In these cases, the control task involves the explicit determination of the optimal behavior and the control action to achieve that behavior. The difficulty with this problem

Perry Y. Li; Roberto Horowitz

1994-01-01

98

Exploiting Problem Structure for Distributed Constraint Optimization  

Microsoft Academic Search

Distributed constraint optimization imposes considerabl e complexity in agents' coordinated search for an optimal so- lution. However, in many application domains, problems often exhibit special structures that can be exploited to fa - cilitate more efficient problem solving. One of the most recurrent structures involves disparity among subproblem s. We present a coordination mechanism, Anchor&Ascend, for distributed constraint optimization that

Jyi-shane Liu; Katia P. Sycara

1995-01-01

99

Multiobjective particle swarm optimization for optimal power flow problem  

Microsoft Academic Search

A novel approach to multiobjective particle swarm optimization (MOPSO) technique for solving optimal power flow (OPF) problem is proposed in this paper. The new MOPSO technique evolves a multiobjective version of PSO by proposing redefinition of global best and local best individuals in multiobjective optimization domain. A clustering algorithm to manage the size of the Pareto-optimal set is imposed. The

M. A. Abido

2008-01-01

100

Optimal control in a macroeconomic problem  

NASA Astrophysics Data System (ADS)

The Pontryagin maximum principle is used to develop an original algorithm for finding an optimal control in a macroeconomic problem. Numerical results are presented for the optimal control and optimal trajectory of the development of a regional economic system. For an optimal control satisfying a certain constraint, an invariant of a macroeconomic system is derived.

Bulgakov, V. K.; Shatov, G. L.

2007-08-01

101

A combination of concave/convex surfaces for field-enhancement optimization: the indented nanocone.  

PubMed

We introduce a design strategy to maximize the Near Field (NF) enhancement near plasmonic antennas. We start by identifying and studying the basic electromagnetic effects that contribute to the electric near field enhancement. Next, we show how the concatenation of a convex and a concave surface allows merging all the effects on a single, continuous nanoantenna. As an example of this NF maximization strategy, we engineer a nanostructure, the indented nanocone. This structure, combines all the studied NF maximization effects with a synergistic boost provided by a Fano-like interference effect activated by the presence of the concave surface. As a result, the antenna exhibits a NF amplitude enhancement of ~ 800, which transforms into ~1600 when coupled to a perfect metallic surface. This strong enhancement makes the proposed structure a robust candidate to be used in field enhancement based technologies. Further elaborations of the concept may produce even larger and more effective enhancements. PMID:23187337

García-Etxarri, Aitzol; Apell, Peter; Käll, Mikael; Aizpurua, Javier

2012-11-01

102

Automated Segmentation of CBCT Image using Spiral CT Atlases and Convex Optimization  

PubMed Central

Cone-beam computed tomography (CBCT) is an increasingly utilized imaging modality for the diagnosis and treatment planning of the patients with craniomaxillofacial (CMF) deformities. CBCT scans have relatively low cost and low radiation dose in comparison to conventional spiral CT scans. However, a major limitation of CBCT scans is the widespread image artifacts such as noise, beam hardening and inhomogeneity, causing great difficulties for accurate segmentation of bony structures from soft tissues, as well as separating mandible from maxilla. In this paper, we presented a novel fully automated method for CBCT image segmentation. In this method, we first estimated a patient-specific atlas using a sparse label fusion strategy from predefined spiral CT atlases. This patient-specific atlas was then integrated into a convex segmentation framework based on maximum a posteriori probability for accurate segmentation. Finally, the performance of our method was validated via comparisons with manual ground-truth segmentations.

Wang, Li; Chen, Ken Chung; Shi, Feng; Liao, Shu; Li, Gang; Gao, Yaozong; Shen, Steve GF; Yan, Jin; Lee, Philip K.M.; Chow, Ben; Liu, Nancy X.; Xia, James J.; Shen, Dinggang

2013-01-01

103

Automated segmentation of CBCT image using spiral CT atlases and convex optimization.  

PubMed

Cone-beam computed tomography (CBCT) is an increasingly utilized imaging modality for the diagnosis and treatment planning of the patients with craniomaxillofacial (CMF) deformities. CBCT scans have relatively low cost and low radiation dose in comparison to conventional spiral CT scans. However, a major limitation of CBCT scans is the widespread image artifacts such as noise, beam hardening and inhomogeneity, causing great difficulties for accurate segmentation of bony structures from soft tissues, as well as separating mandible from maxilla. In this paper, we presented a novel fully automated method for CBCT image segmentation. In this method, we first estimated a patient-specific atlas using a sparse label fusion strategy from predefined spiral CT atlases. This patient-specific atlas was then integrated into a convex segmentation framework based on maximum a posteriori probability for accurate segmentation. Finally, the performance of our method was validated via comparisons with manual ground-truth segmentations. PMID:24505768

Wang, Li; Chen, Ken Chung; Shi, Feng; Liao, Shu; Li, Gang; Gao, Yaozong; Shen, Steve G F; Yan, Jin; Lee, Philip K M; Chow, Ben; Liu, Nancy X; Xia, James J; Shen, Dinggang

2013-01-01

104

Tropical Convexity  

Microsoft Academic Search

The notions of convexity and convex polytopes are introduced in the setting of tropical geometry. Combinatorial types of tropical polytopes are shown to be in bijection with regular triangulations of products of two simplices. Applications to phylogenetic trees are discussed. Theorem 29 and Corollary 30 in the paper, relating tropical polytopes to injective hulls, are incorrect. See the erratum at

Mike Develin; Bernd Sturmfels

2003-01-01

105

Mathematical model and method of searching for a local extremum for the non-convex oriented polygons allocation problem  

Microsoft Academic Search

This work deals with the problem of optimal allocation of objects of a so-called irregular form. The objects are allocated on a strip of given width and with defects. This problem is insufficiently studied, but it is typical for many industries and is also interesting for developing the theory of solving cutting and packing problems. An analytical model of the

Yu. G. Stoyan; M. V. Novozhilova; A. V. Kartashov

1996-01-01

106

Convex Boundary Angle-Based Flattening  

Microsoft Academic Search

Abstract Angle Based Flattening is a robust parameterization method,that finds a quasi-conformal mapping by solving a non-linear optimization problem. We take advantage of a characterization of convex planar drawings of triconnected graphs to introduce new boundary constraints. This prevents boundary intersections and avoids post-processing of the parameterized mesh. We present a simple transformation to eectively,relax the constrained minimization problem, which

Rhaleb Zayer; Christian Rössl; Hans-peter Seidel

2003-01-01

107

Generator of learning data for the TSPs based on the visiting order of the cities on convex hull  

Microsoft Academic Search

The optimal tours of the traveling salesman problems( TSPs) in two dimensional Euclidean space have the characteristics in the visiting order of the cities on the convex hull. Based on this characteristics, the TSPs can be replaced into some shortest Hamiltonian path problems(SHPPs) of which solutions assemble a tour. This reduction is enabled by the calculation of convex hull and

Akihiko Kawashima; Yasuo Sugai

2010-01-01

108

On necessary conditions in an optimization problem for differential inclusions with random initial data  

NASA Astrophysics Data System (ADS)

Necessary conditions in an optimization problem for differential inclusions with convex right-hand side are given. The initial state of the inclusion being a random vector is unknown, or, in the more general case, is contained in some random closed set. We seek a trajectory of the inclusion which minimizes the expectation of a function of the inclusion's final state, or, in the more general case, the similar trajectory which is a minimizer of an max-(or Choquet) integral. The theorem is proved that formulates necessary conditions of optimality for the mentioned problem, conditions which in certain cases are also sufficient.

Ananyev, B. I.

2013-12-01

109

First and Second Order Necessary Conditions for Stochastic Optimal Control Problems  

SciTech Connect

In this work we consider a stochastic optimal control problem with either convex control constraints or finitely many equality and inequality constraints over the final state. Using the variational approach, we are able to obtain first and second order expansions for the state and cost function, around a local minimum. This fact allows us to prove general first order necessary condition and, under a geometrical assumption over the constraint set, second order necessary conditions are also established. We end by giving second order optimality conditions for problems with constraints on expectations of the final state.

Bonnans, J. Frederic, E-mail: Frederic.Bonnans@inria.fr [Ecole Polytechnique, INRIA-Saclay and CMAP (France); Silva, Francisco J., E-mail: fsilva@mat.uniroma1.it [Dipartimento di Matematica Guido Castelnuovo (Italy)

2012-06-15

110

Pseudospectral method for hydropower optimal control problem  

NASA Astrophysics Data System (ADS)

Optimal control is a mathematical optimization problem and optimal control problems seek optimal control design subjective to a system of differential equations. Because of the nonlinearity of problems, it is hard to derive the analytic solutions for optimal control problem. Hence, the research uses an efficient numerical method, pseudospectral method, to solve complex optimal control problem. The design of the algorithm is based on using the pseudo-spectral differentiation matrix to reduce a high-dimensional function to low-dimensional functions, and the low-dimensional functions are more possible to solve difficult optimization problems. The reservoirs generate electricity constantly is built on the basis of steady inflow, but Taiwan's reservoirs unable to provide a stable amount of water. So designing a mathematical model of optimal control is used to deploy water distribution ratio for hydropower of wet and dry seasons. Because of the hydrological and geographical conditions in water resources systems in Taiwan, unstable water flow is hard to provide steady hydropower generation. An optimal control problem of hydropower generation is formulated for water resources system. A case study of Taiwanese water resources system is conducted. This study use monthly rainfall and output hydropower data to analysis the maximum hydropower with steady outflow. The results show the optimal control of water management and hydropower generation.

Lee, T.

2013-12-01

111

Social Emotional Optimization Algorithm for Nonlinear Constrained Optimization Problems  

NASA Astrophysics Data System (ADS)

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.

Xu, Yuechun; Cui, Zhihua; Zeng, Jianchao

112

Convex drawings of graphs with non-convex boundary constraints  

Microsoft Academic Search

In this paper, we study a new problem of convex drawing of planar graphs with non-convex boundary constraints. It is proved that every triconnected plane graph whose boundary is fixed with a star-shaped polygon admits a drawing in which every inner facial cycle is drawn as a convex polygon. We also prove that every four-connected plane graph whose boundary is

Seok-hee Hong; Hiroshi Nagamochi

2008-01-01

113

A Path Following Algorithm for the Graph Matching Problem  

Microsoft Academic Search

We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices.

Mikhail Zaslavskiy; Francis R. Bach; Jean-philippe Vert

2009-01-01

114

Multiobjective Particle Swarm Optimization for Optimal Power Flow Problem  

Microsoft Academic Search

\\u000a A novel approach to multiobjective particle swarm optimization (MOPSO) technique for solving optimal power flow (OPF) problem\\u000a is proposed in this chapter. The new MOPSO technique evolves a multiobjective version of PSO by proposing redefinition of\\u000a global best and local best individuals in multiobjective optimization domain. A clustering algorithm to manage the size of\\u000a the Pareto-optimal set is imposed. The

M. A. Abido

115

Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives  

Microsoft Academic Search

Although there is no universally accepted solution concept for decision problems with multiple noncommensurable objectives, one would agree that agood solution must not be dominated by the other feasible alternatives. Here, we propose a structure of domination over the objective space and explore the geometry of the set of all nondominated solutions. Two methods for locating the set of all

P. L. Yu

1974-01-01

116

Large Scale Computational Problems in Numerical Optimization  

SciTech Connect

Our work under this support broadly falls into five categories: automatic differentiation, sparsity, constraints, parallel computation, and applications. Automatic Differentiation (AD): We developed strong practical methods for computing sparse Jacobian and Hessian matrices which arise frequently in large scale optimization problems [10,35]. In addition, we developed a novel view of "structure" in applied problems along with AD techniques that allowed for the efficient application of sparse AD techniques to dense, but structured, problems. Our AD work included development of freely available MATLAB AD software. Sparsity: We developed new effective and practical techniques for exploiting sparsity when solving a variety of optimization problems. These problems include: bound constrained problems, robust regression problems, the null space problem, and sparse orthogonal factorization. Our sparsity work included development of freely available and published software [38,39]. Constraints: Effectively handling constraints in large scale optimization remains a challenge. We developed a number of new approaches to constrained problems with emphasis on trust region methodologies. Parallel Computation: Our work included the development of specifically parallel techniques for the linear algebra tasks underpinning optimization algorithms. Our work contributed to the nonlinear least-squares problem, nonlinear equations, triangular systems, orthogonalization, and linear programming. Applications: Our optimization work is broadly applicable across numerous application domains. Nevertheless we have specifically worked in several application areas including molecular conformation, molecular energy minimization, computational finance, and bone remodeling.

coleman, thomas f. [cornell university] [cornell university

2000-07-01

117

An evolutionary approach to combinatorial optimization problems  

Microsoft Academic Search

The paper reports on the application of genetic algorithms, probabilistic search algorithms based on the model of organic evolution, to NP-complete combinatorial optimization problems. In particular, the subset sum, max- imum cut, and minimum tardy task problems are considered. Except for the fitness function, no problem-specific changes of the genetic algorithm are required in order to achieve res- ults of

Sami Khuri; Thomas Bäck; Jörg Heitkötter

1994-01-01

118

Scalable multi-objective optimization test problems  

Microsoft Academic Search

After adequately demonstrating the ability to solve different two-objective optimization problems, multi-objective evolutionary algorithms (MOEAs) must show their efficacy in handling problems having more than two objectives. In this paper, we suggest three different approaches for systematically designing test problems for this purpose. The simplicity of construction, scalability to any number of decision variables and objectives, knowledge of exact shape

Kalyanmoy Deb; Lothar Thiele; Marco Laumanns; Eckart Zitzler

2002-01-01

119

Scalable Test Problems for Evolutionary Multiobjective Optimization  

Microsoft Academic Search

After adequately demonstrating the ability to solve different two-objective optimization problems, multiobjective evolutionary algorithms (MOEAs) must demonstrate their efficacy in handling problems having more than two objectives. In this study, we have suggested three different approaches for systematically designing test problems for this purpose. The simplicity of construction, scalability to any number of decision variables and objectives, knowledge of the

Kalyanmoy Deb; Lothar Thiele; Marco Laumanns; Eckart Zitzler

120

Optimal design, inverse problems and parallel computers  

Microsoft Academic Search

Speed has always been a problem in the application of inverse problem methodology in optimal design. This is largely due to the time-consuming operations involved in the computation of gradients with respect to the many parameters. With the advent of parallel computers, this is no longer a problem. The conjugate gradient and Cholesky factorization solution procedures for the computation of

S. R. H. Hoole

1991-01-01

121

A Convex Guidance Algorithm for Formation Reconfiguration  

NASA Technical Reports Server (NTRS)

In this paper, a reconfiguration guidance algorithm for formation flying spacecraft is presented. The formation reconfiguration guidance problem is first formulated as a continuous-time minimum-fuel or minimum-energy optimal control problem with collision avoidance and control constraints. The optimal control problem is then discretized to obtain a finite dimensional parameter optimization problem. In this formulation, the collision avoidance constraints are imposed via separating planes between each pair of spacecraft. A heuristic is introduced to choose these separating planes that leads to the convexification of the collision avoidance constraints. Additionally, convex constraints are imposed to guarantee that no collisions occur between discrete time samples. The resulting finite dimensional optimization problem is a second order cone program, for which standard algorithms can compute the global optimum with deterministic convergence and a prescribed level of accuracy. Consequently, the formation reconfiguration algorithm can be implemented onboard a spacecraft for real-time operations.

Acikmese, A. Behcet; Schar, Daniel P.; Murray, Emmanuell A.; Hadaeghs, Fred Y.

2006-01-01

122

Automatic segmentation for brain MR images via a convex optimized segmentation and bias field correction coupled model.  

PubMed

Accurate segmentation of magnetic resonance (MR) images remains challenging mainly due to the intensity inhomogeneity, which is also commonly known as bias field. Recently active contour models with geometric information constraint have been applied, however, most of them deal with the bias field by using a necessary pre-processing step before segmentation of MR data. This paper presents a novel automatic variational method, which can segment brain MR images meanwhile correcting the bias field when segmenting images with high intensity inhomogeneities. We first define a function for clustering the image pixels in a smaller neighborhood. The cluster centers in this objective function have a multiplicative factor that estimates the bias within the neighborhood. In order to reduce the effect of the noise, the local intensity variations are described by the Gaussian distributions with different means and variances. Then, the objective functions are integrated over the entire domain. In order to obtain the global optimal and make the results independent of the initialization of the algorithm, we reconstructed the energy function to be convex and calculated it by using the Split Bregman theory. A salient advantage of our method is that its result is independent of initialization, which allows robust and fully automated application. Our method is able to estimate the bias of quite general profiles, even in 7T MR images. Moreover, our model can also distinguish regions with similar intensity distribution with different variances. The proposed method has been rigorously validated with images acquired on variety of imaging modalities with promising results. PMID:24832358

Chen, Yunjie; Zhao, Bo; Zhang, Jianwei; Zheng, Yuhui

2014-09-01

123

Coordination and control of distributed spacecraft systems using convex optimization techniques  

Microsoft Academic Search

SUMMARY Formation flying of multiple spacecraft is an enabling technology for many future space science missions. However, the co-ordination and control of these instruments poses many difficult design challenges. This paper presents fuel\\/time-optimal control algorithms for a co-ordination and control architecture that was designed for a fleet of spacecraft. This architecture includes low-level formation-keeping algorithms and a high-level fleet planner

Michael Tillerson; Gokhan Inalhan; Jonathan P. How

2002-01-01

124

Heterogeneous Sensor Networks with convex constraints  

NASA Astrophysics Data System (ADS)

A wireless sensor network design is always subject to constraints. There are constraints on bandwidth, cost, detection robustness, and even false alarm rates to name but a few. This paper studies the design of Heterogeneous Sensor Networks (HSN) performing distributed binary hypothesis testing subject to convex constraints on the total number and types of sensors available. The relationship between real world engineering constraints and a resultant convex set or solution space will be highlighted. Under these convex sets, a theorem will be presented that defines when a homogenous sensor network will have better performance than a HSN. This theorem depends on stationary statistics, which is not the case for most problems of interest. These challenges are explored in detail for a parallel distributed HSN using the Kullback-Leibler (K-L) information number (K-L Divergence) in conjunction with the Chernoff-Stein Lemma. This method allows sensor counts to be optimized across a finite set of hypothesis or events, enabling a robust hypothesis testing solution similar to problems in traditional multiple hypothesis testing or classification problem. This paper also compares and contrast the detection performance of the standard parallel distributed HSN topology and a modified binary relay tree topology that is similar to clustering methods, where the final fusion is done using a logical OR rule. Finally, the asymptotic performance between these two topologies is studied, including the performance relative to optimal bounds. Ultimately providing a methodology to broadly analyze and optimize HSN design.

Rogers, U.; Chen, Hao

125

A compendium of NP optimization problems  

Microsoft Academic Search

ess, we are interestedin studying a class of optimization problems whose feasible solutions are short and easy-torecognize.To this aim, suitable constraints have to be introduced. We thus give the followingdefinition.Definition 1. An NP optimization problem A is a fourtuple (I ; sol; m; goal) such that1. I is the set of the instances of A and it is recognizable in

Pierluigi Crescenzi; Viggo Kann

1994-01-01

126

A bilevel dynamic signal timing optimization problem  

Microsoft Academic Search

This paper formulates the dynamic signal timing optimization (DSTO) problem as a bilevel model. In the upper level, total network travel time is minimized subject to some necessary signalisation constraints. In the lower level, the dynamic user-optimal route choice is formulated as a variational inequality model, which complies with the dynamic extension of Wardrop's first principle. The sensitivity analysis using

Huey-Kuo Chen; Cheng-Yi Chou; Chieh-Tsun Lai

2004-01-01

127

Prox-Method with Rate of Convergence O(1\\/t) for Variational Inequalities with Lipschitz Continuous Monotone Operators and Smooth Convex-Concave Saddle Point Problems  

Microsoft Academic Search

We propose a prox-type method with e-ciency estimate O(†¡1) for approximating saddle points of convex-concave C1;1 functions and solutions of variational inequalities with monotone Lipschitz continuous operators. Application examples include matrix games, eigenvalue minimization and computing Lovasz capacity number of a graph and are illustrated by numerical experiments with large-scale matrix games and Lovasz capacity problems.

Arkadi Nemirovski

2004-01-01

128

Particle swarm optimization for task assignment problem  

Microsoft Academic Search

Task assignment is one of the core steps to effectively exploit the capabilities of distributed or parallel computing systems. The task assignment problem is an NP-complete problem. In this paper, we present a new task assignment algorithm that is based on the principles of particle swarm optimization (PSO). PSO follows a collaborative population-based search, which models over the social behavior

Ayed Salman; Imtiaz Ahmad; Sabah Al-madani

2002-01-01

129

Cubes convexes  

Microsoft Academic Search

In various approaches, data cubes are pre-computed in order to answer efficiently OLAP queries. The notion of data cube has been declined in various ways: iceberg cubes, range cubes or differential cubes. In this paper, we introduce the concept of convex cube which captures all the tuples of a datacube satisfying a constraint combination. It can be represented in a

Sebastien Nedjar; Alain Casali; Rosine Cicchetti; Lotfi Lakhal

2010-01-01

130

Stochastic Linear Quadratic Optimal Control Problems  

SciTech Connect

This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well.

Chen, S. [Department of Mathematics, Zhejiang University, Hangzhou 310027 (China); Yong, J. [Laboratory of Mathematics for Nonlinear Sciences, Department of Mathematics, and Institute of Mathematical Finance, Fudan University, Shanghai 200433 (China)

2001-07-01

131

Minimizing the Moreau Envelope of Nonsmooth Convex Functions over the Fixed Point Set of Certain Quasi-Nonexpansive Mappings  

Microsoft Academic Search

\\u000a The first aim of this paper is to present a useful toolbox of quasi-nonexpansive mappings for convex optimization from the\\u000a viewpoint of using their fixed point sets as constraints. Many convex optimization problems have been solved through elegant\\u000a translations into fixed point problems. The underlying principle is to operate a certain quasi-nonexpansive mapping T iteratively and generate a convergent sequence

Isao Yamada; Masahiro Yukawa; Masao Yamagishi

132

Interior-point methods for convex programming  

Microsoft Academic Search

This work is concerned with generalized convex programming problems, where the objective function and also the constraints belong to a certain class of convex functions. It examines the relationship of two basic conditions used in interior-point methods for generalized convex programming—self-concordance and a relative Lipschitz condition—and gives a short and simple complexity analysis of an interior-point method for generalized convex

Florian Jarre

1992-01-01

133

Cubes convexes  

Microsoft Academic Search

In various approaches, data cubes are pre-computed in order to answer\\u000aefficiently OLAP queries. The notion of data cube has been declined in various\\u000aways: iceberg cubes, range cubes or differential cubes. In this paper, we\\u000aintroduce the concept of convex cube which captures all the tuples of a\\u000adatacube satisfying a constraint combination. It can be represented in a

Sébastien Nedjar; Alain Casali; Rosine Cicchetti; Lotfi Lakhal

2006-01-01

134

The inverse problem of the optimal regulator.  

NASA Technical Reports Server (NTRS)

The inverse problem of the optimal regulator is considered for a general class of multi-input systems with integral-type performance indices. A new phase variable canonical form is shown to be convenient for this analysis. The advantage of the canonical form is to separate the state variables into subvectors of directly controlled, indirectly controlled, and uncontrollable components. Necessary and sufficient conditions for optimized performance indices are given. With the nonlinearities of the system restricted to functions of the directly controlled state variables, additional results are developed about the nonnegative property of optimized loss functions.

Yokoyama, R.; Kinnen, E.

1972-01-01

135

Problem size, parallel architecture and optimal speedup  

NASA Technical Reports Server (NTRS)

The communication and synchronization overhead inherent in parallel processing can lead to situations where adding processors to the solution method actually increases execution time. Problem type, problem size, and architecture type all affect the optimal number of processors to employ. The numerical solution of an elliptic partial differential equation is examined in order to study the relationship between problem size and architecture. The equation's domain is discretized into n sup 2 grid points which are divided into partitions and mapped onto the individual processor memories. The relationships between grid size, stencil type, partitioning strategy, processor execution time, and communication network type are analytically quantified. In so doing, the optimal number of processors was determined to assign to the solution, and identified (1) the smallest grid size which fully benefits from using all available processors, (2) the leverage on performance given by increasing processor speed or communication network speed, and (3) the suitability of various architectures for large numerical problems.

Nicol, David M.; Willard, Frank H.

1987-01-01

136

Problem size, parallel architecture, and optimal speedup  

NASA Technical Reports Server (NTRS)

The communication and synchronization overhead inherent in parallel processing can lead to situations where adding processors to the solution method actually increases execution time. Problem type, problem size, and architecture type all affect the optimal number of processors to employ. The numerical solution of an elliptic partial differential equation is examined in order to study the relationship between problem size and architecture. The equation's domain is discretized into n sup 2 grid points which are divided into partitions and mapped onto the individual processor memories. The relationships between grid size, stencil type, partitioning strategy, processor execution time, and communication network type are analytically quantified. In so doing, the optimal number of processors was determined to assign to the solution, and identified (1) the smallest grid size which fully benefits from using all available processors, (2) the leverage on performance given by increasing processor speed or communication network speed, and (3) the suitability of various architectures for large numerical problems.

Nicol, David M.; Willard, Frank H.

1988-01-01

137

On the linear optimal digital servo problem  

NASA Technical Reports Server (NTRS)

For linear time-invariant digital systems, convergence of the Riccati equation associated with the optimal servo problem is examined. Necessary and sufficient conditions are established for the existence of finite gains when the command input trajectories may fail to be asymptotically stable.

Armstrong, E. S.

1974-01-01

138

Mathematical Optimization for Engineering Design Problems  

NASA Astrophysics Data System (ADS)

Applications in engineering design and the material sciences motivate the development of optimization theory in a manner that additionally draws from other branches of mathematics including the functional, complex, and numerical analyses. The first contribution, motivated by an automotive design application, extends multiobjective optimization theory under the assumption that the problem information is not available in its entirety to a single decision maker as traditionally assumed in the multiobjective optimization literature. Rather, the problem information and the design control are distributed among different decision makers. This requirement appears in the design of an automotive system whose subsystem components themselves correspond to highly involved design subproblems each of whose performance is measured by multiple criteria. This leads to a system/subsystem interaction requiring a coordination whose algorithmic foundation is developed and rigorously examined mathematically. The second contribution develops and analyzes a parameter estimation approach motivated from a time domain modeling problem in the material sciences. In addition to drawing from the theory of least-squares optimization and numerical analysis, the development of a mathematical foundation for comparing a baseline parameter estimation approach with an alternative parameter estimation approach relies on theory from both the functional and complex analyses. The application of the developed theory and algorithms associated with both contributions is also discussed.

Dandurand, Brian C.

139

Application of the two-dimensional differential transform method to heat conduction problem for heat transfer in longitudinal rectangular and convex parabolic fins  

NASA Astrophysics Data System (ADS)

In this article, approximate analytical (series) solutions for the temperature distribution in a longitudinal rectangular and convex parabolic fins with temperature dependent thermal conductivity and heat transfer coefficient are derived. The transient heat conduction problem is solved for the first time using the two-dimensional differential transform method (2D DTM). The effects of some physical parameters such as the thermo-geometric parameter, exponent and thermal conductivity gradient on temperature distribution are studied. Furthermore, we study the temperature profile at the fin tip.

Ndlovu, Partner L.; Moitsheki, Raseelo J.

2013-10-01

140

Evolutionary strategies for solving optimization problems  

NASA Astrophysics Data System (ADS)

We will give a survey of applications of thermodynamically and biologically oriented evolutionary strategies for optimization problems. Primarily, we investigate the solution of discrete optimization problems, most of combinatorial type, using a certain class of coupled differential equations. The problem is to find the minimum on a large set of real numbers (the potential) Ui, defined on the integer set i = 1 ...s, where s is an extremely large nu mber. The stationary states of the system correspond to relative optima on the discrete set. First, several elementary evolutionary strategies are described by simple deterministic equations, leading to a high-dimensional system of coupled differential equations. The known equations for thermodynamic search processes and for simple models of biological evolution are unified by defining a two-parameter family of equations which embed both cases. The unified equations model mixed Boltzmann/Darwin- strategies including basic elements of thermodynamical and biological evolution as well. In a next step a master equation model in the occupation number space is defined. We investigate the transition probabilities and the convergence properties using tools from the theory of stochastic processes. Several examples are analyzed. In particular we study the optimization of theoretical model sequences with simple valuation rules. In order to demonstrate that the strategies developed here may also be used to investigate realistic problems we present an example application to RNA folding (search for a minimum free energy configuration).

Ebeling, Werner; Reimann, Axel; Molgedey, Lutz

141

Multiview Stereo and Silhouette Consistency via Convex Functionals over Convex Domains  

Microsoft Academic Search

We propose a convex formulation for silhouette and stereo fusion in 3D reconstruction from multiple images. The key idea is to show that the reconstruction problem can be cast as one of minimizing a convex functional, where the exact silhouette consistency is imposed as convex constraints that restrict the domain of feasible functions. As a consequence, we can retain the

Daniel Cremers; Kalin Kolev

2011-01-01

142

Pattern Search Algorithms for Mixed Variable General Constrained Optimization Problems.  

National Technical Information Service (NTIS)

A new class of algorithms for solving nonlinearly constrained mixed variable optimization problems is presented The Audet-Dennis Generalized Pattern Search (GPS) algorithm for bound constrained mixed variable optimization problems is extended to problems ...

M. A. Abramson

2002-01-01

143

Interaction prediction optimization in multidisciplinary design optimization problems.  

