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1

Sequential optimality conditions for composed convex optimization problems  

Microsoft Academic Search

Using a general approach which provides sequential optimality conditions for a general convex optimization problem, we derive necessary and sufficient optimality conditions for composed convex optimization problems. Further, we give sequential characterizations for a subgradient of the precomposition of a K-increasing lower semicontinuous convex function with a K-convex and K-epi-closed (continuous) function, where K is a nonempty convex cone. We

Radu Ioan Bo?; Ernö Robert Csetnek; Gert Wanka

2008-01-01

2

A complementarity constraint formulation of convex multiobjective optimization problems.  

SciTech Connect

We propose a new approach to convex nonlinear multiobjective optimization that captures the geometry of the Pareto set by generating a discrete set of Pareto points optimally. We show that the problem of finding a maximally uniform representation of the Pareto surface can be formulated as a mathematical program with complementarity constraints. The complementarity constraints arise from modeling the set of Pareto points, and the objective maximizes some quality measure of this discrete set. We present encouraging numerical experience on a range of test problems collected from the literature.

Leyffer, S.; Mathematics and Computer Science

2009-04-01

3

On the principle of smooth fit for some convex optimal control problems  

Microsoft Academic Search

Proceedings of the 8th International Symposium on Mechatronics and its Applications (ISMA12)1, Sharjah, UAE. The purpose of this work is to show that the principle of smooth fit can fail even for convex problems. Using the dynamic programming approach which involves using differential equation methods, we get the value function for a convex optimal control problem. Then this value function

Jesus Pascal

2012-01-01

4

A recurrent neural network for solving a class of generalized convex optimization problems.  

PubMed

In this paper, we propose a penalty-based recurrent neural network for solving a class of constrained optimization problems with generalized convex objective functions. The model has a simple structure described by using a differential inclusion. It is also applicable for any nonsmooth optimization problem with affine equality and convex inequality constraints, provided that the objective function is regular and pseudoconvex on feasible region of the problem. It is proven herein that the state vector of the proposed neural network globally converges to and stays thereafter in the feasible region in finite time, and converges to the optimal solution set of the problem. PMID:23584134

Hosseini, Alireza; Wang, Jun; Hosseini, S Mohammad

2013-03-25

5

Duality gap of the conic convex constrained optimization problems in normed spaces  

Microsoft Academic Search

In this paper, motivated by a result due to Champion [Math. Program.99, 2004], we introduce a property $${\\\\mathcal{D}(y)}$$ for a conic quasi-convex vector-valued function in a general normed space. We prove that this property $${\\\\mathcal{D}(y)}$$ characterizes the zero duality gap for a class of the conic convex constrained optimization problem in the sense that if\\u000a this property is satisfied and

Liqun Ban; Wen Song

2009-01-01

6

Solving minimum distance problems with convex or concave bodies using combinatorial global optimization algorithms  

Microsoft Academic Search

Determining the minimum distance between convex objects is a problem that has been solved using many difierent approaches. On the other hand, computing the minimum distance between combinations of convex and con- cave objects is known to be a more complicated problem. Most methods propose to partition the concave object into convex sub-objects and then solve the convex problem be-

Juan A. Carretero; Meyer A. Nahon

2005-01-01

7

About the non-convex optimization problem induced by non-positive semidefinite kernel learning  

Microsoft Academic Search

During the last years, kernel based methods proved to be very successful for many real-world learning problems. One of the\\u000a main reasons for this success is the efficiency on large data sets which is a result of the fact that kernel methods like\\u000a support vector machines (SVM) are based on a convex optimization problem. Solving a new learning problem can

Ingo Mierswa; Katharina Morik

2008-01-01

8

Gradient vs. approximation design optimization techniques in low-dimensional convex problems  

NASA Astrophysics Data System (ADS)

Design Optimization methods' application in structural designing represents a suitable manner for efficient designs of practical problems. The optimization techniques' implementation into multi-physical softwares permits designers to utilize them in a wide range of engineering problems. These methods are usually based on modified mathematical programming techniques and/or their combinations to improve universality and robustness for various human and technical problems. The presented paper deals with the analysis of optimization methods and tools within the frame of one to three-dimensional strictly convex optimization problems, which represent a component of the Design Optimization module in the Ansys program. The First Order method, based on combination of steepest descent and conjugate gradient method, and Supbproblem Approximation method, which uses approximation of dependent variables' functions, accompanying with facilitation of Random, Sweep, Factorial and Gradient Tools, are analyzed, where in different characteristics of the methods are observed.

Fedorik, Filip

2013-10-01

9

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

10

Second-order global optimality conditions for convex composite optimization  

Microsoft Academic Search

In recent years second-order sufficient conditions of an isolated local minimizer for convex composite optimization problems have been established. In this paper, second-order optimality conditions are obtained of aglobal minimizer for convex composite problems with a non-finite valued convex function and a twice strictly differentiable function by introducing a generalized representation condition. This result is applied to a minimization problem

Xiaoqi Yang

1998-01-01

11

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

12

MIMO control system design for aircraft via convex optimization  

Microsoft Academic Search

This paper shows how convex optimization may be used to solve control system design problems for multip~e-input multip]e.output( ~~~~) linear time invariant(~~l) finite di. mensional plants. The Youla parameterization is used to convex) convex optimization ideas presented in 171. In this work, we are primarily concerned with 'H\\

Oguzhan Cifdaloz; Marco Shayeb; R. Metzger; Yu-Lung Yi; Armando A. Rodriguez

2003-01-01

13

An algorithm for linearizing convex extremal problems  

NASA Astrophysics Data System (ADS)

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_p-norm of a matrix and of the minimum of the entropy function on a polytope are obtained. Bibliography: 19 titles.

Gorskaya, Elena S.

2010-06-01

14

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

15

Solving an optimization packing problem of circles and non-convex polygons with rotations into a multiply connected region  

Microsoft Academic Search

This paper deals with the packing problem of circles and non-convex polygons, which can be both translated and rotated into a strip with prohibited regions. Using the ?-function technique, a mathematical model of the problem is constructed and its characteristics are investigated. Based on the characteristics, a solution approach to the problem is offered. The approach includes the following methods:

Y G Stoyan; M V Zlotnik; A M Chugay

16

Solving an optimization packing problem of circles and non-convex polygons with rotations into a multiply connected region  

Microsoft Academic Search

This paper deals with the packing problem of circles and non-convex polygons, which can be both translated and rotated into a strip with prohibited regions. Using the ?-function technique, a mathematical model of the problem is constructed and its characteristics are investigated. Based on the characteristics, a solution approach to the problem is offered. The approach includes the following methods:

Y G Stoyan; M V Zlotnik; A M Chugay

2012-01-01

17

Convexification of different classes of non-convex MINLP problems  

Microsoft Academic Search

In the present paper, convexification strategies for certain kinds of discrete and integer non-convex optimization problems are introduced and discussed. We show how to solve problems with both posynomial and negative binomial terms in the constraints. The convexification technique may in some cases be generalized to include continuous variables. Posynomial functions are non-convex and for such functions no straightforward methods

Ray Pörn; Iiro Harjunkoski; Tapio Westerlund

1999-01-01

18

Solving the Convex Cost Integer Dual Network Flow Problem  

Microsoft Academic Search

In this paper, we consider an integer convex optimization problem where the objective functionis the sum of separable convex functions (that is, of the form (i,j)Q ij ij F(w)+ iP ii B( ) ), theconstraints are similar to those arising in the dual of a minimum cost flow problem (that is, of the form i - j w ij ,

Ravindra K. Ahuja; Dorit S. Hochbaum; James B. Orlin

1999-01-01

19

Improved Convexity Cuts for Lattice Point Problems.  

National Technical Information Service (NTIS)

The generalized lattice point (GLP) problem provides a formulation that accommodates a variety of discrete alternative problems. In the paper the authors show how to substantially strengthen the convexity cuts for the GLP problem. The new cuts are based o...

F. Glover D. Klingman

1973-01-01

20

What Is Optimized in Convex Relaxations for Multi-Label Problems: Connecting Discrete and Continuously-Inspired MAP Inference.  

PubMed

In this work we present a unified view on Markov random fields and recently proposed continuous tight convex relaxations for multi-label assignment in the image plane. These relaxations are far less biased towards the grid geometry than Markov random fields (MRFs) on grids. It turns out that the continuous methods are non-linear extensions of the well-established local polytope MRF relaxation. In view of this result a better understanding of these tight convex relaxations in the discrete setting is obtained. Further, a wider range of optimization methods is now applicable to find a minimizer of the tight formulation. We propose two methods to improve the efficiency of minimization. One uses a weaker, but more efficient continuously inspired approach as initialization and gradually refines the energy where it is necessary. The other one reformulates the dual energy enabling smooth approximations to be used for efficient optimization. We demonstrate the utility of our proposed minimization schemes in numerical experiments. Finally, we generalize the underlying energy formulation from isotropic metric smoothness costs to arbitrary non-metric and orientation dependent smoothness terms. PMID:23751286

Zach, Christopher; Hane, Christian; Pollefeys, Marc

2013-06-01

21

A Convex Programming Approach to the Trace Quotient Problem  

Microsoft Academic Search

The trace quotient problem arises in many applications in pattern clas- sification and computer vision, e.g., manifold learning, low-dimension embed- ding, etc. The task is to solve a optimization problem involving maximizing the ratio of two traces, i.e., maxW Tr(f (W ))\\/Tr(h(W )). This optimization prob- lem itself is non-convex in general, hence it is hard to solve it directly.

Chunhua Shen; Hongdong Li; Michael J. Brooks

2007-01-01

22

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

23

A recurrent neural network for nonlinear continuously differentiable optimization over a compact convex subset.  

PubMed

We propose a general recurrent neural-network (RNN) model for nonlinear optimization over a nonempty compact convex subset which includes the bound subset and spheroid subset as special cases. It is shown that the compact convex subset is a positive invariant and attractive set of the RNN system and that all the network trajectories starting from the compact convex subset converge to the equilibrium set of the RNN system. The above equilibrium set of the RNN system coincides with the optimum set of the minimization problem over the compact convex subset when the objective function is convex. The analysis of these qualitative properties for the RNN model is conducted by employing the properties of the projection operator of Euclidean space onto the general nonempty closed convex subset. A numerical simulation example is also given to illustrate the qualitative properties of the proposed general RNN model for solving an optimization problem over various compact convex subsets. PMID:18249977

Liang, X B

2001-01-01

24

On perturbed steepest descent methods with inexact line search for bilevel convex optimization  

Microsoft Academic Search

We use a general framework for solving convex constrained optimization problems introduced in an earlier work to obtain algorithms for problems with a constraint set defined as the set of minimizers of a given function. Also, the algorithms allow the objective function to be decomposed as a sum of other convex functions that can be treated separately. We prove that

Elias Salomão Helou Neto; Álvaro Rodolfo De Pierro

2010-01-01

25

On perturbed steepest descent methods with inexact line search for bilevel convex optimization  

Microsoft Academic Search

We use a general framework for solving convex constrained optimization problems introduced in an earlier work to obtain algorithms for problems with a constraint set defined as the set of minimizers of a given function. Also, the algorithms allow the objective function to be decomposed as a sum of other convex functions that can be treated separately. We prove that

Elias Salomão Helou Neto; Álvaro Rodolfo De Pierro

2011-01-01

26

Solution of non-convex economic dispatch problem considering valve loading effect by a new Modified Differential Evolution algorithm  

Microsoft Academic Search

This paper presents Economic Dispatch (ED) solution considering valve loading effect by a new Modified Differential Evolution (MDE) algorithm. Considering valve loading effect changes ED into a non-convex optimization problem. This non-convexity challenges analytical and heuristic methods in finding optimal solution in reasonable time. Differential Evolution (DE) is one of evolutionary algorithms, which has been used in many optimization problems

Nima Amjady; Hossein Sharifzadeh

2010-01-01

27

Convex Optimization for Nonrigid Stereo Reconstruction  

Microsoft Academic Search

We present a method for recovering 3-D nonrigid structure from an image pair taken with a stereo rig. More specifically, we dedicate to recover shapes of nearly inextensible deformable surfaces. In our approach, we represent the surface as a 3-D triangulated mesh and formulate the reconstruction problem as an optimization problem consisting of data terms and shape terms. The data

Shuhan Shen; Wenjuan Ma; Wenhuan Shi; Yuncai Liu

2010-01-01

28

Machine learning problems from optimization perspective  

Microsoft Academic Search

Both optimization and learning play important roles in a system for intelligent tasks. On one hand, we introduce three types of optimization tasks studied in the machine learning literature, corresponding to the three levels of inverse problems in an intelligent system. Also, we discuss three major roles of convexity in machine learning, either directly towards a convex programming or approximately

Lei Xu

2010-01-01

29

A simplicial branch and duality bound algorithm for the sum of convex-convex ratios problem  

NASA Astrophysics Data System (ADS)

This article presents a simplicial branch and duality bound algorithm for globally solving the sum of convex-convex ratios problem with nonconvex feasible region. To our knowledge, little progress has been made for globally solving this problem so far. The algorithm uses a branch and bound scheme where the Lagrange duality theory is used to obtain the lower bounds. As a result, the lower-bounding subproblems during the algorithm search are all ordinary linear programs that can be solved very efficiently. It has been proved that the algorithm possesses global convergence. Finally, the numerical experiments are given to show the feasibility of the proposed algorithm.

Shen, Pei-Ping; Duan, Yun-Peng; Pei, Yong-Gang

2009-01-01

30

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

31

Convexity Problems on Meshes with Multiple Broadcasting  

Microsoft Academic Search

Our contribution is twofold. First, we show that ?(log n) is a time lower bound on the CREW-PRAM and the mesh with multiple broadcasting for the tasks of computing the perimeter, the area, the diameter, the width, the modality, the smallest-area enclosing rectangle, and the largest-area inscribed triangle of a convex n-gon. We show that the same time lower bound

Dharmavani Bhagavathi; Stephan Olariu; James L. Schwing; W. Shen; Larry Wilson; Jingyuan Zhang

1995-01-01

32

The utility of convex optimization for weight selection in arrays  

Microsoft Academic Search

In this paper, the versatility and usefulness of convex optimization is illustrated. A sidelobe-minimizing weighting method will be presented that returns optimal weights given a set of specifications, including: scan direction, beamwidth, array geometry, set of null constraints and smoothness criteria. The method also takes into account the radiation patterns of the elements, which do not have to be identical.

Peter J. Bevelacqua

2009-01-01

33

Optimal Algorithm for Solving Collision Distance between Convex Polygons in Plane.  

National Technical Information Service (NTIS)

In this paper, we study the problem of calculating the minimum collision distance between two planar convex polygons when one of them moves to another along a given direction. First, several novel concepts and properties are explored, then an optimal algo...

Y. Yan

1994-01-01

34

The Existence Problem for Steiner Networks in Strictly Convex Domains  

NASA Astrophysics Data System (ADS)

We consider the existence problem for `Steiner networks' (trivalent graphs with 2 ?/3 angles at each junction) in strictly convex domains, with `Neumann' boundary conditions. For each of the three possible combinatorial possibilities, sufficient conditions on the domain are derived for existence. In addition, in each case explicit examples of nonexistence are given.

Freire, Alexandre

2011-05-01

35

Online Convex Programming and Generalized Infinitesimal GradientAscent  

Microsoft Academic Search

Convex programming involves a convex set F Rn and a convex cost function c : F ! R. The goal of convex programming is to nd a point in F which minimizes c. In online convex programming, the convex set is known in advance, but in each step of some repeated optimization problem, one must select a point inF before

Martin Zinkevich

2003-01-01

36

Second-Order Global Optimality Conditions for Optimization Problems  

Microsoft Academic Search

Second-order optimality conditions are studied for the constrained optimization problem where the objective function and the\\u000a constraints are compositions of convex functions and twice strictly differentiable functions. A second-order sufficient condition\\u000a of a global minimizer is obtained by introducing a generalized representation condition. Second-order minimizer characterizations\\u000a for a convex program and a linear fractional program are derived using the generalized

X. Q. Yang

2004-01-01

37

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

38

An optimal algorithm for solving collision distance between convex polygons in plane  

Microsoft Academic Search

In this paper, we study the problem of calculating the minimum collision distance between two planar convex polygons when\\u000a one of them moves to another along a given direction. First, several novel concepts and properties are explored, then an optimal\\u000a algorithm OPFIV with time complexityO (log (n+m)) is developed and its correctness and optimization are proved rigorously.

Yong Yan

1993-01-01

39

Rank-Constrained Schur-Convex Optimization With Multiple Trace/Log-Det Constraints  

NASA Astrophysics Data System (ADS)

Rank-constrained optimization problems have received an increasing intensity of interest recently, because many optimization problems in communications and signal processing applications can be cast into a rank-constrained optimization problem. However, due to the non-convex nature of rank constraints, a systematic solution to general rank-constrained problems has remained open for a long time. In this paper, we focus on a rank-constrained optimization problem with a Schur-convex/concave objective function and multiple trace/logdeterminant constraints. We first derive a structural result on the optimal solution of the rank-constrained problem using majorization theory. Based on the solution structure, we transform the rank-constrained problem into an equivalent problem with a unitary constraint. After that, we derive an iterative projected steepest descent algorithm which converges to a local optimal solution. Furthermore, we shall show that under some special cases, we can derive a closed-form global optimal solution. The numerical results show the superior performance of our proposed technique over the baseline schemes.

Yu, Hao; Lau, Vincent K. N.

2011-01-01

40

FIR Filter Design via Spectral Factorization and Convex Optimization  

Microsoft Academic Search

udio, spectrum shaping, ... ) upper bounds are convex in h; lower bounds are notMagnitude filter design problem involves magnitude specsClassical example: lowpass filter designlowpass filter with maximum stopband attenuation:521\\/51IS()l variables: h C R (filter coefficients),52 G R (stopband attenuation) parameters: 51 ( R (logarithmic passband ripple), n (order),Op (passband frequency), Os (stopband frequency)magnitude filter design problems are nonconvex can

Lieven Vandenberghe; Shao-po Wu; Stephen Boyd

1997-01-01

41

QoS and Fairness Constrained Convex Optimization of Resource Allocation for Wireless Cellular and Ad Hoc Networks  

Microsoft Academic Search

For wireless cellular and ad hoc networks with QoS constraints, we propose a suite of problem formulations that allocate network resources to optimize SIR, maximize throughput and minimize de- lay. The distinguishing characteristics of these resource allocation formulations is that, by using convex optimization, they accommo- date a variety of realistic QoS and fairness constraints. Their glob- ally optimal solutions

David Julian; Mung Chiang; Daniel O'neill; Stephen P. Boyd

2002-01-01

42

An Optimal Algorithm for Roundness Determination on Convex Polygons  

Microsoft Academic Search

In tolerancing, the Out-Of-Roundness factor determines the relativecircularity of planar shapes. The measurement of concern in this workis the Minimum Radial Separation, as recommended by the AmericanNational Standards Institute (ANSI). Here we show that the algorithmgiven in Le and Lee [4] runs in \\\\Theta(n2) time even for convex polygons.Furthermore, we present an optimal O(n) time algorithm to computethe Minimum Radial

Kurt Swanson; D. T. Lee; Vanban L. Wu

1995-01-01

43

Existence of Solutions in Vector Optimization Problems  

Microsoft Academic Search

Conditions for the existence of various effective solutions of vector optimization problems with an unbounded convex closed feasible set of solutions are established. The study is based on the use of the properties of recession cones of sets of feasible solutions and cones of perspective directions of optimization problems.

I. V. Sergienko; T. T. Lebedeva; N. V. Semenova

2000-01-01

44

Optimal placement of convex polygons to maximize point containment  

Microsoft Academic Search

Given a convex polygon P with m vertices and a set S ofn points in the plane, we consider the problem of findinga placement of P that contains the maximum number ofpoints in S. We allow both translation and rotation.Our algorithm is self-contained and utilizes the geometricproperties of the containing regions in the parameter space oftransformations. The algorithm requires O(nk2m2log(mk))time

Matthew Dickerson; Daniel Scharstein

1996-01-01

45

A parametric convex programming approach applied to portfolio pelection problems with fuzzy costs  

Microsoft Academic Search

In this work we consider the portfolio selection problems with uncertainties as a kind of multiple objective problem with fuzzy costs in the objective functions. The portfolio selection problems can be classified as convex programming problems. Although convex programming problems are a special class of nonlinear programming, they can also be defined as a general linear programming problem. These problems

Ricardo C. Silva; J. L. Verdegay; A. Yamakami

2010-01-01

46

Analysis of the Criteria of Activation-Based Inverse Electrocardiography using Convex Optimization  

PubMed Central

In inverse electrocardiography (ECG), the problem of finding activation times on the heart noninvasively from body surface potentials is typically formulated as a nonlinear least squares optimization problem. Current solutions rely on iterative algorithms which are sensitive to the presence of local minima. As a result, improved initialization approaches for this problem have been of considerable interest. However, in experiments conducted on a subject with Wolff-Parkinson-White syndrome, we have observed that there may be a mismatch between favorable solutions of the optimization problem and solutions with the desired physiological characteristics. In this work, we use a method based on a convex optimization framework to explore the solution space and analyze whether the optimization criteria target their intended objective.

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

2012-01-01

47

Improving beampatterns of two-dimensional random arrays using convex optimization.  

PubMed

Sensors are becoming ubiquitous and can be combined in arrays for source localization purposes. If classical conventional beamforming is used, then random arrays have poor beampatterns. By pre-computing sensor weights, these beampatterns can be improved significantly. The problem is formulated in the frequency domain as a desired look direction, a frequency-independent transition region, and the power minimized in a rejection-region. Using this formulation, the frequency-dependent sensor weights can be obtained using convex optimization. Since the weights are data independent they can be pre-computed, the beamforming has similar computational complexity as conventional beamforming. The approach is demonstrated for real 2D arrays. PMID:21476620

Gerstoft, Peter; Hodgkiss, William S

2011-04-01

48

Ultrafast Quantum Process Tomography via Continuous Measurement and Convex Optimization  

NASA Astrophysics Data System (ADS)

Quantum process tomography (QPT) is an essential tool to diagnose the implementation of a dynamical map. However, the standard protocol is extremely resource intensive. For a Hilbert space of dimension d, it requires d^2 different input preparations followed by state tomography via the estimation of the expectation values of d^2-1 orthogonal observables. We show that when the process is nearly unitary, we can dramatically improve the efficiency and robustness of QPT through a collective continuous measurement protocol on an ensemble of identically prepared systems. Given the measurement history we obtain the process matrix via a convex program that optimizes a desired cost function. We study two estimators: least-squares and compressive sensing. Both allow rapid QPT due to the condition of complete positivity of the map; this is a powerful constraint to force the process to be physical and consistent with the data. We apply the method to a real experimental implementation, where optimal control is used to perform a unitary map on a d=8 dimensional system of hyperfine levels in cesium atoms, and obtain the measurement record via Faraday spectroscopy of a laser probe.

Baldwin, Charles; Riofrio, Carlos; Deutsch, Ivan

2013-03-01

49

Cooperative Convex Optimization in Networked Systems: Augmented Lagrangian Algorithms With Directed Gossip Communication  

NASA Astrophysics Data System (ADS)

We study distributed optimization in networked systems, where nodes cooperate to find the optimal quantity of common interest, x=x^\\star. The objective function of the corresponding optimization problem is the sum of private (known only by a node,) convex, nodes' objectives and each node imposes a private convex constraint on the allowed values of x. We solve this problem for generic connected network topologies with asymmetric random link failures with a novel distributed, decentralized algorithm. We refer to this algorithm as AL-G (augmented Lagrangian gossiping,) and to its variants as AL-MG (augmented Lagrangian multi neighbor gossiping) and AL-BG (augmented Lagrangian broadcast gossiping.) The AL-G algorithm is based on the augmented Lagrangian dual function. Dual variables are updated by the standard method of multipliers, at a slow time scale. To update the primal variables, we propose a novel, Gauss-Seidel type, randomized algorithm, at a fast time scale. AL-G uses unidirectional gossip communication, only between immediate neighbors in the network and is resilient to random link failures. For networks with reliable communication (i.e., no failures,) the simplified, AL-BG (augmented Lagrangian broadcast gossiping) algorithm reduces communication, computation and data storage cost. We prove convergence for all proposed algorithms and demonstrate by simulations the effectiveness on two applications: l_1-regularized logistic regression for classification and cooperative spectrum sensing for cognitive radio networks.

Jakovetic, Dusan; Xavier, João; Moura, José M. F.

2011-08-01

50

Mixed H2\\/H? control: a convex optimization approach  

Microsoft Academic Search

The problem of finding an internally stabilizing controller that minimizes a mixed H2\\/H? performance measure subject to an inequality constraint on the H? norm of another closed-loop transfer function is considered. This problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint. Both the state-feedback and output-feedback problems are considered. It

Pramod P. Khargonekar; Mario A. Rotea

1991-01-01

51

Perturbed Optimal Control Problems.  

National Technical Information Service (NTIS)

The effects of perturbations of an optimal control problem upon its optimal control are studied for two classes of optimal control problems. The first class consists of fixed-time, fixed-initial-point, free-terminal-point optimal control problems. The sec...

A. Korsak

1966-01-01

52

Computability of Global Solutions to Factorable Nonconvex Programs: Part I. Convex Underestimating Problems.  

National Technical Information Service (NTIS)

For nonlinear programming problems which are factorable, a computable procedure for obtaining tight underestimating convex programs is presented. This is used to exclude from consideration regions where the global minimizer cannot exist.

G. P. McCormick

1975-01-01

53

A fast convex optimization approach to segmenting 3D scar tissue from delayed-enhancement cardiac MR images.  

PubMed

We propose a novel multi-region segmentation approach through a partially-ordered ports (POP) model to segment myocardial scar tissue solely from 3D cardiac delayed-enhancement MR images (DE-MRI). The algorithm makes use of prior knowledge of anatomical spatial consistency and employs customized label ordering to constrain the segmentation without prior knowledge of geometric representation. The proposed method eliminates the need for regional constraint segmentations, thus reduces processing time and potential sources of error. We solve the proposed optimization problem by means of convex relaxation and introduce its duality: the hierarchical continuous max-flow (HMF) model, which amounts to an efficient numerical solver to the resulting convex optimization problem. Experiments are performed over ten DE-MRI data sets. The results are compared to a FWHM (full-width at half-maximum) method and the inter- and intra-operator variabilities assessed. PMID:23285608

Rajchl, Martin; Yuan, Jing; White, James A; Nambakhsh, Cyrus; Ukwatta, Eranga; Li, Feng; Stirrat, John; Peters, Terry M

2012-01-01

54

ON CONVEX STABILITY DOMAIN AND OPTIMIZATION OF IIR FILTERS  

Microsoft Academic Search

We discuss descriptions of convex domains containing Schur polynomials, built around a given Schur polynomial. We show that the domain described by a positive realness constraint always contains the domain characterized by Rouche's theorem. We also show how to handle computa- tionally the positive realness condition, using semidefinite programming, in the context of designing stable IIR filters. Two recent methods

Bogdan Dumitrescu

55

Optimal Choosing Problems.  