PubMed

The distributed strategy of Collaborative Optimization (CO) is suitable for large-scale engineering systems. However, it is hard for CO to converge when there is a high level coupled dimension. Furthermore, the discipline objectives cannot be considered in each discipline optimization problem. In this paper, one large-scale systems control strategy, the interaction prediction method (IPM), is introduced to enhance CO. IPM is utilized for controlling subsystems and coordinating the produce process in large-scale systems originally. We combine the strategy of IPM with CO and propose the Interaction Prediction Optimization (IPO) method to solve MDO problems. As a hierarchical strategy, there are a system level and a subsystem level in IPO. The interaction design variables (including shared design variables and linking design variables) are operated at the system level and assigned to the subsystem level as design parameters. Each discipline objective is considered and optimized at the subsystem level simultaneously. The values of design variables are transported between system level and subsystem level. The compatibility constraints are replaced with the enhanced compatibility constraints to reduce the dimension of design variables in compatibility constraints. Two examples are presented to show the potential application of IPO for MDO. PMID:24744685

Meng, Debiao; Zhang, Xiaoling; Huang, Hong-Zhong; Wang, Zhonglai; Xu, Huanwei

2014-01-01

144

A Reduction Technique for Natural Gas Transmission Network Optimization Problems  

Microsoft Academic Search

We address the problem of minimizing the fuel consumption incurred by compressor stations in steady-state natural gas transmission networks. In the practical world, these type of instances are very large, in terms of the number of decision variables and the number of constraints, and very complex due to the presence of non-linearity and non-convexity in both the set of feasible

Roger Z. Ríos-mercado; Suming Wu; L. Ridgway Scott; E. Andrew Boyd

2002-01-01

145

On domains of convergence in optimization problems  

NASA Technical Reports Server (NTRS)

Numerical optimization algorithms require the knowledge of an initial set of design variables. Starting from an initial design x(sup 0), improved solutions are obtained by updating the design iteratively in a way prescribed by the particular algorithm used. If the algorithm is successful, convergence is achieved to a local optimal solution. Let A denote the iterative procedure that characterizes a typical optimization algorithm, applied to the problem: Find x belonging to R(sup n) that maximizes f(x) subject to x belonging to Omega contained in R(sup n). We are interested in problems with several local maxima (x(sub j))(sup *), j=1, ..., m, in the feasible design space Omega. In general, convergence of the algorithm A to a specific solution (x(sub j))(sup *) is determined by the choice of initial design x(sup 0). The domain of convergence D(sub j) of A associated with a local maximum (x(sub j))(sup *) is a subset of initial designs x(sup 0) in Omega such that the sequence (x(sup k)), k=0,1,2,... defined by x(sup k+1) = A(x(sup k)), k=0,1,... converges to (x(sub j))(sup *). The set D(sub j) is also called the basin of attraction of (x(sub j))(sup *). Cayley first proposed the problem of finding the basin of attraction for Newton's method in 1897. It has been shown that the basin of attraction for Newton's method exhibits chaotic behavior in problems with polynomial objective. This implies that there may be regions in the feasible design space where arbitrarily close starting points will converge to different local optimal solutions. Furthermore, the boundaries of the domains of convergence may have a very complex, even fractal structure. In this paper we show that even simple structural optimization problems solved using standard gradient based (first order) algorithms exhibit similar features.

Diaz, Alejandro R.; Shaw, Steven S.; Pan, Jian

1990-01-01

146

Dynamic multiobjective optimization problems: test cases, approximations, and applications  

Microsoft Academic Search

Abstract—After demonstrating adequately the usefulness of evolutionary multiobjective optimization (EMO) algorithms in finding multiple Pareto-optimal solutions for static multiobjective optimization problems, there is now a growing need for solving dy- namic multiobjective optimization problems in a similar manner. In this paper, we focus on addressing this issue by developing a number of test problems and by suggesting a baseline algorithm.

Marco Farina; Kalyanmoy Deb; Paolo Amato

2004-01-01

147

Stochastic Depletion Problems: Effective Myopic Policies for a Class of Dynamic Optimization Problems  

Microsoft Academic Search

This paper presents a general class of dynamic stochastic optimization problems we refer to as Stochastic Depletion Problems. A number of challenging dynamic optimization problems of practical interest are stochastic depletion problems. Optimal solutions for such problems are difficult to obtain, both from a pragmatic computational perspective as also from a theoretical perspective. As such, simple heuristics are highly desirable.

Carri W. Chan; Vivek F. Farias

2009-01-01

148

Hybrid intelligent optimization methods for engineering problems  

NASA Astrophysics Data System (ADS)

The purpose of optimization is to obtain the best solution under certain conditions. There are numerous optimization methods because different problems need different solution methodologies; therefore, it is difficult to construct patterns. Also mathematical modeling of a natural phenomenon is almost based on differentials. Differential equations are constructed with relative increments among the factors related to yield. Therefore, the gradients of these increments are essential to search the yield space. However, the landscape of yield is not a simple one and mostly multi-modal. Another issue is differentiability. Engineering design problems are usually nonlinear and they sometimes exhibit discontinuous derivatives for the objective and constraint functions. Due to these difficulties, non-gradient-based algorithms have become more popular in recent decades. Genetic algorithms (GA) and particle swarm optimization (PSO) algorithms are popular, non-gradient based algorithms. Both are population-based search algorithms and have multiple points for initiation. A significant difference from a gradient-based method is the nature of the search methodologies. For example, randomness is essential for the search in GA or PSO. Hence, they are also called stochastic optimization methods. These algorithms are simple, robust, and have high fidelity. However, they suffer from similar defects, such as, premature convergence, less accuracy, or large computational time. The premature convergence is sometimes inevitable due to the lack of diversity. As the generations of particles or individuals in the population evolve, they may lose their diversity and become similar to each other. To overcome this issue, we studied the diversity concept in GA and PSO algorithms. Diversity is essential for a healthy search, and mutations are the basic operators to provide the necessary variety within a population. After having a close scrutiny of the diversity concept based on qualification and quantification studies, we improved new mutation strategies and operators to provide beneficial diversity within the population. We called this new approach as multi-frequency vibrational GA or PSO. They were applied to different aeronautical engineering problems in order to study the efficiency of these new approaches. These implementations were: applications to selected benchmark test functions, inverse design of two-dimensional (2D) airfoil in subsonic flow, optimization of 2D airfoil in transonic flow, path planning problems of autonomous unmanned aerial vehicle (UAV) over a 3D terrain environment, 3D radar cross section minimization problem for a 3D air vehicle, and active flow control over a 2D airfoil. As demonstrated by these test cases, we observed that new algorithms outperform the current popular algorithms. The principal role of this multi-frequency approach was to determine which individuals or particles should be mutated, when they should be mutated, and which ones should be merged into the population. The new mutation operators, when combined with a mutation strategy and an artificial intelligent method, such as, neural networks or fuzzy logic process, they provided local and global diversities during the reproduction phases of the generations. Additionally, the new approach also introduced random and controlled diversity. Due to still being population-based techniques, these methods were as robust as the plain GA or PSO algorithms. Based on the results obtained, it was concluded that the variants of the present multi-frequency vibrational GA and PSO were efficient algorithms, since they successfully avoided all local optima within relatively short optimization cycles.

Pehlivanoglu, Yasin Volkan

149

AN ANALYSIS OF THE OPTIMIZATION FORMULATION OF ELASTIC INVERSE PROBLEMS  

Microsoft Academic Search

Inverse problems are often formulated as optimization problems. One seeks the parameter distribution which, when used in a forward model of the problem, gives the best match possible to the measured data. We consider the problem of imaging the elastic modulus distributions of soft tissues in this context. We consider in particular formulating this inverse problem as a constrained optimization

Carlos E. Rivas; Paul E. Barbone; Assad A. Oberai

2003-01-01

150

Nonlinear Optimization Problems in Atmospheric and Oceanic Sciences  

Microsoft Academic Search

A number of problems, arising from both theoretical research in atmospheric and oceanic sciences and numerical implementation of weather and climate prediction, can be formulated as nonlinear optimization problems (NOPs). Firstly the predictability problems in numerical prediction of weather and climate are investigated, of which three sub-problems are classified, and then reduced into nonlinear optimization problems. How to solve these

Mu Mu; Duan Wansuo; Wang Jiafeng

151

First-order convex feasibility algorithms for x-ray CT  

SciTech Connect

Purpose: Iterative image reconstruction (IIR) algorithms in computed tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the optimization problem on which it is based. Often times, however, it is impractical to achieve accurate solution to the optimization of interest, which complicates design of IIR algorithms. This issue is particularly acute for CT with a limited angular-range scan, which leads to poorly conditioned system matrices and difficult to solve optimization problems. In this paper, we develop IIR algorithms which solve a certain type of optimization called convex feasibility. The convex feasibility approach can provide alternatives to unconstrained optimization approaches and at the same time allow for rapidly convergent algorithms for their solution-thereby facilitating the IIR algorithm design process. Methods: An accelerated version of the Chambolle-Pock (CP) algorithm is adapted to various convex feasibility problems of potential interest to IIR in CT. One of the proposed problems is seen to be equivalent to least-squares minimization, and two other problems provide alternatives to penalized, least-squares minimization. Results: The accelerated CP algorithms are demonstrated on a simulation of circular fan-beam CT with a limited scanning arc of 144 Degree-Sign . The CP algorithms are seen in the empirical results to converge to the solution of their respective convex feasibility problems. Conclusions: Formulation of convex feasibility problems can provide a useful alternative to unconstrained optimization when designing IIR algorithms for CT. The approach is amenable to recent methods for accelerating first-order algorithms which may be particularly useful for CT with limited angular-range scanning. The present paper demonstrates the methodology, and future work will illustrate its utility in actual CT application.

Sidky, Emil Y.; Pan Xiaochuan [Department of Radiology, University of Chicago, 5841 South Maryland Avenue, Chicago, Illinois, 60637 (United States); Jorgensen, Jakob S. [Department of Applied Mathematics and Computer Science, Technical University of Denmark, Matematiktorvet, Building 303B, 2800 Kongens Lyngby (Denmark)

2013-03-15

152

Convexity Rule for Shape Decomposition Based on Discrete Contour Evolution  

Microsoft Academic Search

We concentrate here on decomposition of 2D objects into mean- ingful parts of visual form ,o rvisual parts. It is a simple observation that convex parts of objects determine visual parts. However, the problem is that many significant visual parts are not convex, since a visual part may have concavities. We solve this problem by identify- ing convex parts at

Longin Jan Latecki; Rolf Lakämper

1999-01-01

153

Robot Hand Grasping and Related Problems: Optimal Control and Identification  

Microsoft Academic Search

The optimal control problem related to the grasping of ob jects by multifingered grippers of robots is investigated. The Linear Complementarity Problem (LCP), which governs the static unilateral and frictional contact problem, is formulated, and certain propositions concerning necessary and sufficient conditions for its solution are proved. Next the optimal control problem is formulated and studied. Presented also is numeric

P. D. Panagiotopoulos; Ahmad M. Al-fahed Nuseirat

1994-01-01

154

Inverse Optimization: A Survey on Problems, Methods, and Results  

Microsoft Academic Search

Given a (combinatorial) optimization problem and a feasible solution to it, the correspondinginverse optimization problem is to nd a minimal adjustment of the parameters of theproblem (costs, capacities, . . . ) such that the given solution becomes optimum.Several such problems have been studied in the last ten years. After formalizing the notionof an inverse problem and its variants, we

Clemens Heuberger

2003-01-01

155

Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results  

Microsoft Academic Search

Given a (combinatorial) optimization problem and a feasible solution to it, the correspond- ing inverse optimization problem is to nd a minimal adjustment of the cost function such that the given solution becomes optimum. Several such problems have been studied in the last ten years. After formalizing the notion of an inverse problem and its variants, we present various methods

Clemens Heuberger

2004-01-01

156

Analysis, estimation and controller design of parameter-dependent systems using convex optimization based on linear matrix inequalities  

NASA Astrophysics Data System (ADS)

In this thesis, we outline three contributions in robust control. The first is the efficient computation of a lower bound on the robust stability margin (RSM) of uncertain systems. A lower bound on the RSM can be derived using the framework of integral quadratic constraints (IQCs). Current techniques for numerically computing this lower bound use a bisection scheme. We show how this bisection can be avoided altogether by reformulating the lower bound computation problem as a single generalized eigenvalue minimization problem, which can be solved very efficiently using standard algorithms. For the second contribution, we focus on linear systems affected by parametric uncertainties. For these systems, we present sufficient conditions for robust stability. We also derive conditions for the existence of a robustly stabilizing gain-scheduled controller when the system has time-varying parametric uncertainties that can be measured in real time. Our approach is proven to be in general less conservative than existing methods. Our third contribution is on the robust estimation of systems having parametric uncertainties. For systems with mixed deterministic and stochastic uncertainties, we design two optimized steady state filters: (i) the first filter minimizes an upper bound on the worst-case gain in the mean energy between the noise affecting the system and the estimation error; (ii) the second filter minimizes an upper bound on the worst-case asymptotic mean square estimation error when the plant is driven by a white noise process. For time-varying systems with stochastic uncertainties, we derive a robust adaptive Kalman filtering algorithm. This algorithm offers considerable improvement in performance when compared to the standard Kalman filtering techniques. We demonstrate the performance of these robust filters on numerical examples consisting of the design of equalizers for communication channels.

Wang, Fan

157

A convex quadratic semi-definite programming approach to the partial additive constant problem in multidimensional scaling  

Microsoft Academic Search

Bénasséni [Partial additive constant, J. Statist. Comput. Simul. 49 (1994), pp. 179–193] studied the partial additive constant problem in multidimensional scaling. This problem is quite challenging to solve, and Bénasséni proposed a numerical procedure for two special cases: the cross-set partial perturbation and the within-set partial perturbation. This paper casts the problem as a modern quadratic semi-definite programming (QSDP) problem,

Houduo Qi; Naihua Xiu

2012-01-01

158

A convex quadratic semi-definite programming approach to the partial additive constant problem in multidimensional scaling  

Microsoft Academic Search

Bénasséni [Partial additive constant, J. Statist. Comput. Simul. 49 (1994), pp. 179–193] studied the partial additive constant problem in multidimensional scaling. This problem is quite challenging to solve, and Bénasséni proposed a numerical procedure for two special cases: the cross-set partial perturbation and the within-set partial perturbation. This paper casts the problem as a modern quadratic semi-definite programming (QSDP) problem,

Houduo Qi; Naihua Xiu

2011-01-01

159

Mesh refinement strategy for optimal control problems  

NASA Astrophysics Data System (ADS)

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

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

2013-10-01

160

Equal Area Polygons in Convex Bodies  

Microsoft Academic Search

In this paper, we consider the problem of packing two or more equal area polygons with disjoint interiors into a convex body K in E2 such that each of them has at most a given number of sides. We show that for a convex quadrilateral K of area 1, there exist n internally disjoint triangles of equal area such that

Toshinori Sakai; Chie Nara; Jorge Urrutia

2003-01-01

161

Linearithmic time sparse and convex maximum margin clustering.  

PubMed

Recently, a new clustering method called maximum margin clustering (MMC) was proposed and has shown promising performances. It was originally formulated as a difficult nonconvex integer problem. To make the MMC problem practical, the researchers either relaxed the original MMC problem to inefficient convex optimization problems or reformulated it to nonconvex optimization problems, which sacrifice the convexity for efficiency. However, no approaches can both hold the convexity and be efficient. In this paper, a new linearithmic time sparse and convex MMC algorithm, called support-vector-regression-based MMC (SVR-MMC), is proposed. Generally, it first uses the SVR as the core of the MMC. Then, it is relaxed as a convex optimization problem, which is iteratively solved by the cutting-plane algorithm. Each cutting-plane subproblem is further decomposed to a serial supervised SVR problem by a new global extended-level method (GELM). Finally, each supervised SVR problem is solved in a linear time complexity by a new sparse-kernel SVR (SKSVR) algorithm. We further extend the SVR-MMC algorithm to the multiple-kernel clustering (MKC) problem and the multiclass MMC (M3C) problem, which are denoted as SVR-MKC and SVR-M3C, respectively. One key point of the algorithms is the utilization of the SVR. It can prevent the MMC and its extensions meeting an integer matrix programming problem. Another key point is the new SKSVR. It provides a linear time interface to the nonlinear kernel scenarios, so that the SVR-MMC and its extensions can keep a linearthmic time complexity in nonlinear kernel scenarios. Our experimental results on various real-world data sets demonstrate the effectiveness and the efficiency of the SVR-MMC and its two extensions. Moreover, the unsupervised application of the SVR-MKC to the voice activity detection (VAD) shows that the SVR-MKC can achieve good performances that are close to its supervised counterpart, meet the real-time demand of the VAD, and need no labeling for model training. PMID:22645273

Zhang, Xiao-Lei; Wu, Ji

2012-12-01

162

Optimal shape design as a material distribution problem  

Microsoft Academic Search

Shape optimization in a general setting requires the determination of the optimal spatial material distribution for given loads and boundary conditions. Every point in space is thus a material point or a void and the optimization problem is a discrete variable one. This paper describes various ways of removing this discrete nature of the problem by the introduction of a

M. P. Bendsøe

1989-01-01

163

An Alternative Approach to Inverse Planning Optimization: Applying the Projection Theorem to Concave and Convex PTVs for VMAT Delivery  

Microsoft Academic Search

We present an alternative technique for inverse planning optimization and apply it to volumetric modulated arc therapy (VMAT)\\u000a delivery in one rotation with a prior knowledge about the type of leaf motions. The optimization is based on the Projection\\u000a Theorem in inner product spaces. MLC motion is directly considered in the optimization, thus avoiding leaf segmentation. In\\u000a this work we

W. Hoegele; R. Loeschel; P. Zygmanski

164

The mathematics of eigenvalue optimization  

Microsoft Academic Search

Abstract: Optimization problems involving the eigenvalues of symmetric and nonsymmetricmatrices present a fascinating mathematical challenge. Such problems arise often in theoryand practice, particularly in engineering design, and are amenable to a rich blend of classicalmathematical techniques and contemporary optimization theory. This essay presents a personalchoice of some central mathematical ideas, outlined for the broad optimization community. Idiscuss the convex analysis

A. S. Lewis

2003-01-01

165

Cores of convex games  

Microsoft Academic Search

The core of ann-person game is the set of feasible outcomes that cannot be improved upon by any coalition of players. A convex game is defined as one that is based on a convex set function. In this paper it is shown that the core of a convex game is not empty and that it has an especially regular structure.

Lloyd S. Shapley

1971-01-01

166

LDRD Final Report: Global Optimization for Engineering Science Problems.  

National Technical Information Service (NTIS)

For a wide variety of scientific and engineering problems the desired solution corresponds to an optimal set of objective function parameters, where the objective function measures a solution's quality. The main goal of the LDRD 'Global Optimization for E...

Hart

1999-01-01

167

Convergence of pseudospectral discretizations of optimal control problems  

Microsoft Academic Search

A generic nonlinear optimal control problem with a Bolza cost functional is discretized by a Legendre pseudospectral method. According to the covector mapping theorem, the Karush-Kuhn-Tucker multipliers of the discrete problem map linearly to the spectrally discretized covectors of the Bolza problem. Using this result, it is shown that the nonlinear programming problem converges to the continuous Bolza problem at

I. Michael Ross; Fariba Fahroo

2001-01-01

168

Optimal structural design via optimality criteria as a nonsmooth mechanics problem  

Microsoft Academic Search

In the theory of plastic structural design via optimality criteria (due to W. Prager), the optimal design problem is transformed to a nonlinear elastic structural analysis problem with appropriate stress-strain laws, which generally include complete vertical branches. In this context, the concept of structural universe (in the sense of G. Rozvany) permits the treatment of complicated optimal layout problems. Recent

M. Ap. Tzaferopoulos; G. E. Stavroulakis

1995-01-01

169

Progress in design optimization using evolutionary algorithms for aerodynamic problems  

NASA Astrophysics Data System (ADS)

Evolutionary algorithms (EAs) are useful tools in design optimization. Due to their simplicity, ease of use, and suitability for multi-objective design optimization problems, EAs have been applied to design optimization problems from various areas. In this paper we review the recent progress in design optimization using evolutionary algorithms to solve real-world aerodynamic problems. Examples are given in the design of turbo pump, compressor, and micro-air vehicles. The paper covers the following topics that are deemed important to solve a large optimization problem from a practical viewpoint: (1) hybridized approaches to speed up the convergence rate of EAs; (2) the use of surrogate model to reduce the computational cost stemmed from EAs; (3) reliability based design optimization using EAs; and (4) data mining of Pareto-optimal solutions.

Lian, Yongsheng; Oyama, Akira; Liou, Meng-Sing

2010-07-01

170

Nonlinear Approach to a Class of Combinatorial Optimization Problems.  

National Technical Information Service (NTIS)

A special class of combinatorial optimization problems is considered. The authors develop a compact nonconvex quadratic model for these problems that incorporates all inequality constraints in the objective function, and discuss two algorithms for solving...

J. P. Warners

1996-01-01

171

Method of Solving the Isoperimetric Problem of Isotope Irradiation Optimization.  

National Technical Information Service (NTIS)

The algorithm of solving the reactor optimization problem with isoperimetric conditions is drawn. The problem is solved in terms of the iterative method directly using the maximum principle. The thermal and resonance neutron fluxes which ensure maximum yi...

A. I. Volovik

1977-01-01

172

Problems in large-scale structural optimization  

NASA Technical Reports Server (NTRS)

A general design optimization model for large complex systems is defined. Major features of the model that challenge various optimization algorithms are discussed. Requirements of a model optimization algorithm are identified. Objectives of the study of various algorithms are defined and a basis for conducting such a study is developed. Primal as well as transformation methods are analytically studied and a unified viewpoint of various methods is presented. Several numerical examples are solved using different methods to study their performance. Conclusions drawn from the study are presented and discussed. Areas of future research in nonlinear programming as well as structural optimization are identified and discussed.

Arora, J. S.; Belegundu, A. D.

1984-01-01

173

Weak Hamiltonian finite element method for optimal control problems  

NASA Technical Reports Server (NTRS)

A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

Hodges, Dewey H.; Bless, Robert R.

1991-01-01

174

A weak Hamiltonian finite element method for optimal control problems  

NASA Technical Reports Server (NTRS)

A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

Hodges, Dewey H.; Bless, Robert R.

1990-01-01

175

A weak Hamiltonian finite element method for optimal control problems  

NASA Technical Reports Server (NTRS)

A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.

Hodges, Dewey H.; Bless, Robert R.

1989-01-01

176

Difference of convex functions optimization algorithms (DCA) for globally minimizing nonconvex quadratic forms on Euclidean balls and spheres  

Microsoft Academic Search

We present DCA for globally minimizing quadratic forms on Euclidean balls and spheres. Since these problems admit at most one local-nonglobal minimizer, DCA converges in general to a solution for these problems. Numerical simulations show robustness, stability and efficiency of DCA with respect to related standard methods.

Pham Dinh Tao; Le Thi Hoai An

1996-01-01

177

Comparison of Optimal Design Methods in Inverse Problems  

PubMed Central

Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher Information Matrix (FIM). A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criteria with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model [13], the standard harmonic oscillator model [13] and a popular glucose regulation model [16, 19, 29].

Banks, H. T.; Holm, Kathleen; Kappel, Franz

2011-01-01

178

Application of Particle Swarm Optimization for Economic Load Dispatch Problems  

Microsoft Academic Search

This paper presents an efficient and reliable particle swarm optimization (PSO) method for the economic load dispatch (ELD) problems. The PSO method was developed through the simulation of a simplified social system and has been found to be robust in solving continuous nonlinear optimization problems in terms of accuracy of the solution and computation time and it can out perform

M. Sudhakaran; P. Ajay-D-Vimal Raj; T. G. Palanivelu

2007-01-01

179

It looks easy! Heuristics for combinatorial optimization problems  

Microsoft Academic Search

Human performance on instances of computationally intractable optimization problems, such as the travelling salesperson problem (TSP), can be excellent. We have proposed a boundary-following heuristic to account for this finding. We report three experiments with TSPs where the capacity to employ this heuristic was varied. In Experiment 1, participants free to use the heuristic produced solutions significantly closer to optimal

Edward P. Chronicle; James N. MacGregor; Thomas C. Ormerod; Alistair Burr

2006-01-01

180

On some geometric selection and optimization problems via sorted matrices  

Microsoft Academic Search

In this paper we apply the selection and optimization technique of Frederickson and Johnsonto a number of geometric selection and optimization problems, some of which have previouslybeen solved by parametric search, and provide efficient and simple algorithms. Our techniqueimproves the solutions obtained by parametric search by a log n factor. For example, we applythe technique to the two-line center problem,

Alex Glozman; Klara Kedem; Gregory Shpitalnik

1998-01-01

181

Multiobjective particle swarm optimization for environmental\\/economic dispatch problem  

Microsoft Academic Search

A new multiobjective particle swarm optimization (MOPSO) technique for environmental\\/economic dispatch (EED) problem is proposed in this paper. The proposed MOPSO technique evolves a multiobjective version of PSO by proposing redefinition of global best and local best individuals in multiobjective optimization domain. The proposed MOPSO technique has been implemented to solve the EED problem with competing and non-commensurable cost and

M. A. Abido

2009-01-01

182

Simulation Optimization for the Stochastic Economic Lot Scheduling Problem  

Microsoft Academic Search

Löhndorf and Minner Simulation Optimization for the SELSP We study simulation optimization methods for the stochastic economic lot scheduling problem. In contrast to prior research, we focus on methods that treat this problem as a black box. Based on a large-scale numerical study, we compare approximate dynamic programming with a global search for parameters of simple control policies. We propose

Nils Löhndorf; Stefan Minner

2012-01-01

183

Neurocomputing strategies for solving reliability-robust design optimization problems  

Microsoft Academic Search

Purpose – This paper, by taking randomness and uncertainty of structural systems into account aims to implement a combined reliability-based robust design optimization (RRDO) formulation. The random variables to be considered include the cross section dimensions, modulus of elasticity, yield stress, and applied loading. The RRDO problem is to be formulated as a multi-objective optimization problem where the construction cost

Nikos D. Lagaros; Vagelis Plevris; Manolis Papadrakakis

2010-01-01

184

Artificial Bee Colony (ABC) Optimization Algorithm for Solving Constrained Optimization Problems  

Microsoft Academic Search

This paper presents the comparison results on the performance of the Artificial Bee Colony (ABC) algorithm for constrained\\u000a optimization problems. The ABC algorithm has been firstly proposed for unconstrained optimization problems and showed that\\u000a it has superior performance on these kind of problems. In this paper, the ABC algorithm has been extended for solving constrained\\u000a optimization problems and applied to

Dervis Karaboga; Bahriye Basturk

2007-01-01

185

Execution of Multidisciplinary Design Optimization Approaches on Common Test Problems  

NASA Technical Reports Server (NTRS)

A class of synthetic problems for testing multidisciplinary design optimization (MDO) approaches is presented. These test problems are easy to reproduce because all functions are given as closed-form mathematical expressions. They are constructed in such a way that the optimal value of all variables and the objective is unity. The test problems involve three disciplines and allow the user to specify the number of design variables, state variables, coupling functions, design constraints, controlling design constraints, and the strength of coupling. Several MDO approaches were executed on two sample synthetic test problems. These approaches included single-level optimization approaches, collaborative optimization approaches, and concurrent subspace optimization approaches. Execution results are presented, and the robustness and efficiency of these approaches an evaluated for these sample problems.

Balling, R. J.; Wilkinson, C. A.

1997-01-01

186

CONVEX mini manual  

NASA Technical Reports Server (NTRS)

The use of the CONVEX computers that are an integral part of the Supercomputing Network Subsystems (SNS) of the Central Scientific Computing Complex of LaRC is briefly described. Features of the CONVEX computers that are significantly different than the CRAY supercomputers are covered, including: FORTRAN, C, architecture of the CONVEX computers, the CONVEX environment, batch job submittal, debugging, performance analysis, utilities unique to CONVEX, and documentation. This revision reflects the addition of the Applications Compiler and X-based debugger, CXdb. The document id intended for all CONVEX users as a ready reference to frequently asked questions and to more detailed information contained with the vendor manuals. It is appropriate for both the novice and the experienced user.

Tennille, Geoffrey M.; Howser, Lona M.

1993-01-01

187

Duality theory of the optimal two-block H ? problem  

Microsoft Academic Search

SUMMARY This paper provides the Banach duality theory structure of the optimal two-block H1 problem. Alignment conditions are obtained and show that the optimal solution is ?at or allpass in general, and unique in the SISO case. The optimal solution is shown to satisfy an extremal identity, which gives a necessary and su-cient condition for a controller to be optimal.

S. M. Djouadi; J. D. Birdwell

2008-01-01

188

Multi-Swarm Optimization for Dynamic Combinatorial Problems: A Case Study on Dynamic Vehicle Routing Problem  

Microsoft Academic Search

\\u000a Many combinatorial real-world problems are mostly dynamic. They are dynamic in the sense that the global optimum location\\u000a and its value change over the time, in contrast to static problems. The task of the optimization algorithm is to track this\\u000a shifting optimum. Particle Swarm Optimization (PSO) has been previously used to solve continuous dynamic optimization problems,\\u000a whereas only a few

Mostepha Redouane Khouadjia; Enrique Alba; Laetitia Jourdan; El-Ghazali Talbi

2010-01-01

189

Harmony search algorithm: application to the redundancy optimization problem  

Microsoft Academic Search

The redundancy optimization problem is a well known NP-hard problem which involves the selection of elements and redundancy levels to maximize system performance, given different system-level constraints. This article presents an efficient algorithm based on the harmony search algorithm (HSA) to solve this optimization problem. The HSA is a new nature-inspired algorithm which mimics the improvization process of music players.

Nabil Nahas; Dao Thien-My

2010-01-01

190

Constrained Test Problems for Multi-objective Evolutionary Optimization  

Microsoft Academic Search

Over the past few years, researchers have developed a number of multi-objective evolutionary algorithms (MOEAs). Although\\u000a most studies concentrated on solving unconstrained optimization problems, there exists a few studies where MOEAs have been\\u000a extended to solve constrained optimization problems. As the constraint handling MOEAs gets popular, there is a need for developing\\u000a test problems which can evaluate the algorithms well.

Kalyanmoy Deb; Amrit Pratap; T. Meyarivan

191

Approximating convex Pareto surfaces in multiobjective radiotherapy planning  

SciTech Connect

Radiotherapy planning involves inherent tradeoffs: the primary mission, to treat the tumor with a high, uniform dose, is in conflict with normal tissue sparing. We seek to understand these tradeoffs on a case-to-case basis, by computing for each patient a database of Pareto optimal plans. A treatment plan is Pareto optimal if there does not exist another plan which is better in every measurable dimension. The set of all such plans is called the Pareto optimal surface. This article presents an algorithm for computing well distributed points on the (convex) Pareto optimal surface of a multiobjective programming problem. The algorithm is applied to intensity-modulated radiation therapy inverse planning problems, and results of a prostate case and a skull base case are presented, in three and four dimensions, investigating tradeoffs between tumor coverage and critical organ sparing.

Craft, David L.; Halabi, Tarek F.; Shih, Helen A.; Bortfeld, Thomas R. [Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts 02114 (United States)

2006-09-15

192

Optimal bounds for the predecessor problem  

Microsoft Academic Search

We obtain matching upper and lower bounds for the amount of time to find the predecessor of a given element among the elements of a fixed efficiently stored set. Our algorithms are for the unit-cost word-level RAM with multiplication and ex- tend to give optimal dynamic algorithms. The lower bounds are proved in a much stronger communication game model, but

Paul Beame; Faith E. Ficht

1999-01-01

193

The Problem of Local Optimality with OSMOD.  

ERIC Educational Resources Information Center

A revision of the initialization strategy is suggested for OSMOD, a method of nonlinear principal component analysis for multivariate nominal and/or ordinal data. The revision is effective in diminishing the possibility of obtaining locally optimal solutions with categorical data provided by the original version of OSMOD. (SLD)

Otsu, Tatsuo; Saito, Takayuki

1990-01-01

194

Evolutionary structural optimization for dynamic problems  

Microsoft Academic Search

This paper presents a simple method for structural optimization with frequency constraints. The structure is modelled by a fine mesh of finite elements. At the end of each eigenvalue analysis, part of the material is removed from the structure so that the frequencies of the resulting structure will be shifted towards a desired direction. A sensitivity number indicating the optimum

Y. M. Xie; G. P. Steven

1996-01-01

195

Optimal control problems in public health  

Microsoft Academic Search

The health care delivery system in the United States is poorly planned to meet the growing needs of its population. This research establishes the foundations of developing decision-support tools in the emerging field of health care engineering, with special emphasis on public health. It demonstrates the potential of applying engineering methods, especially optimal control theory, to facilitate decision making in

Feng Lin

2010-01-01

196

Divergence of finite element formulations for inverse problems treated as optimization problems  

Microsoft Academic Search

Many inverse problems are formulated and solved as optimization problems. In this approach, the data mismatch between a predicted field and a measured field is minimized, subject to a constraint. The constraint represents the \\

Carlos Rivas; Paul Barbone; Assad Oberai

2008-01-01

197

TSP based Evolutionary optimization approach for the Vehicle Routing Problem  

Microsoft Academic Search

Vehicle Routing and Flexible Job Shop Scheduling Problems (VRP and FJSSP) are two common hard combinatorial optimization problems that show many similarities in their conceptual level [2, 4]. It was proved for both problems that solving techniques like exact methods fail to provide good quality solutions in a reasonable amount of time when dealing with large scale instances [1, 5,

Zoulel Kouki; Besma Fayech Chaar; Mekki Ksouri

2009-01-01

198

Optimizing multi-response surface problems: How to use multi-objective optimization techniques  

Microsoft Academic Search

A common problem encountered in product or process design is the selection of optimal parameter levels that involves the simultaneous consideration of multiple response characteristics, called a multi-response surface problem. Notwithstanding the importance of multi-response surface problems in practice, the development of an optimization scheme has received little attention. In this paper, we note that Multi-Response surface Optimization (MRO) can

KYUNG SAM PARK; KWANG-JAE KIM

2005-01-01

199

Spectral finite-element methods for parametric constrained optimization problems.  

SciTech Connect

We present a method to approximate the solution mapping of parametric constrained optimization problems. The approximation, which is of the spectral finite element type, is represented as a linear combination of orthogonal polynomials. Its coefficients are determined by solving an appropriate finite-dimensional constrained optimization problem. We show that, under certain conditions, the latter problem is solvable because it is feasible for a sufficiently large degree of the polynomial approximation and has an objective function with bounded level sets. In addition, the solutions of the finite-dimensional problems converge for an increasing degree of the polynomials considered, provided that the solutions exhibit a sufficiently large and uniform degree of smoothness. Our approach solves, in the case of optimization problems with uncertain parameters, the most computationally intensive part of stochastic finite-element approaches. We demonstrate that our framework is applicable to parametric eigenvalue problems.

Anitescu, M.; Mathematics and Computer Science

2009-01-01

200

Convex Graph Invariants.  

National Technical Information Service (NTIS)

The structural properties of graphs are usually characterized in terms of invariants, which are functions of graphs that do not depend on the labeling of the nodes. In this paper we study convex graph invariants, which are graph invariants that are convex...

A. S. Willsky P. A. Parrilo V. Chandrasekaran

2010-01-01

201

Optimization Problems in High-Speed Networks.  

National Technical Information Service (NTIS)

The main goal of this project is to develop fundamental algorithmic techniques that can be applied to problems that arise in the context of high- speed communication networks. The explosion in the size and complexity of networks, together with QoS require...

S. Plotkin

2002-01-01

202

Group Testing: Four Student Solutions to a Classic Optimization Problem  

ERIC Educational Resources Information Center

This article describes several creative solutions developed by calculus and modeling students to the classic optimization problem of testing in groups to find a small number of individuals who test positive in a large population.

Teague, Daniel

2006-01-01

203

Direct Multiple Shooting Optimization with Variable Problem Parameters  

NASA Technical Reports Server (NTRS)

Taking advantage of a novel approach to the design of the orbital transfer optimization problem and advanced non-linear programming algorithms, several optimal transfer trajectories are found for problems with and without known analytic solutions. This method treats the fixed known gravitational constants as optimization variables in order to reduce the need for an advanced initial guess. Complex periodic orbits are targeted with very simple guesses and the ability to find optimal transfers in spite of these bad guesses is successfully demonstrated. Impulsive transfers are considered for orbits in both the 2-body frame as well as the circular restricted three-body problem (CRTBP). The results with this new approach demonstrate the potential for increasing robustness for all types of orbit transfer problems.

Whitley, Ryan J.; Ocampo, Cesar A.

2009-01-01

204

Some asymptotic problems in the optimal control of distributed systems  

NASA Technical Reports Server (NTRS)

The optimal control of structures which consist of composite materials or of perforated materials is discussed. Asymptotic formula, derived from the so-called homogenization theory, are presented which allow the replacement of very complicated problems by much simpler ones.

Lions, J. L.

1985-01-01

205

A work-optimal CGM algorithm for the LIS problem  

Microsoft Academic Search

This paper presents a work-optimal CGM algorithm that solves the Longest Increasing Subsequence Problem. It can be implemented in the CGM with P processors in O(N2 ÷P) time and O(P) communication steps. It is the first CGM algorithm for this problem and it is work-optimal since the sequential algorithm has a complexity of O(N2).

Thierry Garcia; Myoupo Jean-Frédéric; David Semé

2001-01-01

206

Implementing Particle Swarm Optimization to Solve Economic Load Dispatch Problem  

Microsoft Academic Search

Economic Load Dispatch (ELD) is one of an important optimization tasks which provides an economic condition for a power systems. In this paper, Particle Swarm Optimization (PSO) as an effective and reliable evolutionary based approach has been proposed to solve the constraint economic load dispatch problem. The proposed method is able to determine, the output power generation for all of

Abolfazl Zaraki; Mohd Fauzi Bin Othman

2009-01-01

207

Hybrid Simplex-Harmony search method for optimization problems  

Microsoft Academic Search

This paper proposes the hybrid simplex algorithm (SA)-harmony search(HS) Method. HS method is, the evolutionary algorithm, conceptualized using the musical process of searching for optimization problems. SA helps HS find optimization solution more accurately and quickly. In this paper, the performances of proposed algorithm are compared with the original HS method and other algorithms through unconstrained functions and constrained functions.

Woo-seok Jang; Hwan-il Kang; Byung-hee Lee

2008-01-01

208

Optimal Policies for a Multi-Echelon Inventory Problem  

Microsoft Academic Search

In the last several years there have been a number of papers discussing optimal policies for the inventory problem. Almost without exception these papers are devoted to the determination of optimal purchasing quantities at a single installation faced with some pattern of demand. It has been customary to make the assumption that when the installation in question requests a shipment

Andrew J. Clark; Herbert Scarf

1960-01-01

209

An optimal distributed solution to the dining philosophers problem  

Microsoft Academic Search

An optimal distributed solution to the dining philosophers problem is presented. The solution is optimal in the sense that it incurs the least communication and computational overhead, and allows the maximum achievable concurrency. The worst case upper bound for concurrency is shown to ben div 3,n being the number of philosophers. There is no previous algorithm known to achieve this

S. P. Rana; D. K. Banerji

1986-01-01

210

Optimal distributed solution to the dining philosophers problem  

SciTech Connect

An optimal distributed solution to the dining philosophers problem is presented. The solution is optimal in the sense that it incurs the least communication and computational overhead, and allows the maximum achievable concurrency. The worst case upper bound for concurrency is shown to be n div 3, n being the number of philosophers. There is no previous algorithm known to achieve this bound.

Rana, S.P.; Banerji, D.K.

1986-08-01

211

On Some Geometric Selection and Optimization Problems via Sorted Matrices  

Microsoft Academic Search

In this paper we apply the selection and optimization technique of Fredrickson and Johnson to a number of geometric selection and optimization problems, some of which have previously been solved by parametric search, and provide efficient and simple algorithms. Our technique improves the solutions obtained by parametric search by a log n factor. For example, we apply the technique to

Alex Glozman; Klara Kedem; Gregory Shpitalnik

1995-01-01

212

Optimal Rendezvous Problem in a Central gravity Field with Drag.  

NASA Astrophysics Data System (ADS)

The work aims at solving the optimal feedback rendezvous problem for a spacecraft moving in a central field of gravity in addition experiencing air drag. We will use the generating function techneque to solve the Hamilton-Jacobi-Bellman equation and compute the optimal control.We will discuss both the hard and soft boundary conditions.

Owis, Ashraf H.

2006-06-01

213

Lagrange multiplier method for convex programs.  

PubMed

The problem of minimizing a convex function that is subject to the constraint that a number of other convex functions be nonpositive can be treated by the Lagrange multiplier method. Such a treatment was revived by Kuhn and Tucker and further studied by many other scientists. These studies led to an associated maximizing problem on the Lagrange function. The aim of this note is to give a short elementary proof that the infimum of the first problem is equal to the supremum of the second problem. To carry this out it is necessary to relax the constraints of the first (or the second) problem so that the constraints are enforced only in the limit. This relaxation of constraints is not necessary should prescribing upper bounds to all the convex functions define a bounded set of points in the domain of the functions. The domain of the functions can be n-dimensional space or a reflexive Banach space. PMID:16578726

Juffin, R J

1975-05-01

214

Formulation of the multimission aircraft design optimization problem  

NASA Astrophysics Data System (ADS)

The conventional single-mission aircraft design optimization problem is reformulated to allow design and optimization for multiple missions. Defining the aircraft mission as a set of continuous scalar variables leads to the concepts of mission vector and mission space. The multimission aircraft design optimization problem becomes one of optimizing a design for several different points in the mission space, simultaneously. In the limit, a design can be optimized simultaneously for all points in the mission space. Mapping various points from the optimization design space into the mission space generates actual and theoretical optimum performance surfaces. The multimission optimum configuration is defined as the single configuration that minimizes the difference between the actual performance and the theoretical optimum performance. The multimission aircraft design optimization method can be applied over several distinct mission by summing the differences between actual and theoretical optimum performance, or over all possible missions by integrating the difference between the actual and theoretical optimum performance surfaces. The concepts associated with the mission vector, mission space, and multimission optimum configuration are presented in mathematical form. The objective function for the multimission optimization problem is expressed both as a summation over discrete mission points and as an integral over the entire mission space. Mathematical expressions for objective functions based on both single and multiple objectives are developed and presented. A weighting function, emphasizing certain parts of the mission space over others, is also discussed. The multimission aircraft design optimization method is applied to an elementary wing-design optimization problem for an executive jet. The optimization problem is solved numerically for single and multiple objectives, with and without a functional constraint. The effect of the different objective functions and the confounding effect of the mission-dependent functional constraint are discussed. The results obtained from the solution of the unconstrained wing-design optimization problem validates the multimission design optimization method in that the overall performance of the multimission optimum configurations is shown to exceed that of the configurations optimized for single missions. An aircraft performance model and numerical optimization code, which were developed for the present work, are also presented.

Straussfogel, Dennis M.

215

Fundamental differences between optimization code test problems in engineering applications  

NASA Technical Reports Server (NTRS)

The purpose here is to suggest that there is at least one fundamental difference between the problems used for testing optimization codes and the problems that engineers often need to solve; in particular, the level of precision that can be practically achieved in the numerical evaluation of the objective function, derivatives, and constraints. This difference affects the performance of optimization codes, as illustrated by two examples. Two classes of optimization problem were defined. Class One functions and constraints can be evaluated to a high precision that depends primarily on the word length of the computer. Class Two functions and/or constraints can only be evaluated to a moderate or a low level of precision for economic or modeling reasons, regardless of the computer word length. Optimization codes have not been adequately tested on Class Two problems. There are very few Class Two test problems in the literature, while there are literally hundreds of Class One test problems. The relative performance of two codes may be markedly different for Class One and Class Two problems. Less sophisticated direct search type codes may be less likely to be confused or to waste many function evaluations on Class Two problems. The analysis accuracy and minimization performance are related in a complex way that probably varies from code to code. On a problem where the analysis precision was varied over a range, the simple Hooke and Jeeves code was more efficient at low precision while the Powell code was more efficient at high precision.

Eason, E. D.

1984-01-01

216

The synthesis of optimal controls for linear, time-optimal problems with retarded controls.  

NASA Technical Reports Server (NTRS)

Optimization problems involving linear systems with retardations in the controls are studied in a systematic way. Some physical motivation for the problems is discussed. The topics covered are: controllability, existence and uniqueness of the optimal control, sufficient conditions, techniques of synthesis, and dynamic programming. A number of solved examples are presented.

Banks, H. T.; Jacobs, M. Q.; Latina, M. R.

1971-01-01

217

The expanded invasive weed optimization metaheuristic for solving continuous and discrete optimization problems.  

PubMed

This paper introduces an expanded version of the Invasive Weed Optimization algorithm (exIWO) distinguished by the hybrid strategy of the search space exploration proposed by the authors. The algorithm is evaluated by solving three well-known optimization problems: minimization of numerical functions, feature selection, and the Mona Lisa TSP Challenge as one of the instances of the traveling salesman problem. The achieved results are compared with analogous outcomes produced by other optimization methods reported in the literature. PMID:24955420

Josi?ski, Henryk; Kostrzewa, Daniel; Michalczuk, Agnieszka; Swito?ski, Adam

2014-01-01

218

The Expanded Invasive Weed Optimization Metaheuristic for Solving Continuous and Discrete Optimization Problems  

PubMed Central

This paper introduces an expanded version of the Invasive Weed Optimization algorithm (exIWO) distinguished by the hybrid strategy of the search space exploration proposed by the authors. The algorithm is evaluated by solving three well-known optimization problems: minimization of numerical functions, feature selection, and the Mona Lisa TSP Challenge as one of the instances of the traveling salesman problem. The achieved results are compared with analogous outcomes produced by other optimization methods reported in the literature.

Josinski, Henryk; Michalczuk, Agnieszka; Switonski, Adam

2014-01-01

219

Adaptive and Accelerated Exploration Particle Swarm Optimizer (AAEPSO) for Solving Constrained Multiobjective Optimization Problems  

NASA Astrophysics Data System (ADS)

Many science and engineering design problems are modeled as constrained multiobjective optimization problem. The major challenges in solving these problems are (i) conflicting objectives and (ii) non linear constraints. These conflicts are responsible for diverging the solution from true Pareto-front. This paper presents a variation of particle swarm optimization algorithm integrated with accelerated exploration technique that adapts to iteration for solving constrained multiobjective optimization problems. Performance of the proposed algorithm is evaluated on standard constrained multiobjective benchmark functions (CEC 2009) and compared with recently proposed DECMOSA algorithm. The comprehensive experimental results show the effectiveness of the proposed algorithm in terms of generation distance, diversity and convergence metric.

Ali, Layak; Sabat, Samrat L.; Udgata, Siba K.

220

An Optimal Algo-Tech-Cuit for the Knapsack Problem  

Microsoft Academic Search

: We present a formal derivation and proof of correctness of a systolic arrayfor the knapsack problem, a well known, NP-complete problem. The dependency graphof the algorithm is not completely known statically, so the derivation also serves as a casestudy for systolic synthesis for this class of programs. The array is itself important sinceit achieves optimal performance on a model

Rumen Andonov; Sanjay Rajopadhye

1994-01-01

221

An algorithm of global optimization for solving layout problems  

Microsoft Academic Search

The two-dimensional layout problem is known to be NP-complete, and the current research work is basically in the heuristic way. In this paper, we mainly discuss the methods for solving layout problem about the artificial satellite module by virtue of graph theory and group theory. Also, an algorithm of global optimization is presented first time. The method given here can

Enmin Feng; Xilu Wang; Xiumei Wang; Hongfei Teng

1999-01-01

222

Optimality of nonequilibrium systems and problems of statistical thermodynamics  

Microsoft Academic Search

This paper reviews advantages which stem from using methods of optimal control theory and variational calculus in nonequilibrium thermodynamics of transport phenomena, focusing on selected problems of statistical thermodynamics rather than on typical phenomenological descriptions. Neglected are aspects of thermodynamic stability and oscillatory phenomena, as those frequently considered earlier. The main problems discussed here are: statistical aspects of nonequilibrium conservation

Stanislaw Sieniutycz

2002-01-01

223

Ordinal optimization and its application to complex deterministic problems  

Microsoft Academic Search

We present in this thesis a new perspective to approach a general class of optimization problems characterized by large deterministic complexities. Many problems of real-world concerns today lack analyzable structures and almost always involve high level of difficulties and complexities in the evaluation process. Advances in computer technology allow us to build computer models to simulate the evaluation process through

Mike Shang-Yu Yang

1998-01-01

224

Neural networks for convex hull computation.  

PubMed

Computing convex hull is one of the central problems in various applications of computational geometry. In this paper, a convex hull computing neural network (CHCNN) is developed to solve the related problems in the N-dimensional spaces. The algorithm is based on a two-layered neural network, topologically similar to ART, with a newly developed adaptive training strategy called excited learning. The CHCNN provides a parallel online and real-time processing of data which, after training, yields two closely related approximations, one from within and one from outside, of the desired convex hull. It is shown that accuracy of the approximate convex hulls obtained is around O[K(-1)(N-1/)], where K is the number of neurons in the output layer of the CHCNN. When K is taken to be sufficiently large, the CHCNN can generate any accurate approximate convex hull. We also show that an upper bound exists such that the CHCNN will yield the precise convex hull when K is larger than or equal to this bound. A series of simulations and applications is provided to demonstrate the feasibility, effectiveness, and high efficiency of the proposed algorithm. PMID:18255663

Leung, Y; Zhang, J S; Xu, Z B

1997-01-01

225

Climate Intervention as an Optimization Problem  

NASA Astrophysics Data System (ADS)

Typically, climate models simulations of intentional intervention in the climate system have taken the approach of imposing a change (eg, in solar flux, aerosol concentrations, aerosol emissions) and then predicting how that imposed change might affect Earth's climate or chemistry. Computations proceed from cause to effect. However, humans often proceed from "What do I want?" to "How do I get it?" One approach to thinking about intentional intervention in the climate system ("geoengineering") is to ask "What kind of climate do we want?" and then ask "What pattern of radiative forcing would come closest to achieving that desired climate state?" This involves defining climate goals and a cost function that measures how closely those goals are attained. (An important next step is to ask "How would we go about producing these desired patterns of radiative forcing?" However, this question is beyond the scope of our present study.) We performed a variety of climate simulations in NCAR's CAM3.1 atmospheric general circulation model with a slab ocean model and thermodynamic sea ice model. We then evaluated, for a specific set of climate forcing basis functions (ie, aerosol concentration distributions), the extent to which the climate response to a linear combination of those basis functions was similar to a linear combination of the climate response to each basis function taken individually. We then developed several cost functions (eg, relative to the 1xCO2 climate, minimize rms difference in zonal and annual mean land temperature, minimize rms difference in zonal and annual mean runoff, minimize rms difference in a combination of these temperature and runoff indices) and then predicted optimal combinations of our basis functions that would minimize these cost functions. Lastly, we produced forward simulations of the predicted optimal radiative forcing patterns and compared these with our expected results. Obviously, our climate model is much simpler than reality and predictions from individual models do not provide a sound basis for action; nevertheless, our model results indicate that the general approach outlined here can lead to patterns of radiative forcing that make the zonal annual mean climate of a high CO2 world markedly more similar to that of a low CO2 world simultaneously for both temperature and hydrological indices, where degree of similarity is measured using our explicit cost functions. We restricted ourselves to zonally uniform aerosol concentrations distributions that can be defined in terms of a positive-definite quadratic equation on the sine of latitude. Under this constraint, applying an aerosol distribution in a 2xCO2 climate that minimized a combination of rms difference in zonal and annual mean land temperature and runoff relative to the 1xCO2 climate, the rms difference in zonal and annual mean temperatures was reduced by ~90% and the rms difference in zonal and annual mean runoff was reduced by ~80%. This indicates that there may be potential for stratospheric aerosols to diminish simultaneously both temperature and hydrological cycle changes caused by excess CO2 in the atmosphere. Clearly, our model does not include many factors (eg, socio-political consequences, chemical consequences, ocean circulation changes, aerosol transport and microphysics) so we do not argue strongly for our specific climate model results, however, we do argue strongly in favor of our methodological approach. The proposed approach is general, in the sense that cost functions can be developed that represent different valuations. While the choice of appropriate cost functions is inherently a value judgment, evaluating those functions for a specific climate simulation is a quantitative exercise. Thus, the use of explicit cost functions in evaluating model results for climate intervention scenarios is a clear way of separating value judgments from purely scientific and technical issues.

Caldeira, Ken; Ban-Weiss, George A.

2010-05-01

226

Nonlinear singularly perturbed optimal control problems with singular arcs  

NASA Technical Reports Server (NTRS)

A third order, nonlinear, singularly perturbed optimal control problem is considered under assumptions which assure that the full problem is singular and the reduced problem is nonsingular. The separation between the singular arc of the full problem and the optimal control law of the reduced one, both of which are hypersurfaces in state space, is of the same order as the small parameter of the problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem. A numerical example is included.

Ardema, M. D.

1977-01-01

227

Does adiabatic quantum optimization fail for NP-complete problems?  

PubMed

It has been recently argued that adiabatic quantum optimization would fail in solving NP-complete problems because of the occurrence of exponentially small gaps due to crossing of local minima of the final Hamiltonian with its global minimum near the end of the adiabatic evolution. Using perturbation expansion, we analytically show that for the NP-hard problem known as maximum independent set, there always exist adiabatic paths along which no such crossings occur. Therefore, in order to prove that adiabatic quantum optimization fails for any NP-complete problem, one must prove that it is impossible to find any such path in polynomial time. PMID:21405383

Dickson, Neil G; Amin, M H S

2011-02-01

228

Solving inverse problems of identification type by optimal control methods  

SciTech Connect

Inverse problems of identification type for nonlinear equations are considered within the framework of optimal control theory. The rigorous solution of any particular problem depends on the functional setting, type of equation, and unknown quantity (or quantities) to be determined. Here the authors present only the general articulations of the formalism. Compared to classical regularization methods (e.g. Tikhonov coupled with optimization schemes), their approach presents several advantages, namely: (i) a systematic procedure to solve inverse problems of identification type; (ii) an explicit expression for the approximations of the solution; and (iii) a convenient numerical solution of these approximations.

Lenhart, S. [Univ. of Tennessee, Knoxville, TN (United States). Mathematics Dept.; Protopopescu, V. [Oak Ridge National Lab., TN (United States); Jiongmin Yong [Fudan Univ., Shanghai (China). Mathematics Dept.

1997-06-01

229

TSP based Evolutionary optimization approach for the Vehicle Routing Problem  

NASA Astrophysics Data System (ADS)

Vehicle Routing and Flexible Job Shop Scheduling Problems (VRP and FJSSP) are two common hard combinatorial optimization problems that show many similarities in their conceptual level [2, 4]. It was proved for both problems that solving techniques like exact methods fail to provide good quality solutions in a reasonable amount of time when dealing with large scale instances [1, 5, 14]. In order to overcome this weakness, we decide in the favour of meta heuristics and we focalize on evolutionary algorithms that have been successfully used in scheduling problems [1, 5, 9]. In this paper we investigate the common properties of the VRP and the FJSSP in order to provide a new controlled evolutionary approach for the CVRP optimization inspired by the FJSSP evolutionary optimization algorithms introduced in [10].

Kouki, Zoulel; Chaar, Besma Fayech; Ksouri, Mekki

2009-03-01

230

Equality Constraints in Multiobjective Robust Design Optimization: Decision Making Problem  

Microsoft Academic Search

Robust design optimization (RDO) problems can generally be formulated by incorporating uncertainty into the corresponding\\u000a deterministic problems. In this context, a careful formulation of deterministic equality constraints into the robust domain\\u000a is necessary to avoid infeasible designs under uncertain conditions. The challenge of formulating equality constraints is\\u000a compounded in multiobjective RDO problems. Modeling the tradeoffs between the mean of the

S. Rangavajhala; A. A. Mullur; A. Messac

2009-01-01

231

Exact and Approximate Sizes of Convex Datacubes  

NASA Astrophysics Data System (ADS)

In various approaches, data cubes are pre-computed in order to efficiently answer Olap queries. The notion of data cube has been explored in various ways: iceberg cubes, range cubes, differential cubes or emerging cubes. Previously, we have introduced the concept of convex cube which generalizes all the quoted variants of cubes. More precisely, the convex cube captures all the tuples satisfying a monotone and/or antimonotone constraint combination. This paper is dedicated to a study of the convex cube size. Actually, knowing the size of such a cube even before computing it has various advantages. First of all, free space can be saved for its storage and the data warehouse administration can be improved. However the main interest of this size knowledge is to choose at best the constraints to apply in order to get a workable result. For an aided calibrating of constraints, we propose a sound characterization, based on inclusion-exclusion principle, of the exact size of convex cube as long as an upper bound which can be very quickly yielded. Moreover we adapt the nearly optimal algorithm HyperLogLog in order to provide a very good approximation of the exact size of convex cubes. Our analytical results are confirmed by experiments: the approximated size of convex cubes is really close to their exact size and can be computed quasi immediately.

Nedjar, Sébastien

232

Time-energy optimal path tracking for robots: a numerically efficient optimization approach  

Microsoft Academic Search

This paper focuses on time-optimal and time-energy optimal path tracking, which are subproblems in optimal motion planning of robot systems. Through a nonlinear change of variables, the time-energy optimal path tracking problem is transformed here into a convex optimal control problem with a single state variable. A direct transcription method is presented that reduces finding the globally optimal trajectory to

Diederik Verscheure; Bram Demeulenaere; Jan Swevers; Joris De Schutter; Moritz Diehl

2008-01-01

233

Sub-problem Optimization With Regression and Neural Network Approximators  

NASA Technical Reports Server (NTRS)

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

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

2003-01-01

234

Integrated network design and scheduling problems : optimization algorithms and applications.  

SciTech Connect

We consider the class of integrated network design and scheduling problems. These problems focus on selecting and scheduling operations that will change the characteristics of a network, while being speci cally concerned with the performance of the network over time. Motivating applications of INDS problems include infrastructure restoration after extreme events and building humanitarian distribution supply chains. While similar models have been proposed, no one has performed an extensive review of INDS problems from their complexity, network and scheduling characteristics, information, and solution methods. We examine INDS problems under a parallel identical machine scheduling environment where the performance of the network is evaluated by solving classic network optimization problems. We classify that all considered INDS problems as NP-Hard and propose a novel heuristic dispatching rule algorithm that selects and schedules sets of arcs based on their interactions in the network. We present computational analysis based on realistic data sets representing the infrastructures of coastal New Hanover County, North Carolina, lower Manhattan, New York, and a realistic arti cial community CLARC County. These tests demonstrate the importance of a dispatching rule to arrive at near-optimal solutions during real-time decision making activities. We extend INDS problems to incorporate release dates which represent the earliest an operation can be performed and exible release dates through the introduction of specialized machine(s) that can perform work to move the release date earlier in time. An online optimization setting is explored where the release date of a component is not known.

Nurre, Sarah G.; Carlson, Jeffrey J.

2014-01-01

235

A Sparse Representation-Based Deployment Method for Optimizing the Observation Quality of Camera Networks  

PubMed Central

Deployment is a critical issue affecting the quality of service of camera networks. The deployment aims at adopting the least number of cameras to cover the whole scene, which may have obstacles to occlude the line of sight, with expected observation quality. This is generally formulated as a non-convex optimization problem, which is hard to solve in polynomial time. In this paper, we propose an efficient convex solution for deployment optimizing the observation quality based on a novel anisotropic sensing model of cameras, which provides a reliable measurement of the observation quality. The deployment is formulated as the selection of a subset of nodes from a redundant initial deployment with numerous cameras, which is an ?0 minimization problem. Then, we relax this non-convex optimization to a convex ?1 minimization employing the sparse representation. Therefore, the high quality deployment is efficiently obtained via convex optimization. Simulation results confirm the effectiveness of the proposed camera deployment algorithms.