National Technical Information Service (NTIS)

The report deals with generalizations of a class of optimal stopping problems often referred to as the secretary problem. Generalizations pursued include a random N, and a more elaborate payoff structure. If the decision maker chooses a candidate its actu...

W. T. Rasmussen

1972-01-01

56

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

57

First Integrals for Problems of Calculus of Variations on Locally Convex Spaces  

Microsoft Academic Search

The fundamental problem of calculus of variations is considered when solutions are differentiable curves on locally convex spaces. Such problems admit an extension of the Euler-Lagrange equations [Orlov 2002] for continuously normally differentiable Lagrangians. Here, we formulate a Legendre condition and an extension of the classical theorem of Emmy Noether, thus obtaining first integrals for problems of the calculus of

Eugenio A. M. Rocha; Delfim F. M. Torres

2005-01-01

58

Approximation Algorithms for the Minimum Convex Partition Problem  

Microsoft Academic Search

We present two algorithms that compute constant factor approximations of a minimum convex partition of a set P of n points in the plane. The first algorithm is very simple and computes a 3-approximation in O(n logn) time. The second algorithm improves the approximation factor to \\u000a\\u000a\\u000a\\u000a\\u000a\\u000a\\\\frac3011 \\\\frac{30}{11} but it is more complex and a straight forward implementation will run

Christian Knauer; Andreas Spillner

2006-01-01

59

Calculating and controlling the error of discrete representations of Pareto surfaces in convex multi-criteria optimization  

PubMed Central

A discrete set of points and their convex combinations can serve as a sparse representation of the Pareto surface in multiple objective convex optimization. We develop a method to evaluate the quality of such a representation, and show by example that in multiple objective radiotherapy planning, the number of Pareto optimal solutions needed to represent Pareto surfaces of up to five dimensions grows at most linearly with the number of objectives. The method described is also applicable to the representation of convex sets.

Craft, David

2009-01-01

60

The role of convexity for solving some shortest path problems in plane without triangulation  

NASA Astrophysics Data System (ADS)

Solving shortest path problems inside simple polygons is a very classical problem in motion planning. To date, it has usually relied on triangulation of the polygons. The question: "Can one devise a simple O(n) time algorithm for computing the shortest path between two points in a simple polygon (with n vertices), without resorting to a (complicated) linear-time triangulation algorithm?" raised by J. S. B. Mitchell in Handbook of Computational Geometry (J. Sack and J. Urrutia, eds., Elsevier Science B.V., 2000), is still open. The aim of this paper is to show that convexity contributes to the design of efficient algorithms for solving some versions of shortest path problems (namely, computing the convex hull of a finite set of points and convex rope on rays in 2D, computing approximate shortest path between two points inside a simple polygon) without triangulation on the entire polygons. New algorithms are implemented in C and numerical examples are presented.

An, Phan Thanh; Hai, Nguyen Ngoc; Hoai, Tran Van

2013-09-01

61

Convexity and the quantum many-body problem  

NASA Astrophysics Data System (ADS)

We recall some properties of convex functions and, in particular, of the sum of the largest eigenvalues of a Hermitian matrix. From these properties a new estimate of an arbitrary eigenvalue of a sum of Hermitian matrices is derived, which in turn is used to compute an approximate associated spectral projector. These estimates are applied for the first time to explain the generic spectral features of quantum systems. As an application of the formalism, we explain the preponderance of certain ground-state angular momenta as observed in the vibron model with random interactions. We show that the evolution of eigenstates can be predicted from the knowledge of a limited number of spectra and investigate the effect of a three-body interaction in the vibron model on eigenenergies and eigenvectors.

Chau Huu-Tai, P.; Van Isacker, P.

2013-05-01

62

The Bargaining Problem Without Convexity:† Extending the Egalitarian and Kalai-Smorodinsky Solutions  

Microsoft Academic Search

Abstract We relax the assumption used in axiomatic bargaining theory that the feasible set be convex. Instead we require only that it be comprehensive. We show that on this domain, Kalai’s (1977) characterization of the Egalitarian solution remains true, as does Kalai and Smorodinsky’s (1975) theorem if we use weak Pareto optimality.

John P. Conley; Simon Wilkie

2000-01-01

63

Reduction of shock induced noise in imperfectly expanded supersonic jets using convex optimization  

NASA Astrophysics Data System (ADS)

Imperfectly expanded jets generate screech noise. The imbalance between the backpressure and the exit pressure of the imperfectly expanded jets produce shock cells and expansion or compression waves from the nozzle. The instability waves and the shock cells interact to generate the screech sound. The mathematical model consists of cylindrical coordinate based full Navier-Stokes equations and large-eddy-simulation turbulence modeling. Analytical and computational analysis of the three-dimensional helical effects provide a model that relates several parameters with shock cell patterns, screech frequency and distribution of shock generation locations. Convex optimization techniques minimize the shock cell patterns and the instability waves. The objective functions are (convex) quadratic and the constraint functions are affine. In the quadratic optimization programs, minimization of the quadratic functions over a set of polyhedrons provides the optimal result. Various industry standard methods like regression analysis, distance between polyhedra, bounding variance, Markowitz optimization, and second order cone programming is used for Quadratic Optimization.

Adhikari, Sam

2007-11-01

64

A chain rule for [var epsilon]-subdifferentials with applications to approximate solutions in convex Pareto problems  

NASA Astrophysics Data System (ADS)

In this work we obtain a chain rule for the approximate subdifferential considering a vector-valued proper convex function and its post-composition with a proper convex function of several variables nondecreasing in the sense of the Pareto order. We derive an interesting formula for the conjugate of a composition in the same framework and we prove the chain rule using this formula. To get the results, we require qualification conditions since, in the composition, the initial function is extended vector-valued. This chain rule extends analogous well-known calculus rules obtained when the functions involved are finite and it gives a complementary simple expression for other chain rules proved without assuming any qualification condition. As application we deduce the well-known calculus rule for the addition and we extend the formula for the maximum of functions. Finally, we use them and a scalarization process to obtain Kuhn-Tucker type necessary and sufficient conditions for approximate solutions in convex Pareto problems. These conditions extend other obtained in scalar optimization problems.

Gutiérrez, César; Jiménez, Bienvenido; Novo, Vicente

2005-10-01

65

Tractable problems in optimal decentralized control  

NASA Astrophysics Data System (ADS)

This thesis considers the problem of constructing optimal decentralized controllers. The problem is formulated as one of minimizing the closed-loop norm of a feedback system subject to constraints on the controller structure. The notion of quadratic invariance of a constraint set with respect to a system is defined. It is shown that quadratic invariance is necessary and sufficient for the constraint set to be preserved under feedback. It is further shown that if the constraint set has this property, this allows the constrained minimum-norm problem to be solved via convex programming. These results are developed in a very general framework, and are shown to hold for continuous-time systems, discrete-time systems, or operators on Banach spaces, for stable or unstable plants, and for the minimization of any norm. The utility of these results is then demonstrated on some specific constraint classes. An explicit test is derived for sparsity constraints on a controller to be quadratically invariant, and thus amenable to convex synthesis. Symmetric synthesis is also shown to be quadratically invariant. The problem of control over networks with delays is then addressed as another constraint class. Multiple subsystems are considered, each with its own controller, such that the dynamics of each subsystem may affect those of other subsystems with some propagation delays, and the controllers may communicate with each other with some transmission delays. It is shown that if the communication delays are less than the propagation delays, then the associated constraints are quadratically invariant, and thus optimal controllers can be synthesized. We further show that this result still holds in the presence of computational delays. This thesis unifies the few previous results on specific tractable decentralized control problems, identifies broad and useful classes of new solvable problems, and delineates the largest known class of convex problems in decentralized control.

Rotkowitz, Michael Charles

66

Convex optimization theory applied to joint beamforming design in multicarrier MIMO channels  

Microsoft Academic Search

This paper addresses the joint design of transmit and receive beamvectors for a multicarrier MIMO channel within the general and powerful framework of convex optimization theory. From this perspective, a great span of design criteria can be easily accommodated and efficiently solved even though closed-form expressions may not be available. Among other criteria, we consider the minimization of the average

Daniel Perez Palomar; John M. Cioffi; Miguel Angel Lagunas; Antonio Pascual Iserte

2003-01-01

67

An optimal algorithm for computing the minimum vertex distance between two crossing convex polygons  

Microsoft Academic Search

LetP={p1,p2, ...,pm} andQ={q1,q2, ...,qn} be two intersecting convex polygons whose vertices are specified by their cartesian coordinates in order. An optimalO(m+n) algorithm is presented for computing the minimum euclidean distance betweena vertexpi inP and a vertexqj inQ.

G. T. Toussaint

1984-01-01

68

First Integrals for Problems of Calculus of Variations on Locally Convex Spaces  

Microsoft Academic Search

The fundamental problem of calculus of variations is considered when\\u000asolutions are differentiable curves on locally convex spaces. Such problems\\u000aadmit an extension of the Euler-Lagrange equations [Orlov 2002] for\\u000acontinuously normally differentiable Lagrangians. Here, we formulate a Legendre\\u000acondition and an extension of the classical theorem of Emmy Noether, thus\\u000aobtaining first integrals for problems of the calculus of

Eugenio A. M. Rocha; Delfim F. M. Torres

2005-01-01

69

Convex duality in constrained mean-variance portfolio optimization  

Microsoft Academic Search

We apply conjugate duality to establish the existence\\u000aof optimal portfolios in an asset-allocation\\u000aproblem, with the goal of minimizing\\u000athe variance of the final wealth which results from\\u000atrading over a fixed, finite horizon in a continuous-time, complete market,\\u000asubject to the constraints that the expected final wealth equal a specified\\u000atarget value and the portfolio of the investor

Chantal Labbé; Andrew J. Heunis

2007-01-01

70

An Optimal Algorithm for Computing the Minimum Vertex Distance Between Two Crossing Convex Polygons  

Microsoft Academic Search

Let P = {p1, p2,..., pm} and Q = {q1, q2,..., qn} be two intersecting polygons whosevertices are specified by their cartesian coordinates in order. An optimal O(m+n) algorithmis presented for computing the minimum euclidean distance between a vertexpiin P and a vertex qjin Q.Key words: Algorithms, complexity, computational geometry, convex polygons, minimumdistance, Voronoi diagrams.1. IntroductionLet P = {p 1

Godfried Toussaint

1984-01-01

71

Convex hull and tour crossings in the Euclidean traveling salesperson problem: Implications for human performance studies  

Microsoft Academic Search

Recently there has been growing interest among psychologists in human performance on the Euclidean traveling salesperson problem\\u000a (E-TSP). A debate has been initiated on what strategy people use in solving visually presented E-TSP instances. The most prominent\\u000a hypothesis is the convex-hull hypothesis, originally proposed by MacGregor and Ormerod (1996). We argue that, in the literature\\u000a so far, there is no

Iris Van Rooij; Ulrike Stege; Alissa Schactman

2003-01-01

72

Efficient Algorithms for Two-Center Problems for a Convex Polygon  

Microsoft Academic Search

Let P be a convex polygon with n vertices. We want to find two congruent disks whose union covers P and whose radius is minimized. We also consider its discrete version with centers restricted to be at vertices of P. Standard and discrete two-center problems are respectively solved in O(n log3\\u000a n log log n) and O(n log2\\u000a n) time.

Sung Kwon Kim; Chan-su Shin

2000-01-01

73

A permutation flow-shop scheduling problem with convex models of operation processing times  

Microsoft Academic Search

The paper is an extension of the classical permutation flow-shop scheduling problem to the case where some of the job operation\\u000a processing times are convex decreasing functions of the amounts of resources (e.g., financial outlay, energy, raw material)\\u000a allocated to the operations (or machines on which they are performed). Some precedence constraints among the jobs are given.\\u000a For this extended

T. C. E. Cheng; A. Janiak

2000-01-01

74

Newton—Goldstein convergence rates for convex constrained minimization problems with singular solutions  

Microsoft Academic Search

Convergence rates of Newton-Goldstein sequences are estimated for convex constrained minimization problems with singular solutions?, i.e., solutions at which the local quadratic approximationQ(?, x) to the objective functionF grows more slowly than ?x - ??2 for admissible vectorsx near?. For a large class of iterative minimization methods with quadratic subproblems, it is shown that the valuesrn =F(xn)-infOF are of orderO(n-1\\/3)

G. C. Hughes; J. C. Dunn

1984-01-01

75

Convex Optimization for Deformable Surface 3-D Tracking  

Microsoft Academic Search

3-D shape recovery of non-rigid surfaces from 3-D to 2-D correspondences is an under-constrained problem that requires prior knowledge of the possible deformations. State-of-the-art solutions involve enforcing smoothness constraints that limit their applicability and prevent the recovery of sharply folding and creasing surfaces. Here, we propose a method that does not require such smoothness constraints. Instead, we represent surfaces as

Mathieu Salzmann; Richard Hartley; Pascal Fua

2007-01-01

76

Optimal structural design via optimality criteria as a nonsmooth mechanics problem  

NASA Astrophysics Data System (ADS)

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 progress in the field of nonsmooth mechanics makes the solution of structural analysis problems with this kind of 'complete' law possible. Elements from the two fields are combined in this paper for the solution of optimal design and layout problems for structures. The optimal layout of plane trusses with various specific cost functions is studied here as a representative problem. The use of convex, continuous and piecewise linear specific cost functions for the structural members leads to problems of linear variational inequalities or equivalently piecewise linear, convex but nonsmooth optimization problems, which are solved by means of an iterative algorithm based on sequential linear programming techniques. Numerical examples illustrate the theory and its applicability to practical engineering structures. Following a parametric investigation of an optimal bridge design, certain aspects of the optimal truss layout problem are discussed, which can be extended to other types of structural systems as well.

Tzaferopoulos, M. Ap.; Stravroulakis, G. E.

1995-06-01

77

Convex hull and tour crossings in the Euclidean traveling salesperson problem: implications for human performance studies.  

PubMed

Recently there has been growing interest among psychologists in human performance on the Euclidean traveling salesperson problem (E-TSP). A debate has been initiated on what strategy people use in solving visually presented E-TSP instances. The most prominent hypothesis is the convex-hull hypothesis, originally proposed by MacGregor and Ormerod (1996). We argue that, in the literature so far, there is no evidence for this hypothesis. Alternatively we propose and motivate the hypothesis that people aim at avoiding crossings. PMID:12749463

Van Rooij, Iris; Stege, Ulrike; Schactman, Alissa

2003-03-01

78

Class and Home Problems: Optimization Problems  

ERIC Educational Resources Information Center

|Optimization problems suitable for all levels of chemical engineering students are available. These problems do not require advanced mathematical techniques, since they can be solved using typical software used by students and practitioners. The method used to solve these problems forces students to understand the trends for the different terms…

Anderson, Brian J.; Hissam, Robin S.; Shaeiwitz, Joseph A.; Turton, Richard

2011-01-01

79

Stochastic Optimization Problems in Telecommunications  

Microsoft Academic Search

We survey dieren t optimization problems under uncertainty which arise in telecommunica- tions. Three levels of decisions are distinguished: design of structural elements of telecommuni- cation networks, top level design of telecommunication networks and design of optimal policies of telecommunication enterprize. Examples of typical problems from each level show that the stochastic programming paradigm is a powerful approach for solving

Alexei A. Gaivoronski

80

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

81

Covering a simple orthogonal polygon with a minimum number of orthogonally convex polygons  

Microsoft Academic Search

The problem of covering a polygon with convex polygons has proven to be very difficult, even when restricted to the class of orthogonal polygons using orthogonally convex covers. We develop a method of analysis based on dent diagrams for orthogonal polygons, and are able to show that Keil's &Ogr;(n2) algorithm for covering horizontally convex polygons is optimal, but can be

Robert A. Reckhow; Joseph C. Culberson

1987-01-01

82

Convex reformulation of biologically-based multi-criteria intensity-modulated radiation therapy optimization including fractionation effects  

NASA Astrophysics Data System (ADS)

Finding fluence maps for intensity-modulated radiation therapy (IMRT) can be formulated as a multi-criteria optimization problem for which Pareto optimal treatment plans exist. To account for the dose-per-fraction effect of fractionated IMRT, it is desirable to exploit radiobiological treatment plan evaluation criteria based on the linear-quadratic (LQ) cell survival model as a means to balance the radiation benefits and risks in terms of biologic response. Unfortunately, the LQ-model-based radiobiological criteria are nonconvex functions, which make the optimization problem hard to solve. We apply the framework proposed by Romeijn et al (2004 Phys. Med. Biol. 49 1991-2013) to find transformations of LQ-model-based radiobiological functions and establish conditions under which transformed functions result in equivalent convex criteria that do not change the set of Pareto optimal treatment plans. The functions analysed are: the LQ-Poisson-based model for tumour control probability (TCP) with and without inter-patient heterogeneity in radiation sensitivity, the LQ-Poisson-based relative seriality s-model for normal tissue complication probability (NTCP), the equivalent uniform dose (EUD) under the LQ-Poisson model and the fractionation-corrected Probit-based model for NTCP according to Lyman, Kutcher and Burman. These functions differ from those analysed before in that they cannot be decomposed into elementary EUD or generalized-EUD functions. In addition, we show that applying increasing and concave transformations to the convexified functions is beneficial for the piecewise approximation of the Pareto efficient frontier.

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

2008-11-01

83

The roles of the convex hull and the number of potential intersections in performance on visually presented traveling salesperson problems  

Microsoft Academic Search

The planar Euclidean version of the traveling salesperson problem requires finding the shortest tour through a two-dimensional\\u000a array of points. MacGregor and Ormerod (1996) have suggested that people solve such problems by using a global-to-local perceptual\\u000a organizing process based on the convex hull of the array. We review evidence for and against this idea, before considering\\u000a an alternative, local-to-global perceptual

Douglas Vickers; Michael D. Lee; Matthew Dry; Peter Hughes

2003-01-01

84

Evaluation of relative entropy of entanglement and derivation of optimal Lewenstein–Sanpera decomposition of bell decomposable states via convex optimization  

Microsoft Academic Search

We provide an analytical expression for optimal Lewenstein–Sanpera decomposition of Bell decomposable states by using semi-definite programming. Also using the Karush–Kuhn–Tucker optimization method, the minimum relative entropy of entanglement of Bell decomposable states has been evaluated and it is shown that the same separable Bell decomposable state lying at the boundary of convex set of separable Bell decomposable states, optimizes

M. A. Jafarizadeh; M. Mirzaee; M. Rezaee

2005-01-01

85

Evaluation of relative entropy of entanglement and derivation of optimal Lewenstein-Sanpera decomposition of Bell decomposable states via convex optimization  

Microsoft Academic Search

We provide an analytical expression for optimal Lewenstein-Sanpera decomposition of Bell decomposable states by using semi-definite programming. Also using the Karush-Kuhn-Tucker optimization method, the minimum relative entropy of entanglement of Bell decomposable states has been evaluated and it is shown that the same separable Bell decomposable state lying at the boundary of convex set of separable Bell decomposable states, optimizes

M. A. Jafarizadeh; M. Mirzaee; M. Rezaee

2006-01-01

86

Minimum strictly convex quadrangulations of convex polygons  

Microsoft Academic Search

We present a linear-time algorithm that decomposes a convex poly- gon conformally into a minimum number of strictly convex quadri- laterals. Moreover, we characterize the polygons that can b e de- composed without additional vertices inside the polygon, and we present a linear-time algorithm for such decompositions, t oo. As an application, we consider the problem of constructing a minimum

Matthias Miiller-Hannemannl; Karsten Weihe

1997-01-01

87

BMI optimization based on unimodal normal distribution crossover GA with relaxed LMI convex estimation  

Microsoft Academic Search

This paper deals with the global optimization of the BMIEP (bilinear matrix inequalities eigenvalue problem) based on the UNDX (unimodal normal distribution crossover) GA. First, analyzing the structure of the BMIEP, the existence of the typical difficult structures is confirmed. Then, based on the results of the problem structures analysis and the consideration of the BMIEP characteristic properties, an efficient

Michihiro Kawanishi; Yuu Ikuyama

2005-01-01

88

Optimization Problems with Cardinality Constraints  

Microsoft Academic Search

\\u000a In this article we review several hybrid techniques that can be used to accurately and efficiently solve large optimization\\u000a problems with cardinality constraints. Exact methods, such as branch-and-bound, require lengthy computations and are, for\\u000a this reason, infeasible in practice. As an alternative, this study focuses on approximate techniques that can identify near-optimal\\u000a solutions at a reduced computational cost. Most of

Rubén Ruiz-Torrubiano; Sergio García-Moratilla; Alberto Suárez

89

About an Optimal Visiting Problem  

SciTech Connect

In this paper we are concerned with the optimal control problem consisting in minimizing the time for reaching (visiting) a fixed number of target sets, in particular more than one target. Such a problem is of course reminiscent of the famous 'Traveling Salesman Problem' and brings all its computational difficulties. Our aim is to apply the dynamic programming technique in order to characterize the value function of the problem as the unique viscosity solution of a suitable Hamilton-Jacobi equation. We introduce some 'external' variables, one per target, which keep in memory whether the corresponding target is already visited or not, and we transform the visiting problem in a suitable Mayer problem. This fact allows us to overcome the lacking of the Dynamic Programming Principle for the originary problem. The external variables evolve with a hysteresis law and the Hamilton-Jacobi equation turns out to be discontinuous.

Bagagiolo, Fabio, E-mail: bagagiol@science.unitn.it; Benetton, Michela [Unversita di Trento, Dipartimento di Matematica (Italy)

2012-02-15

90

Weak convexity in the senses of Vial and Efimov-Stechkin  

NASA Astrophysics Data System (ADS)

Research in convex analysis (in particular, in the theory of strongly convex sets developed in recent years) has made it possible to obtain important results in approximation theory, the theory of extremal problems, optimal control and differential game theory [1]-[3]. In many problems there arise non-convex sets that have weakened convexity properties, which enables one to study them using the methods of convex analysis. In this paper we study new properties of sets that are weakly convex in the sense of Vial or Efimov-Stechkin, that is, in the direct and dual senses. We establish relations between these two concepts of weak convexity. For subsets of Hilbert space that are weakly convex in the sense of Vial we prove a theorem on relative connectedness and a support principle.

Ivanov, G. E.

2005-12-01

91

More on conditions of local and global minima coincidence in discrete optimization problems  

SciTech Connect

In some areas of discrete optimization, it is necessary to isolate classes of problems whose target functions do not have local or strictly local minima that differ from the global minima. Examples include optimizations on discrete metric spaces and graphs, lattices and partially ordered sets, and linear combinatorial problems. A unified schema that to a certain extent generalizes the convexity models on which the above-cited works are based has been presented in articles. This article is a continuation of that research.

Lebedeva, T.T.; Sergienko, I.V.; Soltan, V.P.

1994-05-01

92

A convex characterization of classes of problems in control with specific interaction and communication structures  

Microsoft Academic Search

We present a list of optimal disturbance rejection problems in systems in which the overall control scheme is required to have a certain structure. These structures correspond to various classes of controlled systems which include what we refer to as nested, chained, hierarchical, delayed interaction and communication, and, symmetric systems. The common thread in all of these classes is that

Petros G. Voulgaris

2001-01-01

93

Optimal control problems with switching points  

Microsoft Academic Search

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

Hans Seywald

1991-01-01

94

Necessary Optimality Conditions for Optimal Control Problems with Intermediate Constraints  

Microsoft Academic Search

In this paper we study an optimal control problem with intermediate constraints. Our purpose is to obtain the first- and second-order necessary conditions for an optimal control problem with intermediate constraints.

A. V. Arutyunov; A. I. Okoulevitch

1998-01-01

95

Minimum Strictly Convex Quadrangulations of Convex Polygons  

Microsoft Academic Search

We present a linear--time algorithm that decomposesa convex polygon conformally into a minimumnumber of strictly convex quadrilaterals.Moreover, we characterize the polygons that canbe decomposed without additional vertices insidethe polygon, and we present a linear--time algorithmfor such decompositions, too. As an application,we consider the problem of constructinga minimum conformal refinement of a mesh inthe three--dimensional space, which approximatesthe surface of a

Karsten Weihe; Matthias M Uller-hannemann; Matthias Muller-hannemann

1996-01-01

96

A fast algorithm for assortment optimization problems  

Microsoft Academic Search

Assortment optimization problems intend to seek the best way of placing a given set of rectangles within a minimum-area rectangle. Such problems are often formulated as a quadratic mixed 0–1 program. Many current methods for assortment problems are either unable to find an optimal solution or being computationally inefficient for reaching an optimal solution. This paper proposes a new method

Han-lin Li; Jung-fa Tsai

2001-01-01

97

Uniqueness in the two-dimensional inverse conductivity problems of determining convex polygonal supports: case of variable conductivity  

NASA Astrophysics Data System (ADS)

In a bounded domain {\\Omega} \\subset {\\bb R}^2 , we consider div((ell(x) + m(x)khgrD(x))nablau(x)) + k(x)u(x) = 0, where \\ell, m \\in C^2(\\overline{{\\Omega}}) satisfy ell, ell + m > 0 on \\overline{{\\Omega}} , the subdomain D is the union of a finite number of polygons, khgrD denotes the characteristic function of D and k epsi Linfin(OHgr), k geq 0 on \\overline{{\\Omega}} . We discuss an inverse problem of determining D by the boundary data of u. Our main results are stated as follows. (i) Case k equiv 0: a suitably given single Dirichlet datum of u on partOHgr yields the uniqueness of the convex hull of D. (ii) Case 0 < k(x) < lgr0, where lgr0 is the product of the minimum of ell and the first eigenvalue of -Dgr with the zero Dirichlet boundary condition. By changing Dirichlet inputs to u on partOHgr twice and suitably, the resulting two Neumann data guarantee the uniqueness of the convex hull.

Kim, Sungwhan; Yamamoto, Masahiro

2004-04-01

98

Optimization Problems for Control of Distributed Resources  

NASA Astrophysics Data System (ADS)

We consider a two-level optimization problem of resource allocation in communication networks, which is based on profit maximization of the network subject to capacity constraints. The cost function of the upper level problem involves a sum of non-differentiable functions whose values are computed algorithmically. The corresponding solution methods utilize duality theory and decomposition technique for optimization problems.

Konnov, Igor V.; Kashina, Olga A.; Laitinen, Erkki

2009-08-01

99

First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems  

Microsoft Academic Search

First-order and second-order necessary and sufficient optimality conditions are given for infinite-dimensional programming problems with constraints defined by arbitrary closed convex cones. The necessary conditions are immediate generalizations of those known for the finite-dimensional case. However, this does not hold for the sufficient conditions as illustrated by a counterexample. Here, to go from finite to infinite dimensions, causes an essential

H. Maurer; J. Zowe

1979-01-01

100

Optimal Stopping Problem and Investment Models  

Microsoft Academic Search

\\u000a The paper is devoted to the description of an approach to solving an optimal stopping problems for multidimensional diffusion\\u000a processes. This approach is based on connection between boundary problem for diffusion processes and Dirichlet problem for\\u000a PDE of an elliptic type. The solution of a Dirichlet problem is considered as a functional of the available continuation regions.\\u000a The optimization of

Vadim I. Arkin; Alexander D. Slastnikov

101

An extension of Karmarkar's projective algorithm for convex quadratic programming  

Microsoft Academic Search

We present an extension of Karmarkar's linear programming algorithm for solving a more general group of optimization problems: convex quadratic programs. This extension is based on the iterated application of the objective augmentation and the projective transformation, followed by optimization over an inscribing ellipsoid centered at the current solution. It creates a sequence of interior feasible points that converge to

Yinyu Ye; Edison Tse

1989-01-01

102

Constrained Graph Optimization: Interdiction and Preservation Problems  

SciTech Connect

The maximum flow, shortest path, and maximum matching problems are a set of basic graph problems that are critical in theoretical computer science and applications. Constrained graph optimization, a variation of these basic graph problems involving modification of the underlying graph, is equally important but sometimes significantly harder. In particular, one can explore these optimization problems with additional cost constraints. In the preservation case, the optimizer has a budget to preserve vertices or edges of a graph, preventing them from being deleted. The optimizer wants to find the best set of preserved edges/vertices in which the cost constraints are satisfied and the basic graph problems are optimized. For example, in shortest path preservation, the optimizer wants to find a set of edges/vertices within which the shortest path between two predetermined points is smallest. In interdiction problems, one deletes vertices or edges from the graph with a particular cost in order to impede the basic graph problems as much as possible (for example, delete edges/vertices to maximize the shortest path between two predetermined vertices). Applications of preservation problems include optimal road maintenance, power grid maintenance, and job scheduling, while interdiction problems are related to drug trafficking prevention, network stability assessment, and counterterrorism. Computational hardness results are presented, along with heuristic methods for approximating solutions to the matching interdiction problem. Also, efficient algorithms are presented for special cases of graphs, including on planar graphs. The graphs in many of the listed applications are planar, so these algorithms have important practical implications.

Schild, Aaron V [Los Alamos National Laboratory

2012-07-30

103

Stochastic Convex Programming: Kuhn-Tucker Conditions.  

National Technical Information Service (NTIS)

Optimality criteria are derived for stochastics programs with convex objective and convex constraints. The (basic) Kuhn-Tucker conditions are obtained in terms of conditions on the existence of saddle points of a Lagrangian associated with the stochastic ...

R. T. Rockafellar R. J. B. Wets

1974-01-01

104

A Multivariate Partition Approach to Optimization Problems  

Microsoft Academic Search

In this paper, a general optimization approach called the Multivariate Partition Approach (MPA) is proposed for dealing with the problem of minimization of multivariate functions. The basic idea of the MPA is to partition all the variables appearing in an optimization problem into several groups, each of which consists of some variables, and to regard each group as a set

H. X. Huang; P. M. Pardalos

2002-01-01

105

A Mathematical Optimization Problem in Bioinformatics  

ERIC Educational Resources Information Center

This article describes the sequence alignment problem in bioinformatics. Through examples, we formulate sequence alignment as an optimization problem and show how to compute the optimal alignment with dynamic programming. The examples and sample exercises have been used by the author in a specialized course in bioinformatics, but could be adapted…

Heyer, Laurie J.

2008-01-01

106

A Mathematical Optimization Problem in Bioinformatics  

ERIC Educational Resources Information Center

|This article describes the sequence alignment problem in bioinformatics. Through examples, we formulate sequence alignment as an optimization problem and show how to compute the optimal alignment with dynamic programming. The examples and sample exercises have been used by the author in a specialized course in bioinformatics, but could be adapted…

Heyer, Laurie J.

2008-01-01

107

Local Optimization and the Traveling Salesman Problem  

Microsoft Academic Search

The Traveling Salesman Problem (TSP) is often cited as the prototypical hard combinatorial optimization problem. As such, it would seem to be an ideal candidate for nonstandard algorithmic approaches, such as simulated annealing, and, more recently, genetic algorithms. Both of these approaches can be viewed as variants on the traditional technique called local optimization. This paper surveys the state of

David S. Johnson

1990-01-01

108

Particle swarm optimization method in multiobjective problems  

Microsoft Academic Search

This paper constitutes a first study of the Particle Swarm Optimization (PSO) method in Multiobjective Optimization (MO) problems. The ability of PSO to detect Pareto Optimal points and capture the shape of the Pareto Front is studied through experiments on well-known non-trivial test functions. The Weighted Aggregation technique with fixed or adaptive weights is considered. Furthermore, critical aspects of the

Konstantinos E. Parsopoulos; Michael N. Vrahatis

2002-01-01

109

Solving optimization problems on computational grids  

Microsoft Academic Search

Multiprocessor computing platforms, which have become more and more widely available since the mid-1980s, are now heavily used by organizations that need to solve very demanding computational problems. Parallel computing is now central to the culture of many research communities. Novel parallel approaches were developed for global optimization, network optimization, and direct-search methods for nonlinear optimization. Activity was particularly widespread

S. J. Wright

2001-01-01

110

Mathematical Modeling of Earthwork Optimization Problems  

Microsoft Academic Search

In the past this research efforts in optimizing earthwork processes focused mainly on minimizing transportation costs and mass haul distances, respectively. This kind of optimization problem, well known as earthwork allocation problem can be solved by applying linear programming techniques. As a result, the most cost-efficient cut-to-fill assignments will be found. In this article, starting from an optimal cut-to-fill assignment,

Yang Ji; André Borrmann; Ernst Rank; Florian Seipp; Stefan Ruzika

111

Cones of multipowers and combinatorial optimization problems  

NASA Astrophysics Data System (ADS)

The cone of multipowers is dual to the cone of nonnegative polynomials. The relation of the former cone to combinatorial optimization problems is examined. Tensor extensions of polyhedra of combinatorial optimization problems are used for this purpose. The polyhedron of the MAX-2-CSP problem (optimization version of the two-variable constraint satisfaction problem) of tensor degree 4 k is shown to be the intersection of the cone of 4 k-multipowers and a suitable affine space. Thus, in contrast to SDP relaxations, the relaxation to a cone of multipowers becomes tight even for an extension of degree 4.

Vyalyi, M. N.

2013-05-01

112

Problem Solving through an Optimization Problem in Geometry  

ERIC Educational Resources Information Center

|This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect…

Poon, Kin Keung; Wong, Hang-Chi

2011-01-01

113

Representations in Problem Solving: A Case Study with Optimization Problems  

ERIC Educational Resources Information Center

|Introduction: Representations play an essential role in mathematical thinking. They favor the understanding of mathematical concepts and stimulate the development of flexible and versatile thinking in problem solving. Here our focus is on their use in optimization problems, a type of problem considered important in mathematics teaching and…

Villegas, Jose L.; Castro, Enrique; Gutierrez, Jose

2009-01-01

114

An Analytical Approach to Optimize NC Tool Path Planning for Face Milling Flat Convex Polygonal Surfaces  

Microsoft Academic Search

CAD\\/CAM systems currently generate the tool cutter path for many NC operations. However no mathematical model is available for computing an optimal tool cutter path for face milling. By utilizing such a model, the minimum length of cut can be identified for face milling flat surfaces. In this paper, the authors present an analytical procedure from which the optimal cutting

HSU-PIN WANG; HENG CHANG; RICHARD A. WYSK

1988-01-01

115

Global Optimization for Satisfiability (SAT) Problem  

Microsoft Academic Search

The satisfiability (SAT) problem is a fundamental problem in mathematical logic, inference, automated reasoning, VLSI engineering, and computing theory. Following CNF and DNF local search methods, we introduce the Universal SAT problem model, UniSAT, which transforms the discrete SAT problem on Boolean space {0, 1}\\/sup m\\/ into an unconstrained global optimization problem on real space E\\/sup m\\/. A direct correspondence

Jun Gu

1994-01-01

116

Variations of Base-Station Placement Problem on the Boundary of a Convex Region  

Microsoft Academic Search

Due to the recent growth in the demand of mobile communication services in several typical environments, the development of efficient s ystems for providing specialized services has become an important issue in mobile communication research. An important sub-problem in this area is the base-station placement problem, where the objective is to identify the location for placing the base- stations. Mobile

Gautam K. Das; Sasanka Roy; Sandip Das; Subhas C. Nandy

2008-01-01

117

Convex programming, variational inequalities, and applications to the traffic equilibrium problem  

Microsoft Academic Search

The problem of determining the equilibrium distribution of the traffic flow in a city network is studied when the traffic demands on a set of given routes are known. The problem is formulated in terms of a nonlinear variational inequality over a polyhedron and a solving procedure, different from those shown in [1], [3], [4], is exhibited. This procedure is

Antonino Maugeri; Viale A. Doria

1987-01-01

118

Evolutionary Techniques for Constrained Optimization Problems  

Microsoft Academic Search

: An Evolutionary Algorithm to solve general constrained optimization problems is proposed inthis paper. Mathematical programming problems such as linear, nonlinear, integer, boolean and mixed programmingproblems can be solved by using this technique. Some important characteristics of the EvolutionaryAlgorithm are a natural representation of solutions, a problem-independent technique for constraint satisfaction,tournament selection, complete generational replacement, and elitism strategy....

Fernando Jiménez; José L. Verdegay

1999-01-01

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

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

121

Convex hull or crossing avoidance? Solution heuristics in the traveling salesperson problem  

Microsoft Academic Search

Untrained adults appear to have access to cognitive processes that allow them to perform well in the Euclidean version of\\u000a the traveling salesperson problem (E-TSP). They do so despite the famous computational intractability of the problem, which\\u000a stems from its combinatorial complexity. A current hypothesis is that humans’ good performance is based on following a strategy\\u000a of connecting boundary points

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

2004-01-01

122

Finding Maximum Convex Polygons  

Microsoft Academic Search

This paper considers the situation where one is given a finite set of n points in the plane each of which is labeled either positive or negative. The problem is to find a bounded convex polygon of maximum area, the vertices of which are positive points and which does not contain any negative point. It is shown that this problem

Paul Fischer; Lehrstuhl Informatik II

1993-01-01

123

Phase retrieval, error reduction algorithm, and Fienup variants: a view from convex optimization  

Microsoft Academic Search

The phase retrieval problem is of paramount importance in various areas of applied physics and engineering. The state of the art for solving this problem in two dimensions relies heav- ily on the pioneering work of Gerchberg, Saxton, and Fienup. Despite the widespread use of the algorithms proposed by these three researchers, current mathematical theory cannot ex- plain their remarkable

Heinz H. Bauschke; Patrick L. Combettes; D. Russell Luke

2002-01-01

124

A successive convex approximation method for multistage workforce capacity planning problem with turnover  

Microsoft Academic Search

Workforce capacity planning in human resource management is a critical and essential component of the services supply chain management. In this paper, we consider the planning problem of transferring, hiring, or firing employees among different departments or branches of an organization under an environment of uncertain workforce demands and turnover, with the objective of minimizing the expected cost over a

Haiqing Song; Huei-chuen Huang

2008-01-01

125

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

126

Recent approaches to global optimization problems through Particle Swarm Optimization  

Microsoft Academic Search

This paper presents an overview of our most recent results concerning the Particle Swarm Optimization (PSO) method. Techniques for the alleviation of local minima, and for detecting multiple minimizers are described. Moreover, results on the ability of the PSO in tackling Multiobjective, Minimax, Integer Programming and ? 1 errors-in-variables problems, as well as problems in noisy and continuously changing environments,

Konstantinos E. Parsopoulos; Michael N. Vrahatis

2002-01-01

127

Optimization Problems in Wireless Sensor Networks  

Microsoft Academic Search

The Wireless Sensor Networks (WSNs) design related questions give rise to new complex and difficult the- oretical problems and challenges in operations research and optimization areas. As WSNs become increasingly pervasive, a good understanding of these problems in terms of theoretical complexity is of great help in designing appropriate algorithms. In this paper, we examine some of the most fundamental

Ada Gogu; Dritan Nace; Arta Dilo; Nirvana Meratnia

2011-01-01

128

Dynamic Simulation of Human Motion: Numerically Efficient Inclusion of Muscle Physiology by Convex Optimization  

Microsoft Academic Search

Determining the muscle forces that underlie some experimentally ob- served human motion, is a challenging biomechanical problem, both from an exper- imental and a computational point of view. No non-invasive method is currently available for experimentally measuring muscle forces. The alternative of computing them from the observed motion is complicated by the inherent overactuation of the human body: it has

Goele Pipeleers; Div. PMA; Bram Demeulenaere; Ilse Jonkers; Pieter Spaepen; Div. BMGO; Georges Van der Perre; Arthur Spaepen; Jan Swevers

2006-01-01

129

Planning in Supply Chain Optimization Problem  

Microsoft Academic Search

The SCO planning problem is a tightly coupled plan- ning and scheduling problem. We have identified some important features underlying this problem including the coordination between actions, maintaining tem- poral and numerical constraints and the optimization metric. These features have been modeled separately and experimented with the state-of-the-art planners, Crikey, Lpg-td and SgPlan5. However, none of these planners are able

N. H. Mohamed Radzi; Maria Fox; Derek Long

130

Multiview stereo and silhouette consistency via convex functionals over convex domains.  

PubMed

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 original stereo-weighted surface area as a cost functional without heuristic modifications of this energy by balloon terms or other strategies, yet still obtain meaningful (non-empty) reconstructions which are guaranteed to be silhouette-consistent. We prove that the proposed convex relaxation approach provides solutions that lie within a bound of the optimal solution. Compared to existing alternatives, the proposed method does not depend on initialization and leads to a simpler and more robust numerical scheme for imposing silhouette consistency obtained by projection onto convex sets. We show that this projection can be solved exactly using an efficient algorithm. We propose a parallel implementation of the resulting convex optimization problem on a graphics card. Given a photo-consistency map and a set of image silhouettes, we are able to compute highly accurate and silhouette-consistent reconstructions for challenging real-world data sets. In particular, experimental results demonstrate that the proposed silhouette constraints help to preserve fine-scale details of the reconstructed shape. Computation times depend on the resolution of the input imagery and vary between a few seconds and a couple of minutes for all experiments in this paper. PMID:20820076

Cremers, Daniel; Kolev, Kalin

2011-06-01

131

Dynamic simulation of human motion: numerically efficient inclusion of muscle physiology by convex optimization  

Microsoft Academic Search

Determining the muscle forces that underlie some experimentally observed human motion, is a challenging biomechanical problem,\\u000a both from an experimental and a computational point of view. No non-invasive method is currently available for experimentally\\u000a measuring muscle forces. The alternative of computing them from the observed motion is complicated by the inherent overactuation\\u000a of the human body: it has many more

Goele Pipeleers; Bram Demeulenaere; Ilse Jonkers; Pieter Spaepen; Arthur Spaepen; Jan Swevers

2008-01-01

132

On the Convex Parameterization of Constrained Spacecraft Reorientation  

Microsoft Academic Search

Guiding the rotational motion of a spacecraft subject to constraints on its permissible orientation often leads to nonconvex optimal control problems. In this paper, we consider convex parameterizations of sets associated with the constrained rigid body orientations. We then elaborate on ramifications of such a parameterization in the development of steering laws for autonomous spacecraft reorientation that are based on

Yoonsoo Kim; Mehran Mesbahi; Gurkirpal Singh; Fred Y. Hadaegh

2010-01-01

133

Curvature-Constrained Shortest Paths in a Convex Polygon  

Microsoft Academic Search

Let be a point robot moving in the plane, whose path is con- strained to have curvature at most , and let be a convex polygon with vertices. We study the collision-free, optimal path-plann ing problem for moving between two configurations inside (a con- figuration specifies both a location and a direction of travel ). We present an time algorithm

Pankaj K. Agarwal; Therese C. Biedl; Sylvain Lazard; Steve Robbins; Subhash Suri; Sue Whitesides

2002-01-01

134

Solving constrained optimization problems with hybrid particle swarm optimization  

NASA Astrophysics Data System (ADS)

Constrained optimization problems (COPs) are very important in that they frequently appear in the real world. A COP, in which both the function and constraints may be nonlinear, consists of the optimization of a function subject to constraints. Constraint handling is one of the major concerns when solving COPs with particle swarm optimization (PSO) combined with the Nelder-Mead simplex search method (NM-PSO). This article proposes embedded constraint handling methods, which include the gradient repair method and constraint fitness priority-based ranking method, as a special operator in NM-PSO for dealing with constraints. Experiments using 13 benchmark problems are explained and the NM-PSO results are compared with the best known solutions reported in the literature. Comparison with three different meta-heuristics demonstrates that NM-PSO with the embedded constraint operator is extremely effective and efficient at locating optimal solutions.

Zahara, Erwie; Hu, Chia-Hsin

2008-11-01

135

Decomposing a polygon into its convex parts  

Microsoft Academic Search

A common operation in geometric computing is the decomposition of complex structures into more basic structures. Since it is easier to apply most algorithms to triangles or arbitrary convex polygons, there is considerable interest in finding fast algorithms for such decompositions. We consider the problem of decomposing a simple (non-convex) polygon into the union of a minimal number of convex

Bernard Chazelle; David P. Dobkin

1979-01-01

136

Uncertainty on Multi-objective Optimization Problems  

NASA Astrophysics Data System (ADS)

In general, parameters in multi-objective optimization are assumed as deterministic with no uncertainty. However, uncertainty in the parameters can affect both variable and objective spaces. The corresponding Pareto optimal fronts, resulting from the disturbed problem, define a cloud of curves. In this work, the main objective is to study the resulting cloud of curves in order to identify regions of more robustness and, therefore, to assist the decision making process. Preliminary results, for a very limited set of problems, show that the resulting cloud of curves exhibits regions of less variation, which are, therefore, more robust to parameter uncertainty.

Costa, Lino; Santo, Isabel A. C. P. Espírito; Oliveira, Pedro

2011-09-01

137

Robust Solutions in Unstable Optimization Problems  

Microsoft Academic Search

We consider constraint optimization problems where costs (or preferences) are all given, but some are tagged as possibly unstable, and provided with a range of alternative values. We also allow for some uncontrollable variables, whose value cannot be decided by the agent in charge of taking the decisions, but will be decided by Nature or by some other agent. These

Maria Silvia Pini; Francesca Rossi; Kristen Brent Venable; Rina Dechter

2008-01-01

138

Optimal birth control of population dynamics. II. Problems with free final time, phase constraints, and mini-max costs.  

PubMed

A previous analysis of optimal birth control of population systems of the McKendrick type (a distributed parameter system involving 1st order partial differential equations with nonlocal bilinear boundary control) raised 3 additional issues--free final time problem, system with phase constraints, and the mini-max control problem of a population. The free final time problem considers the minimum time problem to be a special case, but relaxes many convexity assumptions. Theorems (maximum principles) and corollaries are developed that flow from the terminology and mathematical notations set forth in the earlier article. PMID:12316749

Chan, W L; Guo, B Z

1990-03-01

139

The Solution of Groundwater Quality Management Problems with a Nonconvex Feasible Region Using a Cutting Plane Optimization Technique  

NASA Astrophysics Data System (ADS)

In groundwater quality management problems the concentration constraints have a nonlinear behavior which may be described either as a convex or a nonconvex function. Therefore the feasible region, which is defined as the intersection of all of these constraints, can be either a convex or a nonconvex set. A review of existing optimization algorithms for the solution of the groundwater quality management problem indicates that the majority of them have an inability to determine a global optimum when nonconvexity occurs. In an earlier paper that appeared in this journal [Karatzas and Finder, 1993], the outer approximation method, a global optimization technique, was presented for the solution of groundwater management problems with convex constraints. The problem was formulated to minimize a concave objective function over a compact convex set of constraints. In the present study the same concept is applied to problems with nonconvex constraints. While the main concept of the current approach remains the same as that in our earlier study, there is a significant difference in the determination of the cutting hyperplane. The nonconvexity of the domain requires a special approach to insure that the introduction of the cutting hyperplane does not eliminate any part of the nonconvex feasible region. In this work the theory of the developed algorithm is presented and subsequently applied to two groundwater quality problems. In the first example a hypothetical aquifer is considered to illustrate the performance of the methodology. In the second example a groundwater quality management problem in Woburn, Massachusetts, is solved. Results obtained are compared with those generated by MINOS 5.1.

Karatzas, George P.; Finder, George F.

1996-04-01

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

Searching for empty convex polygons  

Microsoft Academic Search

A key problem in computational geometry is the identification of subsets of a point set having particular properties. We study this problem for the properties of convexity and emptiness. We show that finding empty triangles is related to the problem of determining pairs of vertices that see each other in a star-shaped polygon. A linear time algorithm for this problem

David P. Dobkin; Herbert Edelsbrunner; Mark H. Overmars

1988-01-01

142

Parallel Processing of Discrete Optimization Problems  

Microsoft Academic Search

Discrete optimization problems (DOPs) arise in various applications such as planning,scheduling, computer aided design, robotics, game playing and constraint directed reasoning.Often, a DOP is formulated in terms of finding a (minimum cost) solution path in agraph from an initial node to a goal node and solved by graph\\/tree search methods suchas branch-and-bound and dynamic programming. Availability of parallel computers hascreated

Grama Y. Ananth; Vipin Kumar; Panos Pardalos

1992-01-01

143

Sensitivity analysis of hyperbolic optimal control problems  

Microsoft Academic Search

The aim of this paper is to perform sensitivity analysis of optimal control problems defined for the wave equation. The small\\u000a parameter describes the size of an imperfection in the form of a small hole or cavity in the geometrical domain of integration.\\u000a The initial state equation in the singularly perturbed domain is replaced by the equation in a smooth

Adam Kowalewski; Irena Lasiecka; Jan Soko?owski

2012-01-01

144

Combinatorial optimization problems in self-assembly  

Microsoft Academic Search

Self-assembly is the ubiquitous process by which simple objects autonomously assemble into intricate complexes. It has been suggested that intricate self-assembly processes will ultimately be used in circuit fabrication, nano-robotics, DNA computation, and amorphous computing. In this paper, we study two combinatorial optimization problems related to efficient self-assembly of shapes in the Tile Assembly Model of self-assembly proposed by Rothemund

Leonard M. Adleman; Qi Cheng; Ashish Goel; Ming-Deh A. Huang; David Kempe; Pablo Moisset de Espanés; Paul Wilhelm Karl Rothemund

2002-01-01

145

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

146

Interval optimal control problem in a Hilbert space  

NASA Astrophysics Data System (ADS)

An optimal control problem for a system involving an interval parameter is considered. The concepts of a universal optimal state and a universal optimal control are introduced. The existence and uniqueness of a universal solution to the interval optimal control problem is proved, and an algorithm for its determination is presented. The interval optimal control problem for a system described by the boundary value problem for a second-order ordinary differential equation is solved as an example.

Victoria Olegovna, O.

2013-04-01

147

Cutting a cornered convex polygon out of a circle  

Microsoft Academic Search

The problem of cutting a convex polygon P out of a piece of paper Q with minimum total cutting length is a well studied problem in computational geometry. Researchers studied several variations of the problem, such as P and Q are convex or non-convex polygons and the cuts are line cuts or rays cuts. In this paper we consider yet

Syed Ishtiaque Ahmed; M. A. Islam; M. Hasan

2008-01-01

148

Cutting a Cornered Convex Polygon Out of a Circle  

Microsoft Academic Search

The problem of cutting a convex polygon P out of a piece of planar material Q with minimum total cutting length is a well studied problem in computational geometry. Researchers studied several variations of the problem, such as P and Q are convex or non-convex polygons and the cuts are line cuts or ray cuts. In this paper we consider

Syed Ishtiaque Ahmed; Masud Hasan

2010-01-01

149

Dynamic programming approach to a minimum distance optimal control problem  

Microsoft Academic Search

An optimal control problem with minimum-type (non-additive) functional is considered. Such problem has several applications, including air collision avoidance problem for two aircraft. It is known that the Bellman optimality principle is not fulfilled globally for this problem, so that the dynamic programming technique works only in a part of the problem's phase space. The boundary of this part is

Arik Melikyan; N. Hovakimyan; Y. Ikeda

2003-01-01

150

LDRD Final Report: Global Optimization for Engineering Science Problems  

SciTech Connect

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

HART,WILLIAM E.

1999-12-01

151

Asymptotic solution of the optimal control problem for standard systems with delay  

SciTech Connect

The authors consider the construction of an asymptotic solution of the terminal optimal control problem using the averaging method. The optimal process is described by the equation z = eZ (t, z, z(t-l, e, u), u), z/t=[-1,0] = {var_phi}(t), where the delay is constant and of unit magnitude, z {element_of} G is an n-dimensional vector, G {contained_in} R{sup n}, e > 0 is a small parameter, t {element_of} T {triple_bond} [0, e{sup -1}], Z {var_phi} are n-dimensional vector functions, Z is strictly convex in u for any (t, z) {element_of} T X G, u {element_of} U is the r-dimensional control vector, U is a compact set.

Zheltikov, V.P.; Efendiev, V.V.

1995-05-01

152

A Case Study to Test Mozaik for Different Optimization Problems  

Microsoft Academic Search

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

Kursat B Bekar; Yousry Azmy; Kenan Unlu; Jack BrenizerJr

2009-01-01

153

First Order Conditions for Nonsmooth Discretized Constrained Optimal Control Problems  

Microsoft Academic Search

This paper studies first order conditions (Karush-Kuhn-Tucker conditions) for dis- cretized optimal control problems with nonsmooth constraints. We present a simple condition which can be used to verify that a local optimal point satisfies the first order conditions and that a point satisfying the first order conditions is a global or local optimal solution of the optimal control problem.