Wang, Chang; Qi, Fei; Shi, Guangming; Wang, Xiaotian

2013-01-01

236

Pattern search algorithms for mixed variable general constrained optimization problems  

NASA Astrophysics Data System (ADS)

A new class of algorithms for solving nonlinearly constrained mixed variable optimization problems is presented. The Audet-Dennis Generalized Pattern Search (GPS) algorithm for bound constrained mixed variable optimization problems is extended to problems with general nonlinear constraints by incorporating a filter, in which new iterates are accepted whenever they decrease the incumbent objective function value or constraint violation function value. Additionally, the algorithm can exploit any available derivative information (or rough approximation thereof) to speed convergence without sacrificing the flexibility often employed by GPS methods to find better local optima. In generalizing existing GPS algorithms, the new theoretical convergence results presented here reduce seamlessly to existing results for more specific classes of problems. While no local continuity or smoothness assumptions are made, a hierarchy of theoretical convergence results is given, in which the assumptions dictate what can be proved about certain limit points of the algorithm. A new Matlab(c) software package was developed to implement these algorithms. Numerical results are provided for several nonlinear optimization problems from the CUTE test set, as well as a difficult nonlinearly constrained mixed variable optimization problem in the design of a load-bearing thermal insulation system used in cryogenic applications.

Abramson, Mark Aaron

237

Ant colony optimization for solving university facility layout problem  

NASA Astrophysics Data System (ADS)

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

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

2013-04-01

238

Overcoming the Bellman's curse of dimensionality in large optimization problems  

NASA Technical Reports Server (NTRS)

Decomposition of large problems into a hierarchic pyramid of subproblems was proposed in the literature as a means for optimization of engineering systems too large for all-in-one optimization. This decomposition was established heuristically. The dynamic programming (DP) method due to Bellman was augmented with an optimum sensitivity analysis that provides a mathematical basis for the above decomposition, and overcomes the curse of dimensionality that limited the original formulation of DP. Numerical examples are cited.

Sobieszczanski-Sobieski, Jaroslaw

1990-01-01

239

Quadratic Optimization in the Problems of Active Control of Sound  

NASA Technical Reports Server (NTRS)

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

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

2002-01-01

240

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

NASA Astrophysics Data System (ADS)

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

Masuda, Kazuaki; Aiyoshi, Eitaro

241

The expanded LaGrangian system for constrained optimization problems  

NASA Technical Reports Server (NTRS)

Smooth penalty functions can be combined with numerical continuation/bifurcation techniques to produce a class of robust and fast algorithms for constrainted optimization problems. The key to the development of these algorithms is the Expanded Lagrangian System which is derived and analyzed in this work. This parameterized system of nonlinear equations contains the penalty path as a solution, provides a smooth homotopy into the first-order necessary conditions, and yields a global optimization technique. Furthermore, the inevitable ill-conditioning present in a sequential optimization algorithm is removed for three penalty methods: the quadratic penalty function for equality constraints, and the logarithmic barrier function (an interior method) and the quadratic loss function (an interior method) for inequality constraints. Although these techniques apply to optimization in general and to linear and nonlinear programming, calculus of variations, optimal control and parameter identification in particular, the development is primarily within the context of nonlinear programming.

Poore, A. B.

1986-01-01

242

Numerical Solution of Some Types of Fractional Optimal Control Problems  

PubMed Central

We present two different approaches for the numerical solution of fractional optimal control problems (FOCPs) based on a spectral method using Chebyshev polynomials. The fractional derivative is described in the Caputo sense. The first approach follows the paradigm “optimize first, then discretize” and relies on the approximation of the necessary optimality conditions in terms of the associated Hamiltonian. In the second approach, the state equation is discretized first using the Clenshaw and Curtis scheme for the numerical integration of nonsingular functions followed by the Rayleigh-Ritz method to evaluate both the state and control variables. Two illustrative examples are included to demonstrate the validity and applicability of the suggested approaches.

Sweilam, Nasser Hassan; Al-Ajami, Tamer Mostafa; Hoppe, Ronald H. W.

2013-01-01

243

A Discrete Lagrangian Algorithm for Optimal Routing Problems  

SciTech Connect

The ideas of discrete Lagrangian methods for conservative systems are exploited for the construction of algorithms applicable in optimal ship routing problems. The algorithm presented here is based on the discretisation of Hamilton's principle of stationary action Lagrangian and specifically on the direct discretization of the Lagrange-Hamilton principle for a conservative system. Since, in contrast to the differential equations, the discrete Euler-Lagrange equations serve as constrains for the optimization of a given cost functional, in the present work we utilize this feature in order to minimize the cost function for optimal ship routing.

Kosmas, O. T.; Vlachos, D. S.; Simos, T. E. [University of Peloponnese, 22100 Tripoli (Greece)

2008-11-06

244

Determining in Linear Time the Minimum Area Convex Hull of Two Polygons  

Microsoft Academic Search

As preprocessing for the two-dimensional cutting stock problem or pallet loading problem, we compute the minimum area convex hull. Given two polygons P and Q, we find their relative positions such that the convex hull encasing them is minimum in area. Let N be the total number of vertices in P and Q. We determine the minimum area convex hull

HYUN-CHAN LEE; TONY C. WOO

1988-01-01

245

An optimal algo-tech-cuit for the knapsack problem  

Microsoft Academic Search

The authors first present a formal derivation and proof of correctness of a systolic array for the knapsack problem, an NP-complete problem whose dependency graph is not completely known statically. With q PEs, each with a fixed size memory, the arraystretch runs in ?(mc\\/q), which gives optimal speedup of the algorithm. However, it has an intricate tag-based control mechanism which

R. Andonov; Sanjay Rajopadhye

1993-01-01

246

Left ventricle segmentation in MRI via convex relaxed distribution matching.  

PubMed

A fundamental step in the diagnosis of cardiovascular diseases, automatic left ventricle (LV) segmentation in cardiac magnetic resonance images (MRIs) is still acknowledged to be a difficult problem. Most of the existing algorithms require either extensive training or intensive user inputs. This study investigates fast detection of the left ventricle (LV) endo- and epicardium surfaces in cardiac MRI via convex relaxation and distribution matching. The algorithm requires a single subject for training and a very simple user input, which amounts to a single point (mouse click) per target region (cavity or myocardium). It seeks cavity and myocardium regions within each 3D phase by optimizing two functionals, each containing two distribution-matching constraints: (1) a distance-based shape prior and (2) an intensity prior. Based on a global measure of similarity between distributions, the shape prior is intrinsically invariant with respect to translation and rotation. We further introduce a scale variable from which we derive a fixed-point equation (FPE), thereby achieving scale-invariance with only few fast computations. The proposed algorithm relaxes the need for costly pose estimation (or registration) procedures and large training sets, and can tolerate shape deformations, unlike template (or atlas) based priors. Our formulation leads to a challenging problem, which is not directly amenable to convex-optimization techniques. For each functional, we split the problem into a sequence of sub-problems, each of which can be solved exactly and globally via a convex relaxation and the augmented Lagrangian method. Unlike related graph-cut approaches, the proposed convex-relaxation solution can be parallelized to reduce substantially the computational time for 3D domains (or higher), extends directly to high dimensions, and does not have the grid-bias problem. Our parallelized implementation on a graphics processing unit (GPU) demonstrates that the proposed algorithm requires about 3.87 s for a typical cardiac MRI volume, a speed-up of about five times compared to a standard implementation. We report a performance evaluation over 400 volumes acquired from 20 subjects, which shows that the obtained 3D surfaces correlate with independent manual delineations. We further demonstrate experimentally that (1) the performance of the algorithm is not significantly affected by the choice of the training subject and (2) the shape description we use does not change significantly from one subject to another. These results support the fact that a single subject is sufficient for training the proposed algorithm. PMID:23851075

Nambakhsh, Cyrus M S; Yuan, Jing; Punithakumar, Kumaradevan; Goela, Aashish; Rajchl, Martin; Peters, Terry M; Ayed, Ismail Ben

2013-12-01

247

A Case Study to Test Mozaik for Different Optimization Problems  

SciTech Connect

We present four different shape optimization problems based on the existing beam port facility of the Penn State Breazeale Reactor and their results obtained by the modular optimization code package, MOZAIK. Each model problem has a different beam tube configuration with the same optimization goal: to determine an optimal D2O moderator tank shape for the given beam tube arrangement that maximizes the thermal neutron beam intensity at the beam tube exit end. In this study, the power of the automated search process was demonstrated and its capabilities were tested. In addition, the performance of the beam port was analyzed using alternative beam tube arrangements. All alternative arrangements indicate that higher thermal neutron beam intensity can be obtained at the beam tube exit end using a smaller volume of D2O in the system than is used in the existing beam port configuration. Moreover, the results show that MOZAIK is ready for deployment to address shape optimization problems involving radiation transport in nuclear engineering applications.

Bekar, Kursat B [ORNL; Azmy, Yousry [North Carolina State University; Unlu, Kenan [Pennsylvania State University; BrenizerJr., Jack [Pennsylvania State University

2009-01-01

248

A New Local Search Based Ant Colony Optimization Algorithm for Solving Combinatorial Optimization Problems  

NASA Astrophysics Data System (ADS)

Ant Colony Optimization (ACO) algorithms are a new branch of swarm intelligence. They have been applied to solve different combinatorial optimization problems successfully. Their performance is very promising when they solve small problem instances. However, the algorithms' time complexity increase and solution quality decrease for large problem instances. So, it is crucial to reduce the time requirement and at the same time to increase the solution quality for solving large combinatorial optimization problems by the ACO algorithms. This paper introduces a Local Search based ACO algorithm (LSACO), a new algorithm to solve large combinatorial optimization problems. The basis of LSACO is to apply an adaptive local search method to improve the solution quality. This local search automatically determines the number of edges to exchange during the execution of the algorithm. LSACO also applies pheromone updating rule and constructs solutions in a new way so as to decrease the convergence time. The performance of LSACO has been evaluated on a number of benchmark combinatorial optimization problems and results are compared with several existing ACO algorithms. Experimental results show that LSACO is able to produce good quality solutions with a higher rate of convergence for most of the problems.

Hassan, Md. Rakib; Islam, Md. Monirul; Murase, Kazuyuki

249

Multiagent Optimization System for Solving the Traveling Salesman Problem (TSP)  

Microsoft Academic Search

The multiagent optimization system (MAOS) is a nature-inspired method, which supports cooperative search by the self-organization of a group of compact agents situated in an environment with certain sharing public knowledge. Moreover, each agent in MAOS is an autonomous entity with personal declarative memory and behavioral components. In this paper, MAOS is refined for solving the traveling salesman problem (TSP),

Xiao-Feng Xie; Jiming Liu

2009-01-01

250

Biogeography-based Optimization for Economic Load Dispatch Problems  

Microsoft Academic Search

This article presents a biogeography-based optimization technique for solving constrained economic dispatch problems in a power system, considering the non-linear characteristics of generators such as valve point loading, ramp rate limits, prohibited operating zones, and multiple fuels cost functions. In this article, the proposed algorithm has been tested in different systems under various simulated conditions. A comparison of simulation results

P. K. Roy; S. P. Ghoshal; S. S. Thakur

2009-01-01

251

Stochastic programming models for general redundancy-optimization problems  

Microsoft Academic Search

This paper provides a unified modeling idea for both parallel and standby redundancy optimization problems. A spectrum of redundancy stochastic programming models is constructed to maximize the mean system-lifetime, ?-system lifetime, or system reliability. To solve these models, a hybrid intelligent algorithm is presented. Some numerical examples illustrate the effectiveness of the proposed algorithm. This paper considers both parallel redundant

Ruiqing Zhao; Baoding Liu

2003-01-01

252

Some general results on the optimal ramp control problem  

Microsoft Academic Search

In an effort to relieve peak hour congestion on freeways, various ramp metering algorithms have been employed to regulate the inputs to freeways from entry ramps. In this paper, we consider a freeway system comprised of a freeway section and its entry\\/exit ramps, and formulate the ramp control problem as a dynamic optimal process to minimize the total time spent

H. Zhang; S. G. Ritchie; W. W. Recker

1996-01-01

253

Automated optimal design techniques for inverse electromagnetic problems  

Microsoft Academic Search

Two methods are considered for the solution of automated digital optimal design problems. The computer procedures based on these methods have been implemented and tested. The first method, based on a deterministic approach, considers a quadratic approximation of the cost function. The second, based on a stochastic approach, is derived from the simulated annealing algorithm. Both methods, implemented as computer

F. Bellina; P. Campostrini; G. Chitarin; A. Stella; F. Trevisan

1992-01-01

254

Discrete Particle Swarm Optimization for the Orienteering Problem  

Microsoft Academic Search

In this paper a novel discrete Particle Swarm Optimization (PSO) algorithm is proposed to solve the Orienteering Problem (OP). Discrete evolution is achieved by re-defining all operators and operands used in PSO. To obtain better results, Strengthened-PSO which improves both exploration and exploitation during the search process is employed for experimental evaluation. Our proposed algorithm either achieves or improves the

Zülal Sevkli; Fatih Erdogan Sevilgen

2010-01-01

255

Artificial Immune System for Solving Constrained Optimization Problems  

Microsoft Academic Search

In this paper, we present an artificial immune system (AIS) based on the CLONALG algorithm for solving constrained (numerical) optimization problems. We develop a new mutation operator which produces large and small step sizes and which aims to provide better exploration capabilities. We validate our proposed approach with 13 test functions taken from the specialized literature and we compare our

Susana C. Esquivel; Carlos Artemio Coello Coello; Victoria S. Aragón

2007-01-01

256

To the optimization problem in minority game model  

SciTech Connect

The article presents the research results of the optimization problem in minority game model to a gaussian approximation using replica symmetry breaking by one step (1RSB). A comparison to replica symmetry approximation (RS) and the results from literary sources received using other methods has been held.

Yanishevsky, Vasyl [Drogobych Ivan Franko University, 36 Ivan Franko St., 82100 (Ukraine)

2009-12-14

257

Optimal strategy for structured model of fishing problem.  

PubMed

In this work we study a structured fishing model, basically displaying the two stages of the ages of a fish population, which are in our case juvenile, and adults. We associate to this model the maximization of the total discounted net revenues derived by the exploitation of the stock. The exploitation strategy of the optimal control problem is then developed and presented. PMID:15861822

Jerry, Mounir; Raïssi, Nadia

2005-04-01

258

DESIGN OPTIMIZATION OF STRUCTURAL ACOUSTIC PROBLEMS USING FEM-BEM  

Microsoft Academic Search

A design optimization procedure of a noise-vibration- harshness (NVH) problem of a complicated vehicle structure is presented by assuming the acoustic pres- sure does not affect the structural vibration. The steady-state dynamic behavior of the vehicle is calcu- lated from the frequency response finite element analy- sis, while the sound pressure level within the acoustic cavity is calculated from the

Nam H. Kim; Kyung K. Choi; Jun Dong; Christophe Pierre

2003-01-01

259

Solving Globally-Optimal Threading Problems in 'Polynomial-Time'.  

National Technical Information Service (NTIS)

Computational protein is a powerful technique for recognizing native-like folds of a protein sequence from a protein fold database. In this paper, we present an improved algorithm (over our previous work) for solving the globally-optimal threading problem...

E. C. Uberbacher D. Xu Y. Xu

1999-01-01

260

Large Scale Optimization Methods with a Focus on Chemistry Problems.  

National Technical Information Service (NTIS)

Our research under this grant has developed general large-scale global optimization techniques in the context of solving protein structure prediction problems. Over the course of the research period the thrust of the research was primarily in two areas. T...

R. B. Schnabel R. H. Byrd

2002-01-01

261

Lattice point sets for deterministic learning and approximate optimization problems  

Microsoft Academic Search

In this brief, the use of lattice point sets (LPSs) is investigated in the context of general learning problems (including function estimation and dynamic optimization), in the case where the classic empirical risk minimization (ERM) principle is considered and there is freedom to choose the sampling points of the input space. Here it is proved that convergence of the ERM

Cristiano Cervellera

2010-01-01

262

Rees algebras, Monomial Subrings and Linear Optimization Problems  

NASA Astrophysics Data System (ADS)

In this thesis we are interested in studying algebraic properties of monomial algebras, that can be linked to combinatorial structures, such as graphs and clutters, and to optimization problems. A goal here is to establish bridges between commutative algebra, combinatorics and optimization. We study the normality and the Gorenstein property-as well as the canonical module and the a-invariant-of Rees algebras and subrings arising from linear optimization problems. In particular, we study algebraic properties of edge ideals and algebras associated to uniform clutters with the max-flow min-cut property or the packing property. We also study algebraic properties of symbolic Rees algebras of edge ideals of graphs, edge ideals of clique clutters of comparability graphs, and Stanley-Reisner rings.

Dupont, Luis A.

2010-06-01

263

An adiabatic quantum optimization for exact cover 3 problem  

NASA Astrophysics Data System (ADS)

A perturbation method is applied to study the structure of the ground state of the adiabatic quantum optimization for the exact cover 3 problem. It is found that the instantaneous ground state near the end of the evolution is mainly composed of the eigenstates of the problem Hamiltonian, which are Hamming close to the solution state. And the instantaneous ground state immediately after the starting is mainly formed of low energy eigenstates of the problem Hamiltonian. These results are then applied to estimate the minimum gap for a special case.

Zhang, Ying-Yu; Xu, Li-Li; Li, Jun-Qing

2014-03-01

264

Ordinal optimization and its application to complex deterministic problems  

NASA Astrophysics Data System (ADS)

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

Yang, Mike Shang-Yu

1998-10-01

265

Convex Programming and Decomposition of Discrete Frequency Spectra.  

National Technical Information Service (NTIS)

The decomposition of a given empirical frequency distribution into a finite mixture of distributions from an admissible class is posed as a convex programming problem. The convexity is attained with any of the usual statistical principles, e.g., minimum v...

A. Charnes L. Crus-Abad D. Klingman

1971-01-01

266

Parallel Tempering for sampling and optimization in seismic inverse problems  

NASA Astrophysics Data System (ADS)

The field of seismology is rich with inverse problems. Seismologists are constantly seeking new ways to use seismic waveforms, and data products derived from them, to constrain subsurface structure in the form of Earth properties in 1-, 2- and 3 dimensions, as well as seismic sources in space and time. Every approach has its limitations and a virtual smorgasbord of methods exist, and have been applied over thirty years, with varying degrees of success. In this presentation we discuss a new class of approach. Parallel Tempering (PT) is a technique originating in the field of computational statistics that is finding increasing success for probabilistic sampling problems in astro and quantum physics, and more recently ocean acoustics but appears to be virtually unknown in the solid earth geosciences. In seismology two classes of inference approach are common for nonlinear inverse problems, Bayesian (probabilistic) sampling and optimization. Parallel Tempering can be applied to both situations and is related to better known methods such as Simulated Annealing and Metropolis Sampling. PT is distinguished as it has a theoretical basis for being superior to both. PT is best viewed as a `meta' algorithm. In a sense wrapping around existing optimization or Bayesian sampling methods to facilitate more robust performance (optimization) and more rapid exploration of parameter space (sampling). PT has generated much interest across the physical sciences with encouraging results emerging. This presentation will describe the basic ideas, and present results of implementations on seismic waveform inversion for both sampling and optimization.

Sambridge, Malcolm

2013-04-01

267

Vertebral body segmentation in MRI via convex relaxation and distribution matching.  

PubMed

We state vertebral body (VB) segmentation in MRI as a distribution-matching problem, and propose a convex-relaxation solution which is amenable to parallel computations. The proposed algorithm does not require a complex learning from a large manually-built training set, as is the case of the existing methods. From a very simple user input, which amounts to only three points for a whole volume, we compute a multi-dimensional model distribution of features that encode contextual information about the VBs. Then, we optimize a functional containing (1) a feature-based constraint which evaluates a similarity between distributions, and (2) a total-variation constraint which favors smooth surfaces. Our formulation leads to a challenging problem which is not directly amenable to convex-optimization techniques. To obtain a solution efficiently, we split the problem into a sequence of sub-problems, each can be solved exactly and globally via a convex relaxation and the augmented Lagrangian method. Our parallelized implementation on a graphics processing unit (GPU) demonstrates that the proposed solution can bring a substantial speed-up of more than 30 times for a typical 3D spine MRI volume. We report quantitative performance evaluations over 15 subjects, and demonstrate that the results correlate well with independent manual segmentations. PMID:23285591

Ben Ayed, Ismail; Punithakumar, Kumaradevan; Minhas, Rashid; Joshi, Kumradvan Rohit; Garvin, Gregory J

2012-01-01

268

Multicriteria VMAT optimization  

Microsoft Academic Search

Purpose: To make the planning of volumetric modulated arc therapy (VMAT) faster and to explore the tradeoffs between planning objectives and delivery efficiency. Methods: A convex multicriteria dose optimization problem is solved for an angular grid of 180 equi-spaced beams. This allows the planner to navigate the ideal dose distribution Pareto surface and select a plan of desired target coverage

David Craft; Dualta McQuaid; Jeremiah Wala; Wei Chen; Ehsan Salari; Thomas Bortfeld

2011-01-01

269

Computing convex quadrangulations?  

PubMed Central

We use projected Delaunay tetrahedra and a maximum independent set approach to compute large subsets of convex quadrangulations on a given set of points in the plane. The new method improves over the popular pairing method based on triangulating the point set.

Schiffer, T.; Aurenhammer, F.; Demuth, M.

2012-01-01

270

A dynamic convexized method for the TSP  

Microsoft Academic Search

This paper describes a dynamic convexized method for solving the symmetric traveling salesman problem (TSP). We construct an auxiliary function and design an algorithm based on this function. The possibility of sinking into a previous local minimizer can be reduced by adjusting the value of the parameter in the auxiliary function. We have verified the correctness of this approach both

Miaoling Wu; Wenxing Zhu

2010-01-01

271

A Convex Approach to Fault Tolerant Control  

NASA Technical Reports Server (NTRS)

The design of control laws for dynamic systems with the potential for actuator failures is considered in this work. The use of Linear Matrix Inequalities allows more freedom in controller design criteria than typically available with robust control. This work proposes an extension of fault-scheduled control design techniques that can find a fixed controller with provable performance over a set of plants. Through convexity of the objective function, performance bounds on this set of plants implies performance bounds on a range of systems defined by a convex hull. This is used to incorporate performance bounds for a variety of soft and hard failures into the control design problem.

Maghami, Peiman G.; Cox, David E.; Bauer, Frank (Technical Monitor)

2002-01-01

272

Chance-Constrained Guidance With Non-Convex Constraints  

NASA Technical Reports Server (NTRS)

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.

Ono, Masahiro

2011-01-01

273

Analysis of a turning point problem in flight trajectory optimization  

NASA Technical Reports Server (NTRS)

The optimal control policy for the aeroglide portion of the minimum fuel, orbital plane change problem for maneuvering entry vehicles is reduced to the solution of a turning point problem for the bank angle control. For this problem a turning point occurs at the minimum altitude of the flight, when the flight path angle equals zero. The turning point separates the bank angle control into two outer solutions that are valid away from the turning point. In a neighborhood of the turning point, where the bank angle changes rapidly, an inner solution is developed and matched with the two outer solutions. An asymptotic analysis of the turning point problem is given, and an analytic example is provided to illustrate the construction of the bank angle control.

Gracey, C.

1989-01-01

274

Convex Sets in Acyclic Digraphs  

Microsoft Academic Search

A non-empty set X of vertices of an acyclic digraph is called connected if the underlying undirected graph induced by X is connected and it is called convex if no two vertices of X are connected by a directed path in which some vertices are not in X. The set of convex sets (connected convex sets) of an acyclic digraph

Paul Balister; Stefanie Gerke; Gregory Gutin

2009-01-01

275

Compensated optimal grids for elliptic boundary-value problems  

PubMed Central

A method is proposed which allows to efficiently treat elliptic problems on unbounded domains in two and three spatial dimensions in which one is only interested in obtaining accurate solutions at the domain boundary. The method is an extension of the optimal grid approach for elliptic problems, based on optimal rational approximation of the associated Neumann-to-Dirichlet map in Fourier space. It is shown that, using certain types of boundary discretization, one can go from second-order accurate schemes to essentially spectrally accurate schemes in two-dimensional problems, and to fourth-order accurate schemes in three-dimensional problems without any increase in the computational complexity. The main idea of the method is to modify the impedance function being approximated to compensate for the numerical dispersion introduced by a small finite-difference stencil discretizing the differential operator on the boundary. We illustrate how the method can be efficiently applied to nonlinear problems arising in modeling of cell communication.

Posta, F.; Shvartsman, S. Y.; Muratov, C. B.

2008-01-01

276

JABAT Middleware as a Tool for Solving Optimization Problems  

NASA Astrophysics Data System (ADS)

JABAT supports designing and implementing A-Team architectures for solving difficult optimization problems. This paper presents several applications of JABAT as a tool for solving such problems. List of implementations and extensions of JABAT shows how useful and flexible the system can be. The paper summarises experiences of authors gained while developing various A-Teams. Some conclusions concerning such details of the A-Team model like the composition of the team of agents, the choice of rules determining how the agents interact with the population of solutions, or how synchronisation or cooperation of agents influence the quality of results are offered.

Barbucha, Dariusz; Czarnowski, Ireneusz; J?drzejowicz, Piotr; Ratajczak-Ropel, Ewa; Wierzbowska, Izabela

277

Optimal least-squares finite element method for elliptic problems  

NASA Technical Reports Server (NTRS)

An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.

Jiang, Bo-Nan; Povinelli, Louis A.

1991-01-01

278

Asynchronous global optimization techniques for medium and large inversion problems  

SciTech Connect

We discuss global optimization procedures adequate for seismic inversion problems. We explain how to save function evaluations (which may involve large scale ray tracing or other expensive operations) by creating a data base of information on what parts of parameter space have already been inspected. It is also shown how a correct parallel implementation using PVM speeds up the process almost linearly with respect to the number of processors, provided that the function evaluations are expensive enough to offset the communication overhead.

Pereyra, V.; Koshy, M. [Weidlinger Associates, Los Altos, CA (United States); Meza, J.C. [Sandia National Labs., Livermore, CA (United States)

1995-04-01

279

Boundary Search for Constrained Numerical Optimization Problems in ACO Algorithms  

Microsoft Academic Search

This paper presents a novel boundary approach which is included as a constraint-handling technique in an ant colony algorithm.\\u000a The necessity of approaching the boundary between the feasible and infeasible search space for many constrained optimization\\u000a problems is a paramount challenge for every constraint-handling technique. Our proposed technique precisely focuses the search\\u000a on the boundary region and can be either

Guillermo Leguizamón; Carlos A. Coello Coello

2006-01-01

280

The pseudospectral Legendre method for discretizing optimal control problems  

Microsoft Academic Search

This paper presents a computational technique for optimal control problems including state and control inequality constraints. The technique is based on spectral collocation methods used in the solution of differential equations. The system dynamics are collocated at Legendre-Gauss-Lobatto points. The derivative x˙(t) of the state x(t) is approximated by the analytic derivative of the corresponding interpolating polynomial. State and control

G. Elnagar; M. A. Kazemi; M. Razzaghi

1995-01-01

281

A piecewise linear approximation scheme for hereditary optimal control problems  

NASA Technical Reports Server (NTRS)

An approximation scheme based on 'piecewise linear' approximations of L2 spaces is employed to formulate a numerical method for solving quadratic optimal control problems governed by linear retarded functional differential equations. This piecewise linear method is an extension of the so called averaging technique. It is shown that the Riccati equation for the linear approximation is solved by simple transformation of the averaging solution. Thus, the computational requirements are essentially the same. Numerical results are given.

Cliff, E. M.; Burns, J. A.

1977-01-01

282

Block clustering based on difference of convex functions (DC) programming and DC algorithms.  

PubMed

We investigate difference of convex functions (DC) programming and the DC algorithm (DCA) to solve the block clustering problem in the continuous framework, which traditionally requires solving a hard combinatorial optimization problem. DC reformulation techniques and exact penalty in DC programming are developed to build an appropriate equivalent DC program of the block clustering problem. They lead to an elegant and explicit DCA scheme for the resulting DC program. Computational experiments show the robustness and efficiency of the proposed algorithm and its superiority over standard algorithms such as two-mode K-means, two-mode fuzzy clustering, and block classification EM. PMID:23777526

Le, Hoai Minh; Le Thi, Hoai An; Dinh, Tao Pham; Huynh, Van Ngai

2013-10-01

283

Issues and Strategies in Solving Multidisciplinary Optimization Problems  

NASA Technical Reports Server (NTRS)

Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. The accumulated multidisciplinary design activity is collected under a testbed entitled COMETBOARDS. Several issues were encountered during the solution of the problems. Four issues and the strategies adapted for their resolution are discussed. This is followed by a discussion on analytical methods that is limited to structural design application. An optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. Optimum solutions obtained were infeasible for aircraft and airbreathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through a set of problems: Design of an engine component, Synthesis of a subsonic aircraft, Operation optimization of a supersonic engine, Design of a wave-rotor-topping device, Profile optimization of a cantilever beam, and Design of a cylindrical shell. This chapter provides a cursory account of the issues. Cited references provide detailed discussion on the topics. Design of a structure can also be generated by traditional method and the stochastic design concept. Merits and limitations of the three methods (traditional method, optimization method and stochastic concept) are illustrated. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions can be produced by all the three methods. The variation in the weight calculated by the methods was found to be modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliability traced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.