Xiaojun Chen

2004-01-01

154

Dynamic optimization of constrained chemical engineering problems using dynamic programming  

Microsoft Academic Search

In many chemical engineering process control applications, one frequently encounters differential-algebraic optimization problems. Such optimal control problems are difficult to solve, in general, because of the presence of singular arcs for systems whose Hamiltonian is linear with respect to the control variable. We propose the use of absolute error penalty functions (AEPF) in handling constrained optimal control problems in chemical

S. A. Dadebo; K. B. Mcauley

1995-01-01

155

Necessary Conditions for Optimal Control Problems with Infinite Horizons.  

National Technical Information Service (NTIS)

In a classical optimal control problem the terminal time, either prescribed a priori or not, is always a real number. In many dynamic optimization problems in economics one is lead to consider optimal control problems in which the terminal time is the ext...

H. Halkin

1972-01-01

156

Second Order Sufficient Optimality Conditions for a Control Problem with Continuous and Bang-Bang Control Components: Riccati Approach  

NASA Astrophysics Data System (ADS)

Second order sufficient optimality conditions for bang-bang control problems in a very general form have been obtained in [15,21,13,12,1]. These conditions require the positive definiteness (coercivity) of an associated quadratic form on the finite-dimensional critical cone. In the present paper, we investigate similar conditions for optimal control problems with a control variable having two components: a continuous unconstrained control appearing nonlinearly and a bang-bang control appearing linearly and belonging to a convex polyhedron. The coercivity of the quadratic form can be verified by checking solvability of an associated matrix Riccati equation. The results are applied to an economic control problem in optimal production and maintenance, where existing sufficient conditions fail to hold.

Osmolovskii, Nikolai P.; Maurer, Helmut

157

Solving Large-Scale Symmetric Travelling Salesman Problems to Optimality  

Microsoft Academic Search

We report the solution to optimality of ten large-scale symmetric travelling salesman problems. The travelling salesman problem (TSP) is one of the standard problems of the Operations Research\\/Management Science literature and is cited in virtually every textbook on this subject. The TSP is a hard combinatorial optimization problem for which to date no technically good algorithm is known. All known

Harlan Crowder; Manfred W. Padberg

1980-01-01

158

Generalized Surrogate Problem Methodology for Online Stochastic Discrete Optimization  

Microsoft Academic Search

We consider stochastic discrete optimization problems where the decision variables are nonnegative integers and propose a generalized surrogate problem methodology that modifies and extends previous work in Ref. 1. Our approach is based on an online control scheme which transforms the problem into a surrogate continuous optimization problem and proceeds to solve the latter using standard gradient-based approaches while simultaneously

Kagan Gokbayrak; Christos G. Cassandras

2002-01-01

159

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

NASA Astrophysics Data System (ADS)

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

Nguyen, Duc T.

1990-09-01

160

The subdifferential and the directional derivatives of the maximum of a family of convex functions. II  

NASA Astrophysics Data System (ADS)

The paper deals with calculating the directional derivatives and the subdifferential of the maximum of convex functions with no compactness conditions on the indexing set. We apply our results to the problems of minimax theory in which the Lagrange function is not assumed to be concave. We also apply these results to the duality theory of non-convex extremum problems, and strengthen earlier results of Yakubovich, Matveev and the author. We illustrate our results by investigating a problem of optimal design of experiments.

Solov'ev, V. N.

2001-02-01

161

Optimal Stopping with Sampling Cost: The Secretary Problem  

Microsoft Academic Search

A secretary problem is an optimal stopping problem based on relative ranks. To the usual formulation of the secretary problem we add a cumulative interview cost function $h(\\\\cdot)$, no longer obtaining \\

Thomas J. Lorenzen

1981-01-01

162

Solution of Optimal Control Problems Using Hybrid Computers.  

National Technical Information Service (NTIS)

By employing Pontryagin's maximum principle, the problem of finding optimal control for a system described by n first order simultaneous differential equations is reduced to a two point boundary value problem. Two schemes for solution of these problems on...

G. W. Hubbard

1968-01-01

163

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

164

A Fuzzy Optimal Routing Problem for Sightseeing  

NASA Astrophysics Data System (ADS)

The purpose of this study is to apply the fuzzy theory to an Optimal Routing Problem for Sightseeing (ORPS) in which we consider time varying travel time and location value. In the conventional ORPS, the travel time or the location value has been treated as a crisp number. However, it is better that these values are expressed by ambiguous value like “about 10 minutes" rather than by crisp number. In this paper we propose a Fuzzy ORPS (FORPS) considering time-varying and ambiguity. FORPS is defined on a complete graph in which location value is associated with a node weight while travel time depends on an edge weight. The aim of the problem is to construct a path with maximal total value under the condition that a time constraint has to be satisfied. In order to confirm that a candidate solution satisfies the time constraint, we introduce an agreement index which is proposed by Kaufmann and Gupta. The value of the agreement index is regarded as the degree of satisfying the time constraint. Moreover, the location value and the travel time are calculated by introducing the expectation value. Finally, comparing the result of ORPS and FORPS which are obtained by the numerical example, we discuss the characteristic of results obtained by FORPS.

Matsuda, Yoshitaka; Nakamura, Morikazu; Kang, Dongshik; Miyagi, Hayao

165

Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems  

Microsoft Academic Search

Whether or not the general asymmetric variational inequality problem can be formulated as a differentiable optimization problem has been an open question. This paper gives an affirmative answer to this question. We provide a new optimization problem formulation of the variational inequality problem, and show that its objective function is continuously differentiable whenever the mapping involved in the latter problem

Masao Fukushima

1992-01-01

166

Searching for Empty Convex Polygons  

Microsoft Academic Search

A key problem in computational geometry is the identification of subsets of a point set having particular properties. We study\\u000a this problem for the properties of convexity and emptiness. We show that finding empty triangles is related to the problem\\u000a of determining pairs of vertices that see each other in a star-shaped polygon. A linear-time algorithm for this problem which

David P. Dobkin; Herbert Edelsbrunner; Mark H. Overmars

1990-01-01

167

on a Partition into Convex Polygons  

Microsoft Academic Search

In this paper we study the problem of partitioning point sets in the plane so that each equivalence class is a convex polygon with some conditions on the intersection properties of such sets. Let P be a set of n points in the plane. We define f(P) to be the minimum number of sets in a partition into disjoint convex

Masatsugu Urabe

1996-01-01

168

Level set method for optimization of contact problems  

Microsoft Academic Search

This paper deals with the numerical solution of topology and shape optimization problems of an elastic body in unilateral contact with a rigid foundation. The contact problem with the prescribed friction is described by an elliptic variational inequality of the second order governing a displacement field. The structural optimization problem consists in finding such shape of the boundary of the

Andrzej My?li?ski

2008-01-01

169

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

170

Magnetic resonance image reconstruction using trained geometric directions in 2D redundant wavelets domain and non-convex optimization.  

PubMed

Reducing scanning time is significantly important for MRI. Compressed sensing has shown promising results by undersampling the k-space data to speed up imaging. Sparsity of an image plays an important role in compressed sensing MRI to reduce the image artifacts. Recently, the method of patch-based directional wavelets (PBDW) which trains geometric directions from undersampled data has been proposed. It has better performance in preserving image edges than conventional sparsifying transforms. However, obvious artifacts are presented in the smooth region when the data are highly undersampled. In addition, the original PBDW-based method does not hold obvious improvement for radial and fully 2D random sampling patterns. In this paper, the PBDW-based MRI reconstruction is improved from two aspects: 1) An efficient non-convex minimization algorithm is modified to enhance image quality; 2) PBDW are extended into shift-invariant discrete wavelet domain to enhance the ability of transform on sparsifying piecewise smooth image features. Numerical simulation results on vivo magnetic resonance images demonstrate that the proposed method outperforms the original PBDW in terms of removing artifacts and preserving edges. PMID:23992629

Ning, Bende; Qu, Xiaobo; Guo, Di; Hu, Changwei; Chen, Zhong

2013-08-29

171

Multiobjective evolutionary algorithms for complex portfolio optimization problems  

Microsoft Academic Search

This paper investigates the ability of Multiobjective Evolutionary Algorithms (MOEAs), namely the Non-dominated Sorting Genetic\\u000a Algorithm II (NSGA-II), Pareto Envelope-based Selection Algorithm (PESA) and Strength Pareto Evolutionary Algorithm 2 (SPEA2),\\u000a for solving complex portfolio optimization problems. The portfolio optimization problem is a typical bi-objective optimization\\u000a problem with objectives the reward that should be maximized and the risk that should be

Konstantinos P. Anagnostopoulos; Georgios Mamanis

2011-01-01

172

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)

Application of the two dimensional differential transform method.New analytical solutions to nonlinear transient heat transfer in longitudinal rectangular and convex parabolic fins.Study of the effects of thermal parameters on temperature distribution.Comparison of the heat transfer in longitudinal rectangular against convex parabolic fins

Ndlovu, Partner L.; Moitsheki, Raseelo J.

2013-10-01

173

Dual support method for solving convex quadratic programs  

Microsoft Academic Search

In this article, we present a new dual method for solving convex (but not strictly convex) quadratic programs (QPs). Our method is the generalization of the dual support method, developed by Gabasov and co-workers in 1981, for solving convex QPs. It proceeds in two phases: the first is to construct the initial support, called coordinator support, for the problem and

Belkacem Brahmi; Mohand Ouamer Bibi

2010-01-01

174

Quadratic Kernelization for Convex Recoloring of Trees  

Microsoft Academic Search

The Convex Recoloring (CR) problem measures how far a tree of characters differs from exhibiting a so-called “perfect phylogeny”. For an input\\u000a consisting of a vertex-colored tree T, the problem is to determine whether recoloring at most k vertices can achieve a convex coloring, meaning by this a coloring where each color class induces a subtree. The problem\\u000a was introduced

Hans L. Bodlaender; Michael R. Fellows; Michael A. Langston; Mark A. Ragan; Frances A. Rosamond; Mark Weyer

175

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

176

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

177

Reconfiguring convex polygons  

Microsoft Academic Search

We prove that there is a motion from any convex polygon to any convex polygon with the same counterclockwise sequence of edge lengths, that preserves the lengths of the edges, and keeps the polygon convex at all times. Furthermore, the motion is “direct” (avoiding any intermediate canonical configuration like a subdivided triangle) in the sense that each angle changes monotonically

Oswin Aichholzer; Erik D. Demaine; Jeff Erickson; Ferran Hurtado; Mark H. Overmars; Michael A. Soss; Godfried T. Toussaint

2001-01-01

178

Optimization of process synthesis and design problems: A modified differential evolution approach  

Microsoft Academic Search

A large number of process synthesis and design problems in chemical engineering can be modeled as mixed integer nonlinear programming (MINLP) problems. They involve continuous (floating point) and integer variables. A common feature of this class of mathematical problems is the potential existence of non-convexities due to the particular form of the objective function and\\/or the set of constraints. Due

Rakesh Angira; B. V. Babu

2006-01-01

179

An Ant Colony Optimization Algorithm for Shop Scheduling Problems  

Microsoft Academic Search

We deal with the application of ant colony optimization to group shop scheduling, which is a general shop scheduling problem that includes, among others, the open shop scheduling problem and the job shop scheduling problem as special cases. The contributions of this paper are twofold. First, we propose a neighborhood structure for this problem by extending the well-known neighborhood structure

Christian Blum; Michael Sampels

2004-01-01

180

Problem Size, Parallel Architecture and Optimal Speedup.  

National Technical Information Service (NTIS)

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 optima...

D. M. Nicol F. H. Willard

1987-01-01

181

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

182

The Role of Intuition in the Solving of Optimization Problems  

ERIC Educational Resources Information Center

|This article presents the partial results obtained in the first stage of the research, which sought to answer the following questions: (a) What is the role of intuition in university students' solutions to optimization problems? (b) What is the role of rigor in university students' solutions to optimization problems? (c) How is the combination of…

Malaspina, Uldarico; Font, Vicenc

2010-01-01

183

Imposing Radiality Constraints in Distribution System Optimization Problems  

Microsoft Academic Search

Distribution systems commonly operate with a radial topology, so all models of optimization problems in these distribution systems should consider radiality in their formulation. This work presents a literature review, a critical analysis, and a proposal for incorporating the radiality constraints in mathematical models of optimization problems for radial distribution systems. The objective is to show that the radiality constraints

Marina Lavorato; John F. Franco; Marcos J. Rider; Rubén Romero

2012-01-01

184

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

185

Abnormal equality-constrained optimization problems: sensitivity theory  

Microsoft Academic Search

For the equality-constrained optimization problem, we consider the case when the customary regularity of constraints can be violated. Under the assumptions substantially weaker than those previously used in the literature, we develop a reasonably complete local sensitivity theory for this class of problems, including upper and lower bounds for the rate of change of the optimal value function subject to

A. V. Arutyunov; A. F. Izmailov

2004-01-01

186

Exact Solution of a Constrained Optimization Problem in Thermoelectric Cooling  

Microsoft Academic Search

We consider an optimization problem in thermoelectric cooling. The maximum achievable cooling temperature in thermoelectric cooling is, among other things, affected by the Seebeck coefficient profile of the inhomogeneous materials. Mathematically, the maximum cooling tem- perature is a non-linear functional of the Seebeck coefficient function. In this study, we solve this optimization problem exactly.

Hongyun Wang; Hong Zhou

2008-01-01

187

The Traveling Salesman Problem: A Case Study in Local Optimization  

Microsoft Academic Search

This is a preliminary version of a chapter that appeared in the book Local Search in Combinatorial Optimization, E. H. L. Aarts and J. K. Lenstra (eds.), John Wiley and Sons, London, 1997, pp. 215-310. The traveling salesman problem (TSP) has been an early proving ground for many approaches to combinatorial optimization, including clas- sical local optimization techniques as well

David S. Johnson; Lyle A. McGeoch

188

Optimal quantization methods and applications to numerical problems in flnance  

Microsoft Academic Search

We review optimal quantization methods for numerically solving nonlinear problems in higher dimension associated with Markov processes. Quantization of a Markov pro- cess consists in a spatial discretization on flnite grids optimally fltted to the dynamics of the process. Two quantization methods are proposed: the flrst one, called marginal quantization, relies on an optimal approximation of the marginal distributions of

Gilles PAG; Jacques PRINTEMS

2003-01-01

189

Interpolation on a Net of Convex Quadrilaterals.  

National Technical Information Service (NTIS)

The problem of forming a surface of interpolation over a mesh of convex quadrilateral cells is investigated. The requirements that the surface be continuous and practical to generate lead to the consideration of interpolation across a space quadrilateral ...

M. A. Kaplan R. A. Papetti

1969-01-01

190

Coevolutionary Particle Swarm Optimization Using Gaussian Distribution for Solving Constrained Optimization Problems  

Microsoft Academic Search

In this correspondence, an approach based on coevolutionary particle swarm optimization to solve constrained optimization problems formulated as min-max problems is presented. In standard or canonical particle swarm optimization (PSO), a uniform probability distribution is used to generate random numbers for the accelerating coefficients of the local and global s. We propose a Gaussian probability distribution to generate the accelerating

Renato A. Krohling; Leandro dos Santos Coelho

2006-01-01

191

Continuous-time optimization problems involving invex functions  

Microsoft Academic Search

In [D.H. Martin, The essence of invexity, J. Optim. Theory Appl. 47 (1985) 65-76] Martin introduced the notions of KKT-invexity and WD-invexity for mathematical programming problems. These notions are relaxations of invexity. In this work we generalize these concepts for continuous-time nonlinear optimization problems. We prove that the notion of KKT-invexity is a necessary and sufficient condition for global optimality

V. A. de Oliveira; M. A. Rojas-Medar

2007-01-01

192

Continuous-time optimization problems involving invex functions  

Microsoft Academic Search

In [D.H. Martin, The essence of invexity, J. Optim. Theory Appl. 47 (1985) 65–76] Martin introduced the notions of KKT-invexity and WD-invexity for mathematical programming problems. These notions are relaxations of invexity. In this work we generalize these concepts for continuous-time nonlinear optimization problems. We prove that the notion of KKT-invexity is a necessary and sufficient condition for global optimality

V. A. de Oliveira; M. A. Rojas-Medar

2007-01-01

193

Topology optimization of 3D Stokes flow problems  

Microsoft Academic Search

Topology optimization has been applied to a multitude of physical systems and is now a mature technology used in industrial\\u000a practice, see [1] for an overview. Borrvall and Petersson [2] introduced topology optimization of Stokes flow problems which initiated works on extending topology optimization to different\\u000a flow problems. However, this research has focused on 2D fluid modelling, which limits the

A. Gersborg-Hansen

194

New Hybrid Optimization Algorithms for Machine Scheduling Problems  

Microsoft Academic Search

Dynamic programming, branch-and-bound, and constraint programming are the standard solution principles for finding optimal solutions to machine scheduling problems. We propose a new hybrid optimization framework that integrates all three methodologies. The hybrid framework leads to powerful solution procedures. We demonstrate our approach through the optimal solution of the single-machine total weighted completion time scheduling problem subject to release dates,

Yunpeng Pan; Leyuan Shi

2008-01-01

195

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

196

Optimal solutions to multi-objective robust fault detection problems  

Microsoft Academic Search

This paper will give complete, analytic, and optimal solutions to several robust fault detection problems that have been considered in the research community in the last twenty years. It is shown that several well-recognized robust fault detection problems, such as H-\\/Hinfin, H2\\/Hinfin, and Hinfin\\/Hinfin problems, have a very simple optimal solution in an observer form by solving a standard algebraic

Nike Liu; Kemin Zhou

2007-01-01

197

Some Optimization Problems for p-Laplacian Type Equations  

SciTech Connect

In this paper we study some optimization problems for nonlinear elastic membranes. More precisely, we consider the problem of optimizing the cost functional over some admissible class of loads f where u is the (unique) solution to the problem -{delta}{sub p}u+ vertical bar u vertical bar {sup p-2}u=0 in {omega} with vertical bar {nabla}u vertical bar {sup p-2}u{sub {nu}}=f on {partial_derivative}{omega}.

Del Pezzo, L. M., E-mail: ldpezzo@dm.uba.ar; Fernandez Bonder, J. [Universidad de Buenos Aires, Departamento de Matematica, FCEyN (Argentina)], E-mail: jfbonder@dm.uba.ar

2009-06-15

198

Level Set Method for Optimization of Contact Problems  

Microsoft Academic Search

This paper deals with the numerical solution of structural optimization problems of an elastic body in unilateral contact\\u000a with a rigid foundation. The contact problem with a given friction is described by an elliptic inequality of the second order\\u000a governing a displacement field. The optimization problem consists in finding, in a contact region, such topology and shape\\u000a of the boundary

Andrzej My?li?ski

199

An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems.  

PubMed

We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly nonsmooth) regularizer is minimized under the constraint that the solution explains the observations sufficiently well. Although the regularizer and constraint are usually convex, several particular features of these problems (huge dimensionality, nonsmoothness) preclude the use of off-the-shelf optimization tools and have stimulated a considerable amount of research. In this paper, we propose a new efficient algorithm to handle one class of constrained problems (often known as basis pursuit denoising) tailored to image recovery applications. The proposed algorithm, which belongs to the family of augmented Lagrangian methods, can be used to deal with a variety of imaging IPLIP, including deconvolution and reconstruction from compressive observations (such as MRI), using either total-variation or wavelet-based (or, more generally, frame-based) regularization. The proposed algorithm is an instance of the so-called alternating direction method of multipliers, for which convergence sufficient conditions are known; we show that these conditions are satisfied by the proposed algorithm. Experiments on a set of image restoration and reconstruction benchmark problems show that the proposed algorithm is a strong contender for the state-of-the-art. PMID:20840899

Afonso, Manya V; Bioucas-Dias, José M; Figueiredo, Mário A T

2010-09-13

200

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

201

Research on Constrained Layout Optimization Problem Using Multi-adaptive Strategies Particle Swarm Optimizer  

Microsoft Academic Search

\\u000a The complex layout optimization problems with behavioral constraints belong to NP-hard problem in math. Due to its complexity,\\u000a the general particle swarm optimization algorithm converges slowly and easily to local optima. Taking the layout problem of\\u000a satellite cabins as background, a novel adaptive particle swarm optimizer based on multi-modified strategies is proposed in\\u000a the paper, which can not only escape

Kaiyou Lei

2009-01-01

202

Problems in taxation: An optimization approach for loss offset options  

Microsoft Academic Search

We solve an optimization problem which arises in the German tax system. Here losses in some period can be tranferred to other periods reducing tax in these periods. Two variants of taxation can be applied. We formulate the problem as a mixed binary mathematical program and solve it via branch and bound using binary search. Special cases of the problem

Sebastian Schanz; Günter Schmidt; Hai-Dung Dinh; Mike Kersch

2012-01-01

203

Optimal Control of the Obstacle Problem in a Perforated Domain  

SciTech Connect

We study the problem of optimally controlling the solution of the obstacle problem in a domain perforated by small periodically distributed holes. The solution is controlled by the choice of a perforated obstacle which is to be chosen in such a fashion that the solution is close to a given profile and the obstacle is not too irregular. We prove existence, uniqueness and stability of an optimal obstacle and derive necessary and sufficient conditions for optimality. When the number of holes increase indefinitely we determine the limit of the sequence of optimal obstacles and solutions. This limit depends strongly on the rate at which the size of the holes shrink.

Stroemqvist, Martin H., E-mail: stromqv@kth.se [Royal Institute of Technology, Department of Mathematics (Sweden)

2012-10-15

204

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

205

Optimization Problems in Supply Chain Management  

Microsoft Academic Search

Maria Dolores Romero Morales was born on Augustus 5th, 1971, in Sevilla (Spain).\\u000aShe studied Mathematics at University of Sevilla from 1989 to 1994 and specialized\\u000ain Statistics and Operations Research. She wrote her Master's thesis on Global Optimization\\u000ain Location Theory under the supervision of Dr. Emilio Carrizosa Priego\\u000aand Dr. Eduardo Conde S?nchez. During the academic year 1995-1996

D. Romero Morales

2000-01-01

206

Optimal Design and Relaxation of Variational Problems. I.  

National Technical Information Service (NTIS)

The focus of this three-part paper is the interrelation between structural design optimization, relaxation of variational problems, and homogenization. Our principal contribution is a set of methods for computing examples. From one point of view we obtain...

R. V. Kohn G. Strang

1986-01-01

207

Two improved harmony search algorithms for solving engineering optimization problems  

NASA Astrophysics Data System (ADS)

This paper describes two new harmony search (HS) meta-heuristic algorithms for engineering optimization problems with continuous design variables. The key difference between these algorithms and traditional (HS) method is in the way of adjusting bandwidth (bw). bw is very important factor for the high efficiency of the harmony search algorithms and can be potentially useful in adjusting convergence rate of algorithms to optimal solution. First algorithm, proposed harmony search (PHS), introduces a new definition of bandwidth (bw). Second algorithm, improving proposed harmony search (IPHS) employs to enhance accuracy and convergence rate of PHS algorithm. In IPHS, non-uniform mutation operation is introduced which is combination of Yang bandwidth and PHS bandwidth. Various engineering optimization problems, including mathematical function minimization problems and structural engineering optimization problems, are presented to demonstrate the effectiveness and robustness of these algorithms. In all cases, the solutions obtained using IPHS are in agreement or better than those obtained from other methods.

Jaberipour, Majid; Khorram, Esmaile

2010-11-01

208

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

209

Integral-functional equations for optimal renovation problems  

Microsoft Academic Search

The integral-functional equations with the unknown variable in the upper limit of integration are introduced and studied. They arise in the optimization problems for integral dynamical models and allow to analyze the variable aftereffect duration of dynamical system

N. Hritonenko; Y. U. Yatsenko

1996-01-01

210

Exact Solution of a Constrained Optimization Problem in Thermoelectric Cooling.  

National Technical Information Service (NTIS)

We consider an optimization problem in thermoelectric cooling. The maximum achievable cooling temperature in thermoelectric cooling is, among other things, affected by the Seebeck coefficient profile of the inhomogeneous materials. Mathematically, the max...

H. Wang H. Zhou

2008-01-01

211

Hybrid Evolutionary Algorithm for Solving Global Optimization Problems  

Microsoft Academic Search

Differential Evolution (DE) is a novel evolutionary approach capable of handling non-differentiable, non-linear and multi-modal objective functions. DE has been consistently ranked as one of the best search algorithm for solving global optimization problems in several case studies. This paper presents a simple and modified hybridized Differential Evolution algorithm for solving global optimization problems. The proposed algorithm is a hybrid

Radha Thangaraj; Millie Pant; Ajith Abraham; Youakim Badr

2009-01-01

212

Optimal control problem for impulsive systems with integral boundary conditions  

NASA Astrophysics Data System (ADS)

In the present work the optimal control problem is considered, when the state of the system is described by the impulsive differential equations with integral boundary conditions. Applying the Banach contraction principle the existence and uniqueness of solution is proved for the corresponding boundary problem by the fixed admissible control. The first and second variation of the functional is calculated. Various necessary conditions of optimality of the first and second order are obtained by the help of the variation of the controls.

Ashyralyev, Allaberen; Sharifov, Y. A.

2012-08-01

213

Probabilistic Model of Ant Colony Optimization for Multiple Knapsack Problem  

Microsoft Academic Search

The Ant Colony Optimization (ACO) algorithms are being applied successfully to a wide range of problems. ACO algorithms could\\u000a be good alternatives to existing algorithms for hard combinatorial optimization problems (COPs). In this paper we investigate\\u000a the influence of the probabilistic model in model-based search as ACO. We present the effect of four different probabilistic\\u000a models for ACO algorithms to

Stefka Fidanova; G. Bonchev

2007-01-01

214

Some Optimal Stochastic Control Problems in Neuroscience — a Review  

NASA Astrophysics Data System (ADS)

Nervous systems are probability machines and, as such, modeling their activities should incorporate stochastic processes. In this review, we present two examples of optimal stochastic control problems with an analytic methodology on how to find optimal signals. The first example deals with neuronal activity and the second example is concerned with a higher level task: arm movement. In both cases we find optimal signals for particular tasks and find our results in agreement with the experimental Fitts Law.

Feng, Jianfeng; Chen, Xiaojiang; Tuckwell, Henry C.; Vasilaki, Eleni

215

Russian Doll Search for Solving Constraint Optimization Problems  

Microsoft Academic Search

If the Constraint Satisfactionframework has been extended to deal with Constraint Optimization problems, it appears that optimization is far more complex than satisfaction. One of the causes of the inefficiency of complete tree search methods, like Depth First Branch and Bound , lies in the poor quality of the lower bound on the global valuation of a partial assignment, even

Gérard Verfaillie; Michel Lemaître; Thomas Schiex

1996-01-01

216

Multiagent Search Strategy for Combinatorial Optimization Problems in Ant Model  

Microsoft Academic Search

Ant colony system (ACS) is a meta heuristic approach based on biology in order to solve combinatorial optimization problem. It is based on the tracing action of real ants that accumulate pheromone on the passed path and uses as communication medium. In order to search the optimal path, it is necessary to make a search for various edges. In existing

Seok Mi Hong; SeungGwan Lee

2006-01-01

217

The Vector Model of Artificial Physics Optimization Algorithm for Global Optimization Problems  

Microsoft Academic Search

To solve complex global optimization problems, Artificial Physics Optimization (APO) algorithm is presented based on Physicomimetics framework, which is a population-based stochastic algorithm inspired by physical force. The solutions (particles) sampled from the feasible region of the problems are treated as physical individuals. Each individual has a mass, position and velocity. The mass of each individual corresponds to a user-defined

Liping Xie; Jianchao Zeng; Zhuihua Cui

2009-01-01

218

Tractable fitting with convex polynomials via sum-of-squares  

Microsoft Academic Search

We consider the problem of fitting given data (u1,y1),...,(um,ym) where ui? Rnand yi? R with a convex polynomial f. A technique to solve this problem using sum of squares polynomials is presented. This technique is extended to enforce convexity of f only on a specified region. Also, an algorithm to fit the convex hull of a set of points with

Alessandro Magnani; Sanjay Lall; Stephen Boyd

2005-01-01

219

Random Convex Hulls and Extreme Value Statistics  

Microsoft Academic Search

In this paper we study the statistical properties of convex hulls of N random points in a plane chosen according to a given distribution. The points may be chosen independently or they may be\\u000a correlated. After a non-exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex\\u000a hull problem, we present a unifying approach, based

Satya N. Majumdar; Alain Comtet; Julien Randon-Furling

2010-01-01

220

A Bacterial foraging PSO-DE algorithm for solving dynamic economic dispatch problem with security constraints  

Microsoft Academic Search

This paper presents a heuristic optimization methodology, Bacterial foraging and PSO-DE (BPSO-DE) algorithm by integrating Bacterial foraging optimization Algorithm (BFOA), Particle Swarm Optimization (PSO) and Differential Evolution (DE) for solving Non-Convex Dynamic Economic Dispatch problem (DED). The DED problem exhibits non-convex nature due to valve-point loading effects, ramp rate limits, spinning reserve capacity and security constraints. Even though PSO and

P. Praveena; K. Vaisakh; S. R. M. Rao

2010-01-01

221

Convex and Polaroid Extensions.  

National Technical Information Service (NTIS)

In an effort towards a comprehensive and unified theory, this note represents some new results in the area of non-convex programming within the framework of convex (sets and function) analysis. The entire study is primarily devoted to the development of u...

C. A. Burdet

1974-01-01

222

Competitive Problem Solving and the Optimal Prize Schemes  

Microsoft Academic Search

Agents compete to solve a problem. Each agent knows own computational capacity as private information and simultaneously chooses either a risky or a safe problem solving method. This paper analyzes the optimal prize schemes from the perspective of the prize designer who wishes to find a solution as quick as possible. It is shown that (i) the winner- take-all scheme

Toru Suzuki

2010-01-01

223

Optimization and improvement of Genetic Algorithms solving Traveling Salesman Problem  

Microsoft Academic Search

Traveling salesman problem (TSP) is a typical NP-complete problem, of which the search space increases with the number of cities. Genetic algorithm (GA) is an efficient optimization algorithm characterized with explicit parallelism and robustness, applicable to TSP. In this paper, we compare the performance of the existing GAs in searching the solution for TSP and find a superior combination of

Liping Zhang; Min Yao; Nenggan Zheng

2009-01-01

224

A General Ant Colony Model to solve Combinatorial Optimization Problems  

Microsoft Academic Search

An Ants System is an artificial system based on the behavior of real ant colonies, which is used to solve combinatorial problems. This is a distributed algorithm composed by a set of cooperating agents called ants which cooperate among them to find good solutions to combinatorial optimization problems. The cooperation follows the behavior of real ants using an indirect form

Jose Aguilar

2001-01-01

225

Multiobjective optimization approach to sensitivity analysis: Waste treatment costs in discrete process synthesis and optimization problems  

SciTech Connect

This paper presents an approach for determining the sensitivity of the maximum net profits of a chemical process to changes in the waste treatment cost when discrete terms must be optimized. The approach employs a basic relationship between the sensitivity problem and a multiobjective optimization problem that maximizes profiles and minimizes waste. It is shown that all solutions of the original process optimization problem must lie in the concave portions of the solution set of the multiobjective problem and that a simple transform exists between the multiobjective optimization problem and the sensitivity problem. The proposed approach uses a modified form of the outer approximation method to identify discretely different regions of the multiobjective solution set. The complete solution set is generated with a sequential approximation algorithm. The approach is illustrated with a case study of the production of ethylene glycol from ethylene oxide and water.

Ciric, A.R.; Huchette, S.G. (Univ. of Cincinnati, OH (United States). Dept. of Chemical Engineering)

1993-11-01

226

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

227

A sparse representation-based deployment method for optimizing the observation quality of camera networks.  

PubMed

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. PMID:23989826

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

2013-08-28

228

A path following algorithm for the graph matching problem.  

PubMed

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. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We, therefore, construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore, perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four data sets: simulated graphs, QAPLib, retina vessel images, and handwritten Chinese characters. In all cases, the results are competitive with the state of the art. PMID:19834143

Zaslavskiy, Mikhail; Bach, Francis; Vert, Jean-Philippe

2009-12-01

229

Topologies m -Convexes dans les algebres a-convexes  

Microsoft Academic Search

\\u000a Abstract  We endow anyA-convex algebra (E, ?) with a multiplicatively-convex topologyM(?) finer than ?. We then show that this is the weakestm-convex topology finer than ?. We are then led to consider two classes ofA-convex algebras examples and (or) characterizations of which are given.

Lahbib Oubbi

1992-01-01

230

A spatial domain decomposition method for parabolic optimal control problems  

NASA Astrophysics Data System (ADS)

We present a non-overlapping spatial domain decomposition method for the solution of linear-quadratic parabolic optimal control problems. The spatial domain is decomposed into non-overlapping subdomains. The original parabolic optimal control problem is decomposed into smaller problems posed on space-time cylinder subdomains with auxiliary state and adjoint variables imposed as Dirichlet boundary conditions on the space-time interface boundaryE The subdomain problems are coupled through Robin transmission conditions. This leads to a Schur complement equation in which the unknowns are the auxiliary state adjoint variables on the space-time interface boundary. The Schur complement operator is the sum of space-time subdomain Schur complement operators. The application of these subdomain Schur complement operators is equivalent to the solution of an subdomain parabolic optimal control problem. The subdomain Schur complement operators are shown to be invertible and the application of their inverses is equivalent to the solution of a related subdomain parabolic optimal control problem. We introduce a new family of Neumann-Neumann type preconditioners for the Schur complement system including several different coarse grid corrections. We compare the numerical performance of our preconditioners with an alternative approach recently introduced by Benamou.

Heinkenschloss, Matthias; Herty, Michael

2007-04-01

231

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

232

Solving Portfolio Optimization Problem Based on Extension Principle  

Microsoft Academic Search

\\u000a Conventional portfolio optimization models have an assumption that the future condition of stock market can be accurately\\u000a predicted by historical data. However, no matter how accurate the past data is, this premise will not exist in the financial\\u000a market due to the high volatility of market environment. This paper discusses the fuzzy portfolio optimization problem where\\u000a the asset returns are

Shiang-Tai Liu

2010-01-01

233

Problems in the Optimization of Manned Interplanetary Expeditions  

NASA Astrophysics Data System (ADS)

Within the scope of the unified variation problem the authors discuss the optimization of parameters, choosing flight trajectories and optimal flight control as well as control of life support systems in spacecraft in manned interplanetary expeditions. They examine the efficiency of ejecting the life support systems waste by jets from high-thrust rocket engines as compared to partial waste regeneration. They confirm the possibility of manned expeditions to Mars before efficient life support systems based on biological regeneration are developed.

Kiforenko, B. N.; Vasil'Ev, I. Yu.

234

Multiagent Search Strategy for Combinatorial Optimization Problems in Ant Model  

Microsoft Academic Search

Ant Colony System (ACS) is a meta heuristic approach based on biology in order to solve combinatorial optimization problem.\\u000a It is based on the tracing action of real ants that accumulate pheromone on the passed path and uses as communication medium.\\u000a In order to search the optimal path, it is necessary to make a search for various edges. In existing

Seokmi Hong; Seunggwan Lee

2006-01-01

235

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

236

Hybrid optimization schemes for simulation-based problems.  

SciTech Connect

The inclusion of computer simulations in the study and design of complex engineering systems has created a need for efficient approaches to simulation-based optimization. For example, in water resources management problems, optimization problems regularly consist of objective functions and constraints that rely on output from a PDE-based simulator. Various assumptions can be made to simplify either the objective function or the physical system so that gradient-based methods apply, however the incorporation of realistic objection functions can be accomplished given the availability of derivative-free optimization methods. A wide variety of derivative-free methods exist and each method has both advantages and disadvantages. Therefore, to address such problems, we propose a hybrid approach, which allows the combining of beneficial elements of multiple methods in order to more efficiently search the design space. Specifically, in this paper, we illustrate the capabilities of two novel algorithms; one which hybridizes pattern search optimization with Gaussian Process emulation and the other which hybridizes pattern search and a genetic algorithm. We describe the hybrid methods and give some numerical results for a hydrological application which illustrate that the hybrids find an optimal solution under conditions for which traditional optimal search methods fail.

Fowler, Katie (Clarkson University, NY); Gray, Genetha Anne; Griffin, Joshua D. (SAS Institute, NC)

2010-05-01

237

Social interaction as a heuristic for combinatorial optimization problems.  

PubMed

We investigate the performance of a variant of Axelrod's model for dissemination of culture--the Adaptive Culture Heuristic (ACH)--on solving an NP-Complete optimization problem, namely, the classification of binary input patterns of size F by a Boolean Binary Perceptron. In this heuristic, N agents, characterized by binary strings of length F which represent possible solutions to the optimization problem, are fixed at the sites of a square lattice and interact with their nearest neighbors only. The interactions are such that the agents' strings (or cultures) become more similar to the low-cost strings of their neighbors resulting in the dissemination of these strings across the lattice. Eventually the dynamics freezes into a homogeneous absorbing configuration in which all agents exhibit identical solutions to the optimization problem. We find through extensive simulations that the probability of finding the optimal solution is a function of the reduced variable F/N(¼) so that the number of agents must increase with the fourth power of the problem size, N?F?, to guarantee a fixed probability of success. In this case, we find that the relaxation time to reach an absorbing configuration scales with F? which can be interpreted as the overall computational cost of the ACH to find an optimal set of weights for a Boolean binary perceptron, given a fixed probability of success. PMID:21230556

Fontanari, José F

2010-11-29

238

Optimization of solutions for the one plant protection problem.  

PubMed

Plant protection problems are simulated by a system of ordinary differential equations with given initial conditions. The sensitivity and resistance of pathogen subpopulations to fungicide mixtures, fungicide weathering, plant growth, etc. are taken into consideration. The system of equations is solved numerically for each set of initial conditions and parameters of the disease and fungicide applications. Optimization algorithms were investigated and a computer program was developed for optimization of these solutions. 14 typical cases of the disease were simulated and optimized in order to determine optimal fungicide treatments. The optimized strategy for fungicide application differs considerably from the commonly used method and seems to be an important new principle in plant protection. The approach developed in this study may be useful for a wide spectrum of purposes in the simulation of leaf diseases. It may also help the biologist to decrease or pinpoint experimental work and analyze its results and is perspective for plant disease control. PMID:11368479

Kelman, E; Levy, R S; Levy, Y

2001-03-01

239

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

240

Approximate convex decomposition of polygons  

Microsoft Academic Search

We propose a strategy to decompose a polygon, containing zero or more holes, into ``approximately convex'' pieces. For many applications, the approximately convex components of this decomposition provide similar benefits as convex components, while the resulting decomposition is significantly smaller and can be computed more efficiently. Moreover, our approximate convex decomposition (ACD) provides a mechanism to focus on key structural

Jyh-Ming Lien; Nancy M. Amato

2004-01-01

241

PCE: Piecewise Convex Endmember Detection  

Microsoft Academic Search

A new hyperspectral endmember detection method that represents endmembers as distributions, autonomously partitions the input data set into several convex regions, and simultaneously determines endmember distributions (EDs) and proportion values for each convex region is presented. Spectral unmixing methods that treat endmembers as distributions or hyperspectral images as piecewise convex data sets have not been previously developed. Piecewise convex endmember

Alina Zare; Paul Gader

2010-01-01

242

Generalized convexity and inequalities  

NASA Astrophysics Data System (ADS)

Let and let be the family of all mean values of two numbers in (some examples are the arithmetic, geometric, and harmonic means). Given , we say that a function is (m1,m2)-convex if f(m1(x,y))[less-than-or-equals, slant]m2(f(x),f(y)) for all . The usual convexity is the special case when both mean values are arithmetic means. We study the dependence of (m1,m2)-convexity on m1 and m2 and give sufficient conditions for (m1,m2)-convexity of functions defined by Maclaurin series. The criteria involve the Maclaurin coefficients. Our results yield a class of new inequalities for several special functions such as the Gaussian hypergeometric function and a generalized Bessel function.

Anderson, G. D.; Vamanamurthy, M. K.; Vuorinen, M.

2007-11-01

243

On Optimal AMLI Solvers for Incompressible Navier-Stokes Problems  

NASA Astrophysics Data System (ADS)

We consider the incompressible Navier-Stokes problem and a projection scheme based on Crouzeix-Raviart finite element approximation of the velocities and piece-wise constant approximation of the pressure. These non-conforming finite elements guarantee that the divergence of the velocity field is zero inside each element, i.e., the approximation is locally conservative. We propose optimal order Algebraic MultiLevel Iteration (AMLI) preconditioners for both, the decoupled scalar parabolic problems at the prediction step as well as to the mixed finite element method (FEM) problem at the projection step. The main contribution of the current paper is the obtained scalability of the AMLI methods for the related composite time-stepping solution method. The algorithm for the Navier-Stokes problem has a total computational complexity of optimal order. We present numerical tests for the efficiency of the AMLI solvers for the case of lid-driven cavity flow for different Reynolds numbers.

Boyanova, P.; Margenov, S.

2010-11-01

244

A new global optimization algorithm and its application to a Magnetic Resonance optimal design problem 1  

Microsoft Academic Search

In this paper we are concerned with the design of a small low-cost, low-field multipolar magnet for Magnetic Resonance Imaging with a high field uniformity. By introducing appropriate variables, the considered design problem is converted into a global optimization one. This latter problem is solved by means of a new derivative free global optimization method which is a distributed multi-start

Giampaolo LiuzziT; Stefano LucidiT; Veronica PiccialliT; Antonello Sotgiu

245

Optimal scheduling of reservoir releases during flood: Deterministic optimization problem, part 2, case study  

Microsoft Academic Search

This paper applies the optimization procedure developed in Part 1 to the problem of the optimal scheduling of reservoir releases during flood in the case study concerning the river system of Upper Vistula in Poland. Technical details related to the implementation of the proposed algorithm are discussed.

R. Pytlak; K. Malinowski

1989-01-01

246

A Class of Fuzzy Portfolio Optimization Problems: ES Models  

Microsoft Academic Search

\\u000a This paper adopts the spread of fuzzy variable as a new criteria in practical risk management problems, and develops a novel\\u000a fuzzy expectation-spread (E-S) model for portfolio optimization problem. Since the spread is defined by Lebesgue-Stieltjes\\u000a (L-S) integral, its computation for general fuzzy variables is a challenge issue for research, and usually depends on approximation\\u000a scheme and soft computing. But

Yankui Liu; Xiaoli Wu

2010-01-01

247

Optimization models for the dynamic facility location and allocation problem  

Microsoft Academic Search

The design of logistic distribution systems is one of the most critical and strategic issues in industrial facility management. The aim of this study is to develop and apply innovative mixed integer programming optimization models to design and manage dynamic (i.e. multi-period) multi-stage and multi-commodity location allocation problems (LAP). LAP belong to the NP-hard complexity class of decision problems, and

Riccardo Manzini; Elisa Gebennini

2008-01-01

248

On destination optimality in asymmetric distance Fermat-Weber problems  

Microsoft Academic Search

This paper introduces skewed norms, i.e. norms perturbed by a linear function, which are useful for modelling asymmetric distance\\u000a measures. The Fermat-Weber problem with mixed skewed norms is then considered. Using subdifferential calculus we derive exact\\u000a conditions for a destination point to be optimal, thereby correcting and completing some recent work on asymmetric distance\\u000a location problems. Finally the classical dominance

Frank Plastria

1992-01-01

249

Optimal Control of Newton-Type Problems of Minimal Resistance  

Microsoft Academic Search

We address Newton-type problems of minimal resistance from an optimal control\\u000aperspective. It is proven that for Newton-type problems the Pontryagin maximum\\u000aprinciple is a necessary and sufficient condition. Solutions are then computed\\u000afor concrete situations, including the new case when the flux of particles is\\u000anon-parallel.

Delfim F. M. Torres; Alexander Yu. Plakhov

2004-01-01

250

Minimum Distance to the Complement of a Convex Set: Duality Result  

Microsoft Academic Search

The subject of this paper is to study the problem of the minimum distance to the complement of a convex set. Nirenberg has stated a duality theorem treating the minimum norm problem for a convex set. We state a duality result which presents some analogy with the Nirenberg theorem, and we apply this result to polyhedral convex sets. First, we

W. Briec

1997-01-01

251

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

252

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

253

Identification problem for a wave equation via optimal control  

SciTech Connect

The authors approximate an identification problem by applying optimal control techniques to a Tikhonov`s regularization. They seek to identify the dispersive coefficient in a wave equation and allow for the case of error or uncertainty in the observations used for the identification.

Lenhart, S.; Liang, M. [Univ. of Tennessee, Knoxville, TN (United States). Mathematics Dept.; Protopopescu, V. [Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.

1998-11-01

254

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

255

Two improved harmony search algorithms for solving engineering optimization problems  

Microsoft Academic Search

This paper describes two new harmony search (HS) meta-heuristic algorithms for engineering optimization problems with continuous design variables. The key difference between these algorithms and traditional (HS) method is in the way of adjusting bandwidth (bw). bw is very important factor for the high efficiency of the harmony search algorithms and can be potentially useful in adjusting convergence rate of

Majid Jaberipour; Esmaile Khorram

2010-01-01

256

An improved harmony search algorithm for solving optimization problems  

Microsoft Academic Search

This paper develops an Improved harmony search (IHS) algorithm for solving optimization problems. IHS employs a novel method for generating new solution vectors that enhances accuracy and convergence rate of harmony search (HS) algorithm. In this paper the impacts of constant parameters on harmony search algorithm are discussed and a strategy for tuning these parameters is presented. The IHS algorithm

M. Mahdavi; M. Fesanghary; E. Damangir

2007-01-01

257

THEORY OF OPTIMAL CONTROL APPLIED TO PROBLEMS OF AMBIENTAL POLLUTION  

Microsoft Academic Search

We study the theory of optimal control of systems of distributed parameters and apply to problems of ambient pollution. The model consists of a partial dierential equation of parabolic type that models the transport of a pollutant in an incompressi- ble viscous uid, with boundary conditions and initial value; that is, in our model we consider the velocity that the

F ATIMA ARANTES; JAIME E. MU; NOZ RIVERA

2009-01-01

258

Ant colony optimization techniques for the vehicle routing problem  

Microsoft Academic Search

This research applies the meta-heuristic method of ant colony optimization (ACO) to an established set of vehicle routing problems (VRP). The procedure simulates the decision-making processes of ant colonies as they forage for food and is similar to other adaptive learning and artificial intelligence techniques such as Tabu Search, Simulated Annealing and Genetic Algorithms. Modifications are made to the ACO

John E. Bell; Patrick R. McMullen

259

Ant colony optimization techniques for the vehicle routing problem  

Microsoft Academic Search

Abstract This research applies the meta-heuristic method of ant colony optimization (ACO) to an established set of vehicle routing problems (VRP). The procedure simulates the decision-making processes of ant colonies as they forage for food and is similar to other adaptive learning and artificial intelligence techniques such as Tabu Search, Simulated Annealing and Genetic Algorithms. Modifications are made to the

John E. Bell; Patrick R. Mcmullen

2004-01-01

260

Mapping tree-structured combinatorial optimization problems onto parallel computers  

Microsoft Academic Search

this paper, we present effective mapping and load-balancing functions thatyield nearly linear performance on large systems, when the inherent parallelism ofthe given optimization problem is large enough. After giving an overview of techniquesfor dynamically mapping tree structured computations onto parallel computerarchitectures, we will present detailed results of some techniques found to be veryefficient even on large scale parallel computing systems.

Reinhard Lfiling; Burkhard Monien; Alexander Reinefeld; Stefan Tschöke

1996-01-01

261

Algorithms for Noisy Problems in Gas Transmission Pipeline Optimization  

Microsoft Academic Search

In this paper we describe some algorithms for noisy optimization in the context of problems from the gas transmission industry. The algorithms are implicit filtering, DIRECT, and a new hybrid of these methods, which uses DIRECT to find an intitial iterate for implicit filtering. We report on numerical results that illustrate the performance of the methods.

R. G. Carter; J. M. Gablonsky; A. Patrick; C. T. Kelley; O. J. Eslinger

2001-01-01

262

Level Set Methods for Optimization Problems Involving Geometry and Constraints  

Microsoft Academic Search

Many problems in engineering design involve optimizing the geometry to maximize a certain design objective. Geometrical constraints are often imposed. In this paper, we use the level set method devised in (Osher and Sethian, J. Comput. Phys.79, 12 (1988)), the variational level set calculus presented in (Zhao et al., J. Comput. Phys.127, 179 (1996)), and the projected gradient method, as

Stanley J. Osher; Fadil Santosa

2001-01-01

263

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

264

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

265

Second Order Necessary Conditions for Optimal Impulsive Control Problems  

Microsoft Academic Search

First and second order necessary conditions of optimality for an impulsive control problem are presented and derived. One of the main features of these results is that no a priori normality assumptions are required and they are informative for abnormal control processes as well. This feature follows from the fact that the conditions are derived from an extremal principle, which

A. Arutyunov; V. Ja?imovi?; F. Pereira

2003-01-01

266

Alternative solutions for optimization problems in generalizability theory  

Microsoft Academic Search

Solutions for the problem of maximizing the generalizability coefficient under a budget constraint are presented. It is shown\\u000a that the Cauchy-Schwarz inequality can be applied to derive optimal continuous solutions for the number of conditions of each\\u000a facet.

Piet F. Sanders

1992-01-01

267

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

268

Drug resistance in cancer chemotherapy as an optimal control problem  

Microsoft Academic Search

We analyze non cell-cycle specific mathematical models for drug resistance in cancer chemotherapy. In each model developing drug resistance is inevitable and the issue is how to prolong its onset. Distinguishing between sensitive and resistant cells we consider a model which includes interactions of two killing agents which generate separate resistant populations. We formu- late an associated optimal control problem

Urszula Ledzewicz

2005-01-01

269

Towards Grid Implementations of Metaheuristics for Hard Combinatorial Optimization Problems  

Microsoft Academic Search

Metaheuristics are approximation algorithms that nd very good solutions to hard combinatorial optimization problems at the expense of large computational require- ments. They do, however, offer a wide range of possibili- ties for implementations of effective robust parallel algo- rithms which run in much smaller computation times. We present four strategies for the parallelization of an extended GRASP with ILS

Cristina Boeres; Vinod E. F. Rebello; Celso C. Ribeiro

270

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

PubMed Central

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

Acuna, Daniel E.; Parada, Victor

2010-01-01

271

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 3.87s 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

2013-06-10

272

Necessary and Sufficient Conditions for Optimal Control of Quasilinear Partial Differential Systems.  

National Technical Information Service (NTIS)

This paper studies the problem of optimal control of quasilinear partial differential systems. A maximum principle necessary condition is derived and shown to be sufficient when the Hamiltonian and boundary conditions satisfy a convexity condition. The de...

N. A. Derzko S. P. Sethi G. L. Thompson

1979-01-01

273

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

274

Solving Optimal Control Problems by Exploiting Inherent Dynamical Systems Structures  

NASA Astrophysics Data System (ADS)

Computing globally efficient solutions is a major challenge in optimal control of nonlinear dynamical systems. This work proposes a method combining local optimization and motion planning techniques based on exploiting inherent dynamical systems structures, such as symmetries and invariant manifolds. Prior to the optimal control, the dynamical system is analyzed for structural properties that can be used to compute pieces of trajectories that are stored in a motion planning library. In the context of mechanical systems, these motion planning candidates, termed primitives, are given by relative equilibria induced by symmetries and motions on stable or unstable manifolds of e.g. fixed points in the natural dynamics. The existence of controlled relative equilibria is studied through Lagrangian mechanics and symmetry reduction techniques. The proposed framework can be used to solve boundary value problems by performing a search in the space of sequences of motion primitives connected using optimized maneuvers. The optimal sequence can be used as an admissible initial guess for a post-optimization. The approach is illustrated by two numerical examples, the single and the double spherical pendula, which demonstrates its benefit compared to standard local optimization techniques.

Flaßkamp, Kathrin; Ober-Blöbaum, Sina; Kobilarov, Marin

2012-08-01

275

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

276

Parallel algorithms for separation of two sets of points and recognition of digital convex polygons  

SciTech Connect

Given two finite sets of points in a plane, the polygon separation problem is to construct a separating convex k-gon with smallest k. In this paper, we present a parallel algorithm for the polygon separation problem. The algorithm runs in O(log n) time on a CREW PRAM with n processors, where n is the number of points in the two given sets. The algorithm is cost-optimal, since [Omega](n log n) is a lower-bound for the first time needed by any sequential algorithm. We apply this algorithm to the problem of finding a convex region is its digital image. The algorithm in this paper constructs one such polygon with possibly two more edges than the minimal one.