Patnaik, Surya

2013-01-01

284

Linear and nonlinear model predictive control using a general purpose optimal control problem solver RIOTS 95  

Microsoft Academic Search

In this paper, we introduce the general purpose optimal control problem solver RIOTS_95, Matlab toolbox, as a solver for general linear and nonlinear model predictive control (MPC) problems. This optimization toolbox is designed to solve a wide variety of optimal control problems and therefore constitutes a good candidate as a optimization solver in the MPC framework. The illustrative example of

Christophe Tricaud; Yang Quan Chen

2008-01-01

285

Convex Quantum Logic  

NASA Astrophysics Data System (ADS)

In this work we study the convex set of quantum states from a quantum logical point of view. We consider an algebraic structure based on the convex subsets of this set. The relationship of this algebraic structure with the lattice of propositions of quantum logic is shown. This new structure is suitable for the study of compound systems and shows new differences between quantum and classical mechanics. These differences are linked to the nontrivial correlations which appear when quantum systems interact. They are reflected in the new propositional structure, and do not have a classical analogue. This approach is also suitable for an algebraic characterization of entanglement and it provides a new entanglement criteria.

Holik, Federico; Massri, Cesar; Ciancaglini, Nicolás

2012-05-01

286

A self-learning particle swarm optimizer for global optimization problems.  

PubMed

Particle swarm optimization (PSO) has been shown as an effective tool for solving global optimization problems. So far, most PSO algorithms use a single learning pattern for all particles, which means that all particles in a swarm use the same strategy. This monotonic learning pattern may cause the lack of intelligence for a particular particle, which makes it unable to deal with different complex situations. This paper presents a novel algorithm, called self-learning particle swarm optimizer (SLPSO), for global optimization problems. In SLPSO, each particle has a set of four strategies to cope with different situations in the search space. The cooperation of the four strategies is implemented by an adaptive learning framework at the individual level, which can enable a particle to choose the optimal strategy according to its own local fitness landscape. The experimental study on a set of 45 test functions and two real-world problems show that SLPSO has a superior performance in comparison with several other peer algorithms. PMID:22067435

Li, Changhe; Yang, Shengxiang; Nguyen, Trung Thanh

2012-06-01

287

An optimization spiking neural p system for approximately solving combinatorial optimization problems.  

PubMed

Membrane systems (also called P systems) refer to the computing models abstracted from the structure and the functioning of the living cell as well as from the cooperation of cells in tissues, organs, and other populations of cells. Spiking neural P systems (SNPS) are a class of distributed and parallel computing models that incorporate the idea of spiking neurons into P systems. To attain the solution of optimization problems, P systems are used to properly organize evolutionary operators of heuristic approaches, which are named as membrane-inspired evolutionary algorithms (MIEAs). This paper proposes a novel way to design a P system for directly obtaining the approximate solutions of combinatorial optimization problems without the aid of evolutionary operators like in the case of MIEAs. To this aim, an extended spiking neural P system (ESNPS) has been proposed by introducing the probabilistic selection of evolution rules and multi-neurons output and a family of ESNPS, called optimization spiking neural P system (OSNPS), are further designed through introducing a guider to adaptively adjust rule probabilities to approximately solve combinatorial optimization problems. Extensive experiments on knapsack problems have been reported to experimentally prove the viability and effectiveness of the proposed neural system. PMID:24875789

Zhang, Gexiang; Rong, Haina; Neri, Ferrante; Pérez-Jiménez, Mario J

2014-08-01

288

A New Approach to Duality in Vector Optimization  

Microsoft Academic Search

In this article we develop a new approach to duality theory for convex vector optimization problems. We modify a given (set-valued) vector optimization problem such that the image space becomes a complete lattice (a sublattice of the power set of the original image space), where the corresponding infimum and supremum are sets that are related to the set of (minimal

Andreas Lohne; Christiane Tammer

2005-01-01

289

Optimality Conditions for A Two-Stage Reservoir Operation Problem  

NASA Astrophysics Data System (ADS)

This paper discusses the optimality conditions for standard operation policy (SOP) and hedging rule (HR) for a two-stage reservoir operation problem within a consistent theoretical framework. The effects of three typical constraints, which are mass balance, non-negative release and storage constraints under both certain and uncertain conditions have been analyzed. When all non-negative constraints and storage constraints are non-binding, HR results in optimal reservoir operation following the marginal benefit (MB) principle (the MB is equal over the two stages); while if any of the non-negative release or storage constraints is binding, in general SOP results in the optimal solution except two special cases. One of them is a complement of the traditional SOP/HR curve, which happens while the capacity constraint is binding; the other is a special hedging rule, which should be employed to carry over all water in the current stage to the future, when extreme drought is certain and higher marginal utility exists for the second stage. Furthermore, uncertainty complicates the effects of the various constraints but in general higher uncertainty level in the future makes HR a more favorable since water needs to be reserved to defense the risk caused by the uncertainty. Using the derived optimality conditions, an algorithm for solving the model numerically has been developed and tested with hypothetical examples.

Zhao, J.; Cai, X.; Wang, Z.

2010-12-01

290

Optimality conditions for a two-stage reservoir operation problem  

NASA Astrophysics Data System (ADS)

This paper discusses the optimality conditions for standard operation policy (SOP) and hedging rule (HR) for a two-stage reservoir operation problem using a consistent theoretical framework. The effects of three typical constraints, i.e., mass balance, nonnegative release, and storage constraints under both certain and uncertain conditions are analyzed. When all nonnegative constraints and storage constraints are unbinding, HR results in optimal reservoir operation following the marginal benefit (MB) principle (the MB is equal over current and future stages. However, if any of those constraints are binding, SOP results in the optimal solution, except in some special cases which need to carry over water in the current stage to the future stage, when extreme drought is certain and a higher marginal utility exists for the second stage. Furthermore, uncertainty complicates the effects of the various constraints. A higher uncertainty level in the future makes HR more favorable as water needs to be reserved to defend against the risk caused by uncertainty. Using the derived optimality conditions, an algorithm for solving a numerical model is developed and tested with the Miyun Reservoir in China.

Zhao, Jianshi; Cai, Ximing; Wang, Zhongjing

2011-08-01

291

Application of modified Kohnen's network to optimization problems  

NASA Astrophysics Data System (ADS)

The traveling salesman problem, which is one of combinatorial optimization problems, is solved by using two different methods: the Hopfield type network and the Kohonen type network. In the Hopfield type network the energy function is defined, whose global minimum must be searched. The energy is shown analytically to decrease monotonically. The time behavior can be discussed analytically, because the input-output function is piecewise linear. The network can always find the optimum solution. In the Kohonen type network the modified version is proposed, in which the mechanism of choice of winner neuron is included automatically in the time evolution equation of the internal state. In usual Hopfield 's network N x N neurons are needed to solve TSP with N cities. It is shown that only N neurons are needed in modified Kohonen's network, which means that the network has a great advantage in the case of the application to TSP with higher number of cities or in the application to more complicated combinatorial optimization problems. The relation between the Hopfield type network and the modified Kohonen type network is discussed.

Shimizu, Toshihiro

2007-03-01

292

Mathematical theory of a relaxed design problem in structural optimization  

NASA Technical Reports Server (NTRS)

Various attempts have been made to construct a rigorous mathematical theory of optimization for size, shape, and topology (i.e. layout) of an elastic structure. If these are represented by a finite number of parametric functions, as Armand described, it is possible to construct an existence theory of the optimum design using compactness argument in a finite dimensional design space or a closed admissible set of a finite dimensional design space. However, if the admissible design set is a subset of non-reflexive Banach space such as L(sup infinity)(Omega), construction of the existence theory of the optimum design becomes suddenly difficult and requires to extend (i.e. generalize) the design problem to much more wider class of design that is compatible to mechanics of structures in the sense of variational principle. Starting from the study by Cheng and Olhoff, Lurie, Cherkaev, and Fedorov introduced a new concept of convergence of design variables in a generalized sense and construct the 'G-Closure' theory of an extended (relaxed) optimum design problem. A similar attempt, but independent in large extent, can also be found in Kohn and Strang in which the shape and topology optimization problem is relaxed to allow to use of perforated composites rather than restricting it to usual solid structures. An identical idea is also stated in Murat and Tartar using the notion of the homogenization theory. That is, introducing possibility of micro-scale perforation together with the theory of homogenization, the optimum design problem is relaxed to construct its mathematical theory. It is also noted that this type of relaxed design problem is perfectly matched to the variational principle in structural mechanics.

Kikuchi, Noboru; Suzuki, Katsuyuki

1990-01-01

293

A Discriminative Sentence Compression Method as Combinatorial Optimization Problem  

NASA Astrophysics Data System (ADS)

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

Hirao, Tsutomu; Suzuki, Jun; Isozaki, Hideki

294

A novel weight-improved particle swarm optimization algorithm for optimal power flow and economic load dispatch problems  

Microsoft Academic Search

The optimization problems of optimal power flow (OPF) and the economic load dispatch (ELD) with valve-point effects in power systems are recently solved by some types of artificial intelligent (AI) algorithms. In this paper, based on improving the function of weight parameters, we present a novel weight-improved particle swarm optimization (WIPSO) method for computing two above problems. To evaluate the

PhanTu Vu; DinhLuong Le; NgocDieu Vo; Josef Tlusty

2010-01-01

295

Radar rainfall estimation as an optimal prediction problem  

NASA Astrophysics Data System (ADS)

A formulation of the radar rainfall estimation problem as optimal statistical prediction of area-averaged rainfall accumulations based on the radar measured reflectivity is presented. Questions of the estimation and validation of such optimal prediction procedures based on large samples of synchronous radar and raingage measurement are analyzed. Our approach accepts the truth that radar cannot mimic the near-point raingage sampling and that proper quantification of the area-point difference is necessary. The questions and consequences which originate from our formulation of the radar rainfall estimation/validation problem are formalized statistically and investigated using both statistical modeling and data analysis. A general definition of the error of the radar rainfall predictions in terms of bivariate probability distributions of the radar and true rainfalls is discussed. The raingage representativeness error structure is analyzed based on the available data. An analytically tractable statistical model of the radar-raingage comparisons is developed. It shows the large impact of the estimation method on the resulting reflectivity-rainrate conversion and the incompleteness of the system due to the radar and raingage errors. These effects prove the need of additional data on the raingage area-point difference structure. Next, an Error Separation Method for the error variance estimation of the radar rainfall predictions is developed. This method is based on additional data on the rainfield small scale correlation structure. Finally, a global optimization approach to the multiparameter radar rainfall prediction is developed. The prediction algorithm is designed to minimize the error variance of the final radar rainfall product. The general radar rainfall estimation/validation methodologies developed here can also be applied to other remote sensing rainfall estimation problems. The work is concluded with a summary discussion of the obtained results and of the research directions that might stem from those results.

Ciach, Grzegorz Jan

296

Computational and statistical tradeoffs via convex relaxation  

PubMed Central

Modern massive datasets create a fundamental problem at the intersection of the computational and statistical sciences: how to provide guarantees on the quality of statistical inference given bounds on computational resources, such as time or space. Our approach to this problem is to define a notion of “algorithmic weakening,” in which a hierarchy of algorithms is ordered by both computational efficiency and statistical efficiency, allowing the growing strength of the data at scale to be traded off against the need for sophisticated processing. We illustrate this approach in the setting of denoising problems, using convex relaxation as the core inferential tool. Hierarchies of convex relaxations have been widely used in theoretical computer science to yield tractable approximation algorithms to many computationally intractable tasks. In the current paper, we show how to endow such hierarchies with a statistical characterization and thereby obtain concrete tradeoffs relating algorithmic runtime to amount of data.

Chandrasekaran, Venkat; Jordan, Michael I.

2013-01-01

297

CONVERGENCE OF COSTS IN AN OPTIMAL STOPPING PROBLEM FOR A PARTIALLY OBSERVABLE MODEL  

Microsoft Academic Search

UThe problem of optimal stopping of a stochastic process with incomplete data is reduced to the problem of optimal stopping of a stochastic process with complete data and the convergence of payofis is proved when \\

P. Babilua; I. Bokuchava; B. Dochviri; M. Shashiashvili

298

Feed Forward Neural Network and Optimal Control Problem with Control and State Constraints  

SciTech Connect

A feed forward neural network based optimal control synthesis is presented for solving optimal control problems with control and state constraints. The paper extends adaptive critic neural network architecture proposed by [5] to the optimal control problems with control and state constraints. The optimal control problem is transcribed into a nonlinear programming problem which is implemented with adaptive critic neural network. The proposed simulation method is illustrated by the optimal control problem of nitrogen transformation cycle model. Results show that adaptive critic based systematic approach holds promise for obtaining the optimal control with control and state constraints.

Kmet', Tibor [Department of Informatics, Constantine the Philosopher University, Tr. A. Hlinku 1, 949 74 Nitra (Slovakia); Kmet'ova, Maria [Department of Mathematics, Constantine the Philosopher University, Tr. A. Hlinku 1, 949 74 Nitra (Slovakia)

2009-09-09

299

Analysis of a Path Following Method for Nonsmooth Convex Programs  

Microsoft Academic Search

Recently Gilbert, Gonzaga and Karas (7) constructed examples of ill-behaved central paths for convex programs. In this paper we show that under mild conditions the central path has sucient smoothness to allow construction of a path-following interior point algorithm for non-dierentiable convex programs. We show that starting from a point near the cen- ter of the first set an †-optimal

Sanjay Mehrotra

300

Affine Buildings and Tropical Convexity  

Microsoft Academic Search

The notion of convexity in tropical geometry is closely related to notions of convexity in the theory of affine buildings. We explore this relationship from a combinatorial and computational perspective. Our results include a convex hull algorithm for the Bruhat--Tits building of SL$_d(K)$ and techniques for computing with apartments and membranes. While the original inspiration was the work of Dress

Michael Joswig; Bernd Sturmfels; Josephine Yu

2007-01-01

301

Hybrid Particle Swarm Optimization Approach for Solving the Discrete OPF Problem Considering the Valve Loading Effects  

Microsoft Academic Search

This paper presents a hybrid particle swarm optimization algorithm (HPSO) as a modern optimization tool to solve the discrete optimal power flow (OPF) problem that has both discrete and continuous optimization variables. The problem is classified as constrained mixed integer nonlinear programming with multimodal characteristics. The objective functions considered are the system real power losses, fuel cost, and the gaseous

M. R. AlRashidi; M. E. El-Hawary

2007-01-01

302

A non-parametric heuristic algorithm for convex and non-convex data clustering based on equipotential surfaces  

Microsoft Academic Search

In this paper, using the concepts of field theory and potential functions a sub-optimal non-parametric algorithm for clustering of convex and non-convex data is proposed. For this purpose, equipotential surfaces, created by interaction of the potential functions, are applied. Equipotential surfaces are the geometric location of the points in the space on which the potential is constant. It means all

Farhad Bayat; Ehsan Adeli Mosabbeb; Ali Akbar Jalali; Farshad Bayat

2010-01-01

303

On the problem of optimal thrust programming for a lunar soft landing  

Microsoft Academic Search

The problem of minimal fuel thrust programming for the terminal phase of a lunar soft landing mission is shown to be equivalent to the minimal time problem for the mission. The existence of an optimal (minimal fuel) thrust program for the problem is then assured by appealing to existence theorems for time optimal controls, and the optimal thrust program is

J. Meditch; V. G. Boltyanskii; R. V. Gamkrelidze; E. F. Llischenko

1964-01-01

304

Convex trace functions on quantum channels and the additivity conjecture  

SciTech Connect

We study a natural generalization of the additivity problem in quantum information theory: given a pair of quantum channels, then what is the set of convex trace functions that attain their maximum on unentangled inputs if they are applied to the corresponding output state? We prove several results on the structure of the set of those convex functions that are 'additive' in this more general sense. In particular, we show that all operator convex functions are additive for the Werner-Holevo channel in 3x3 dimensions, which contains the well-known additivity results for this channel as special cases.

Mueller, Markus [Institut fuer Mathematik, Technische Universitaet Berlin, Strasse des 17. Juni 136, 10623 Berlin (Germany) and Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig (Germany)

2009-05-15

305

Optimal order multilevel preconditioners for regularized ill-posed problems  

NASA Astrophysics Data System (ADS)

In this article we design and analyze multilevel preconditioners for linear systems arising from regularized inverse problems. Using a scale-independent distance function that measures spectral equivalence of operators, it is shown that these preconditioners approximate the inverse of the operator to optimal order with respect to the spatial discretization parameter h . As a consequence, the number of preconditioned conjugate gradient iterations needed for solving the system will decrease when increasing the number of levels, with the possibility of performing only one fine-level residual computation if h is small enough. The results are based on the previously known two-level preconditioners of Rieder (1997) (see also Hanke and Vogel (1999)), and on applying Newton-like methods to the operator equation X^{-1} - A = 0 . We require that the associated forward problem has certain smoothing properties; however, only natural stability and approximation properties are assumed for the discrete operators. The algorithm is applied to a reverse-time parabolic equation, that is, the problem of finding the initial value leading to a given final state. We also present some results on constructing restriction operators with preassigned approximating properties that are of independent interest.

Draganescu, Andrei; Dupont, Todd F.

2008-12-01

306

[Design method of convex master gratings for replicating flat-field concave gratings].  

PubMed

Flat-field concave diffraction grating is the key device of a portable grating spectrometer with the advantage of integrating dispersion, focusing and flat-field in a single device. It directly determines the quality of a spectrometer. The most important two performances determining the quality of the spectrometer are spectral image quality and diffraction efficiency. The diffraction efficiency of a grating depends mainly on its groove shape. But it has long been a problem to get a uniform predetermined groove shape across the whole concave grating area, because the incident angle of the ion beam is restricted by the curvature of the concave substrate, and this severely limits the diffraction efficiency and restricts the application of concave gratings. The authors present a two-step method for designing convex gratings, which are made holographically with two exposure point sources placed behind a plano-convex transparent glass substrate, to solve this problem. The convex gratings are intended to be used as the master gratings for making aberration-corrected flat-field concave gratings. To achieve high spectral image quality for the replicated concave gratings, the refraction effect at the planar back surface and the extra optical path lengths through the substrate thickness experienced by the two divergent recording beams are considered during optimization. This two-step method combines the optical-path-length function method and the ZEMAX software to complete the optimization with a high success rate and high efficiency. In the first step, the optical-path-length function method is used without considering the refraction effect to get an approximate optimization result. In the second step, the approximate result of the first step is used as the initial value for ZEMAX to complete the optimization including the refraction effect. An example of design problem was considered. The simulation results of ZEMAX proved that the spectral image quality of a replicated concave grating is comparable with that of a directly recorded concave grating. PMID:19839358

Zhou, Qian; Li, Li-Feng

2009-08-01

307

Algorithms for bilevel optimization  

NASA Technical Reports Server (NTRS)

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

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

1994-01-01

308

Human opinion dynamics: An inspiration to solve complex optimization problems  

PubMed Central

Human interactions give rise to the formation of different kinds of opinions in a society. The study of formations and dynamics of opinions has been one of the most important areas in social physics. The opinion dynamics and associated social structure leads to decision making or so called opinion consensus. Opinion formation is a process of collective intelligence evolving from the integrative tendencies of social influence with the disintegrative effects of individualisation, and therefore could be exploited for developing search strategies. Here, we demonstrate that human opinion dynamics can be utilised to solve complex mathematical optimization problems. The results have been compared with a standard algorithm inspired from bird flocking behaviour and the comparison proves the efficacy of the proposed approach in general. Our investigation may open new avenues towards understanding the collective decision making.

Kaur, Rishemjit; Kumar, Ritesh; Bhondekar, Amol P.; Kapur, Pawan

2013-01-01

309

Human opinion dynamics: An inspiration to solve complex optimization problems  

NASA Astrophysics Data System (ADS)

Human interactions give rise to the formation of different kinds of opinions in a society. The study of formations and dynamics of opinions has been one of the most important areas in social physics. The opinion dynamics and associated social structure leads to decision making or so called opinion consensus. Opinion formation is a process of collective intelligence evolving from the integrative tendencies of social influence with the disintegrative effects of individualisation, and therefore could be exploited for developing search strategies. Here, we demonstrate that human opinion dynamics can be utilised to solve complex mathematical optimization problems. The results have been compared with a standard algorithm inspired from bird flocking behaviour and the comparison proves the efficacy of the proposed approach in general. Our investigation may open new avenues towards understanding the collective decision making.

Kaur, Rishemjit; Kumar, Ritesh; Bhondekar, Amol P.; Kapur, Pawan

2013-10-01

310

A scatter learning particle swarm optimization algorithm for multimodal problems.  

PubMed

Particle swarm optimization (PSO) has been proved to be an effective tool for function optimization. Its performance depends heavily on the characteristics of the employed exemplars. This necessitates considering both the fitness and the distribution of exemplars in designing PSO algorithms. Following this idea, we propose a novel PSO variant, called scatter learning PSO algorithm (SLPSOA) for multimodal problems. SLPSOA contains some new algorithmic features while following the basic framework of PSO. It constructs an exemplar pool (EP) that is composed of a certain number of relatively high-quality solutions scattered in the solution space, and requires particles to select their exemplars from EP using the roulette wheel rule. By this means, more promising solution regions can be found. In addition, SLPSOA employs Solis and Wets' algorithm as a local searcher to enhance its fine search ability in the newfound solution regions. To verify the efficiency of the proposed algorithm, we test it on a set of 16 benchmark functions and compare it with six existing typical PSO algorithms. Computational results demonstrate that SLPSOA can prevent premature convergence and produce competitive solutions. PMID:24108491

Ren, Zhigang; Zhang, Aimin; Wen, Changyun; Feng, Zuren

2014-07-01

311

Convexity, complexity, and high dimensions  

Microsoft Academic Search

We discuss metric, algorithmic and geometric issues related to broadly understood complexity of high dimensional convex sets. The specific topics we bring up include metric entropy and its duality, derandomization of constructions of normed spaces or of convex bodies, and different fundamental questions related to geometric diversity of such bodies, as measured by various isomorphic (as opposed to isometric) invariants.

Stanislaw J. Szarek

312

Convex sets in acyclic digraphs  

Microsoft Academic Search

A non-empty set X of vertices of an acyclic digraph is called con- nected if the underlying undirected graph induced by X is connected and it is called convex if no two vertices of X are connected by a directed path in which some vertices are not in X. The set of con- vex sets (connected convex sets) of an

Paul N. Balister; Stefanie Gerke; Gregory Gutin

2007-01-01

313

Mathematical programs with a two-dimensional reverse convex constraint  

Microsoft Academic Search

We consider the problem min {f(x): x ? G, T(x) ? int D}, where f is a lower semicontinuous function, G a compact, nonempty set in Rn, D a closed convex set in R2 with nonempty interior and T a continuous mapping from Rn to R2. The constraint T(x) ? int D is a reverse convex constraint, so the feasible

P. T. Thach; R. E. Burkard; W. Oettli

1991-01-01

314

Probabilistic and Worst Case Analyses of Classical Problems of Combinatorial Optimization in Euclidean Space.  

National Technical Information Service (NTIS)

The classical problems reviewed are the traveling salesman problem, minimal spanning tree, minimal matching, greedy matching, minimal triangulation, and others. Each optimization problem is considered for finite sets of points in R to the d power, and the...

J. M. Steele

1990-01-01

315

A Method for Solving Optimization Problems in Continuous Space Using Ant Colony Algorithm  

Microsoft Academic Search

We state our algorithm using the nonlinear programming (NLP) problem, objective function G is a given non-linear function.\\u000a Constraint conditions that represented by a set of inequalities form a convex domain of R\\u000a n. We can obtain the minimal n-d hypercube that can be defined as the following inequalities: l\\u000a i?x\\u000a i?U\\u000a i (I = 1, 2, …, n). Let

Ling Chen; Jie Sheng; Ling Qin; Hongjian Chen

2002-01-01

316

Multiagent optimization system for solving the traveling salesman problem (TSP).  

PubMed

The multiagent optimization system (MAOS) is a nature-inspired method, which supports cooperative search by the self-organization of a group of compact agents situated in an environment with certain sharing public knowledge. Moreover, each agent in MAOS is an autonomous entity with personal declarative memory and behavioral components. In this paper, MAOS is refined for solving the traveling salesman problem (TSP), which is a classic hard computational problem. Based on a simplified MAOS version, in which each agent manipulates on extremely limited declarative knowledge, some simple and efficient components for solving TSP, including two improving heuristics based on a generalized edge assembly recombination, are implemented. Compared with metaheuristics in adaptive memory programming, MAOS is particularly suitable for supporting cooperative search. The experimental results on two TSP benchmark data sets show that MAOS is competitive as compared with some state-of-the-art algorithms, including the Lin-Kernighan-Helsgaun, IBGLK, PHGA, etc., although MAOS does not use any explicit local search during the runtime. The contributions of MAOS components are investigated. It indicates that certain clues can be positive for making suitable selections before time-consuming computation. More importantly, it shows that the cooperative search of agents can achieve an overall good performance with a macro rule in the switch mode, which deploys certain alternate search rules with the offline performance in negative correlations. Using simple alternate rules may prevent the high difficulty of seeking an omnipotent rule that is efficient for a large data set. PMID:19095545

Xie, Xiao-Feng; Liu, Jiming

2009-04-01

317

Optimization methods applied for solving the short-term hydrothermal coordination problem  

Microsoft Academic Search

Short-term hydrothermal coordination (STHTC) is a very complicated optimization problem. It is a dynamic large-scale non-linear problem and requires solving unit commitment and economic power load dispatch problems. From this perspective, many successful and powerful optimization methods and algorithms have been employed to solve this problem. These optimization methodologies and techniques are widely diverse and have been the subject of

I. A. Farhat; M. E. El-Hawary

2009-01-01

318

Improved Particle Swarm Optimization with a Collective Local Unimodal Search for Continuous Optimization Problems  

PubMed Central

A new local search technique is proposed and used to improve the performance of particle swarm optimization algorithms by addressing the problem of premature convergence. In the proposed local search technique, a potential particle position in the solution search space is collectively constructed by a number of randomly selected particles in the swarm. The number of times the selection is made varies with the dimension of the optimization problem and each selected particle donates the value in the location of its randomly selected dimension from its personal best. After constructing the potential particle position, some local search is done around its neighbourhood in comparison with the current swarm global best position. It is then used to replace the global best particle position if it is found to be better; otherwise no replacement is made. Using some well-studied benchmark problems with low and high dimensions, numerical simulations were used to validate the performance of the improved algorithms. Comparisons were made with four different PSO variants, two of the variants implement different local search technique while the other two do not. Results show that the improved algorithms could obtain better quality solution while demonstrating better convergence velocity and precision, stability, robustness, and global-local search ability than the competing variants.

Arasomwan, Martins Akugbe; Adewumi, Aderemi Oluyinka

2014-01-01

319

Improved particle swarm optimization with a collective local unimodal search for continuous optimization problems.  

PubMed

A new local search technique is proposed and used to improve the performance of particle swarm optimization algorithms by addressing the problem of premature convergence. In the proposed local search technique, a potential particle position in the solution search space is collectively constructed by a number of randomly selected particles in the swarm. The number of times the selection is made varies with the dimension of the optimization problem and each selected particle donates the value in the location of its randomly selected dimension from its personal best. After constructing the potential particle position, some local search is done around its neighbourhood in comparison with the current swarm global best position. It is then used to replace the global best particle position if it is found to be better; otherwise no replacement is made. Using some well-studied benchmark problems with low and high dimensions, numerical simulations were used to validate the performance of the improved algorithms. Comparisons were made with four different PSO variants, two of the variants implement different local search technique while the other two do not. Results show that the improved algorithms could obtain better quality solution while demonstrating better convergence velocity and precision, stability, robustness, and global-local search ability than the competing variants. PMID:24723827

Arasomwan, Martins Akugbe; Adewumi, Aderemi Oluyinka

2014-01-01

320

Solving a class of geometric programming problems by an efficient dynamic model  

NASA Astrophysics Data System (ADS)

In this paper, a neural network model is constructed on the basis of the duality theory, optimization theory, convex analysis theory, Lyapunov stability theory and LaSalle invariance principle to solve geometric programming (GP) problems. The main idea is to convert the GP problem into an equivalent convex optimization problem. A neural network model is then constructed for solving the obtained convex programming problem. By employing Lyapunov function approach, it is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the original problem. The simulation results also show that the proposed neural network is feasible and efficient.

Nazemi, Alireza; Sharifi, Elahe

2013-03-01

321

Swarm intelligence for hybrid cost dispatch problem  

Microsoft Academic Search

The paper presents a modified particle swarm optimizer (PSO) to solve the economic power dispatch problem with piecewise quadratic cost function. Practically, operating conditions of many generating units require that the cost function be segmented as piecewise quadratic functions instead of using one convex function for each generator. The proposed technique is applied to a case study of multiple intersecting

A. I. El-Gallad; M. El-Hawary; A. A. Sallam; A. Kalas

2001-01-01

322

Bank Assets and Liabilities Portfolio Optimization Model Based on the Dual-Gap Immunity of the Directional Duration and Directional Convexity  

Microsoft Academic Search

Changes in market interest rates led to the changes of bank's assets and liabilities values, which led to the change of the owner's equity of the bank and bring in risk to the bank owners. As a result, interest rate risk management of commercial banks is extremely important. We built a portfolio optimal model for bank assets and liabilities management

Haowen Wu; Guotai Chi

2009-01-01

323

An implementation of harmony search algorithm to unit commitment problem  

Microsoft Academic Search

This paper presents a harmony search algorithm (HSA) to solve unit commitment (UC) problem. HSA was conceptualized using the\\u000a musical process of searching for a perfect state of harmony, just as the optimization process seeks to find a global solution\\u000a that is determined by an objective function. HSA can be used to optimize a non-convex optimization problem with both continuous

M. Afkousi-Paqaleh; M. Rashidinejad; M. Pourakbari-Kasmaei

2010-01-01

324

SAT-decoding in evolutionary algorithms for discrete constrained optimization problems  

Microsoft Academic Search

For complex optimization problems, several population-based heuristics like Multi-Objective Evolutionary Algorithms have been developed. These algorithms are aiming to deliver sufficiently good solutions in an acceptable time. However, for discrete problems that are restricted by several constraints it is mostly a hard problem to even find a single feasible solution. In these cases, the optimization heuristics typically perform poorly as

Martin Lukasiewycz; Michael Glaß; Christian Haubelt; Jürgen Teich

2007-01-01

325

Some Problems of Soil Media Ecology and Optimal Control Processes in Them  

Microsoft Academic Search

New multicomponent soil media ecology problems and respective optimal control problems are considered in the paper. Existence theorems for the unique optimal control are proved for all the cases considered. Computation algorithms of high-accuracy discretization are constructed for some new classes of problems with discontinuous solutions.