Sarkar, D. (Univ. of Miami, Coral Gables, FL (United States)); Stojmenovic, I. (Univ. of Ottawa, Ontario (Canada))

1992-04-01

277

On Fixed Convex Combinations of No-Regret Learners  

Microsoft Academic Search

Abstract No-regret algorithms are powerful tools for learning in online convex problems that have received increased attention in recent years. Considering affine and external regret, we investigate what happens when a set of no-regret learners (voters) merge their respective strategies in each learn- ing iteration to a single, common one in form of a convex combination. We show that an

Jan-P. Calliess

2009-01-01

278

A Scalable Multi-objective Test Problem Toolkit  

Microsoft Academic Search

Abstract. This paper presents a new toolkit for creating scalable multiobjective test problems. The WFG Toolkit is ?exible, allowing characteristics such as bias, multi-modality, and non-separability to be incorporated and combined as desired. A wide variety of Pareto optimal geometries are also supported, including convex, concave, mixed convex\\/concave, linear, degenerate, and disconnected geometries. All problems created by the WFG Toolkit

Simon Huband; Luigi Barone; R. Lyndon While; Philip Hingston

2005-01-01

279

An ordinal optimization theory-based algorithm for solving the optimal power flow problem with discrete control variables  

Microsoft Academic Search

The optimal power flow (OPF) problem with discrete control variables is an NP-hard problem in its exact formulation. To cope with the immense computational-difficulty of this problem, we propose an ordinal optimization theory-based algorithm to solve for a good enough solution with high probability. Aiming for hard optimization problems, the ordinal optimization theory, in contrast to heuristic methods, guarantee to

Shin-Yeu Lin; Yu-Chi Ho; Ch'i-Hsin Lin

2004-01-01

280

Multiresolution strategies for the numerical solution of optimal control problems  

NASA Astrophysics Data System (ADS)

There exist many numerical techniques for solving optimal control problems but less work has been done in the field of making these algorithms run faster and more robustly. The main motivation of this work is to solve optimal control problems accurately in a fast and efficient way. Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. The algorithm adapted dynamically to any existing or emerging irregularities in the solution by automatically allocating more grid points to the region where the solution exhibited sharp features and fewer points to the region where the solution was smooth. Thereby, the computational time and memory usage has been reduced significantly, while maintaining an accuracy equivalent to the one obtained using a fine uniform mesh. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a nonlinear programming (NLP) problem that is solved using standard NLP codes. The novelty of the proposed approach hinges on the automatic calculation of a suitable, nonuniform grid over which the NLP problem is solved, which tends to increase numerical efficiency and robustness. Control and/or state constraints are handled with ease, and without any additional computational complexity. The proposed algorithm is based on a simple and intuitive method to balance several conflicting objectives, such as accuracy of the solution, convergence, and speed of the computations. The benefits of the proposed algorithm over uniform grid implementations are demonstrated with the help of several nontrivial examples. Furthermore, two sequential multiresolution trajectory optimization algorithms for solving problems with moving targets and/or dynamically changing environments have been developed. For such problems, high accuracy is desirable only in the immediate future, yet the ultimate mission objectives should be accommodated as well. An intelligent trajectory generation for such situations is thus enabled by introducing the idea of multigrid temporal resolution to solve the associated trajectory optimization problem on a non-uniform grid across time that is adapted to: (i) immediate future, and (ii) potential discontinuities in the state and control variables.

Jain, Sachin

281

Lagrange's principle in extremum problems with constraints  

NASA Astrophysics Data System (ADS)

In this paper a general result concerning Lagrange's principle for so-called smoothly approximately convex problems is proved which encompasses necessary extremum conditions for mathematical and convex programming, the calculus of variations, Lyapunov problems, and optimal control problems with phase constraints. The problem of local controllability for a dynamical system with phase constraints is also considered. In an appendix, results are presented that relate to the development of a 'Lagrangian approach' to problems where regularity is absent and classical approaches are meaningless. Bibliography: 33 titles.

Avakov, E. R.; Magaril-Il'yaev, G. G.; Tikhomirov, V. M.

2013-06-01

282

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

283

An optimized spectral difference scheme for CAA problems  

NASA Astrophysics Data System (ADS)

In the implementation of spectral difference (SD) method, the conserved variables at the flux points are calculated from the solution points using extrapolation or interpolation schemes. The errors incurred in using extrapolation and interpolation would result in instability. On the other hand, the difference between the left and right conserved variables at the edge interface will introduce dissipation to the SD method when applying a Riemann solver to compute the flux at the element interface. In this paper, an optimization of the extrapolation and interpolation schemes for the fourth order SD method on quadrilateral element is carried out in the wavenumber space through minimizing their dispersion error over a selected band of wavenumbers. The optimized coefficients of the extrapolation and interpolation are presented. And the dispersion error of the original and optimized schemes is plotted and compared. An improvement of the dispersion error over the resolvable wavenumber range of SD method is obtained. The stability of the optimized fourth order SD scheme is analyzed. It is found that the stability of the 4th order scheme with Chebyshev-Gauss-Lobatto flux points, which is originally weakly unstable, has been improved through the optimization. The weak instability is eliminated completely if an additional second order filter is applied on selected flux points. One and two dimensional linear wave propagation analyses are carried out for the optimized scheme. It is found that in the resolvable wavenumber range the new SD scheme is less dispersive and less dissipative than the original scheme, and the new scheme is less anisotropic for 2D wave propagation. The optimized SD solver is validated with four computational aeroacoustics (CAA) workshop benchmark problems. The numerical results with optimized schemes agree much better with the analytical data than those with the original schemes.

Gao, Junhui; Yang, Zhigang; Li, Xiaodong

2012-05-01

284

Minimax-Optimal Stop Rules and Distributions in Secretary Problems  

Microsoft Academic Search

For the secretary (or best-choice) problem with an unknown number $N$ of objects, minimax-optimal stop rules and (worst-case) distributions are derived, under the assumption that $N$ is a random variable with unknown distribution, but known upper bound $n$. Asymptotically, the probability of selecting the best object in this situation is of order of $(\\\\log n)^{-1}$. For example, even if the

Theodore P. Hill; Ulrich Krengel

1991-01-01

285

Optimization of Order Fulfillment in Distribution Network Problems  

Microsoft Academic Search

This paper focuses on optimization of order due date fulfillment reliability in multi-echelon distribution network problems\\u000a with uncertainties present in the production lead time, transportation lead time, and due date of orders. Reliability regarding\\u000a order due date fulfillment is critical in customer service, and customer retention. However, this reliability can be seriously\\u000a influenced by supply chain uncertainties, which may induce

Felix T. S. Chan; S. H. Chung; K. L. Choy

2006-01-01

286

Optimal Dynamic Order Submission Strategies in Some Stylized Trading Problems  

Microsoft Academic Search

Abstract This study derives optimal dynamic,order submission strategies for trading problems faced by three stylized traders: an uninformed liquidity trader, an informed trader and a value- motivated trader. Separate solutions are obtained for quote- and order-driven markets. The results provide practicable rules for how to trade small orders and how to manage traders. Transaction cost measurement,methods,based on implementation shortfall are

Lawrence Harris

1998-01-01

287

Multiagent Elite Search Strategy for Combinatorial Optimization Problems  

Microsoft Academic Search

\\u000a Ant Colony System is a new meta heuristics algorithms to solve hard combinatorial optimization problems. It is a population\\u000a based approach that uses exploitation of positive feedback as well as greedy search. In this paper, we propose a multi colony\\u000a interaction ant model that achieves positive·negative interaction through an elite strategy divided by intensification strategy\\u000a and diversification strategy to improve

Seunggwan Lee

2005-01-01

288

Second order necessary and sufficient conditions for convex composite NDO  

Microsoft Academic Search

In convex composite NDO one studies the problem of minimizing functions of the formF:=h ?f whereh:?\\u000a m\\u000a ? ? is a finite valued convex function andf:?\\u000a n\\u000a ? ?\\u000a m\\u000a is continuously differentiable. This problem model has a wide range of application in mathematical programming since many\\u000a important problem classes can be cast within its framework, e.g. convex inclusions, minimax

James V. Burke

1987-01-01

289

An Algorithm on Collision Detection by Computing the Minimum Distance between Two Convex Polyhedra  

Microsoft Academic Search

The problem of tracking the distance between two convex polyhedra is finding applications in many areas of robotics, including intersection detection, collision detection, and path planning. An algorithm for computing the minimum distance between two convex polyhedra is presented. The algorithm applies to polyhedral objects that can be represented as convex hulls of its vertex value in three-dimensional space. Nonlinear

Hanjun Jin; Yanlin Wang; Xiaorong Wang; Jia Fu

2006-01-01

290

On the Minimum Perimeter Triangle Enclosing a Convex Polygon  

Microsoft Academic Search

\\u000a We consider the problem of computing a minimum perimeter triangle enclosing a convex polygon. This problem defied a linear-time\\u000a solution due to the absence of a property called the interspersing property. This property was crucial in the linear-time solution for the minimum area triangle enclosing a convex polygon. We have\\u000a discovered a non-trivial interspersing property for the minimum perimeter problem.

Binay K. Bhattacharya; Asish Mukhopadhyay

2002-01-01

291

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

2013-06-18

292

Convex Hull Algorithms  

NSDL National Science Digital Library

An applet that demonstrates some algorithms for computing the convex hull of points in three dimensions. See the points from different viewpoints; see how the Incremental algorithm constructs the hull, face by face; while it's playing, look at it from different directions; see how the gift-wrapping or divide-and-conquer algorithms construct the hull; look at animations of Delaunay triangulation algorithms.

Lambert, Tim

2007-08-09

293

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

294

Optimum packing of convex-polygons by a new data structure sequence-table  

Microsoft Academic Search

The convex-polygon packing problem is to arrange given convex-polygons without overlapping each other in a bounding box of minimum area. This paper proposes a new algorithm. A solution space of convex-polygon packings is constructed by a new data-structure called the sequence-table which can represent topological relations between two convex-polygons. The algorithm searches the solution space stochastically for an optimum packing.

Hiroyuki Yamazaki; Keishi Sakanushi; Yoji Kajitani

2000-01-01

295

Isotonic, Convex and Related Splines  

Microsoft Academic Search

In this paper, we consider the estimation of isotonic, convex or related functions by means of splines. It is shown that certain classes of isotone or convex functions can be represented as a positive cone embedded in a Hilbert space. Using this representation, we give an existence and characterization theorem for isotonic or convex splines. Two special cases are examined

Ian W. Wright; Edward J. Wegman

1980-01-01

296

Optimal Parametric Discrete Event Control: Problem and Solution  

SciTech Connect

We present a novel optimization problem for discrete event control, similar in spirit to the optimal parametric control problem common in statistical process control. In our problem, we assume a known finite state machine plant model $G$ defined over an event alphabet $\\Sigma$ so that the plant model language $L = \\LanM(G)$ is prefix closed. We further assume the existence of a \\textit{base control structure} $M_K$, which may be either a finite state machine or a deterministic pushdown machine. If $K = \\LanM(M_K)$, we assume $K$ is prefix closed and that $K \\subseteq L$. We associate each controllable transition of $M_K$ with a binary variable $X_1,\\dots,X_n$ indicating whether the transition is enabled or not. This leads to a function $M_K(X_1,\\dots,X_n)$, that returns a new control specification depending upon the values of $X_1,\\dots,X_n$. We exhibit a branch-and-bound algorithm to solve the optimization problem $\\min_{X_1,\\dots,X_n}\\max_{w \\in K} C(w)$ such that $M_K(X_1,\\dots,X_n) \\models \\Pi$ and $\\LanM(M_K(X_1,\\dots,X_n)) \\in \\Con(L)$. Here $\\Pi$ is a set of logical assertions on the structure of $M_K(X_1,\\dots,X_n)$, and $M_K(X_1,\\dots,X_n) \\models \\Pi$ indicates that $M_K(X_1,\\dots,X_n)$ satisfies the logical assertions; and, $\\Con(L)$ is the set of controllable sublanguages of $L$.

Griffin, Christopher H [ORNL

2008-01-01

297

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

298

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

299

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

300

Optimal Resource Allocation for OFDMA Downlink Systems  

Microsoft Academic Search

This paper proposes efficient rate and power allocation algorithms for OFDMA downlink systems where each tone is taken by at most one user. Weighted sum rate maximization (WSRmax) and weighted sum power minimization (WSPmin) problems are considered. Since these resource allocation problems are non-convex, complexity of finding the optimal solutions is prohibitively high. This paper employs the Lagrange dual decomposition

Kibeom Seong; Mehdi Mohseni; John M. Cioffi

2006-01-01

301

The Synthesis of Optimal Controls for Linear Problems with Retarded Controls.  

National Technical Information Service (NTIS)

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 cont...

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

1970-01-01

302

Integer Partitions and Convexity  

NASA Astrophysics Data System (ADS)

Let n be an integer >=1, and let p(n,k) and P(n,k) count the number of partitions of n into k parts, and the number of partitions of n into parts less than or equal to k, respectively. In this paper, we show that these functions are convex. The result includes the actual value of the constant of Bateman and Erdos.

Bouroubi, Sadek

2007-06-01

303

Nonlinear Programming Global Optimization Techniques.  

National Technical Information Service (NTIS)

This report summarizes the results obtained in the area of optimization with non-convex functions. The difficulty is in determining when a local minimum is also a global minimum. The results can be classified into four areas: separable problems, factorabl...

J. E. Falk A. V. Fiacco G. P. McCormick

1978-01-01

304

Topics in optimization and sparse linear systems  

NASA Astrophysics Data System (ADS)

In the first part of the thesis, we study three problems in optimization-Network Optimization Problem, A Convex Optimization Problem arising out of Timing Analysis of VLSI circuits, and A Geometric Solution to two variable Convex Optimization Problems. In the second part of the thesis, we analyze the quality of a new graph-based preconditioner for large sparse Symmetric Positive Definite Diagonally Dominant (SPDDD) linear systems. These kinds of linear systems arise in the solution of scalar second order PDEs for Heat Transfer, Electrostatics, Electromagnetics, Ground Water Flow, and Diffusion (with or without reaction) when they are discretized using finite differences. They also arise in discrete problems like Network Flow Problems (Assignment, Maximum Flow, and Minimum Cost Flow), Large Resistive Networks, and Laminar Flow in Pipe Networks.

Joshi, Anil

1997-06-01

305

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

SciTech Connect

Computational protein threading 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, and illustrate how the computational complexity and the fold recognition accuracy of the algorithm change as the cutoff distance for pairwise interactions changes. For a given fold of m residues and M core secondary structures (or simply cores) and a protein sequence of n residues, the algorithm guarantees to find a sequence-fold alignment (threading) that is globally optimal, measured collectively by (1) the singleton match fitness, (2) pairwise interaction preference, and (3) alignment gap penalties, in O(mn + MnN{sup 1.5C-1}) time and O(mn + nN{sup C-1}) space. C, the topological complexity of a fold as we term, is a value which characterizes the overall structure of the considered pairwise interactions in the fold, which are typically determined by a specified cutoff distance between the beta carbon atoms of a pair of amino acids in the fold. C is typically a small positive integer. N represents the maximum number of possible alignments between an individual core of the fold and the protein sequence when its neighboring cores are already aligned, and its value is significantly less than n. When interacting amino acids are required to see each other, C is bounded from above by a small integer no matter how large the cutoff distance is. This indicates that the protein threading problem is polynomial-time solvable if the condition of seeing each other between interacting amino acids is sufficient for accurate fold recognition. A number of extensions have been made to our basic threading algorithm to allow finding a globally-optimal threading under various constraints, which include consistencies with (1) specified secondary structures (both cores and loops), (2) disulfide bonds, (3) active sites, etc.

Uberbacher, E.C.; Xu, D.; Xu, Y.

1999-04-12

306

Difficulties in Evolutionary Multiobjective Optimization for Many-Objective Optimization Problems and Their Scalability Improvement Techniques  

NASA Astrophysics Data System (ADS)

In this paper, we examine the behavior of evolutionary multiobjective optimization (EMO) algorithms to clarify the difficulties in their scalability to many-objective optimization problems. Whereas EMO algorithms usually work well on two-objective problems, it has also been reported that they do not work well on many-objective problems. First, we examine the behavior of the most well-known and frequently-used Pareto-based EMO algorithm (i. e. , NSGA-II) on many-objective 0/1 knapsack problems. Experimental results show that the search ability of NSGA-II is severely deteriorated by the increase in the number of objectives. This is because the selection pressure toward the Pareto front is severely weakened by the increase in the number of non-dominated solutions. Next we briefly review some approaches to the scalability improvement of EMO algorithms to many-objective problems. Then we examine their effects on the search ability of NSGA-II. Experimental results show that the improvement in the convergence of solutions to the Pareto front often leads to the decrease in their diversity.

Tsukamoto, Noritaka; Nojima, Yusuke; Ishibuchi, Hisao

307

Finding Quadratic Schedules for Affine Recurrence Equations Via Nonsmooth Optimization  

Microsoft Academic Search

Frequently, affine recurrence equations can be scheduled more efficiently by quadratic scheduling functions than by linear scheduling functions. In this paper, the problem of finding optimal quadratic schedules for affine recurrence equations is formulated as a convex nonsmooth programming problem. In particular, sufficient constraints for causality are used generalizing Lamport's condition. In this way, the presented problem formulation becomes independent

Wolfgang Achtziger; Karl-heinz Zimmermann

2000-01-01

308

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

309

Composite optimization: Second order conditions, value functions and sensityvity  

Microsoft Academic Search

By composite optimization we mean a class of optimization problems without constraints involving composite functions of the\\u000a form f(X)=g(F(X)), where F is a smooth map and g is a convex (in general non-smooth) function. Such problems typically appear as reduction forms for many (if not practically\\u000a all) important classes of optimization problems with constraints. In the paper we give a

Alexander Ioffe

310

Convex bodies of states and maps  

NASA Astrophysics Data System (ADS)

We give a general solution to the question of when the convex hulls of orbits of quantum states on a finite-dimensional Hilbert space under unitary actions of a compact group have a non-empty interior in the surrounding space of all density operators. The same approach can be applied to study convex combinations of quantum channels. The importance of both problems stems from the fact that, usually, only sets with non-vanishing volumes in the embedding spaces of all states or channels are of practical importance. For the group of local transformations on a bipartite system we characterize maximally entangled states by the properties of a convex hull of orbits through them. We also compare two partial characteristics of convex bodies in terms of the largest balls and maximum volume ellipsoids contained in them and show that, in general, they do not coincide. Separable states, mixed-unitary channels and k-entangled states are also considered as examples of our techniques.

Grabowski, Janusz; Ibort, Alberto; Ku?, Marek; Marmo, Giuseppe

2013-10-01

311

Human opinion dynamics: An inspiration to solve complex optimization problems.  

PubMed

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. PMID:24141795

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

2013-10-21

312

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

313

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

314

Frame-based deconvolution of Poissonian images using alternating direction optimization  

Microsoft Academic Search

Restoration of Poissonian images is a class of inverse problem arising in fields such medical and astronomical imaging. Regularization criteria that combine the Poisson log-likelihood with a non-smooth convex regularizer lead to optimization problems with several difficulties: the log-likelihood does not have a Lipschitzian gradient; the regularizer is non-smooth; there is a non-negativity constraint. Using convex analysis tools, we give

Mário A. T. Figueiredo; José M. Bioucas-Dias

2010-01-01

315

Error rates of the maximum-likelihood detector for arbitrary constellations: convex\\/concave behavior and applications  

Microsoft Academic Search

Motivated by a recent surge of interest in convex optimization techniques, convexity\\/concavity properties of error rates of the maximum likelihood detector operating in the AWGN channel are studied and extended to frequency-flat slow-fading channels. Generic conditions are identified under which the symbol error rate (SER) is convex\\/concave for arbitrary multidimensional constellations. In particular, the SER is convex in SNR for

Sergey Loyka; Victoria Kostina; François Gagnon

2010-01-01

316

Permutations Defining Convex Permutominoes  

NASA Astrophysics Data System (ADS)

A permutomino of size n is a polyomino determined by particular pairs (n_1,n_1) of permutations of size n, such that n_1(i) <> n_2i) for 1<=iconvex permutominoes. Using such a characterization, these permutations can be uniquely represented in terms of the so-called square permutations, introduced by Mansour and Severini. We provide a closed formula for the number of these permutations with size n.

Bernini, Antonio; Disanto, Filippo; Pinzani, Renzo; Rinaldi, Simone

2007-09-01

317

[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

318

DC Optimal Power Flow Formulation and Solution Using QuadProgJ  

Microsoft Academic Search

Nonlinear AC Optimal Power Flow (OPF) problems are commonly approximated by linearized DC OPF problems to obtain real power solutions for restructured wholesale power markets. We first present a standard DC OPF problem, which has the numerically desirable form of a strictly convex quadratic programming (SCQP) problem when voltage angles are eliminated by substitution. We next augment this standard DC

Junjie Sun; Leigh Tesfatsion

2006-01-01

319

Partially constrained ant colony optimization algorithm for the solution of constrained optimization problems: Application to storm water network design  

Microsoft Academic Search

This paper exploits the unique feature of the Ant Colony Optimization Algorithm (ACOA), namely incremental solution building mechanism, to develop partially constraint ACO algorithms for the solution of optimization problems with explicit constraints. The method is based on the provision of a tabu list for each ant at each decision point of the problem so that some constraints of the

M. H. Afshar

2007-01-01

320

Supplementary optimality properties of the restoration phase of sequential gradient-restoration algorithms for optimal control problems  

Microsoft Academic Search

In this paper, sequential gradient-restoration algorithms for optimal control problems are considered, and attention is focused on the restoration phase. It is shown that the Lagrange multipliers associated with the restoration phase not only solve the auxiliary minimization problem of the restoration phase, but are also endowed with a supplementary optimality property: they minimize a special functional, quadratic in the

A. Miele; T. Wang

1983-01-01

321

Triangulating a non-convex polytype  

Microsoft Academic Search

This paper is concerned with the problem of partitioning a three-dimensional polytope into a small number of elementary convex parts. The need for such decompositions arises in tool design, computer-aided manufacturing, finite-element methods, and robotics. Our main result is an algorithm for decomposing a polytope with n vertices and r reflex edges into &Ogr;(n+r2) tetrahedra. This bound is asymptotically tight

Bernard Chazelle; Leonidas Palios

1989-01-01

322

Non-Euler–Lagrangian Pareto-optimality Conditions for Dynamic Multiple Criterion Decision Problems  

Microsoft Academic Search

In this paper the problem of verifying the Pareto-optimality of a given solution to a dynamic multiple-criterion decision (DMCD) problem is investigated. For this purpose, some new conditions are derived for Pareto-optimality of DMCD problems. In the literature, Pareto-optimality is characterized by means of Euler-Lagrangian differential equations. There exist problems in production and inventory control to which these conditions cannot

Augustine O. Esogbue; Qiang Song; Donovan Young

2006-01-01

323

Polynomial Time Approximation Schemes for Some Dense Instances of NP-Hard Optimization Problems  

Microsoft Academic Search

.    We survey recent results on the existence of polynomial time approximation schemes for some dense instances of NP-hard combinatorial\\u000a optimization problems. We indicate some inherent limits for the existence of such schemes for some other dense instances of\\u000a optimization problems. We also go beyond the dense optimization problems and show how other approximation problems can be\\u000a solved by

Marek Karpinski

2001-01-01

324

New Hybrid Intelligent Systems to Solve Linear and Quadratic Optimization Problems and Increase Guaranteed Optimal Convergence Speed of Recurrent ANN  

Microsoft Academic Search

\\u000a This chapter deals with the study of artificial neural networks (ANNs) and Heuristic Rules (HR) to solve optimization problems.\\u000a The study of ANN as optimization tools for solving large scale problems was due to the fact that this technique has great\\u000a potential for hardware VLSI implementation, in which it may be more efficient than traditional optimization techniques. However,\\u000a the implementation

Otoni Nóbrega Neto; Ronaldo R. B. Aquino; Milde M. S. Lira

325

The two-convex-polygons TSP: A solvable case  

Microsoft Academic Search

In this paper, the Travelling Salesman Problem whenm points are on one convex polygonP, andn points are on another convex polygonQ, insideP, is polynomially solved. For this specific case, anO(m\\u000a 3\\u000a n\\u000a 3) time andO(m\\u000a 2\\u000a n\\u000a 2) space algorithm to obtain the tour with minimum length is provided.

Alfredo García; F. Javier Tejel

1997-01-01

326

Design of progressively censored group sampling plans for Weibull distributions: An optimization problem  

Microsoft Academic Search

Optimization algorithms provides efficient solutions to many statistical problems. Essentially, the design of sampling plans for lot acceptance purposes is an optimization problem with several constraints, usually related to the quality levels required by the producer and the consumer. An optimal acceptance sampling plan is developed in this paper for the Weibull distribution with unknown scale parameter. The proposed plan

Arturo J. Fernández; Carlos J. Pérez-González; Muhammad Aslam; Chi-Hyuck Jun

2011-01-01

327

Optimization of short-time gasoline blending scheduling problem with a DNA based hybrid genetic algorithm  

Microsoft Academic Search

Gasoline blending is a key process in the petroleum refinery industry posed as a nonlinear optimization problem with heavily nonlinear constraints. This paper presents a DNA based hybrid genetic algorithm (DNA-HGA) to optimize such nonlinear optimization problems. In the proposed algorithm, potential solutions are represented with nucleotide bases. Based on the complementary properties of nucleotide bases, operators inspired by DNA

Xiao Chen; Ning Wang

2010-01-01

328

ON APPROXIMATE t–CONVEXITY  

Microsoft Academic Search

Abstract. Areal valued function f defined on an open convex set D is called (?,?,p,t)-convex if it satisfies f (tx +( 1 ? t)y) tf (x )+( 1 ? t)f (y )+ ? + ?|x ? y|, for x,y ? D. The main result of the paper states that if f is locally bounded,from above at a point of D

Attila Hazy

329

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

330

Robust convex quadratically constrained programs  

Microsoft Academic Search

In this paper we study robust convex quadratically constrained programs, a subset of the class of robust convex programs introduced by Ben-Tal and Nemirovski (4). Unlike (4), our focus in this paper is to identify uncertainty structures that allow the corresponding robust quadratically constrained programs to be reformulated as second-order cone programs. We propose three classes of uncertainty sets that

Donald Goldfarb; Garud Iyengar

2003-01-01

331

A sparse superlinearly convergent SQP with applications to two-dimensional shape optimization.  

SciTech Connect

Discretization of optimal shape design problems leads to very large nonlinear optimization problems. For attaining maximum computational efficiency, a sequential quadratic programming (SQP) algorithm should achieve superlinear convergence while preserving sparsity and convexity of the resulting quadratic programs. Most classical SQP approaches violate at least one of the requirements. We show that, for a very large class of optimization problems, one can design SQP algorithms that satisfy all these three requirements. The improvements in computational efficiency are demonstrated for a cam design problem.

Anitescu, M.

1998-04-15

332

Application of l1 optimal control to the engine idle speed control problem  

Microsoft Academic Search

In this paper, the engine idle speed control (ISC) problem is revisited with the l1 optimization design methodology. A controller configuration consisting of a feedback linear quadratic Gaussian (LQG) optimal controller and a feedforward l1 optimal controller is chosen to satisfy the design objectives. The main goal of this work is to demonstrate the application of the l1 optimal control

Kenneth R. Butts; N. Sivashankar; Jing Sun

1999-01-01

333

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

334

Multiobjective optimization and hybrid evolutionary algorithm to solve constrained optimization problems.  

PubMed

This paper presents a novel evolutionary algorithm (EA) for constrained optimization problems, i.e., the hybrid constrained optimization EA (HCOEA). This algorithm effectively combines multiobjective optimization with global and local search models. In performing the global search, a niching genetic algorithm based on tournament selection is proposed. Also, HCOEA has adopted a parallel local search operator that implements a clustering partition of the population and multiparent crossover to generate the offspring population. Then, nondominated individuals in the offspring population are used to replace the dominated individuals in the parent population. Meanwhile, the best infeasible individual replacement scheme is devised for the purpose of rapidly guiding the population toward the feasible region of the search space. During the evolutionary process, the global search model effectively promotes high population diversity, and the local search model remarkably accelerates the convergence speed. HCOEA is tested on 13 well-known benchmark functions, and the experimental results suggest that it is more robust and efficient than other state-of-the-art algorithms from the literature in terms of the selected performance metrics, such as the best, median, mean, and worst objective function values and the standard deviations. PMID:17550112

Wang, Yong; Cai, Zixing; Guo, Guanqi; Zhou, Yuren

2007-06-01

335

Optimization of Very Large Nonlinear Problems (Design of a Flexible Separation Process)  

Microsoft Academic Search

We faced a common problem for those solving industrial sized process optimization problems. We had a problem that was much too nonlinear, large and combinatorially explosive to be solved by any of the commercial optimization codes we had available. Our goal was to find an \\

Arthur W. Westerberg; Kenneth H. Tyner

336

Optimization of the keyboard arrangement problem using an Ant Colony algorithm  

Microsoft Academic Search

In order to solve the problem of the arrangement of letters on a computer keyboard, an abstract representation of a keyboard is introduced and an evaluation function taking account of ergonomic criteria is proposed. It results in a new optimization problem that we name the keyboard arrangement problem. Based on the generic framework of Ant Colony optimization, an algorithm is

Jan Eggers; Dominique Feillet; Steffen Kehl; Marc Oliver Wagner; Bernard Yannou

2003-01-01

337

The minimum cost optimal power flow problem solved via the restart homotopy continuation method  

Microsoft Academic Search

The potential of the continuation method to solve the minimum-cost optimal power flow (OPF) problem is assessed. Initially, the complete OPF problem is simplified by creating a subproblem in which limits on functional variables are ignored. A restart homotopy continuation algorithm is developed that solves the sub-problem by manipulating the control variables to satisfy the optimality conditions of a family

R. A. Ponrajah; F. D. Galiana

1989-01-01

338

IDENTIFYING ALTERNATE OPTIMAL SOLUTIONS TO THE DESIGN APPROXIMATION PROBLEM IN STOCK CUTTING  

Microsoft Academic Search

The design approximation problem is a well known problem in stock cutting, where, in order to facilitate the optimization techniques used in the cutting process, it is required to approximate complex designs by simpler ones. Although there are algorithms available to solve this problem, they all suffer from an undesirable feature that they only produce one optimal solution to the

J. BHADURY; R. CHANDRASEKARAN

1999-01-01

339

Methods and Program Products for Optimizing Problem Clustering.  

National Technical Information Service (NTIS)

Exemplary embodiments of the present invention are directed to methods and program products for optimizing clustering of a design structure matrix. An embodiment of the present invention includes the steps of using a genetic operator to achieve an optimal...

D. E. Goldberg T. L. Yu A. Yassine

2004-01-01

340

Nash points, Ky Fan inequality and equilibria of abstract economies in Max-Plus and -convexity  

NASA Astrophysics Data System (ADS)

-convexity was introduced in [W. Briec, C. Horvath, -convexity, Optimization 53 (2004) 103-127]. Separation and Hahn-Banach like theorems can be found in [G. Adilov, A.M. Rubinov, -convex sets and functions, Numer. Funct. Anal. Optim. 27 (2006) 237-257] and [W. Briec, C.D. Horvath, A. Rubinov, Separation in -convexity, Pacific J. Optim. 1 (2005) 13-30]. We show here that all the basic results related to fixed point theorems are available in -convexity. Ky Fan inequality, existence of Nash equilibria and existence of equilibria for abstract economies are established in the framework of -convexity. Monotone analysis, or analysis on Maslov semimodules [V.N. Kolokoltsov, V.P. Maslov, Idempotent Analysis and Its Applications, Math. Appl., volE 401, Kluwer Academic, 1997; V.P. Litvinov, V.P. Maslov, G.B. Shpitz, Idempotent functional analysis: An algebraic approach, Math. Notes 69 (2001) 696-729; V.P. Maslov, S.N. Samborski (Eds.), Idempotent Analysis, Advances in Soviet Mathematics, Amer. Math. Soc., Providence, RI, 1992], is the natural framework for these results. From this point of view Max-Plus convexity and -convexity are isomorphic Maslov semimodules structures over isomorphic semirings. Therefore all the results of this paper hold in the context of Max-Plus convexity.

Briec, Walter; Horvath, Charles

2008-05-01

341

Solving multi-contingency transient stability constrained optimal power flow problems with an improved GA  

Microsoft Academic Search

In this paper, an improved genetic algorithm has been proposed for solving multi-contingency transient stability constrained optimal power flow (MC-TSCOPF) problems. The MC-TSCOPF problem is formulated as an extended optimal power flow (OPF) with additional generator rotor angle constraints and is converted into an unconstrained optimization problem, which is suitable for genetic algorithms to deal with, using a penalty function.

K. Y. Chan; S. H. Ling; K. W. Chan; Herbert H. C. Iu; G. T. Y. Pong

2007-01-01

342

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

343

Structural approaches to spin glasses and optimization problems  

NASA Astrophysics Data System (ADS)

We introduce the concept of Random Multi-Overlap Structure (RaMOSt) as a generalization of the one introduced by M. Aizenman et al. for non-diluted spin glasses. We use this concept to find generalized bounds for the free energy of the Viana-Bray model of diluted spin glasses and to formulate and prove the Extended Variational Principle that implicitly provides the free energy of the model. Then we exhibit a theorem for the limiting RaMOSt, analogous to the one found by F. Guerra for the Sherrington-Kirkpatrick model, that describes some stability properties of the model. We also show how our technique can be used to prove the existence of the thermodynamic limit of the free energy. We then propose an ultrametric breaking of replica symmetry for diluted spin glasses in the framework of Random Multi-Overlap Structures (RaMOSt). Such a proposal is closer to the Parisi theory for non-diluted spin glasses than the theory based on the iterative approach. Our approach allows to formulate an ansatz in which the Broken Replica Symmetry trial function depends on a set of numbers, over which one has to take the infimum (as opposed to a nested chain of probabilty distributions). Our scheme suggests that the order parameter is determined by the probability distribution of the multi-overlap in a similar sense as in the non-diluted case, and it is not necessarily a functional. Such results are then extended to the K-SAT and p-XOR-SAT optimization problems, and to the spherical mean field spin glass. The ultrametric structure exhibits a factorization property similar to the one of the optimal structures for the Viana-Bray model. The present work paves the way to a revisited Parisi theory for diluted spin systems. Moreover, it emphasizes some structural analogies among different models, which also seem to be plausible for models that still escape good mathematical control. This structural analysis seems quite promising both mathematically and physically.

de Sanctis, Luca

344

Optimization of stiffened plates by genetic search  

Microsoft Academic Search

This paper deals with the optimization of stiffeners on plates by varying their positions, while having well-defined dimensions. Considering the nonlinearity, the non-convexity and the discontinuity of this problem, we have chosen to use a stochastic method, that is the genetic algorithm (GA). This work is above all a study of feasibility. Some improvements in the GA have been used

A. Kallassy; J.-L. Marcelin

1997-01-01

345

Approximation of the optimal-time problem for controlled differential inclusions  

SciTech Connect

One of the common methods for numerical solution of optimal control problems constructs an approximating sequence of discrete control problems. The approximation method is also attractive because it can be used as an effective tool for analyzing optimality conditions and other topics in optimization theory. In this paper, we consider the approximation of optimal-time problems for controlled differential inclusions. The sequence of approximating problems is constructed using a finite-difference scheme, i.e., the differential inclusions are replaced with difference inclusions.

Otakulov, S.

1995-01-01

346

A comparative study of three simulation optimization algorithms for solving high dimensional multi-objective optimization problems in water resources  

NASA Astrophysics Data System (ADS)

Some real-world optimization problems in water resources have a high-dimensional space of decision variables and more than one objective function. In this work, we compare three general-purpose, multi-objective simulation optimization algorithms, namely NSGA-II, AMALGAM, and CMA-ES-MO when solving three real case Multi-objective Optimization Problems (MOPs): (i) a high-dimensional soil hydraulic parameter estimation problem; (ii) a multipurpose multi-reservoir operation problem; and (iii) a scheduling problem in deficit irrigation. We analyze the behaviour of the three algorithms on these test problems considering their formulations ranging from 40 up to 120 decision variables and 2 to 4 objectives. The computational effort required by each algorithm in order to reach the true Pareto front is also analyzed.

Schütze, Niels; Wöhling, Thomas; de Play, Michael

2010-05-01

347

New approach for the solution of optimal control problems on parallel machines. Doctoral thesis  

SciTech Connect

This thesis develops a highly parallel solution method for nonlinear optimal control problems. Balakrishnan's epsilon method is used in conjunction with the Rayleigh-Ritz method to convert the dynamic optimization of the optimal control problem into a static optimization problem. Walsh functions and orthogonal polynomials are used as basis functions to implement the Rayleigh-Ritz method. The resulting static optimization problem is solved using matrix operations which have well defined massively parallel solution methods. To demonstrate the method, a variety of nonlinear optimal control problems are solved. The nonlinear Raleigh problem with quadratic cost and nonlinear van der Pol problem with quadratic cost and terminal constraints on the states are solved in both serial and parallel on an eight processor Intel Hypercube. The solutions using both Walsh functions and Legendre polynomials as basis functions are given. In addition to these problems which are solved in parallel, a more complex nonlinear minimum time optimal control problem and nonlinear optimal control problem with an inequality constraint on the control are solved. Results show the method converges quickly, even from relatively poor initial guesses for the nominal trajectories.

Stech, D.J.

1990-01-01

348

Global optimization approach to the linear complementarity problem  

Microsoft Academic Search

The linear complementarity problem is formulated as a constrained quadratic global minimization problem. A computational method is presented and justified, which does not depend on any special properties of the problem matrix M. The method is based on the use of a multiple-cost-row linear program with 2n cost rows, where n is the number of problem variables. The method has

P. M. Pardalos; J. B. Rosen

1988-01-01

349

A global optimization approach for the BMI problem  

Microsoft Academic Search

The biaffine matrix inequality (BMI) is a potentially very flexible new framework for approaching complex robust control system synthesis problems with multiple plants, multiple objectives and controller order constraints. The BMI problem may be viewed as the nondifferentiable biconvex programming problem of minimizing the maximum eigenvalue of a biaffine combination of symmetric matrices. The BMI problem is non-local-global in general,

K.-C. Goh; M. G. Safonovt; G. P. Papavassilopoulos

1994-01-01

350

A domain decomposition method for the Helmholtz equation and related optimal control problems  

SciTech Connect

In this paper the Helmholtz equation and optimal control problems are solved by an iterative domain decomposition method. Proof of convergence is discussed based on energy methods. This method gives efficient numerical solutions to harmonic wave propagation problems.

Benamou, J.D. [Domaine de Voluceau, Le Chesnay (France); Despres, B. [Commissariat a l`Energie Atomique, Saint Georges (France)

1997-09-01

351

A compaction algorithm for non-convex polygons and its application  

Microsoft Academic Search

Given a two dimensional, non-overlapping layout of convex and non-convex polygons, compaction can be thought of as simulating the motion of the polygons as a result of applied “forces.” Compaction can be modeled as a motion of the polygons that reduces the value of some linear functional on their positions. Optimal compaction, planning a motion that finds the global minimum

Zhenyu Li; Victor Milenkovicf

1993-01-01

352

An effective hybrid immune-hill climbing optimization approach for solving design and manufacturing optimization problems in industry  

Microsoft Academic Search

The focus of this research is on a hybrid method combining immune algorithm with a hill climbing local search algorithm for solving complex real-world optimization problems. The objective is to contribute to the development of more efficient optimization approaches with the help of immune algorithm and hill climbing algorithm. The hybrid algorithm combines the exploration speed of immune algorithm with

Ali R?za Y?ld?z

2009-01-01

353

Discrete-Continuous Optimization for Optical Flow Estimation  

Microsoft Academic Search

The accurate estimation of optical flow is a challenging task, which is often posed as an energy minimization problem. Most\\u000a top-performing methods approach this using continuous optimization algorithms. In many cases, the employed models are assumed\\u000a to be convex to ensure tractability of the optimization problem. This is in contrast to the related problem of narrow-baseline\\u000a stereo matching, where the

Stefan Roth; Victor Lempitsky; Carsten Rother

354

Continuous Optimization A smoothing heuristic for a bilevel pricing problem  

Microsoft Academic Search

In this paper, we provide a heuristic procedure, that performs well from a global optimality point of view, for an important and difficult class of bilevel programs. The algorithm relies on an interior point approach that can be inter- preted as a combination of smoothing and implicit programming techniques. Although the algorithm cannot guarantee global optimality, very good solutions can

Jean-Pierre Dussault; Patrice Marcotte; Gilles Savard

355

Synthesis using approximately bisimilar abstractions: time-optimal control problems  

Microsoft Academic Search

In this paper, we present a hierarchical approach to time-optimal control using approximately bisimilar abstractions. Given a time-optimal controller for an abstraction, we present a specific procedure that allows us to compute a suboptimal controller for the original system. While the usual controller refinement procedure produces dynamic controllers that may have limitations in terms of implementation cost and robustness, the

Antoine Girard

2010-01-01

356

Optimizing edge detection in quantitative coronary arteriography: problems and proposals  

Microsoft Academic Search

Optimum geometric edge detection in quantitative coronary arteriography (QCA) is determined by the accuracy of measurements of known phantom diameters. The authors optimized the edge detection for different calibration methods, diameter ranges, accuracy measures and performance strategies. They found, that the optimization process itself is ill-defined, depending on the calibration method used, the included range of small diameters and the

W. Wunderlich; T. Linderer; B. Backs; F. Fischer; J. Noering; R. Schroeder

1993-01-01

357

MULTI-OBJECTIVE APPROACH FOR ROBUST DESIGN OPTIMIZATION PROBLEMS  

Microsoft Academic Search

The paper demonstrates the main capabilities of IOSO (Indirect Optimization based on Self - Organization) technology algorithms, tools and software, which can be used for the optimization of complex systems and objects. IOSO algorithms have higher efficiency, provide a wider range of capabilities, and are practically insensitive with respect to the types of objective function and constraints. They could be

Egorov N. Igor; Kretinin V. Gennadiy; Leshchenko A. Igor; Kuptzov V. Sergey

358

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

359

Noah, Joseph and Convex Hulls  

NASA Astrophysics Data System (ADS)

The idea of describing animal movement by mathematical models based on diffusion and Brownian motion has a long heritage. It has thus been natural to account for those aspects of motion that depart from the Brownian by the use of models incorporating long memory & subdiffusion (“the Joseph effect”) and/or heavy tails & superdiffusion (“the Noah effect”). My own interest in this problem was originally from a geoscience perspective, and was triggered by the need to model time series in space physics where both effects coincide. Subsequently I have been involved in animal foraging studies [e.g. Edwards et al, Nature, 2007]. I will describe some recent work [Watkins et al, PRE, 2009] which studies how fixed-timestep and variable-timestep formulations of anomalous diffusion are related in the presence of heavy tails and long range memory (stable processes versus the CTRW). Quantities for which different scaling relations are predicted between the two approaches are of particular interest, to aid testability. I will also present some of work in progress on the convex hull of anomalously diffusing walkers, inspired by its possible relevance to the idea of home range in biology, and by Randon-Furling et al’s recent analytical results in the Brownian case [PRL, 2009].

Watkins, N. W.; Chau, Y.; Chapman, S. C.

2010-12-01

360

Multi-label Moves for MRFs with Truncated Convex Priors  

NASA Astrophysics Data System (ADS)

Optimization with graph cuts became very popular in recent years. As more applications rely on graph cuts, different energy functions are being employed. Recent evaluation of optimization algorithms showed that the widely used swap and expansion graph cut algorithms have an excellent performance for energies where the underlying MRF has Potts prior. Potts prior corresponds to assuming that the true labeling is piecewise constant. While surprisingly useful in practice, Potts prior is clearly not appropriate in many circumstances. However for more general priors, the swap and expansion algorithms do not perform as well. Both algorithms are based on moves that give each pixel a choice of only two labels. Therefore such moves can be referred to as binary moves. Recently, range moves that act on multiple labels simultaneously were introduced. As opposed to swap and expansion, each pixel has a choice of more than two labels in a range move. Therefore we call them multi-label moves. Range moves were shown to work better for problems with truncated convex priors, which imply a piecewise smooth labeling. Inspired by range moves, we develop several different variants of multi-label moves. We evaluate them on the problem of stereo correspondence and discuss their relative merits.

Veksler, Olga

361

Convex polytopes and quantum separability  

SciTech Connect

We advance a perspective of the entanglement issue that appeals to the Schlienz-Mahler measure [Phys. Rev. A 52, 4396 (1995)]. Related to it, we propose a criterium based on the consideration of convex subsets of quantum states. This criterium generalizes a property of product states to convex subsets (of the set of quantum states) that is able to uncover an interesting geometrical property of the separability property.

Holik, F.; Plastino, A. [Departamento de Matematica - Ciclo Basico Comun, Universidad de Buenos Aires - Pabellon III, Ciudad Universitaria, Buenos Aires, Argentina and CONICET (Argentina); National University La Plata and CONICET IFLP-CCT, C.C. 727 - 1900 La Plata (Argentina)

2011-12-15

362

A dual method for solving general convex quadratic programs  

Microsoft Academic Search

In this paper, we present a new method for solving quadratic programming problems, not strictly convex. Constraints of the problem are linear equalities and inequalities, with bounded variables. The suggested method combines the active-set strategies and support methods. The algorithm of the method and numerical experiments are presented, while comparing our approach with the active set method on randomly generated

Belkacem BRAHMI; Mohand Ouamer BIBI

2009-01-01

363

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

364

A faster optimization method based on support vector regression for aerodynamic problems  

NASA Astrophysics Data System (ADS)

In this paper, a new strategy for optimal design of complex aerodynamic configuration with a reasonable low computational effort is proposed. In order to solve the formulated aerodynamic optimization problem with heavy computation complexity, two steps are taken: (1) a sequential approximation method based on support vector regression (SVR) and hybrid cross validation strategy, is proposed to predict aerodynamic coefficients, and thus approximates the objective function and constraint conditions of the originally formulated optimization problem with given limited sample points; (2) a sequential optimization algorithm is proposed to ensure the obtained optimal solution by solving the approximation optimization problem in step (1) is very close to the optimal solution of the originally formulated optimization problem. In the end, we adopt a complex aerodynamic design problem, that is optimal aerodynamic design of a flight vehicle with grid fins, to demonstrate our proposed optimization methods, and numerical results show that better results can be obtained with a significantly lower computational effort than using classical optimization techniques.

Yang, Xixiang; Zhang, Weihua

2013-09-01

365

Coarse-grained parallel genetic algorithm applied to a nuclear reactor core design optimization problem  

Microsoft Academic Search

This work extends the research related to genetic algorithms (GA) in core design optimization problems, which basic investigations were presented in previous work. Here we explore the use of the Island Genetic Algorithm (IGA), a coarse-grained parallel GA model, comparing its performance to that obtained by the application of a traditional non-parallel GA. The optimization problem consists on adjusting several

Cláudio M. N. A. Pereira; Celso M. F. Lapa

2003-01-01

366

An Ant Colony Optimization algorithm to solve a 2-machine bicriteria flowshop scheduling problem  

Microsoft Academic Search

Consider the 2-machine flowshop scheduling problem with the objective of minimizing both the total completion time and the makespan criteria. The latter is assumed to be optimized prior to the former. In view of the NP-hardness of the problem an Ant Colony Optimization approach is proposed to solve it. The heuristic also uses feature of Simulated Annealing search and local

Vincent T'kindt; Nicolas Monmarché; Fabrice Tercinet; Daniel Laügt

2002-01-01

367

Optimization of the quadratic assignment problem using an ant colony algorithm  

Microsoft Academic Search

Ant algorithm is a multi-agent systems inspired by the behaviors of real ant colonies function to solve optimization problems. In this paper an ant colony optimization algorithm is developed to solve the quadratic assignment problem. The local search process of the algorithm is simulated annealing. In the exploration of the search space, the evaluation of pheromones which are laid on

Nihan Çetin Demirel; M. Duran Toksari

2006-01-01

368

SOLUTION OF SOME COMBINATORIAL OPTIMIZATION PROBLEMS ENCOUNTERED IN WATER RESOURCES DEVELOPMENT  

Microsoft Academic Search

The solution of some constrained combinatorial optimization problems encountered in the preinvestment planning of large-scale water resources systems is discussed. Mathematical structures are formulated for several problems involving the optimal selection, sequencing and timing of a set of water resources development projects which, in the aggregate, must satisfy a number of continuous time demand projections at every point in a

THOMAS L. MORIN

1975-01-01

369

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

370

Finite difference approximations of optimal control problems for semilinear elliptic equations with discontinuous coefficients and solutions  

NASA Astrophysics Data System (ADS)

Mathematical formulation of nonlinear optimal control problems for semilinear elliptic equations with discontinuous coefficients and discontinuous solutions are examined. Finite difference approximations of optimization problems are constructed, and the approximation error is estimated with respect to the state and the cost functional. Weak convergence of the approximations with respect to the control is proved. The approximations are regularized using Tikhonov regularization.

Lubyshev, F. V.

2012-08-01

371

A Particle Swarm Optimization and Differential Evolution Algorithms for Job Shop Scheduling Problem  

Microsoft Academic Search

In this paper, we present particle swarm optimization (PSO) and differential evolution (DE) algorithms for the job shop scheduling problem with the makespan criterion. The applications of PSO and DE on combinatorial optimization problems are still considered limited, but the advantages of PSO and DE algorithms such as structural simplicity, accessibility to practical applications, ease of implementatio n, speed to

M. Fatih Tasgetiren; Mehmet Sevkli; Yun-Chia Liang; M. Mutlu Yenisey

2006-01-01

372

Distributed Solution of Optimal Hybrid Control Problems on Networks of Workstations  

Microsoft Academic Search

The design of an optimal control strategy for a hybrid sys- tem is a matter of growing interest in computational en- gineering. The solution of optimization problems in most engineering disciplines often requires efficient parallelop- timization algorithms to solve these kinds of problems in reasonable time. Instead of introducing parallelism to selected components of an existing sequential algorithm, the algorithm

Thomas Barthl; Bernd Freisleben; Manfred Grauer; Frank Thilol

2000-01-01

373

An ant colony optimization approach to addressing a JIT sequencing problem with multiple objectives  

Microsoft Academic Search

This research presents an application of the relatively new approach of ant colony optimization (ACO) to address a production-sequencing problem when two objectives are present — simulating the artificial intelligence agents of virtual ants to obtain desirable solutions to a manufacturing logistics problem. The two objectives are minimization of setups and optimization of stability of material usage rates. This type

Patrick R. Mcmullen

2001-01-01

374

A generalization of Arcangeli's method for ill-posed problems leading to optimal rates  

Microsoft Academic Search

Schock (1984) considered a general a posteriori parameter choice strategy for the regularization of ill-posed problems which provide nearly the optimal rate of convergence. We improve the result of Schock and give a class of parameter choice strategies leading to optimal rates As a particular case we prove that the Arcangeli's method do give optimal rate of convergence.

M. Thamban Nair

1992-01-01

375

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

376

Multi-objective Evolutionary Algorithms to Solve Coverage and Lifetime Optimization Problem in Wireless Sensor Networks  

NASA Astrophysics Data System (ADS)

Multi-objective optimization problem formulations reflect pragmatic modeling of several real-life complex optimization problems. In many of them, the considered objectives are competitive with each other and emphasizing only one of them during solution generation and evolution, incurs high probability of producing one sided solution which is unacceptable with respect to other objectives. This paper investigates the concept of boundary search and also explores the application of a special evolutionary operator on a multi-objective optimization problem; Coverage and Lifetime Optimization Problem in Wireless Sensor Network (WSN). The work in this paper explores two competing objectives of WSN;network coverage and network lifetime using two efficient, robust MOEAs. It also digs into the impact of special operators in the multi-objective optimization problems of sensor node's design topology.

Chaudhuri, Koyel; Dasgupta, Dipankar

377

Optimization problems and calculation of electrical networks work regimes  

Microsoft Academic Search

For calculation of established regimes of electrical network and minimization of energetical losses numerical methods are offered. These are the methods of non-linear equations solving and methods of optimization. The methods possess the high speed of convergence

N. N. Redkovsky; V. A. Goureev

1997-01-01

378

Optimal Conditions for the Control Problem Associated to a Biomedical Process  

NASA Astrophysics Data System (ADS)

This paper considers a mathematical model of infectious disease of SIS type. We will analyze the problem of minimizing the cost of diseases trough medical treatment. Mathematical modeling of this process leads to an optimal control problem with a finite horizon. The necessary conditions for optimality are given. Using the optimality conditions we prove the existence, uniqueness and stability of the steady state for a differential equations system.

Bund?u, O.; Juratoni, A.; Chevere?an, A.