I. V. Sergienko; V. S. Deineka

2003-01-01

326

Comparison of derivative-free optimization methods for groundwater supply and hydraulic capture community problems  

Microsoft Academic Search

Management decisions involving groundwater supply and remediation often rely on optimization techniques to determine an effective strategy. We introduce several derivative-free sampling methods for solving constrained optimization problems that have not yet been considered in this field, and we include a genetic algorithm for completeness. Two well-documented community problems are used for illustration purposes: a groundwater supply problem and a

K. R. Fowler; J. P. Reese; C. E. Kees; J. E. Dennis; C. T. Kelley; C. T. Miller; C. Audet; A. J. Booker; G. Couture; R. W. Darwin; M. W. Farthing; D. E. Finkel; J. M. Gablonsky; G. Gray; T. G. Kolda

2008-01-01

327

On the minimal convex annulus of a planar convex body  

Microsoft Academic Search

In this paper we introduce the notion of a minimal convex annulusK (C) of a convex bodyC, generalizing the concept of a minimal circular annulus. Then we prove the existence — as for the minimal circular annulus — of a Radon partition of the set of contact points of the boundaries ofK (C) andC. Subsequently, the uniqueness ofK (C) is

Carla Peri; Andreana Zucco

1992-01-01

328

Mathematical Optimization--A Successful Tool for Logistics Problems.  

National Technical Information Service (NTIS)

Recent developments in mathematical optimization are substantially enhancing the scope and power of logistics planning systems. Based on these advances, successful applications of sophisticated mathematical optimization logistics systems are occurring wor...

F. Glover D. Klingman

1981-01-01

329

Utilizing Problem Structure in Optimization of Radiation Therapy.  

National Technical Information Service (NTIS)

In this thesis, optimization approaches for intensity-modulated radiation therapy are developed and evaluated with focus on numerical efficiency and treatment delivery aspects. The first two papers deal with strategies for solving fluence map optimization...

F. Carlsson

2008-01-01

330

Hybrid Solution of Stochastic Optimal Control Problems Using Gauss Pseudospectral Method and Generalized Polynomial Chaos Algorithms.  

National Technical Information Service (NTIS)

Two numerical methods, Gauss Pseudospectral Method and Generalized Polynomial Chaos Algorithm, were combined to form a hybrid algorithm for solving nonlinear optimal control and optimal path planning problems with uncertain parameters. The algorithm was a...

G. C. Cottrill

2012-01-01

331

Matrix Eigenvalue Problems, Jacobi-type Methods, and Optimization on Graf3mannians  

Microsoft Academic Search

A differential geometry approach for the design of algorithms for solving the generalized eigenvalue problem AZ = M?z is presented. In a first step the generalized eigenvalue problem is reformulated as an intersection problem of subspaces. The square matrices A and B are possibly singular. This intersection problem is then formulated as an optimization problem for smooth functions on Graf3mann

K. Hiiper; J. B. Moore; U. Helmke

332

Ant colony optimization and local search for bin packing and cutting stock problems  

Microsoft Academic Search

The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimization problems. Exact solution methods can only be used for very small instances, so for real-world problems, we have to rely on heuristic methods. In recent years, researchers have started to apply evolutionary approaches to these problems, including Genetic Algorithms and Evolutionary Programming. In

J Levine; F Ducatelle

2004-01-01

333

Shock Diffraction by Convex Cornered Wedges for the Nonlinear Wave System  

NASA Astrophysics Data System (ADS)

We are concerned with rigorous mathematical analysis of shock diffraction by two-dimensional convex cornered wedges in compressible fluid flow, through the nonlinear wave system. This shock diffraction problem can be formulated as a boundary value problem for second-order nonlinear partial differential equations of mixed elliptic-hyperbolic type in an unbounded domain. It can be further reformulated as a free boundary problem for nonlinear degenerate elliptic equations of second order with a degenerate oblique derivative boundary condition. We establish a global theory of existence and optimal regularity for this shock diffraction problem. To achieve this, we develop several mathematical ideas and techniques, which are also useful for other related problems involving similar analytical difficulties.

Chen, Gui-Qiang; Deng, Xuemei; Xiang, Wei

2014-01-01

334

Particle Swarm Optimization for multimodal combinatorial problems and its application to protein design  

Microsoft Academic Search

Particle Swarm Optimization (PSO) is a well-known technique for numerical optimization with real-parameter representation. Like other meta-heuristics, PSO is usually designed for the goal of finding a single optimal solution for a given problem. However, many scientific and engineering optimization problems have convoluted search spaces with a large number of optima. This paper explores the ability of a cooperative combinatorial

Grecia Lapizco-Encinas; Carl Kingsford; James A. Reggia

2010-01-01

335

Necessary Optimality Conditions for Some Control Problems of Elliptic Equations with Venttsel Boundary Conditions  

SciTech Connect

In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The control is applied to the state equation via the boundary and a functional of the control together with the solution of the state equation under such a control will be minimized. A constraint on the solution of the state equation is also considered.

Luo Yousong, E-mail: yluo@rmit.edu.a [RMIT University, School of Mathematical and Geospatial Sciences (Australia)

2010-06-15

336

OPTIMIZATION MODEL FOR LARGE-SCALE BUS TRANSIT SCHEDULING PROBLEMS  

Microsoft Academic Search

A procedure is presented for solving real-world large-scale multiple depot vehicle scheduling (MDVS) problems considering the route time constraints (RTCs). The procedure is applied to some test problems and then to a real-world problem. The real-world problem is the transit bus scheduling problem of the mass transit administration (MTA) in Baltimore, Maryland. The RTCs are added to the MDVS problem

Mohamadreza Banihashemi; Ali Haghani

2000-01-01

337

Convex preserving scattered data interpolation using bivariate C1 cubic splines  

NASA Astrophysics Data System (ADS)

We use bivariate C1 cubic splines to deal with convexity preserving scattered data interpolation problem. Using a necessary and sufficient condition on Bernstein-Bézier polynomials, we set the convexity-preserving interpolation problem into a quadratically constraint quadratic programming problem. We show the existence of convexity preserving interpolatory surfaces under certain conditions on the data. That is, under certain conditions on the data, there always exists a convexity preservation C1 cubic spline interpolation if the triangulation is refined sufficiently many times. We then replace the quadratical constrains by three linear constrains and formulate the problem into linearly constraint quadratic programming problems in order to be able to solve it easily. Certainly, the existence of convexity preserving interpolatory surfaces is equivalent to the feasibility of the linear constrains. We present a numerical experiment to test which of these three linear constraints performs the best.

Lai, Ming-Jun

2000-07-01

338

A Primal-Dual Iterative Scheme for Solving Capacity Planning Problems under Uncertainty  

NASA Astrophysics Data System (ADS)

In this paper we present an application of robust optimization to capacity planning problems under uncertainty. We present the framework to handle uncertainty and discuss the computational complexity of capacity planning problems under this framework. We show that the formulation is not only intuitive but the computational complexity of a large variety of problems is the same as linear (in general convex) programming.

Aswal, Abhilasha; Prasanna, G. N. Srinivasa

2010-10-01

339

A Procedure for Computing the K Best Solutions to Discrete Optimization Problems and Its Application to the Shortest Path Problem  

Microsoft Academic Search

A general procedure is presented for computing the best, 2nd best,..., Kth best solutions to a given discrete optimization problem. If the number of computational steps required to find an optimal solution to a problem with n(0, 1) variables is c(n), then the amount of computation required to obtain the if best solutions is O(Knc<\\/sub>(n)). The procedure specializes to published

Eugene L. Lawler

1972-01-01

340

An optimal control model for human postural regulation  

Microsoft Academic Search

This paper proposes a convex optimal control problem as a mathematical model of human postural control during quiet standing. The human body is modeled as a two-segment inverted pendulum controlled by a single ankle torque. Several performance criteria that are quartic in the state and quadratic in the control are utilized. The discrete-time approximation to each of these problems is

Yao Li; W. S. Levine

2009-01-01

341

An optimal model predictive control model for human postural regulation  

Microsoft Academic Search

A series of convex optimal control problems is proposed as mathematical models of human postural control during quiet standing. The human body is modeled as a two-segment inverted pendulum controlled by a joint torque. Several performance criteria that are quartic in the state and quadratic in the control are utilized. The discrete-time approximation to each of these problems is a

Yao Li; W. S. Levine

2009-01-01

342

Convergence of Newton's Method for Convex Best Interpolation 1  

Microsoft Academic Search

In this paper, we consider the problem of nding a convex function which interpolates given points and has a minimal L 2 norm of the second derivative. This problem reduces to a system of equations involving semismooth functions. We study a Newton-type method utilizing Clarke's generalized Jacobian and prove that its local convergence is superlinear. For a special choice of

Asen L. Dontchev; Houduo Qi; Liqun Qi

1999-01-01

343

Multi-criteria Human Resource Allocation for Optimization Problems Using Multi-objective Particle Swarm Optimization Algorithm  

Microsoft Academic Search

Multi-criteria human resource allocation involves deciding how to divide human resource of limited availability among multiple demands in a way that optimizes current objectives. This paper aims to solve the multi-criteria optimal allocation of human resources issues using multi-objective particle swarm optimization (MOPSO). In this paper, we tackled this problem via a multi-objective decision-making model using a multi-objective PSO. We

Zhengyuan Jia; Lihua Gong

2008-01-01

344

Hybrid genetic algorithm research and its application in problem optimization  

Microsoft Academic Search

There is a lot of research in genetic algorithm about structural optimization. But as far as the large multi-goal program is concerned, it limits the application of genetic algorithm for the reason of its specialty and large calculation. In order to explore a new resolution, the author proposed a combining algorithm for structural optimization, which is based on genetic algorithm

Weijin Jiang I; Dingti Luol; Yusheng Xu; Xingming Sun

2004-01-01

345

Optimal experimental design and some related control problems  

Microsoft Academic Search

This paper traces the strong relations between experimental design and control, such as the use of optimal inputs to obtain precise parameter estimation in dynamical systems and the introduction of suitably designed perturbations in adaptive control. The mathematical background of optimal experimental design is briefly presented, and the role of experimental design in the asymptotic properties of estimators is emphasized.

Luc Pronzato

2008-01-01

346

Strengthening the conditions of Clarke and Smirnov for convex-valued differential inclusions  

SciTech Connect

Assume that a Lipschitz continuous differential inclusion with convex images and locally compact graph is fixed on a certain time interval. For trajectories of this inclusion the problem of the minimization of a smooth end-point function is considered under smooth end-point constraints of equality and inequality types. This problem is approximated by a sequence of smooth optimal control problems with regular mixed constraints, which are treated using the maximum principle obtained earlier by the author in conjunction with Dubovitskii. Passing to the limit in the conditions of the maximum principle one obtains necessary conditions for strong minimality in the initial problem which refine the well-known conditions of Clarke and Smirnov.

Milyutin, A A [N.N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow (Russian Federation)

2003-02-28

347

Ant colony optimization algorithm to solve split delivery vehicle routing problem  

Microsoft Academic Search

As a combinatorial optimization problem, vehicle routing problem (VRP) is a typical NP-hard problem; an assumption that the demand of customers can not be split is given to the traditional VRP formulation. However, the transportation cost can be reduced by means of splitting the demand of customers in practical logistics operation. This paper solved the split delivery vehicle routing problem

Lu-si Sui; Jia-fu Tang; Zhendong Pan; Shu-an Liu

2008-01-01

348

The Dynamic Programming Approach to the Multicriterion Optimization Problem.  

National Technical Information Service (NTIS)

Decision makers are often confronted with problems for which there exist several distinct measures of success. Such problems can often be expressed in terms of linear or nonlinear programming models with several 'criterion' functions instead of single obj...

K. K. Bog

1978-01-01

349

Optimization of Distribution Routing Problem Based on Travel Time Reliability  

Microsoft Academic Search

As part of solutions to the technical problem of logistics distribution, vehicle routing problem (VRP) is getting more and more attention in academics and enterprises, it belongs to the NP-hard problem theoretically. VRP with time windows and capacity constraint in stochastic traffic network was studied based on travel time reliability . Firstly, travel time was expressed as a random variable

Jie Gao

2009-01-01

350

Stability Analysis of Gradient-Based Neural Networks for Optimization Problems  

Microsoft Academic Search

The paper introduces a new approach to analyze the stability of neural network models without using any Lyapunov function. With the new approach, we investigate the stability properties of the general gradient-based neural network model for optimization problems. Our discussion includes both isolated equilibrium points and connected equilibrium sets which could be unbounded. For a general optimization problem, if the

Qiaoming Han; Li-Zhi Liao; Houduo Qi; Liqun Qi

2001-01-01

351

Solving Continuous-Time Optimal-Control Problems with a Spreadsheet.  

ERIC Educational Resources Information Center

Explains how optimal control problems can be solved with a spreadsheet, such as Microsoft Excel. Suggests the method can be used by students, teachers, and researchers as a tool to find numerical solutions for optimal control problems. Provides several examples that range from simple to advanced. (JEH)

Naevdal, Eric

2003-01-01

352

Constrained and bicriteria inverse bottleneck optimization problems under weighted Hamming distance  

Microsoft Academic Search

A bottleneck optimization problem (BOP) is to find a feasible solution that minimizes the maximum weight w of edges. While in an inverse (BOP), a candidate solution F?* is first given, and the aim is to modify weights w to w* under some measure such that F?* becomes an optimal bottleneck solution with respect to w*. The constrained inverse problem

Xiucui Guan; Yangbo Cao

2012-01-01

353

Solving the optimal process target problem using response surface designs in heteroscedastic conditions  

Microsoft Academic Search

The contemporary industrial environment continues to rely on the identification of the optimal process target as a means to minimise the product defect rate and ultimately reduce manufacturing costs. Within the context of the optimal process target problem, this paper will offer three distinct contributions. First, a review of literature associated with the process target problem indicates that most research

Paul L. Goethals; Byung Rae Cho

2011-01-01

354

Semi-smooth Newton methods for state-constrained optimal control problems  

Microsoft Academic Search

A regularized optimality system for state-constrained optimal control problems is introduced and semi-smooth Newton methods for its solution are analyzed. Convergence of the regularized problems is proved. Numerical tests confirm the theoretical results and demonstrate the efficiency of the proposed methodology.

Kazufumi Ito; Karl Kunisch

2003-01-01

355

A sequential approximation method using neural networks for engineering design optimization problems  

Microsoft Academic Search

There are three characteristics in engineering design optimization problems: (1) the design variables are often discrete physical quantities; (2) the constraint functions often cannot be expressed analytically in terms of design variables; (3) in many engineering design applications, critical constraints are often ‘pass–fail’, ‘0–1’ type binary constraints. This paper presents a sequential approximation method specifically for engineering optimization problems with

Yeh-Liang Hsu; Shu-Gen Wang; Chia-Chieh Yu

2003-01-01

356

Boolean Query Optimization and the 0-1 Hyperbolic Sum Problem  

Microsoft Academic Search

An “intelligent front-end” or “logic assistant” is an interactive program devised to assist the users of an information retrieval system in the formulation of their queries. In order to provide knowledge usable in such a program, we study a problem of query optimization with an average efficiency criterion. We formulate it as a new combinatorial optimization problem, which we call

Pierre Hansen; Marcus V. Poggi de Aragão; Celso C. Ribeiro

1990-01-01

357

Efficient Initial Solution to Extremal Optimization Algorithm for Weighted MAXSAT Problem  

Microsoft Academic Search

Stochastic local search algorithms are proved to be one of the most effective approach for computing approximate solutions of hard combinatorial problems. Most of them are based on a typical randomness related to some uniform distributions for generating initial solutions. Particularly, Extremal Optimization is a recent meta-heuristic proposed for finding high quality solutions to hard optimization problems. In this paper,

Mohamed El-bachir Menai; Mohamed Batouche

2003-01-01

358

Optimal harvesting control problem for linear periodic age-dependent population dynamics  

Microsoft Academic Search

In this paper, we investigate an optimal harvesting problem for linear periodic age-dependent population dynamics. Namely, we consider the Lotka–Mckendrick model with periodic vital rates and a periodic forcing term that sustains oscillations. By Mazur's Theorem, we demonstrate existence of solutions of the optimal control problem (OH) and by the conception of normal cone, we also obtain the first order

Zhixue Luo; Wan-Tong Li; Miansen Wang

2004-01-01

359

A framework of multi-objective particle swarm optimization in motion segmentation problem  

Microsoft Academic Search

Research in motion segmentation and robust tracking have been getting more attention recently. In video sequence, motion segmentation is considered as multi-objective problem. Better representation and processing of the standard image in video sequence, with efficient segmentation algorithm is required. Thus, multi-objective optimization approach is an appropriate method to solve the optimization problem in motion segmentation. In this paper, we

Nilam Nur Amir Sjarif; Siti Mariyam Shamsuddin; Siti Zaiton Mohd Hashim

2012-01-01

360

A Decomposition Methodology Applied to the Multi-Area Optimal Power Flow Problem  

Microsoft Academic Search

This paper describes a decomposition methodology applied to the multi-area optimal power flow problem in the context of an electric energy system. The proposed procedure is simple and efficient, and presents some advantages with respect to other common decomposition techniques such as Lagrangian relaxation and augmented Lagrangian decomposition. The application to the multi-area optimal power flow problem allows the computation

Francisco J. Nogales; Francisco J. Prieto; Antonio J. Conejo

2003-01-01

361

Solving traveling salesman problems with time windows by genetic particle swarm optimization  

Microsoft Academic Search

The genetic particle swarm optimization (GPSO) was derived from the original particle swarm optimization (PSO), which is incorporated with the genetic reproduction mechanisms, namely crossover and mutation. To solve traveling salesman problems (TSP), a modified genetic particle swarm optimization (MGPSO) was introduced, where the new solution was generated with local best and individual best solutions with crossover and mutation operators.

Wang Cheng; Zeng Maimai; Li Jian

2008-01-01

362

ADVANCES FOR THE POOLING PROBLEM: MODELING, GLOBAL OPTIMIZATION, AND COMPUTATIONAL STUDIES  

Microsoft Academic Search

The pooling problem, an optimization challenge of maximizing proflt subject prod- uct availability, storage capacity, demand, and product speciflcation constraints, has applica- tions to petroleum reflning, wastewater treatment, supply-chain operations, and communica- tions. This review illustrates the long-standing symbiosis between the industrial challenge of optimally combining feed stocks into products and the mathematical fleld of global optimization. We present flve

RUTH MISENER; CHRISTODOULOS A. FLOUDAS

363

State evaluation strategy for exemplar-based policy optimization of dynamic decision problems  

Microsoft Academic Search

Direct policy search (DPS) that optimizes the parameters of a decision making model, combined with evolutionary algorithms which enable robust optimization, is a promising approach to dynamic decision problems. Exemplar- based policy (EBP) optimization is a novel framework for DPS in which the policy is composed of a set of exemplars and a case- based action selector, with the set

Kokolo Ikeda; Hajime Kita

2007-01-01

364

Convex ultrasound image reconstruction with log-Euclidean priors.  

PubMed

Image reconstruction from noisy and incomplete observations is usually an ill-posed problem. A Bayesian framework may be adopted do deal with this such inverse task by well posing the reconstruction problem. In this approach, the ill poseness nature of the reconstruction is removed by minimizing a two-term energy function. The first term pushes the solution toward the data and the second regularizes the solution. A Bayesian algorithm for ultrasound image reconstruction and de-noising is proposed where an edge preserving prior is used to reduce the smoothing effect at the transitions. The prior distribution is based on log-Euclidean potential functions that are particular suitable in reconstruction problems under the constraint of positivity, that is, when the unknowns to be estimated should be positive, which is the case, where the noisy observations are modeled by a Rayleigh distribution. In this paper, the reconstruction procedure is formulated as the optimization of a convex function and a Newton method is adopted to obtain the minimizer. This strategy guarantees a convergence to the global minimum in a small number of iterations. Experimental results, using synthetic and real medical images are shown. The proposed method produces images where speckle noise is effectively suppressed and important clinical details (organ and tissue transitions) are preserved. PMID:19162686

Seabra, José; Xavier, João; Sanches, João

2008-01-01

365

A Computational Approach to Solve Optimal Control Problems Using Differential Transformation  

Microsoft Academic Search

A computational approach based on differential transformation is proposed to solve optimal control problems of dynamical systems. The optimal control law is constructed by solving a two-point-boundary value problem or a Hamilton-Jacobi-Bellman partial differential equation. Using differential transformation, ordinary or partial differential equations are transformed into a system of nonlinear algebraic equations. By using the inverse transformation, the optimal solution

Dzung Du; Inseok Hwang

2007-01-01

366

Problem Formulation for Optimal Array Modeling and Planning  

NASA Technical Reports Server (NTRS)

In this paper we describe an optimal modeling and planning framework for the future large array of DSN antennas. This framework takes into account the array link performance models, reliability models, constrain models, and objective functions, and determines the optimal sub-array clusters configuration that will support the maximum number of concurrent missions based on mission link properties, antenna element reliabilities, mission requests, and array operation constraints. ..

Cheung, Kar-Ming; Lee, Charles H.; Ho, Jeannie

2006-01-01

367

Multidimensional Hermite-Hadamard inequalities and the convex order  

NASA Astrophysics Data System (ADS)

The problem of establishing inequalities of the Hermite-Hadamard type for convex functions on n-dimensional convex bodies translates into the problem of finding appropriate majorants of the involved random vector for the usual convex order. We present two results of partial generality which unify and extend the most part of the multidimensional Hermite-Hadamard inequalities existing in the literature, at the same time that lead to new specific results. The first one fairly applies to the most familiar kinds of polytopes. The second one applies to symmetric random vectors taking values in a closed ball for a given (but arbitrary) norm on . Related questions, such as estimates of approximation and extensions to signed measures, also are briefly discussed.

de La Cal, J.; Carcamo, J.

2006-12-01

368

A Local Collision Avoidance Method for Non-strictly Convex Polyhedra  

Microsoft Academic Search

This paper proposes a local collision avoidance method for non-strictly convex polyhedra with continuous veloc- ities. The main contribution of the method is that non-strictly convex polyhedra can be used as geometric models of the robot and the environment without any approximation. The problem of the continuous interaction generation between polyhedra is re- duced to the continuous constraints generation between

Fumio Kanehiro; Florent Lamiraux; Oussama Kanoun; Eiichi Yoshidaand; Jean-Paul Laumond

369

Using adaptive resonance theory and local optimization to divide and conquer large scale traveling salesman problems  

Microsoft Academic Search

The traveling salesman problem (TSP) is a very hard optimization problem in the field of operations research. It has been shown to be NP-complete, and is an often-used benchmark for new optimization techniques. One of the main challenges with this problem is that standard, non-AI heuristic approaches such as the Lin-Kernighan algorithm (LK) and the chained LK variant are currently

Samuel A. Mulder; Donald C. Wunsch

2003-01-01

370

Topology optimization of heat conduction problems using the finite volume method  

Microsoft Academic Search

This note addresses the use of the finite volume method (FVM) for topology optimization of a heat conduction problem. Issues\\u000a pertaining to the proper choice of cost functions, sensitivity analysis, and example test problems are used to illustrate\\u000a the effect of applying the FVM as an analysis tool for design optimization. This involves an application of the FVM to problems

A. Gersborg-Hansen; M. P. Bendsøe; O. Sigmund

2006-01-01

371

A permutation-based dual genetic algorithm for dynamic optimization problems  

Microsoft Academic Search

Adaptation to dynamic optimization problems is currently receiving growing interest as one of the most important applications\\u000a of genetic algorithms. Inspired by dualism and dominance in nature, genetic algorithms with the dualism mechanism have been\\u000a applied for several dynamic problems with binary encoding. This paper investigates the idea of dualism for combinatorial optimization\\u000a problems in dynamic environments, which are also

Lili Liu; Dingwei Wang; W. H. Ip

2009-01-01

372

Valid Inequalities for a Shortest-Path Routing Optimization Problem  

Microsoft Academic Search

In autonomous systems of the Internet packets are routed on shortest paths to their destinations, for example according to the ECMP principle. The problem of finding a feasible traffic routing configuration realized on paths which can be generated by a system of weights assigned to IP links is NP-hard. This problem can be formulated as a mixed-integer program and attempted

M. Dzida; M. Mycek; M. Zago

373

Impulse control for the optimal dividend and reinvestment problem  

Microsoft Academic Search

In this paper, we mainly consider the dividend payments and reinvestments with both fixed and proportional transaction costs in the diffusion model. Because we have taken into account the fixed transaction costs, the problem was changed the impulse stochastic control problem. The final goal is to maximize the expected value of discounted net cash flow, i.e. dividends paid minus reinvestments,it

Song Yijie; Zhao Xiuping

2010-01-01

374

Optimization Problems in Multisensor and Multitarget Target Tracking.  

National Technical Information Service (NTIS)

The central problem in any surveillance system is the data association problem of partitioning observations into tracks and false alarms. Over the last fifteen years and with support from AFOSR, a new approach has been developed based on the use of multi-...

A. B. Poore

2004-01-01

375

Initial parameters problem of WNN based on particle swarm optimization  

NASA Astrophysics Data System (ADS)

The stock price prediction by the wavelet neural network is about minimizing RMSE by adjusting the parameters of initial values of network, training data percentage, and the threshold value in order to predict the fluctuation of stock price in two weeks. The objective of this dissertation is to reduce the number of parameters to be adjusted for achieving the minimization of RMSE. There are three kinds of parameters of initial value of network: w , t , and d . The optimization of these three parameters will be conducted by the Particle Swarm Optimization method, and comparison will be made with the performance of original program, proving that RMSE can be even less than the one before the optimization. It has also been shown in this dissertation that there is no need for adjusting training data percentage and threshold value for 68% of the stocks when the training data percentage is set at 10% and the threshold value is set at 0.01.

Yang, Chi-I.; Wang, Kaicheng; Chang, Kueifang

2014-04-01

376

A Decomposition-based Multi-objective Particle Swarm Optimization Algorithm for Continuous Optimization Problems  

Microsoft Academic Search

Particle swarm optimization (PSO) is a heuristic optimization technique that uses previous personal best experience and global best experience to search global optimal solutions. This paper studies the application of PSO techniques to multi-objective optimization using decomposition methods. A new decomposition-based multi-objective PSO algorithm is proposed, called MOPSO\\/D. It integrates PSO into a multiobjective evolutionary algorithm based on decomposition (MOEA\\/D).

Wei Peng; Qingfu Zhang

2008-01-01

377

An Optimal Lower Bound for the Frobenius Problem  

Microsoft Academic Search

Given N ? 2 positive integers a1, a2, . . . , aN with GCD(a1, . . . , aN) = 1, let fN denote the largest natural number which is not a positive integer combination of a1, . . . , aN. This paper gives an optimal lower bound for fN in terms of the absolute inhomogeneous minimum of

Peter M. Gruber

2006-01-01

378

Some Marginalist Intuition Concerning the Optimal Commodity Tax Problem  

ERIC Educational Resources Information Center

The author offers a simple intuition that can be exploited to derive and to help interpret some canonical results in the theory of optimal commodity taxation. He develops and explores the principle that the marginal social welfare loss per last unit of tax revenue generated be equalized across tax instruments. A simple two-consumer,…

Brett, Craig

2006-01-01

379

Improved shuffled frog leaping algorithm for continuous optimization problem  

Microsoft Academic Search

Shuffled frog leaping algorithm (SFLA) is mainly used for the discrete space optimization. For SFLA, the population is divided into several memeplexes, several frogs of each memeplex are selected to compose a submemeplex for local evolvement, according to the mechanism that the worst frog learns from the best frog in submemeplex or the best frog in population, and the memeplexes

Ziyang Zhen; DaoBo Wang; Yuanyuan Liu

2009-01-01

380

Optimal Website Design with the Constrained Subtree Selection Problem  

Microsoft Academic Search

We introduce the Constrained Subtree Selection (CSS) prob- lem as a model for the optimal design of websites. Given a hierarchy of topics represented as a DAG G and a probability distribution over the topics, we select a subtree of the transitive closure of G which minimizes the expected path cost. We define path cost as the sum of the

Brent Heeringa; Micah Adler

2004-01-01

381

Unconstrained optimization of coupled magneto-thermal problems  

Microsoft Academic Search

The shape optimization of coupled systems by a gradients-based method is presented. The design specifications are in one system, while the critical parameters are in both systems. The method is demonstrated using an induction heating system. The magnetic and thermal models coexist in the same geometry. The eddy currents calculated from the electromagnetic solution is used as the thermal sources

Tan H. Pham; S. R. H. Hoole

1995-01-01

382

A hybrid particle swarm optimization for vehicle routing problem with simultaneous pickup and delivery  

Microsoft Academic Search

Vehicle routing problem (VRP) is an important and well-known combinatorial optimization problem encountered in many transport logistics and distribution systems. The VRP has several variants depending on tasks performed and on some restrictions, such as time windows, multiple vehicles, backhauls, simultaneous delivery and pick-up, etc. In this paper, we consider vehicle routing problem with simultaneous pickup and delivery (VRPSPD). The

Fatma Pinar GOKSAL; Fulya ALTIPARMAK; Ismail KARAOGLAN

2010-01-01

383

A discrete particle swarm optimization algorithm for the generalized traveling salesman problem  

Microsoft Academic Search

Dividing the set of nodes into clusters in the well-known traveling salesman problem results in the generalized traveling salesman problem which seeking a tour with minimum cost passing through only a single node from each cluster. In this paper, a discrete particle swarm optimization is presented to solve the problem on a set of benchmark instances. The discrete particle swarm

Mehmet Fatih Tasgetiren; Ponnuthurai N. Suganthan; Quan-qe Pan

2007-01-01

384

The potential of optimization in communal routing problems: case studies from Finland  

Microsoft Academic Search

In many European countries, municipalities offer their inhabitants a wide variety of social services. In this paper we will focus on efficiently scheduling home care, transportation of the elderly, and home meal delivery. These so-called municipal or communal routing problems can be modeled as different variants of the vehicle routing problem, a well-known optimization problem from the literature. We present

Olli Bräysy; Wout Dullaert; Pentti Nakari

2009-01-01

385

Ant Colony Optimization for the Single Vehicle Pickup and Delivery Problem with Time Window  

Microsoft Academic Search

The single vehicle pickup and delivery problem with time window (1-PDPTW) is an important class of vehicle routing problem. This problem aims to find a shortest route for a single vehicle to deliver objects from origin to destination, subject to load limit and time window of delivery. This study develops an ant colony optimization (ACO) method for the 1-PDPTW. Specifically,

Yu-Hsuan Huang; Chuan-Kang Ting

2010-01-01

386

Generalized Orienteering Problem for Optimal Search and Interdiction Planning.  

National Technical Information Service (NTIS)

In order to support search planning for counterdrug operations, we introduce a generalized Orienteering Problem (OP) where transit on arcs in a network and reward collection at nodes both consume a variable amount of the same limited resource. We exploit ...

J. Pietz

2013-01-01

387

Optimal Production Growth for the Machine Loading Problem.  

National Technical Information Service (NTIS)

This paper investigates a production growth logistics system for the machine loading problem (generalized transportation model), with a linear cost structure and minimum levels on total machine hours (resources) and product types (demands). An algorithm i...

V. Balachandran

1975-01-01

388

Bit-string optimization in a brachytherapy dosimetry problem  

Microsoft Academic Search

A problem in radiotherapy planning is solved by applying the following search algorithms: artificial genetic search, with fixed crossover probability, with variable crossover probability, and with cut-point distribution; simulated annealing, serial and parallel; stochastic hill-climbing; next-ascent hill-climbing; and steepest-ascent hill-climbing. Given a number of points at each of which a predetermined dose of radiation is required, the problem is to

U. K. Chakraborty; D. Ghosh Dastidar

1992-01-01

389

Reducing computation time in DFP (Davidon, Fletcher & Powell) update method for solving unconstrained optimization problems  

NASA Astrophysics Data System (ADS)

Solving the unconstrained optimization problems is not easy and DFP update method is one of the methods that we can work with to solve the problems. In unconstrained optimization, the time computing needed by the method's algorithm to solve the problems is very vital and because of that, we proposed a hybrid search direction for DFP update method in order to reduce the computation time needed for solving unconstrained optimization problems. Some convergence analysis and numerical results of the hybrid search direction were analyzed and the results showed that the proposed hybrid search direction strictly reduce the computation time needed by DFP update method and at the same time increase the method's efficiency which is sometimes fail for some complicated unconstrained optimization problems.

Sofi, A. Z. M.; Mamat, M.; Ibrahim, M. A. H.

2013-04-01

390

Optimal control problems with switching points. Ph.D. Thesis, 1990 Final Report  

NASA Technical Reports Server (NTRS)

An overview is presented of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.

Seywald, Hans

1991-01-01

391

Topology Optimization of Flow Problems Modeled by the Incompressible Navier-Stokes Equations  

NASA Astrophysics Data System (ADS)

This work is concerned with topology optimization of incompressible flow problems. While size and shape optimization methods are limited to modifying existing boundaries, topology optimization allows for merging boundaries as well as creating new ones. Since topology optimization methods do not require a good initial guess, they are powerful tools for finding new and non-intuitive designs. The latter is particularly beneficial for flow problems which are typically nonlinear as well as transient. Depending on the complexity of the flow problem, predicting a solution may be challenging. Determining an improved or optimized design for complex flow problems is an even greater challenge as it not only requires a solution to the flow problem for a given design, but also a prediction on how a design change will affect the flow. Fluid topology optimization commonly uses a material interpolation approach for describing the geometry during the optimization process: solid material is modeled via an artificial porosity that penalizes the flow velocities. While this approach works well for simple steady-state problems aiming to minimize the dissipated energy, the current study shows that using the porosity approach may cause issues for more complex problems such as coupled fluid-structure-interaction (FSI) systems, unsteady flow problems or problems aiming to match a target performance. To overcome these issues a geometric boundary description based on level sets is developed. This geometric boundary description is applied to both, a steady-state hydrodynamic lattice Boltzmann formulation and a stabilized finite element formulation of the steady-state Navier-Stokes equations. The enforcement of the no-slip condition along the fluid-solid interface is handled via an immersed boundary technique in case of the lattice Boltzmann method, while the Navier-Stokes formulation uses an extended finite element method (XFEM). Through the research conducted in this work, the spectrum of flow problems that can be solved by topology optimization techniques has been broadened significantly.

Kreissl, Sebastian

392

Optimal spread spectrum watermark embedding via a multistep feasibility formulation.  

PubMed

We consider optimal formulations of spread spectrum watermark embedding where the common requirements of watermarking, such as perceptual closeness of the watermarked image to the cover and detectability of the watermark in the presence of noise and compression, are posed as constraints while one metric pertaining to these requirements is optimized. We propose an algorithmic framework for solving these optimal embedding problems via a multistep feasibility approach that combines projections onto convex sets (POCS) based feasibility watermarking with a bisection parameter search for determining the optimum value of the objective function and the optimum watermarked image. The framework is general and can handle optimal watermark embedding problems with convex and quasi-convex formulations of watermark requirements with assured convergence to the global optimum. The proposed scheme is a natural extension of set-theoretic watermark design and provides a link between convex feasibility and optimization formulations for watermark embedding. We demonstrate a number of optimal watermark embeddings in the proposed framework corresponding to maximal robustness to additive noise, maximal robustness to compression, minimal frequency weighted perceptual distortion, and minimal watermark texture visibility. Experimental results demonstrate that the framework is effective in optimizing the desired characteristic while meeting the constraints. The results also highlight both anticipated and unanticipated competition between the common requirements for watermark embedding. PMID:19131302

Altun, H Oktay; Orsdemir, Adem; Sharma, Gaurav; Bocko, Mark F

2009-02-01

393

Rearrangement, convection, convexity and entropy.  

PubMed

The concepts of convexity and entropy play a crucial role in the mathematical theory of hyperbolic systems of conservation laws. We show that they also play an important role in the mathematical analysis of convection theory, through the mathematical concept of rearrangement. PMID:24249771

Brenier, Yann

2013-12-28

394

Online Routing in Convex Subdivisions  

Microsoft Academic Search

We consider online routing algorithms for nding paths between the vertices of plane graphs. We show (1) there exists a routing algorithm for arbitrary triangulations that has no memory and uses no randomization, (2) no equivalent result is possible for convex subdivisions, (3) there is no competitive online routing algorithm under the Euclidean distance metric in arbitrary triangulations, and (4)

Prosenjit Bose; Pat Morin; Andrej Brodnik; Svante Carlsson; Erik D. Demaine; Rudolf Fleischer; J. Ian Munro; Alejandro López-ortiz

2000-01-01

395

An aggregate subgradient method for nonsmooth convex minimization  

Microsoft Academic Search

A class of implementable algorithms is described for minimizing any convex, not necessarily differentiable, functionf of several variables. The methods require only the calculation off and one subgradient off at designated points. They generalize Lemarechal's bundle method. More specifically, instead of using all previously computed\\u000a subgradients in search direction finding subproblems that are quadratic programming problems, the methods use an

Krzysztof Czes?aw Kiwiel

1983-01-01

396

An optimal lower bound for the Frobenius problem  

Microsoft Academic Search

Given N?2 positive integers a1,a2,…,aN with GCD(a1,…,aN)=1, let fN denote the largest natural number which is not a positive integer combination of a1,…,aN. This paper gives an optimal lower bound for fN in terms of the absolute inhomogeneous minimum of the standard (N?1)-simplex.

Iskander M. Aliev; Peter M. Gruber

2007-01-01

397

Single and multiobjective optimization problems in robust parameter design  

Microsoft Academic Search

This paper reviews the evolution of off-line quality engineering methods with respect to one or more quality criteria, and\\u000a presents some recent results. The fundamental premises that justify the use of robust product\\/process design are established\\u000a with an illustrative example. The use of designed experiments to model quality criteria and their optimization is briefly\\u000a reviewed. The fact that most design-for-quality

Amit Mathur; Krishna R Pattipati

1997-01-01

398

Convex Four-Body Central Configurations with Some Equal Masses  

NASA Astrophysics Data System (ADS)

We prove that there is an unique convex noncollinear central configuration of the planar Newtonian four-body problem when two equal masses are located at opposite vertices of a quadrilateral and, at most, only one of the remaining masses is larger than the equal masses. Such a central configuration possesses a symmetry line and it is a kite-shaped quadrilateral. We also show that there is exactly one convex noncollinear central configuration when the opposite masses are equal. Such a central configuration also possesses a symmetry line and it is a rhombus.

Perez-Chavela, Ernesto; Santoprete, Manuele

2007-09-01

399

Identifying Model Inaccuracies and Solution Uncertainties in Non-Invasive Activation-Based Imaging of Cardiac Excitation using Convex Relaxation  

PubMed Central

Noninvasive imaging of cardiac electrical function has begun to move towards clinical adoption. Here we consider one common formulation of the problem, in which the goal is to estimate the spatial distribution of electrical activation times during a cardiac cycle. We address the challenge of understanding the robustness and uncertainty of solutions to this formulation. This formulation poses a non-convex, non-linear least squares optimization problem. We show that it can be relaxed to be convex, at the cost of some degree of physiological realism of the solution set, and that this relaxation can be used as a framework to study model inaccuracy and solution uncertainty. We present two examples, one using data from a healthy human subject and the other synthesized with the ECGSIM software package. In the first case, we consider uncertainty in the initial guess and regularization parameter. In the second case, we mimic the presence of an ischemic zone in the heart in a way which violates a model assumption. We show that the convex relaxation allows understanding of spatial distribution of parameter sensitivity in the first case, and identification of model violation in the second.

Erem, Burak; van Dam, Peter M.; Brooks, Dana H.

2014-01-01

400

Solution of transient optimization problems by using an algorithm based on nonlinear programming  

NASA Technical Reports Server (NTRS)

An algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.

Teren, F.

1977-01-01

401

On copositive programming and standard quadratic optimization problems  

Microsoft Academic Search

A standard quadratic problem consists of finding global maximizers of a quadratic form over the standard simplex. In this paper, the usual semidefinite programming relaxation is strengthened by replacing the cone of positive semidefinite matrices by the cone of completely positive matrices (the positive semidefinite matrices which allow a factorization FFT whereF is some non-negative matrix). The dual of this

Immanuel M. Bomze; Mirjam Dür; Etienne de Klerk; Cornelis Roos; Arie J. Quist; Tamás Terlaky

2000-01-01

402

On finding the optimal genetic algorithms for robot control problems  

Microsoft Academic Search

Describes a C++ package used to analyze a class of genetic algorithms. The parameters of the best genetic algorithms have been searched by a genetic algorithm. The ultimate goal of the work is to find out if it would be possible to utilize genetic algorithm techniques in certain difficult and complex robot control problems, such as task planning, adaptation, error

Jarmo T. Alander

1991-01-01

403

Solving the Prize-Collecting Steiner Tree Problem to Optimality  

Microsoft Academic Search

The Prize-Collecting Steiner Tree Problem (PCST) on a graph with edge costs and vertex profits asks for a subtree minimizing the sum of the total cost of all edges in the subtree plus the total profit of all vertices not contained in the subtree. PCST appears in the design of utility networks (eg. fiber optics or district heating) where profit

Ivana Ljubic; René Weiskircher; Ulrich Pferschy; Gunnar W. Klau; Petra Mutzel; Matteo Fischetti

2005-01-01

404

Research on Optimal Coverage Problem of Wireless Sensor Networks  

Microsoft Academic Search

In a wireless sensor network, the size of radio nodes has direct relation to the cost of total wireless sensor networks, and at the same time, the problem is closely connected to wireless sensor networks' performance, such as robust, fault-tolerance, and further more, it is considered at first as wireless sensor networks are designed. Therefore, the research on the size

Xueqing Wang; Fayi Sun; Xiangsong Kong

2009-01-01

405

Multi-agent Optimization Design for Multi-resource Job Shop Scheduling Problems  

Microsoft Academic Search

As a practical generalization of the job shop scheduling problem, multi-resource job shop scheduling problem (MRJSSP) is discussed\\u000a in this paper. In this problem, operations may be processed by a type of resources and jobs have individual deadlines. How\\u000a to design and optimize this problem with DSAFO, a novel multi-agent algorithm, is introduced in detail by a case study, including

Fan Xue; Wei Fan

2007-01-01

406

Optimal Linear Estimation Applied to Generate Suboptimal Numerical Solutions for Control Problems.  

National Technical Information Service (NTIS)

A procedure for the generation of suboptimal numerical solutions in dynamical systems optimal control problems is described. The approximation of the control by a functional dependent upon a finite number of parameters and the adoption of a linear perturb...

A. R. Neto

1980-01-01

407

Application of Particle Swarm Optimization Algorithm in the Heating System Planning Problem  

PubMed Central

Based on the life cycle cost (LCC) approach, this paper presents an integral mathematical model and particle swarm optimization (PSO) algorithm for the heating system planning (HSP) problem. The proposed mathematical model minimizes the cost of heating system as the objective for a given life cycle time. For the particularity of HSP problem, the general particle swarm optimization algorithm was improved. An actual case study was calculated to check its feasibility in practical use. The results show that the improved particle swarm optimization (IPSO) algorithm can more preferably solve the HSP problem than PSO algorithm. Moreover, the results also present the potential to provide useful information when making decisions in the practical planning process. Therefore, it is believed that if this approach is applied correctly and in combination with other elements, it can become a powerful and effective optimization tool for HSP problem.

Ma, Rong-Jiang; Yu, Nan-Yang; Hu, Jun-Yi

2013-01-01

408

Tackling the problems of tumour chemotherapy by optimal drug scheduling.  

PubMed

Introduction: There are various strategies for overcoming the major pitfalls of cancer chemotherapy, such as toxicity and drug resistance. The scientific computing of drug scheduling by optimisation before drug administration is one among them. In a majority of these strategies, the pharmacodynamic variations are given more importance than the pharmacokinetic variations. This study was meant to analyse the importance of the pharmacokinetic parameters (?) of the individual patients in cancer chemotherapy scheduling, along with the pharmacodynamic factors. Methods: A mathematical model is developed and it is implemented in the open source OCTAVE GNU LINUX. Optimisation is done by using an optimization tool in OCTAVE. The present study was aimed at evaluating the daily drug dosaging and cyclic chemotherapy which are commonly practised in the chemotherapy scheduling. Four cases were analyzed with and without considering the pharmacokinetic parameters. The optimal therapy was meant to reduce the number of cancer cells to a minimum at the end of the therapy and to minimise the emergence of resistant cancer cells. Since the dose was within tolerable limits, the toxic effects could also be minimised. Results: Even with the consideration of a 1 per cent effect (?), the maximum possible dose and the performance index were increased in the daily scheduling. But in the cyclic therapy, even though the maximum tolerated dose or the performance index was not altered, the cumulative toxicity was greatly reduced. Conclusion: Daily scheduling and cyclic chemotherapy can be applied alternatively more effectively, by considering the interindividual variations in the pharmacokinetic effect (?). PMID:23998076

Remesh, Ambili

2013-07-01

409

General Robust-Optimization Formulation for Nonlinear Programming  

Microsoft Academic Search

Most research in robust optimization has been focused so far on inequality-only, convex conic programming with simple linear\\u000a models for the uncertain parameters. Many practical optimization problems, however, are nonlinear and nonconvex. Even in linear\\u000a programming, the coefficients may still be nonlinear functions of the uncertain parameters. In this paper, we propose robust\\u000a formulations that extend the robust-optimization approach to

Y. Zhang

2007-01-01

410

A link-based variational inequality formulation of ideal dynamic user-optimal route choice problem  

Microsoft Academic Search

The ideal dynamic user-optimal (DUO) route choice problem is to determine vehicle flows on each link at each instant of time resulting from drivers using actual minimal-time routes. Actual route time is the travel time incurred while driving along the route. In a previous paper, we presented a route-based optimal control model for the ideal DUO route choice problem. However,

Bin Ran; David E. Boyce

1996-01-01

411

Cost Equality and Inequality Results for a Partially Observed Stochastic Optimization Problem  

Microsoft Academic Search

A finite-horizon partially observed stochastic optimization problem is presented, where the underlying (or core) process subject to control is a finite-state discrete-time controlled semi-Markov vector process, the information pattern is classical, and times of control reset and noise corrupted observation occur at times of core process transition. Conditions for optimality are stated. The new problem formulation is shown to generalize

Chelsea C. White

1975-01-01

412

A dual method for optimal control problems with initial and final boundary constraints.  

NASA Technical Reports Server (NTRS)

This paper presents two new algorithms belonging to the family of dual methods of centers. The first can be used for solving fixed time optimal control problems with inequality constraints on the initial and terminal states. The second one can be used for solving fixed time optimal control problems with inequality constraints on the initial and terminal states and with affine instantaneous inequality constraints on the control. Convergence is established for both algorithms. Qualitative reasoning indicates that the rate of convergence is linear.

Pironneau, O.; Polak, E.

1973-01-01

413

An algorithm for solving optimal control problems with control and terminal-state constraints  

Microsoft Academic Search

The authors (1993) introduced an algorithm to solve continuous-time optimal control problems where the control variables are constrained. In this paper, the algorithm is extended to solve optimal control problems with not only hard control constraints but also terminal-state constraints. An exact penalty type of function is employed to penalize any violated terminal-state constraints. The authors then show that the

Baoming Ma; William S. Levine

1994-01-01

414

Study of the vehicle routing problem with time windows based on improved particle swarm optimization algorithm  

Microsoft Academic Search

To overcome that the standard particle swarm optimization algorithms can not find good solutions of solving the vehicle routing problem with tim windows,an improved particle swarm optimization algorithm for vehicle routing problem with time windows (VRPTW)was proposed. In the improved algorithm,different particles are assigned specific tasks. Better particles are given smaller inertial weights, while worse ones are given larger inertialweights.

Anxin Ye

2011-01-01

415

Genetic Algorithm for Mulicriteria Optimization of a Multi-Pickup and Delivery Problem with Time Windows  

Microsoft Academic Search

In This paper we present a genetic algorithm for mulicriteria optimization of\\u000aa multipickup and delivery problem with time windows (m-PDPTW). The m-PDPTW is\\u000aan optimization vehicles routing problem which must meet requests for transport\\u000abetween suppliers and customers satisfying precedence, capacity and time\\u000aconstraints. This paper purposes a brief literature review of the PDPTW,\\u000apresent an approach based on

Imen Harbaoui Dridi; Ryan Kammarti; Mekki Ksouri; Pierre Borne

2010-01-01

416

Multi-objective Optimization For The Dynamic Multi-Pickup and Delivery Problem with Time Windows  

Microsoft Academic Search

The PDPTW is an optimization vehicles routing problem which must meet\\u000arequests for transport between suppliers and customers satisfying precedence,\\u000acapacity and time constraints. We present, in this paper, a genetic algorithm\\u000afor multi-objective optimization of a dynamic multi pickup and delivery problem\\u000awith time windows (Dynamic m-PDPTW). We propose a brief literature review of\\u000athe PDPTW, present our approach

Imen Harbaoui Dridi; Ryan Kammarti; Pierre Borne; Mekki Ksouri

2011-01-01

417

Reduction of dimension of optimal estimation problems for dynamical systems with singular perturbations  

NASA Astrophysics Data System (ADS)

The possibility of applying the method of integral manifolds to the reduction of optimal filtering problems for systems with low energy dissipation is explored. For such systems, it is shown that the slow subsystem of matrix Riccati differential equations turns out to have a higher dimension than expected, which leads to an increase in the dimension of the reduced problems. An optimal filter is constructed for the Langevin equation and for a dynamic model of a single-link flexible manipulator.

Osintsev, M. S.; Sobolev, V. A.

2014-01-01

418

Multi-objective optimization and selection for the PI control of ALSTOM gasifier problem  

Microsoft Academic Search

Based on the baseline PI control structure, the control parameters of non-linear ALSTOM gasifier benchmark problem are optimized. Firstly, taking all the input and output limits under three load conditions as constraints, the relative IAE indices at six scenarios are calculated and optimized by using multi-objective optimization algorithm NSGA-II. A set of non-dominated solutions are obtained which facilitate the further

Yali Xue; Donghai Li; Furong Gao

2010-01-01

419

Variational optimality condition in the problem of control of initial boundary conditions for semilinear hyperbolic systems  

Microsoft Academic Search

Consideration is given to the problem of optimal control of a system of semilinear hyperbolic equations at finite-dimensional\\u000a (pointwise) relations between initial boundary states of the system and control actions. In this case, the optimality condition\\u000a in the form of a pointwise maximum principle is invalid. A nonclassical optimality condition of a variational type is proved.\\u000a The sense of the

A. V. Arguchintsev; V. P. Poplevko

2008-01-01

420

Absence of self-averaging in global optimization problems  

NASA Astrophysics Data System (ADS)

We study the distribution of (1+1)-dimensional self-affine lines resulting from the zero-temperature directed polymer in a random medium or from critical directed percolation problems. The related amplitude ratios depend on whether the finite size scaling statistics is made over finite segments of the infinite objects or over the finite objects of diverging size. As a by-product we obtain the correction to scaling exponents for the finite size scaling of the distribution functions.

Hansen, Alex; Kertész, János

1996-06-01

421

On optimality of Bayesian testimation in the normal means problem  

Microsoft Academic Search

We consider a problem of recovering a high-dimensional vector $\\\\mu$ observed in white noise, where the unknown vector $\\\\mu$ is assumed to be sparse. The objective of the paper is to develop a Bayesian formalism which gives rise to a family of $l_0$-type penalties. The penalties are associated with various choices of the prior distributions $\\\\pi_n(\\\\cdot)$ on the number of

Felix Abramovich; Vadim Grinshtein; Marianna Pensky

2007-01-01

422

Optimization models and algorithms for the hyperplane clustering problem  

Microsoft Academic Search

This is a summary of the author’s PhD thesis supervised by Edoardo Amaldi and defended on 3 April 2009 at the Politecnico\\u000a di Milano. The thesis is written in English and is available from the author upon request. In this work, we extensively study\\u000a two challenging variants of the general problem of clustering a given set of data points with respect

Kanika Dhyani

2010-01-01

423

Optimized constraints for the linearized geoacoustic inverse problem.  

PubMed

A geoacoustic inversion scheme to estimate the depth-dependent sound speed characteristics of the shallow-water waveguide is presented. The approach is based on the linearized perturbative technique developed by Rajan et al. [J. Acoust. Soc. Am. 82, 998-1017 (1987)]. This method is applied by assuming a background starting model for the environment that includes both the water column and the seabed. Typically, the water column properties are assumed to be known and held fixed in the inversion. Successful application of the perturbative inverse technique lies in handling issues of stability and uniqueness associated with solving a discrete ill-posed problem. Conventionally, such problems are regularized, a procedure which results in a smooth solution. Past applications of this inverse technique have been restricted to cases for which the water column sound speed profile was known and sound speed in the seabed could be approximated by a smooth profile. In this work, constraints that are better suited to specific aspects of the geoacoustic inverse problem are applied. These techniques expand on the original application of the perturbative inverse technique by including the water column sound speed profile in the solution and by allowing for discontinuities in the seabed sound speed profile. PMID:21361424

Ballard, Megan S; Becker, Kyle M

2011-02-01

424

Metamodel-assisted distributed genetic algorithms applied to structural shape optimization problems  

Microsoft Academic Search

This article is concerned with the development of a general optimization tool based on distributed real genetic algorithms (DRGAs) assisted by metamodel evaluation and applied to structural shape optimization problems of general boundary-element models (BEMs). The evaluation fitness function is performed by a surrogate function based on multidimensional Gaussian random field models (MGRFMs) in order to minimize the computational cost

W. Annicchiarico

2007-01-01

425

Incremental Local Search in Ant Colony Optimization: Why It Fails for the Quadratic Assignment Problem  

Microsoft Academic Search

Ant colony optimization algorithms are currently among the best performing algorithms for the quadratic assignment problem. These algorithms contain two main search procedures: solution construction by articial ants and local search to improve the solutions constructed by the ants. Incremental local search is an approach that consists in re- optimizing partial solutions by a local search algorithm at regular inter-

Prasanna Balaprakash; Mauro Birattari; Thomas Stützle; Marco Dorigo

2006-01-01

426

A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems  

Microsoft Academic Search

Several extensions to evolutionary algorithms (EAs) and particle swarm optimization (PSO) have been suggested during the last decades offering improved performance on selected benchmark problems. Recently, another search heuristic termed differential evolution (DE) has shown superior performance in several real-world applications. In this paper, we evaluate the performance of DE, PSO, and EAs regarding their general applicability as numerical optimization

J. Vesterstrom; R. Thomsen

2004-01-01

427

An Investigation of Optimal Decision Rules for Several Single-Period Stochastic Inventory Problems.  

National Technical Information Service (NTIS)

The single-period inventory model, known as the newsboy or Christmas tree problem, is extended for several cost expressions and optimal decision rules for these variations are derived. A two-echelon single-period inventory model is developed and optimal d...

S. Swasdikiat

1973-01-01

428

UFO: Uncertainty Feature Optimization, an Implicit Paradigm for Problems with Noisy Data  

Microsoft Academic Search

Optimization problems due to noisy data are usually solved using stochastic programming or robust optimization approaches. Both requiring the explicit characterization of an uncertainty set that models the nature of the noise. Such approaches tightly depend on the modeling of the uncertainty set. In this paper, we introduce a framework that implicitly models the uncertain data. We define the general

Niklaus Eggenberg; Matteo Salani; Michel Bierlaire

2008-01-01

429

CALIBRATING NON-CONVEX PENALIZED REGRESSION IN ULTRA-HIGH DIMENSION  

PubMed Central

We investigate high-dimensional non-convex penalized regression, where the number of covariates may grow at an exponential rate. Although recent asymptotic theory established that there exists a local minimum possessing the oracle property under general conditions, it is still largely an open problem how to identify the oracle estimator among potentially multiple local minima. There are two main obstacles: (1) due to the presence of multiple minima, the solution path is nonunique and is not guaranteed to contain the oracle estimator; (2) even if a solution path is known to contain the oracle estimator, the optimal tuning parameter depends on many unknown factors and is hard to estimate. To address these two challenging issues, we first prove that an easy-to-calculate calibrated CCCP algorithm produces a consistent solution path which contains the oracle estimator with probability approaching one. Furthermore, we propose a high-dimensional BIC criterion and show that it can be applied to the solution path to select the optimal tuning parameter which asymptotically identifies the oracle estimator. The theory for a general class of non-convex penalties in the ultra-high dimensional setup is established when the random errors follow the sub-Gaussian distribution. Monte Carlo studies confirm that the calibrated CCCP algorithm combined with the proposed high-dimensional BIC has desirable performance in identifying the underlying sparsity pattern for high-dimensional data analysis.

Wang, Lan; Kim, Yongdai; Li, Runze

2014-01-01

430

Optimal Throughput-Oriented Power Control by Linear Multiplicative Fractional Programming  

Microsoft Academic Search

This paper studies optimal power control for throughput maximization in wireless ad hoc networks. Optimal power control problem in ad hoc networks is known to be non-convex due to the co-channel interference between links. As a result, a global optimal solution is difficult to obtain. Previous work either simplified the problem by assuming that the signal- to-interference-and-noise-radio (SINR) of each

Liping Qian; Ying Jun Zhang

2008-01-01

431

Evaluation of Genetic Algorithm Concepts using Model Problems. Part 1; Single-Objective Optimization  

NASA Technical Reports Server (NTRS)

A genetic-algorithm-based optimization approach is described and evaluated using a simple hill-climbing model problem. The model problem utilized herein allows for the broad specification of a large number of search spaces including spaces with an arbitrary number of genes or decision variables and an arbitrary number hills or modes. In the present study, only single objective problems are considered. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all problems attempted. The most difficult problems - those with large hyper-volumes and multi-mode search spaces containing a large number of genes - require a large number of function evaluations for GA convergence, but they always converge.

Holst, Terry L.; Pulliam, Thomas H.

2003-01-01

432

Formulations and Methods for Robust and Efficient Optimization of Acoustic Radiated Noise Problems  

NASA Astrophysics Data System (ADS)

A new optimization methodology for solving broad -band radiated noise design problems is presented. Design parameters of numerical models of radiating structures are modified by the optimizer to find low-weight and low -cost designs with radiated sound spectra below user-specified goal levels. The methods presented in this dissertation are based on a combination of state-of-the-art optimization techniques, and provide to the noise control community a robust, globally-convergent structural-acoustic optimization tool. The general purpose methods will allow acoustic analysts and designers to use optimization techniques in early computer-aided design stages to effect potentially large performance gains in radiated noise spectra. The key difficulties associated with optimizing structural-acoustic systems are the complexity of the fluid -structure interaction problem, the high computational expense associated with computing radiated noise for a wide range of frequencies, and the ill-conditioning of the optimization design space due to resonance phenomena in structural-acoustic response. New optimization methods based on first-order Taylor and half-quadratic series approximations and global search methods are developed which are relatively insensitive to the ill-conditioned design spaces of structural-acoustic systems. The optimization methods were applied to several complex test problems solved using finite element analysis, and converged to global optimum designs starting from a wide range of initial designs. The first-order Taylor optimizer had a 77% global convergence rate for all test problems considered, and the half-quadratic optimizer had a 66% global convergence rate. The first-order Taylor optimizer is shown to be significantly more efficient than the half-quadratic optimizer, since it requires only half the design evaluations (numerical analyses of radiated noise spectra) compared to the half-quadratic approach. The accuracy of the sensitivity analysis of broad -band radiated noise levels, computed using low-order finite difference approximations, is also investigated. Large perturbations of design variables which cause high second order sensitivities were found to improve significantly the half-quadratic optimizer robustness for the most complex test problem considered. For general problems, however, the first-order Taylor optimization method is recommended due to its high efficiency and, in most cases, its high robustness.

Hambric, Stephen Andre

1995-01-01

433

Surgical treatment of congenital convex pes valgus.  

PubMed

Congenital convex pes valgus is a rare, complex and heterogeneous anomaly of the foot, which is difficult to treat. From 1985 to 1994, we treated 14 patients (20 feet) with this deformity. There were six boys and eight girls. Six patients had bilateral involvement. Their ages at the time of surgery ranged from 4 to 32 months (mean, 13 mo). In eight patients (10 feet), the etiology was arthrogryposis multiplex congenita. The eitiology was unknown in six patients (10 feet). Associated problems included hip dislocation in seven patients, flexion or extension contractures of the knee in six patients, and clubfoot deformity in three patients. One patient had undergone previous surgery for release of a knee contracture. To achieve a plantigrade and balanced foot, all patients had one-stage surgical open reduction and circumferential release for the correction of deformities. At a minimum of 2 years following surgery, 11 patients (16 feet) had satisfactory results determined by a 10-point evaluation system based on both clinical and radiographic features. Satisfactory results and ambulatory prognosis were related to the etiology and severity of each patient's condition. Two patients (two feet) had scars with poor cosmetic appearance and two patients (three feet) had inadequate correction. We concluded that with adequate soft tissue release and complete talocalcaneonavicular joint reduction in one-stage surgery, proper postoperative maintenance, and physical therapy, satisfactory results in the treatment of congenital convex pes valgus can be achieved. PMID:9216165

Yen, C C; Huang, S C

1997-06-01

434

Economic dispatch using particle swarm optimization: A review  

Microsoft Academic Search

Electrical power industry restructuring has created highly vibrant and competitive market that altered many aspects of the power industry. In this changed scenario, scarcity of energy resources, increasing power generation cost, environment concern, ever growing demand for electrical energy necessitate optimal economic dispatch. Practical economic dispatch (ED) problems have nonlinear, non-convex type objective function with intense equality and inequality constraints.

Amita Mahor; Vishnu Prasad; Saroj Rangnekar

2009-01-01

435

On the Optimality of Generalized (S,S) Policies.  

National Technical Information Service (NTIS)

A standard inventory model is examined with a concave increasing ordering cost function rather than simply a linear one with a setup cost. A generalized (s,S) policy is shown to be optimal in the n-period problem. A generalization of K-convex and quasi-co...

E. L. Porteus

1970-01-01

436

New high performing hybrid particle swarm optimization for permutation flow shop scheduling problem with minimization of makespan  

Microsoft Academic Search

The well-known particle swarm optimization (PSO) proposed by Kennedy and Eberhart has been widely applied to the continuous optimal problems. However, it is still intractable to apply PSO to discrete optimization problems, such as permutation flow shop scheduling problems (PFSSP). In this paper, a new high performing metaheuristic algorithm hybridizing PSO with variable neighborhood search (VNS) is proposed to solve

Y. Sun; M. Liu; C. Y. Zhang; L. Gao; K. L. Lian

2010-01-01

437

Applications of Euclidean Geometry to Various Optimization Problems  

Microsoft Academic Search

\\u000a The method of least squares is a way of “solving” an overdetermined system of linear equations \\u000a \\u000a Ax = b,\\u000aAx = b,\\u000a\\u000a \\u000a \\u000a i.e., a system in which A is a rectangular m × n matrix with more equations than unknowns (when m > n). Historically, the method of least squares was used by Gauss and Legendre to solve problems in

Jean Gallier

438

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

NASA Technical Reports Server (NTRS)

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

Holst, Terry L.; Pulliam, Thomas H.

2003-01-01

439

Ant Colony Optimization with Memory and Its Application to Traveling Salesman Problem  

NASA Astrophysics Data System (ADS)

Ant Colony Optimization (ACO) is one of the most recent techniques for solving combinatorial optimization problems, and has been unexpectedly successful. Therefore, many improvements have been proposed to improve the performance of the ACO algorithm. In this paper an ant colony optimization with memory is proposed, which is applied to the classical traveling salesman problem (TSP). In the proposed algorithm, each ant searches the solution not only according to the pheromone and heuristic information but also based on the memory which is from the solution of the last iteration. A large number of simulation runs are performed, and simulation results illustrate that the proposed algorithm performs better than the compared algorithms.

Wang, Rong-Long; Zhao, Li-Qing; Zhou, Xiao-Fan

440

Optimal Distributed Beamforming for MISO Interference Channels  

NASA Astrophysics Data System (ADS)

We consider the problem of quantifying the Pareto optimal boundary in the achievable rate region over multiple-input single-output (MISO) interference channels, where the problem boils down to solving a sequence of convex feasibility problems after certain transformations. The feasibility problem is solved by two new distributed optimal beamforming algorithms, where the first one is to parallelize the computation based on the method of alternating projections, and the second one is to localize the computation based on the method of cyclic projections. Convergence proofs are established for both algorithms.

Qiu, Jiaming; Zhang, Rui; Luo, Zhi-Quan; Cui, Shuguang

2011-11-01

441

Polynomial-Time Verification of PCTL Properties of MDPs with Convex Uncertainties.  

National Technical Information Service (NTIS)

We address the problem of verifying Probabilistic Computation Tree Logic (PCTL) properties of Markov Decision Processes (MDPs) whose state transition probabilities are only known to lie within uncertainty sets. We first introduce the model of Convex-MDPs ...

A. A. Puggelli A. L. Sangiovanni-Vincentelli S. A. Seshia W. Li

2013-01-01

442

Application of Biogeography-based Optimization for Solving Multi-objective Economic Emission Load Dispatch Problems  

Microsoft Academic Search

This article presents a biogeography-based optimization algorithm to solve complex economic emission load dispatch problems of thermal generators of power systems. Different emission substances, such as NOX, SOX, and COX, are considered for case studies. The methodology considers the power demand equality constraint and the operating limit constraint during the time of solving economic emission load dispatch problems. Biogeography deals

Aniruddha Bhattacharya; P. K. Chattopadhyay

2010-01-01

443

Biogeography Based Optimization technique applied to multi-constraints economic load dispatch problems  

Microsoft Academic Search

This paper presents biogeography-based optimization (BBO) technique for solving constrained economic dispatch problems in power system. Many nonlinear characteristics of generators, like valve point loading, ramp rate limits, prohibited zone, and multiple fuels cost functions are considered. Two Economic Load Dispatch (ELD) problems with different characteristics are applied and compared its solution quality and computation efficiency to genetic algorithm (GA),

P. K. Roy; S. P. Ghoshal; S. S. Thakur

2009-01-01

444

An Optimization-Based Heuristic for the Split Delivery Vehicle Routing Problem  

Microsoft Academic Search

The split delivery vehicle routing problem is concerned with serving the demand of a set of customers with a fleet of capacitated vehicles at minimum cost. A customer, contrary to what is assumed in the classical vehicle routing problem, can be served by more than one vehicle, if convenient. We present a solution approach that integrates heuristic search with optimization

Claudia Archetti; Maria Grazia Speranza; Martin W. P. Savelsbergh

2008-01-01

445

Ant Colony Optimization Algorithms with Local Search for the Dynamic Vehicle Routing Problem  

Microsoft Academic Search

Abstract This report demonstrates the use of eective,local search to im- prove the performance of simple Ant Colony Optimization (ACO) algorithms as applied to an extension of the Vehicle Routing Problem (VRP) known as the Dynamic Vehicle Routing Problem (DVRP). The static VRP presents all orders a priori, however the DVRP requires scheduling to begin without a complete knowledge of

Andrew Runka

446

Parallel Full Space SQP Lagrange-Newton-Krylov-Schwarz Algorithms for PDE-Constrained Optimization Problems  

Microsoft Academic Search

Optimization problems constrained by nonlinear partial difierential equations have been the focus of intense research in scientiflc computing lately. Current methods for the parallel numerical solution of such problems involve sequential quadratic programming (SQP), with either reduced or full space approaches. In this paper we propose and investigate a class of parallel full space SQP Lagrange-Newton-Krylov-Schwarz (LNKSz) algorithms. In LNKSz,

Ernesto E. Prudencio; Richard H. Byrd; Xiao-chuan Cai

2006-01-01

447

A well-posed optimal spectral element approximation for the Stokes problem  

NASA Technical Reports Server (NTRS)

A method is proposed for the spectral element simulation of incompressible flow. This method constitutes in a well-posed optimal approximation of the steady Stokes problem with no spurious modes in the pressure. The resulting method is analyzed, and numerical results are presented for a model problem.

Maday, Y.; Patera, A. T.; Ronquist, E. M.

1987-01-01

448

An improved Particle Swarm Optimization algorithm and its application to a class of JSP problem  

Microsoft Academic Search

In this paper, we analyze the special job shop scheduling problem (JSP) of actual production system in large-scale structure workshops. With regard to this kind of JSP problem, two novel mathematical models (deterministic model and stochastic model) are proposed. In addition, particle swarm optimization (PSO) algorithm is used in the paper because of its high efficiency, and binary PSO algorithm

Kun Fan; Ren-qian Zhang; Guoping Xia

2007-01-01

449

Determination of functional gradient in an optimal control problem related to metal solidification  

NASA Astrophysics Data System (ADS)

The gradient of the cost functional in the discrete optimal control problem of metal solidification in casting is exactly evaluated. The mathematical model describing the solidification process is based on a three-dimensional two-phase initial-boundary value problem of the Stefan type. Formulas determining exact gradient determination are derived using the fast automatic differentiation technique.

Albu, A. F.; Zubov, V. I.

2009-01-01

450

Global optimization for the phase and chemical equilibrium problem: Application to the NRTL equation  

Microsoft Academic Search

Several approaches have been proposed for the computation of solutions to the phase and chemical equilibrium problem when the problem is posed as the minimization of the Gibbs free energy function. None of them can guarantee convergence to the true optimal solution, and are highly dependent on the supplied initial point. Convergence to local solutions often occurs, yielding incorrect phase

C. M. McDonald; C. A. Floudas

1995-01-01

451

Necessary and sufficient conditions of optimality for some classical scheduling problems  

Microsoft Academic Search

A scheduling problem is generally to order the jobs such that a certain objective function f(?) is minimized. For some classical scheduling problems, only sufficient conditions of optimal solutions are concerned in the literature. In this paper, we study the necessary and sufficient conditions by means of the concept of critical ordering (critical jobs and their relations). These results are

Yixun Lin; Xiumei Wang

2007-01-01

452

Pyramid Implementation Of Optimal Step Conjugate Search Algorithms For Some Computer Vision Problems  

Microsoft Academic Search

Optimization of a cost function arises in several computer vision problems. The cost functions in these problems are usually derived from discretization of functionals obtained from regularization principles or stochastic estimation techniques using Markov random field models. In this paper we present a parallel implementation on a pyramid of the line search conjugate gradient algorithm for minimizing the cost functions

T. Simchony; R. Chellappa; Z. Lichtenstein

1988-01-01

453

On a global optimization technique for solving a nonlinear hyperboloid least squares problem  

Microsoft Academic Search

We present a numerical experimentation of the global optimization algorithm presented by Velazquez et al. (2001) applied to a nonlinear hyperboloid least squares problem. This problem arises when beta sheet residues from an allosteric enzyme are fitted onto a hyperboloid by using Newton type methods. The results show that the algorithm performs well on three test cases. An important side

Leticia Velázquez; Miguel Argáez; Brenda Bueno; Boguslaw Stec

2005-01-01

454

On a global optimization technique for solving a nonlinear hyperboloid least squares problem  

Microsoft Academic Search

We present a numerical experimentation of the global optimization algorithm presented by Velázquez et. al. [3] applied to a nonlinear hyperboloid least squares problem. This problem arises when beta sheet residues from an allosteric enzyme are fitted onto a hyperboloid by using Newton type methods. The results show that the algorithm performs well on three testcases. An important side result

Leticia Velázquez; Miguel Argáez; Brenda Bueno; Boguslaw Stec

2005-01-01

455

Convergence of Newton's method for convex best interpolation  

Microsoft Academic Search

  \\u000a \\u000a \\u000a Summary. In this paper, we consider the problem of finding a convex function which interpolates given points and has a minimal norm of the second derivative. This problem reduces to a system of equations involving semismooth functions. We study a Newton-type\\u000a method utilizing Clarke's generalized Jacobian and prove that its local convergence is superlinear. For a special choice of

Asen L. Dontchev; Houduo Qi; Liqun Qi

2001-01-01

456

A global optimization method for the molecular replacement problem in X-ray crystallography  

Microsoft Academic Search

Abstract.,The primary,technique,for determining,the three-dimensional structure,of a protein molecule is X-ray crystallography, from which the molecular replacement (MR) problem often arises as a critical step. The MR problem,is a global optimization problem,to locate an optimal position of a model,protein so that at this position the model,will produce,calculated,intensities closest to those observed,from,an X-ray crystallography experiment involving a protein with unknown,but similar atomic,structure.

Diane C. Jamrog; George N. Phillips Jr.; Richard A. Tapia; Yin Zhang

2005-01-01

457

Varying fitness functions in genetic algorithm constrained optimization: the cutting stock and unit commitment problems.  

PubMed

We present a specific varying fitness function technique in genetic algorithm (GA) constrained optimization. This technique incorporates the problem's constraints into the fitness function in a dynamic way. It consists of forming a fitness function with varying penalty terms. The resulting varying fitness function facilitates the GA search. The performance of the technique is tested on two optimization problems: the cutting stock, and the unit commitment problems. Also, new domain-specific operators are introduced. Solutions obtained by means of the varying and the conventional (nonvarying) fitness function techniques are compared. The results show the superiority of the proposed technique. PMID:18255983

Petridis, V; Kazarlis, S; Bakirtzis, A

1998-01-01

458

MultiChannel $l_{1}$ Regularized Convex Speech Enhancement Model and Fast Computation by the Split Bregman Method  

Microsoft Academic Search

A convex speech enhancement (CSE) method is presented based on convex optimization and pause detection of the speech sources. Channel spatial difference is identified for enhancing each speech source individually while suppressing other interfering sources. Sparse unmixing filters indicating channel spatial differences are sought by $l_{1}$ norm regularization and the split Bregman method. A subdivided split Bregman method is developed

Meng Yu; Wenye Ma; Jack Xin; Stanley Osher

2012-01-01

459

Finite termination of a dual Newton method for convex best C 1 interpolation and smoothing  

Microsoft Academic Search

Summary. Given the data ( x i, y i)?R 2, ${{i=0,1,\\\\ldots,n}}$ which are in convex position, the problem is to choose the convex best C 1 interpolant with the smallest mean square second derivative among all admissible cubic C 1-splines on the grid. This problem can be efficiently solved by its dual program, developed by Schmdit and his collaborators in

Houduo Qi; Liqun Qi

2003-01-01

460

Variational principles and optimal solutions of the inverse problems of creep bending of plates  

NASA Astrophysics Data System (ADS)

It is shown that inverse problems of steady-state creep bending of plates in both the geometrically linear and nonlinear formulations can be represented in a variational formulation. Steady-state values of the obtained functionals corresponding to the solutions of the problems of inelastic deformation and elastic unloading are determined by applying a finite element procedure to the functionals. Optimal laws of creep deformation are formulated using the criterion of minimizing damage in the functionals of the inverse problems. The formulated problems are reduced to the problems solved by the finite element method using MSC.Marc software.

Bormotin, K. S.; Oleinikov, A. I.

2012-09-01

461

Genetic algorithms applied to the solution of hybrid optimal control problems in astrodynamics  

Microsoft Academic Search

Many space mission planning problems may be formulated as hybrid optimal control problems, i.e. problems that include both\\u000a continuous-valued variables and categorical (binary) variables. There may be thousands to millions of possible solutions;\\u000a a current practice is to pre-prune the categorical state space to limit the number of possible missions to a number that may\\u000a be evaluated via total enumeration.

Bradley J. Wall; Bruce A. Conway

2009-01-01

462

Almost Optimal Interior Penalty Discontinuous Approximations of Symmetric Elliptic Problems on Non-Matching Grids  

SciTech Connect

We consider an interior penalty discontinuous approximation for symmetric elliptic problems of second order on non-matching grids in this paper. The main result is an almost optimal error estimate for the interior penalty approximation of the original problem based on the partition of the domain into a finite number of subdomains. Further, an error analysis for the finite element approximation of the penalty formulation is given. Finally, numerical experiments on a series of model second order problems are presented.

Lazarov, R D; Pasciak, J E; Schoberl, J; Vassilevski, P S

2001-08-08

463

An immunity-based ant colony optimization algorithm for solving weapon-target assignment problem  

Microsoft Academic Search

In this paper, an immunity-based ant colony optimization (ACO) algorithm for solving weapon–target assignment (WTA) problems is proposed. The WTA problem, known as a NP-complete problem, is to find a proper assignment of weapons to targets with the objective of minimizing the expected damage of own-force assets. The general idea of the proposed algorithm is to combine the advantages of

Zne-jung Lee; Chou-yuan Lee; Shun-feng Su

2002-01-01

464

An Interactive Satisficing Method Based on Level Set Optimization for Fuzzy Random Multiobjective Linear Programming Problems  

NASA Astrophysics Data System (ADS)

This paper focuses on multiobjective linear programming problems involving fuzzy random variable coefficients. A new decision making model and Pareto optimal solution concept are proposed using ?-level cuts of membership function. It is shown that the problem including both randomness and fuzziness is equivalently transformed into a deterministic problem. An interactive algorithm is proposed in order to obtain a satisficing solution for a decision maker through interaction.

Katagiri, Hideki; Sakawa, Masatoshi; Kato, Kosuke; Nishizaki, Ichiro

2009-01-01

465

Hybrid solution of stochastic optimal control problems using Gauss pseudospectral method and generalized polynomial chaos algorithms  

NASA Astrophysics Data System (ADS)

A hybrid numerical algorithm combining the Gauss Pseudospectral Method (GPM) with a Generalized Polynomial Chaos (gPC) method to solve nonlinear stochastic optimal control problems with constraint uncertainties is presented. TheGPM and gPC have been shown to be spectrally accurate numerical methods for solving deterministic optimal control problems and stochastic differential equations, respectively. The gPC uses collocation nodes to sample the random space, which are then inserted into the differential equations and solved by applying standard differential equation methods. The resulting set of deterministic solutions is used to characterize the distribution of the solution by constructing a polynomial representation of the output as a function of uncertain parameters. Optimal control problems are especially challenging to solve since they often include path constraints, bounded controls, boundary conditions, and require solutions that minimize a cost functional. Adding random parameters can make these problems even more challenging. The hybrid algorithm presented in this dissertation is the first time the GPM and gPC algorithms have been combined to solve optimal control problems with random parameters. Using the GPM in the gPC construct provides minimum cost deterministic solutions used in stochastic computations that meet path, control, and boundary constraints, thus extending current gPC methods to be applicable to stochastic optimal control problems. The hybrid GPM-gPC algorithm was applied to two concept demonstration problems: a nonlinear optimal control problem with multiplicative uncertain elements and a trajectory optimization problem simulating an aircraft flying through a threat field where exact locations of the threats are unknown. The results show that the expected value, variance, and covariance statistics of the polynomial output function approximations of the state, control, cost, and terminal time variables agree with Monte-Carlo simulation results while requiring on the order of (1/40)th to (1/100)th the number of collocation points and computation time. It was shown that the hybrid algorithm demonstrated an ability to effectively characterize how the solutions to optimization problems vary with uncertainty, and has the potential with continued development and availability of more powerful computer workstations, to be a powerful tool applicable to more complex control problems of interest to the Department of Defense.

Cottrill, Gerald C.

466

Selecting radiotherapy dose distributions by means of constrained optimization problems.  

PubMed

The main steps in planning radiotherapy consist in selecting for any patient diagnosed with a solid tumor (i) a prescribed radiation dose on the tumor, (ii) bounds on the radiation side effects on nearby organs at risk and (iii) a fractionation scheme specifying the number and frequency of therapeutic sessions during treatment. The goal of any radiotherapy treatment is to deliver on the tumor a radiation dose as close as possible to that selected in (i), while at the same time conforming to the constraints prescribed in (ii). To this day, considerable uncertainties remain concerning the best manner in which such issues should be addressed. In particular, the choice of a prescription radiation dose is mostly based on clinical experience accumulated on the particular type of tumor considered, without any direct reference to quantitative radiobiological assessment. Interestingly, mathematical models for the effect of radiation on biological matter have existed for quite some time, and are widely acknowledged by clinicians. However, the difficulty to obtain accurate in vivo measurements of the radiobiological parameters involved has severely restricted their direct application in current clinical practice.In this work, we first propose a mathematical model to select radiation dose distributions as solutions (minimizers) of suitable variational problems, under the assumption that key radiobiological parameters for tumors and organs at risk involved are known. Second, by analyzing the dependence of such solutions on the parameters involved, we then discuss the manner in which the use of those minimizers can improve current decision-making processes to select clinical dosimetries when (as is generally the case) only partial information on model radiosensitivity parameters is available. A comparison of the proposed radiation dose distributions with those actually delivered in a number of clinical cases strongly suggests that solutions of our mathematical model can be instrumental in deriving good quality tests to select radiotherapy treatment plans in rather general situations. PMID:24599739

Alfonso, J C L; Buttazzo, G; García-Archilla, B; Herrero, M A; Núñez, L

2014-05-01

467

THE SELBERG ZETA FUNCTION FOR CONVEX CO-COMPACT  

Microsoft Academic Search

We give a new upper bound on the Selberg zeta function for a convex co-compact Schottky group acting on the hyperbolic space Hn+1: in strips parallel to the imaginary axis the zeta function is bounded by exp(C|s|?) whereis the dimension of the limit set of the group. This bound is more precise than the optimal global bound exp(C|s|n+1), and it

LAURENT GUILLOP ´; KEVIN K. LIN; MACIEJ ZWORSKI

468

The Sizing and Optimization Language, (SOL): Computer language for design problems  

NASA Technical Reports Server (NTRS)

The Sizing and Optimization Language, (SOL), a new high level, special purpose computer language was developed to expedite application of numerical optimization to design problems and to make the process less error prone. SOL utilizes the ADS optimization software and provides a clear, concise syntax for describing an optimization problem, the OPTIMIZE description, which closely parallels the mathematical description of the problem. SOL offers language statements which can be used to model a design mathematically, with subroutines or code logic, and with existing FORTRAN routines. In addition, SOL provides error checking and clear output of the optimization results. Because of these language features, SOL is best suited to model and optimize a design concept when the model consits of mathematical expressions written in SOL. For such cases, SOL's unique syntax and error checking can be fully utilized. SOL is presently available for DEC VAX/VMS systems. A SOL package is available which includes the SOL compiler, runtime library routines, and a SOL reference manual.

Lucas, Stephen H.; Scotti, Stephen J.

1988-01-01

469

A Class of Global Optimization Problems as Models of the Phase Unwrapping Problem  

Microsoft Academic Search

Let I={(i,j)?? i=1, 2,..., N1, j=1, 2,..., N2} and let U=Ui,j, (i,j)?I be a discrete real function defined on I. Let [c]2p be c modulus 2p, we define W:I ? p, p) as follows W=[U]2p. The function U will be called phase function and the function W will be called wrapped phase function. The phase unwrapping problem consists in recovering

Pierluigi Maponi; Francesco Zirilli

2001-01-01

470

On performance metrics and particle swarm methods for dynamic multiobjective optimization problems  

Microsoft Academic Search

This paper describes two performance measures for measuring an EMO (evolutionary multiobjective optimization) algorithm's ability to track a time-varying Pareto-front in a dynamic environment. These measures are evaluated using a dynamic multiobjective test function and a dynamic multiobjective PSO, maximinPSOD, which is capable of handling dynamic multiobjective optimization problems. maximinPSOD is an extension from a previously proposed multiobjective PSO, maximinPSO.

Xiaodong Li; J. Branke; M. Kirley

2007-01-01

471

Probability-based least square support vector regression metamodeling technique for crashworthiness optimization problems  

Microsoft Academic Search

This paper presents a crashworthiness design optimization method based on a metamodeling technique. The crashworthiness optimization\\u000a is a highly nonlinear and large scale problem, which is composed various nonlinearities, such as geometry, material and contact\\u000a and needs a large number expensive evaluations. In order to obtain a robust approximation efficiently, a probability-based\\u000a least square support vector regression is suggested to

Hu Wang; Enying Li; G. Y. Li

2011-01-01

472

Solution of a Sub-Riemannian Optimal Control Problem for a Quantum Spin System  

Microsoft Academic Search

Experiments in nuclear magnetic resonance (NMR) spectroscopy and NMR quantum computing require control of ensembles of quantum mechanical systems. The controlled transfer of coherence along a one-dimensional chain of spin systems plays a key role in NMR spectroscopy of proteins, and spin chains have also been proposed for NMR quantum information processing. The problem of time-optimal or energy-optimal control of

Amit K. Sanyal; Christopher Moseley; Anthony Bloch

473

C-NSGA-II-MOPSO: An Effective Multi-objective Optimizer for Engineering Design Problems  

Microsoft Academic Search

This paper extends the NSGA-II-MOPSO algorithm, which is based on the combination of NSGA-II and multi-objective particle\\u000a swarm optimizer (MOPSO) for unconstrained multi-objective optimization problems, to accommodate constraints and mixed variables.\\u000a In order to utilize the valuable information from the objective function values of infeasible solutions, a method called M+1\\u000a nondominated sorting is proposed to check the nondomination levels of

Jinhua Wang; Zeyong Yin

474

Proper efficiency for set-valued vector optimization problems and vector variational inequalitiesRID=\\  

Microsoft Academic Search

.   We obtain the necessary and sufficient conditions of many kinds of proper efficiency in vector set-valued optimization by\\u000a using the concept of contingent epiderivative introduced by Jahn and Rauh, also we disclose the closed relations between proper\\u000a efficiency of vector set-valued optimization problem and proper efficiency of a certain kind of vector variational inequality.

Wei Liu; Xunhua Gong

2000-01-01

475

Solution of the boundary value problem for optimal escape in continuous stochastic systems and maps  

NASA Astrophysics Data System (ADS)

Topologies of invariant manifolds and optimal trajectories are investigated in stochastic continuous systems and maps. A topological method is introduced that simplifies the solution of boundary value problems: The activation energy is calculated as a function of a set of parameters characterizing the initial conditions of the escape path. The method is applied explicitly to compute the optimal escape path and the activation energy for a variety of dynamical systems and maps.

Beri, S.; Mannella, R.; Luchinsky, D. G.; Silchenko, A. N.; McClintock, P. V. E.

2005-09-01

476

Optimization of the time-dependent traveling salesman problem with Monte Carlo methods.  

PubMed

A problem often considered in operations research and computational physics is the traveling salesman problem, in which a traveling salesperson has to find the shortest closed tour between a certain set of cities. This problem has been extended to more realistic scenarios, e.g., the "real" traveling salesperson has to take rush hours into consideration. We will show how this extended problem is treated with physical optimization algorithms. We will present results for a specific instance of Reinelt's library TSPLIB95, in which we define a zone with traffic jams in the afternoon. PMID:11580476

Bentner, J; Bauer, G; Obermair, G M; Morgenstern, I; Schneider, J

2001-09-01

477

Flat tori in three-dimensional space and convex integration  

PubMed Central

It is well-known that the curvature tensor is an isometric invariant of C2 Riemannian manifolds. This invariant is at the origin of the rigidity observed in Riemannian geometry. In the mid 1950s, Nash amazed the world mathematical community by showing that this rigidity breaks down in regularity C1. This unexpected flexibility has many paradoxical consequences, one of them is the existence of C1 isometric embeddings of flat tori into Euclidean three-dimensional space. In the 1970s and 1980s, M. Gromov, revisiting Nash’s results introduced convex integration theory offering a general framework to solve this type of geometric problems. In this research, we convert convex integration theory into an algorithm that produces isometric maps of flat tori. We provide an implementation of a convex integration process leading to images of an embedding of a flat torus. The resulting surface reveals a C1 fractal structure: Although the tangent plane is defined everywhere, the normal vector exhibits a fractal behavior. Isometric embeddings of flat tori may thus appear as a geometric occurrence of a structure that is simultaneously C1 and fractal. Beyond these results, our implementation demonstrates that convex integration, a theory still confined to specialists, can produce computationally tractable solutions of partial differential relations.

Borrelli, Vincent; Jabrane, Said; Lazarus, Francis; Thibert, Boris

2012-01-01

478

Two Point Exponential Approximation Method for structural optimization of problems with frequency constraints  

NASA Technical Reports Server (NTRS)

The point exponential approximation method was introduced by Fadel et al. (Fadel, 1990), and tested on structural optimization problems with stress and displacement constraints. The reports in earlier papers were promising, and the method, which consists of correcting Taylor series approximations using previous desi