2010-09-01

379

Two stages optimization problem: New variant of Bin Packing Problem for decision making  

Microsoft Academic Search

In this paper, we present a new multi-criteria assignment problem that groups characteristics from the well known Bin Packing Problem (BPP) and Generalized Assign- ment Problem (GAP). Similarities and differences between these problems are discussed, and a new variant of BPP is presented. The new variant will be called generalized assignment problem with identified first-use bins (GAPIFB). The GAPIFB will

Ahmad H. Shraideh; Hervé G. Camus; Pascal G. M. Yim

2008-01-01

380

Approximation schemes for NP-hard geometric optimization problems: A survey  

Microsoft Academic Search

gnpolynomial time algorithms to solve these problems optimally. However, wemight be able to design approximation algorithms: algorithms that computenear-optimal solutions in polynomial time for every problem instance. For1 we say that an algorithm approximates the problem within a factor# if it computes, for every instance I, a solution of cost at most #OPT(I),where OPT(I) is the cost of the optimum

Sanjeev Arora

2002-01-01

381

An optimization method for overdetermined kinematic problems formulated with natural coordinates  

Microsoft Academic Search

In this paper, we present an optimization method for solving the nonlinear constrained optimization problem arising from a\\u000a motion reconstruction problem formulated with natural coordinates. A motion reconstruction problem consists in a kinematic\\u000a analysis of a rigid multibody system whose motion is usually overdetermined by an excess of data. The method has been applied\\u000a to the analysis of human motion which

Sergio Ausejo; Ángel Suescun; Juan Celigüeta

382

Superresolution of passive millimeter-wave images using a combined maximum-likelihood optimization and projection-onto-convex-sets approach  

NASA Astrophysics Data System (ADS)

Imagery data acquired from Passive Millimeter-Wave (PMMW) radiometers have inherently poor resolution due to limited aperture dimensions and the consequent diffraction limits thus requiring processing by a sophisticated super- resolution algorithm before the images can be used for nay useful purposes such as surveillance, fusion, navigation and missile guidance. Recent research has produced a class of powerful algorithms that employ a Bayesian framework in order to iteratively optimize a likelihood function in the resolution enhancement process. These schemes, popularly called ML algorithms, enjoy several advantages such as simple digital implementation and robustness of performance to inaccurate estimation of sensor parameters. However, the convergence of iterations could in some cases become rather slow and practical implementations may require executing a large number of iterations before desired resolution levels can be achieved. The quality of restoration and the extent of achievable super-resolution depend on the accuracy and the amount of a prior information that could be utilized in processing the input imagery dat. Projection-based set- theoretic methods offer a considerable flexibility in incorporating available a priori information and hence provide an attractive framework for tailoring powerful restoration and super-resolution algorithms. The prior information, which is used as constraints during the processing, can be derived form a number of sources such as the phenomenology of the sensor employed, known conditions at the time of recording data, and scene-related information that could be extracted from the image. In this paper, we shall describe a POCS approach to image restoration and use it to enhance the super-resolution performance of ML algorithms. A new algorithm, termed POCS-assisted ML algorithm, that combines the strong points of ML and POCS approaches will be outlined. A quantitative evaluation of the performance of this algorithm for restoring and super- resolving PMMW image data will also be presented.

Sundareshan, Malur K.; Bhattacharjee, Supratik

2001-08-01

383

A Decomposition-Based Global Optimization Approach for Solving Bilevel Linear and Quadratic Programs  

Microsoft Academic Search

. The paper presents a decomposition based global optimization approach to bilevellinear and quadratic programming problems. By replacing the inner problem by its correspondingKKT optimality conditions, the problem is transformed to a single yet non-convex, due to thecomplementarity condition, mathematical program. Based on the primal-dual global optimizationapproach of Floudas and Visweswaran (1990, 1993), the problem is decomposed into a series

V. Visweswaran; C. A. Floudas

1996-01-01

384

Real-Time Mass Passenger Transport Network Optimization Problems  

Microsoft Academic Search

The aim of the real-time mass transport vehicle routing problem (MTVRP) is to find a solution to route n vehicles in real time to pick up and deliver m passengers. This problem is described in the context of flexible large-scale mass transportation options that use new technologies for communication among passengers and vehicles. This study does not focus on the

Laia Pages; R. Jayakrishnan

2006-01-01

385

Nonlinear switched capacitor `neural' networks for optimization problems  

Microsoft Academic Search

A systematic approach is presented for the design of analog neural nonlinear programming solvers using switched-capacitor (SC) integrated circuit techniques. The method is based on formulating a dynamic gradient system whose state evolves in time toward the solution point of the corresponding programming problem. A neuron cell for the linear and the quadratic problem suitable for monolithic implementation is introduced.

A. Rodriguez-Vazquez; R. Dominguez-Castro; A. Rueda; J. L. Huertas; E. Sanchez-Sinencio

1990-01-01

386

On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems  

Microsoft Academic Search

Deconvolution problems arise in a variety of situations in statistics. An interesting problem is to estimate the density $f$ of a random variable $X$ based on $n$ i.i.d. observations from $Y = X + \\\\varepsilon$, where $\\\\varepsilon$ is a measurement error with a known distribution. In this paper, the effect of errors in variables of nonparametric deconvolution is examined. Insights

Jianqing Fan

1991-01-01

387

An approximately global optimization method for assortment problems  

Microsoft Academic Search

Assortment problems occur when we want to cut a number of small rectangular pieces from a large rectangle to get the minimum area within the rectangle. Recently, Chen et al. proposed a useful model for assortment problems. Although Chen et al.'s model is quite promising to find solutions, there are two inadequacies in their model: firstly, the objective function in

Han-Lin Li; Ching-Ter Chang

1998-01-01

388

Algebraic Optimization: The Fermat-Weber Location Problem  

Microsoft Academic Search

The Fermat-Weber location problem is to find a point in Rn that minimizes the sum of the (weighted) Euclidean distances fromm given points in Rn. In this work we discuss some relevant complexity and algorithmic issues. First, using Tarski's theory on solvability over real closed fields we argue that there is an infinite scheme to solve the problem, where the

R. Chandrasekaran; Arie Tamir

1990-01-01

389

A global optimization method, ?BB, for general twice-differentiable constrained NLPs—II. Implementation and computational results  

Microsoft Academic Search

Part I of this paper (Adjiman et al., 1998a) described the theoretical foundations of a global optimization algorithm, the ?BB algorithm, which can be used to solve problems belonging to the broad class of twicedifferentiable NPLs. For any such problem, the ability to automatically generate progressively tighter convex lower bounding problems at each iteration guarantees the convergence of the branch-and-bound

C. S. Adjiman; I. P. Androulakis; C. A. Floudas

1998-01-01

390

A Convex Approach to Validation-Based Learning of the Regularization Constant  

Microsoft Academic Search

This letter investigates a tight convex relaxation to the problem of tuning the regularization constant with respect to a validation based criterion. A number of algorithms is covered including ridge regression, regularization networks, smoothing splines, and least squares support vector machines (LS-SVMs) for regression. This convex approach allows the application of reliable and efficient tools, thereby improving computational cost and

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

2007-01-01

391

Decomposing a simple polygon into pseudo-triangles and convex polygons  

Microsoft Academic Search

In this paper we consider the problem of decomposing a simple polygon into subpolygons that exclusively use vertices of the given polygon. We allow two types of subpolygons: pseudo- triangles and convex polygons. We call the resulting decomposition PT-convex. We are interested in minimum decompositions, i.e., in decomposing the input polygon into the least number of subpolygons. Allowing subpolygons of

Stefan Gerdjikov; Alexander Wolff

2008-01-01

392

A Linear-Time Algorithm for Computing the Voronoi Diagram of a Convex Polygon  

Microsoft Academic Search

We present an algorithm for computing certain kinds of three-dimensional convex hulls in linear time. Using this algorithm, we show that the Voronoi diagram ofn sites in the plane can be computed in ?(n) time when these sites form the vertices of a convex polygon in, say, counterclockwise order. This settles an open problem in computational geometry. Our techniques can

Alok Aggarwal; Leonidas J. Guibas; James B. Saxe; Peter W. Shor

1989-01-01

393

A Linear time algorithm for computing the Voronoi diagram of a convex polygon  

Microsoft Academic Search

We present an algorithm for computing certain kinds of three-dimensional convex hulls in linear time. Using this algorithm, we show that the Voronoi diagram of n points in the plane can be computed in &THgr;(n) time when these points form the vertices of a convex polygon in, say, counterclockwise order. This settles an outstanding open problem in computational geometry. Our

Alok Aggarwal; Leonidas J. Guibas; James B. Saxe; Peter W. Shor

1987-01-01

394

UAV Coordination on Convex Curves in Wind: An Environmental Sampling Application  

Microsoft Academic Search

This paper is concerned with synchronization of UAVs, modeled as particles, moving along convex curves in the plane, in the presence of a steady wind. The method presented here integrates previous results on synchronization along convex loops, in still air, and synchronization on circles in an external flow field. The method is applied to a control-volume sampling problem, in which

Derek A. Pale; Craig A. Woolsey

395

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

NASA Astrophysics Data System (ADS)

As a practical generalization of the job shop scheduling problem, multi-resource job shop scheduling problem (MRJSSP) is discussed in this paper. In this problem, operations may be processed by a type of resources and jobs have individual deadlines. How to design and optimize this problem with DSAFO, a novel multi-agent algorithm, is introduced in detail by a case study, including problem analysis, agent role specification, and parameter selection. Experimental results show the effectiveness and efficiency of designing and optimizing MRJSSPs with multi-agent.

Xue, Fan; Fan, Wei

396

Parallel evolutionary algorithms for optimization problems in aerospace engineering  

Microsoft Academic Search

This paper presents the recent developments in hierarchical genetic algorithms (HGAs) to speed up the optimization of aerodynamic shapes. It first introduces HGAs, a particular instance of parallel GAs based on the notion of interconnected sub-populations evolving independently. Previous studies have shown the advantages of introducing a multi-layered hierarchical topology in parallel GAs. Such a topology allows the use of

J. F. Wang; J. Periaux; M. Sefrioui

2002-01-01

397

Optimization of Flight Test Maneuvers for Aerodynamic Derivatives Inverse Problem  

Microsoft Academic Search

1. Abstract This work deals with the application of optimization techniques to the determination of aircraft light test input maneuvers for aircraft model identification and aerodynamic parameter estimation. The optimum flight test maneuvers are necessary to increase the efficiency of aircraft identification and parameter estimation algorithms, respecting operational restrictions related to flight safety and limits of the assumed mathematical models.

Nei Salis; Brasil Neto; Luiz Carlos; S. Góes; Benedito Carlos; O. Maciel; Elder Moreira Hemerly

398

Optimizing ACS for Big TSP Problems Distributing Ant Parameters  

Microsoft Academic Search

Ant colony algorithms are a group of heuristic optimization algorithms that have been inspired by ants foraging for food. In these algorithms there are some agents, the ants, that for finding the suitable solution, search the solution space. Ant colony algorithms have some parameters like relative pheromone importance on trail and pheromone decay coefficient that convergence and efficiency of algorithms

Fardin Abdali Mohammadi; Abdol Hossein Fathi; Mohammad Taghi Manzurit

2006-01-01

399

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

400

Optimal Pricing Strategy for Queuing Systems with Capacity Constraint Problem  

Microsoft Academic Search

Although the lost profit from lost business is quite difficult to estimate for the queuing systems with cyclic demands, my previous work presents a creative and effective approach to formulate waiting cost as balking loss. Using the estimation of waiting cost allows decision maker to have the capability of determining the optimal number of servers for each planning period by

Pen-Yuan Liao

2007-01-01

401

Global convergence of nonmonotone descent methods for unconstrained optimization problems  

NASA Astrophysics Data System (ADS)

Global convergence results are established for unconstrained optimization algorithms that utilize a nonmonotone line search procedure. This procedure allows the user to specify a flexible forcing function and includes the nonmonotone Armijo rule, the nonmonotone Goldstein rule, and the nonmonotone Wolfe rule as special cases.

Sun, Wenyu; Han, Jiye; Sun, Jie

2002-09-01

402

On optimization algorithms for the reservoir oil well placement problem  

Microsoft Academic Search

Determining optimal locations and operation parameters for wells in oil and gas reservoirs has a potentially high economic impact. Finding these optima depends on a complex combination of geological, petrophysical, flow regimen, and economical parameters that are hard to grasp intuitively. On the other hand, automatic approaches have in the past been hampered by the overwhelming computational cost of running

W. Bangerth; H. Klie; M. F. Wheeler; P. L. Stoffa; M. K. Sen

2006-01-01

403

A heuristic solution to the transformer manufacturing cost optimization problem  

Microsoft Academic Search

The aim of the transformer design is to completely obtain the dimensions of all the parts of the transformer based on the given specification, using available materials economically in order to achieve lower cost, lower weight, reduced size and better operating performance. In this paper, a transformer design optimization method is proposed aiming at designing the transformer so as to

Pavlos S. Georgilakis; Marina A. Tsili; Athanassios T. Souflaris

2007-01-01

404

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

405

Free terminal time optimal control problem of an HIV model based on a conjugate gradient method.  

PubMed

The minimum duration of treatment periods and the optimal multidrug therapy for human immunodeficiency virus (HIV) type 1 infection are considered. We formulate an optimal tracking problem, attempting to drive the states of the model to a "healthy" steady state in which the viral load is low and the immune response is strong. We study an optimal time frame as well as HIV therapeutic strategies by analyzing the free terminal time optimal tracking control problem. The minimum duration of treatment periods and the optimal multidrug therapy are found by solving the corresponding optimality systems with the additional transversality condition for the terminal time. We demonstrate by numerical simulations that the optimal dynamic multidrug therapy can lead to the long-term control of HIV by the strong immune response after discontinuation of therapy. PMID:21271294

Jang, Taesoo; Kwon, Hee-Dae; Lee, Jeehyun

2011-01-27

406

A Parallel Global Optimization Method for Solving Molecular Cluster and Polymer Conformation Problems  

Microsoft Academic Search

Identifying the conformations that a molecular cluster or polymer assumes in natureis an important problem with many practical applications in biology and medicine. Itis believed that the naturally occurring molecular conformations minimize or nearlyminimize the potential energy of the molecular cluster or polymer. The problem offinding the molecular configuration(s) with the lowest potential energy is a challengingglobal optimization problem with

Richard H. Byrd; Elizabeth Eskow; André Van Der Hoek; Robert B. Schnabel; Klaas P. B. Oldenkamp

1995-01-01

407

Communications Maintenance and Optimization Problem in Robotic Multi-hop Networks: Assumptions, Models, and Algorithms.  

National Technical Information Service (NTIS)

An important problem in robotics is the Communications Maintenance and Optimization Problem (CMOP). In this problem, we have a set of robots that are communicating with one another across a multi-hop wireless network. The primary constraint is that the ro...

C. Karan

2013-01-01

408

An interior point nonlinear programming for optimal power flow problems with a novel data structure  

Microsoft Academic Search

This paper presents a new interior point nonlinear programming algorithm for optimal power flow problems (OPF) based on the perturbed KKT conditions of the primal problem. Through the concept of the centering direction, the authors extend this algorithm to classical power flow (PF) and approximate OPF problems. For the latter, CPU time can be reduced substantially. To efficiently handle functional

Hua Wei; H. Sasaki; J. Kubokawa; R. Yokoyama

1998-01-01

409

Large scale hydrothermal optimal power flow problems based on interior point nonlinear programming  

Microsoft Academic Search

This paper presents an interior point algorithm for hydrothermal optimal power flow problems (HTOPF) which is derived from the perturbed KKT conditions of the primal problem. Moreover, the algorithm is extended successfully to solve approximate HTOPF problems (A-HTOPF) to find a suboptimal solution with much less execution time. For large scale systems, A-HTOPF can reduce CPU time by half and

Hau Wei; Hiroshi Sasaki; Junji Kubokawa; Ryuichi Yokoyama

2000-01-01

410

A columnar competitive model for solving combinatorial optimization problems  

Microsoft Academic Search

The major drawbacks of the Hopfield network when it is applied to some combinatorial problems, e.g., the traveling salesman problem (TSP), are invalidity of the obtained solutions, trial-and-error setting value process of the network parameters and low-computation efficiency. This letter presents a columnar competitive model (CCM) which incorporates winner-takes-all (WTA) learning rule for solving the TSP. Theoretical analysis for the

Huajin Tang; K. C. Tan; Zhang Yi

2004-01-01

411

A fast algorithm for the constrained formulation of compressive image reconstruction and other linear inverse problems  

Microsoft Academic Search

Ill-posed linear inverse problems (ILIP), such as restoration and reconstruction, are a core topic of signal\\/image processing. A standard formulation for dealing with ILIP consists in a constrained optimization problem, where a regularization function is minimized under the constraint that the solution explains the observations sufficiently well. The regularizer and constraint are usually convex; however, several particular features of these

Manya V. Afonso; José M. Bioucas-Dias; Mário A. T. Figueiredo

2010-01-01

412

Solving Rank-Constrained LMI Problems With Application to Reduced-Order Output Feedback Stabilization  

Microsoft Academic Search

This paper presents an iterative penalty function method for solving rank-constrained linear matrix inequality (LMI) problems and illustrates its application to reduced-order output feedback stabilization. We propose a penalized objective function to replace the rank condition, so that a solution to the original nonconvex LMI feasibility problem can be obtained by solving a series of convex LMI optimization subproblems. Numerical

Seog-Joo Kim; Young-Hyun Moon; Soonman Kwon

2007-01-01

413

On Finding a Better Position of a Convex Polygon Inside a Circle to Minimize the Cutting Cost  

Microsoft Academic Search

\\u000a The problem of cutting a convex polygon P out of a planar piece of material Q (P is already drawn on Q) with minimum total cutting cost is a well studied problem in computational geometry that has been studied with several variations\\u000a such as P and Q are convex or non-convex polygons, Q is a circle, and the cuts are

Syed Ishtiaque Ahmed; Masud Hasan; Ishita Kamal Khan

2010-01-01

414

A New Differential Evolution for Constrained Optimization Problems  

Microsoft Academic Search

Differential evolution (DE) is a novel evolutionary approach capable of handling non-differentiable, nonlinear and multi-modal objective functions. Previous studies have shown that DE is an efficient, effective and robust evolutionary algorithm, but usually it takes large computational time for optimizing the computationally expensive objective function, therefore it is necessary to find a trade-off between convergence speed and robustness. For this

Jihui Zhang; Junqin Xu; Qiyuan Zhou

2006-01-01

415

Applications of genetic algorithms to optimization problems in the solvent extraction process for spent nuclear fuel  

SciTech Connect

Applications of genetic algorithms (GAs) to optimization problems in the solvent extraction process for spent nuclear fuel are described. Genetic algorithms have been considered a promising tool for use in solving optimization problems in complicated and nonlinear systems because they require no derivatives of the objective function. In addition, they have the ability to treat a set of many possible solutions and consider multiple objectives simultaneously, so they can calculate many pareto optimal points on the trade-off curve between the competing objectives in a single iteration, which leads to small computing time. Genetic algorithms were applied to two optimization problems. First, process variables in the partitioning process were optimized using a weighted objective function. It was observed that the average fitness of a generation increased steadily as the generation proceeded and satisfactory solutions were obtained in all cases, which means that GAs are an appropriate method to obtain such an optimization. Secondly, GAs were applied to a multiobjective optimization problem in the co-decontamination process, and the trade-off curve between the loss of uranium and the solvent flow rate was successfully obtained. For both optimization problems, CPU time with the present method was estimated to be several tens of times smaller than with the random search method.

Omori, Ryota, Sakakibara, Yasushi; Suzuki, Atsuyuki [Univ. of Tokyo (Japan). Dept. of Quantum Engineering and Systems Science

1997-04-01

416

Optimal investment, consumption and retirement choice problem with disutility and subsistence consumption constraints  

NASA Astrophysics Data System (ADS)

In this paper we consider a general optimal consumption-portfolio selection problem of an infinitely-lived agent whose consumption rate process is subject to subsistence constraints before retirement. That is, her consumption rate should be greater than or equal to some positive constant before retirement. We integrate three optimal decisions which are the optimal consumption, the optimal investment choice and the optimal stopping problem in which the agent chooses her retirement time in one model. We obtain the explicit forms of optimal policies using a martingale method and a variational inequality arising from the dual function of the optimal stopping problem. We treat the optimal retirement time as the first hitting time when her wealth exceeds a certain wealth level which will be determined by a free boundary value problem and duality approaches. We also derive closed forms of the optimal wealth processes before and after retirement. Some numerical examples are presented for the case of constant relative risk aversion (CRRA) utility class.

Lim, Byung Hwa; Shin, Yong Hyun; Choi, U. Jin

2008-09-01

417

The Knaster-Kuratowski-Mazurkiewicz theorem and abstract convexities  

NASA Astrophysics Data System (ADS)

The Knaster-Kuratowski-Mazurkiewicz covering theorem (KKM), is the basic ingredient in the proofs of many so-called "intersection" theorems and related fixed point theorems (including the famous Brouwer fixed point theorem). The KKM theorem was extended from Rn to Hausdorff linear spaces by Ky Fan. There has subsequently been a plethora of attempts at extending the KKM type results to arbitrary topological spaces. Virtually all these involve the introduction of some sort of abstract convexity structure for a topological space, among others we could mention H-spaces and G-spaces. We have introduced a new abstract convexity structure that generalizes the concept of a metric space with a convex structure, introduced by E. Michael in [E. Michael, Convex structures and continuous selections, Canad. J. MathE 11 (1959) 556-575] and called a topological space endowed with this structure an M-space. In an article by Shie Park and Hoonjoo Kim [S. Park, H. Kim, Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl. 197 (1996) 173-187], the concepts of G-spaces and metric spaces with Michael's convex structure, were mentioned together but no kind of relationship was shown. In this article, we prove that G-spaces and M-spaces are close related. We also introduce here the concept of an L-space, which is inspired in the MC-spaces of J.V. Llinares [J.V. Llinares, Unified treatment of the problem of existence of maximal elements in binary relations: A characterization, J. Math. Econom. 29 (1998) 285-302], and establish relationships between the convexities of these spaces with the spaces previously mentioned.

Cain, George L., Jr.; González, Luis

2008-02-01

418

Generating coefficients for optimization test problems with implicit correlation induction  

Microsoft Academic Search

We consider methods for inducing correlation between the objective function and constraint coefficients in 0-1 Knapsack, generalized assignment, capital budgeting, and set covering problems. Each of the methods that we examine is an implicit correlation-induction (ICI) method that has been featured in the literature. However, the correlation levels used in the corresponding computational experiments are typically neither quantified nor systematically

Charles H. Reilly

1997-01-01

419

Automated Knowledge Elicitation and Flowchart Optimization for Problem Diagnosis  

Microsoft Academic Search

The established procedure for problem diag- nosis in a wide variety of systems is often em- bodied in a ?owchart or decision tree. These procedures are usually authored manually, which is extremely expensive and results in ?owcharts that are di-cult to maintain and often quite ine-cient. A better diagnostic procedure would be one that automatically modifles itself in response to

Alina Beygelzimer; Mark Brodie; Jonathan Lenchner; Irina Rish

420

Individual Differences in Optimization Problem Solving: Reconciling Conflicting Results  

Microsoft Academic Search

Results on human performance on the Traveling Salesman Problem (TSP) from different laboratories show high consistency. However, one exception is in the area of individual differences. While one research group has consistently failed to find systematic individual differences across instances of TSPs (Chronicle, MacGregor and Ormerod), another group (Vickers, Lee and associates) has found individual differences both within TSP performance

Edward P. Chronicle; James N. MacGregor; Michael Lee; Thomas C. Ormerod; Peter Hughes

2008-01-01

421

SECOND ORDER NECESSARY CONDITIONS FOR OPTIMAL IMPULSIVE CONTROL PROBLEMS  

Microsoft Academic Search

Abstract. First and second order necessary conditions of optimali- ty for an impulsive control problem are presented and derived. One of the main features of these results is that no a priori normality assumptions are required and they are informative for abnormal con- trol processes as well. This feature follows fromthe fact that the conditions are derived froman extremal principle,

A. Arutyunov; V. Ja Cimovic; F. Pereira

2003-01-01

422

An optimal strategy for a conflict resolution problem  

Microsoft Academic Search

A problem of relevance to the design of multiple access protocols is the following: Let X1,...,XN be i.i.d, random variables uniformly distributed in [0,1]. We have to determine the largest Xi,1 ¿i ¿N, as follows: Given N, we pick a set A(1) ¿ [0,1] and ask \\

V. Anantharam; Pravin Varaiya

1985-01-01

423

Generating optimal Sturmian basis functions for atomic problems  

SciTech Connect

In this paper we discuss the optimization of Sturmian basis functions by studying bound atomic systems within the configuration interaction method. Our investigation clearly shows how the fulfillment of correct physical boundary conditions at short and large distances from the nucleus improves the convergence rate of the method. This is illustrated first through a one-electron atom, and then with the two-electron systems. For the ground state of the helium atom, and with 35 Sturmian functions per electron and angular momenta, we obtain an energy of -2.903 712 820 a.u., outperforming previous similar calculations [Bromley and Mitroy, Int. J. Quantum Chem. 107, 1150 (2007)].

Randazzo, J. M.; Frapiccini, A. L.; Colavecchia, F. D. [Centro Atomico Bariloche and CONICET, 8400 Bariloche, Rio Negro (Argentina); Ancarani, L. U. [Laboratoire de Physique Moleculaire et des Collisions, Universite Paul Verlaine-Metz France, F-57078 Metz (France); Gasaneo, G. [Departamento de Fisica, Universidad Nacional del Sur and CONICET, 8000 Bahia Blanca, Buenos Aires (Argentina)

2010-04-15

424

Luus-Jaakola optimization procedure for some problems in optics  

NASA Astrophysics Data System (ADS)

In today's technology an increasing use is made of materials consisting of thin layers with thicknesses in the range of a few nanometers. Applications of these types of materials can be found in integrated circuits, magnetic heads and tapes, solid-state lasers, X-ray mirrors and coated window glass, etc. They are used for their mechanical, magnetic, optical and/or electrical properties. These properties are related to the structural parameters of these materials, such as the elemental composition, thickness, roughness and number of layers in the material. The first part of this thesis explores both the thickness of layers and the number of layers in x-ray multilayer mirrors by using the Luus-Jaakola optimization procedure in order to achieve a desired reflectivity. The reflectivity of multilayer coatings shows a strong dependence on the thickness of each layer and the number of layers. In the first chapter we present and modify the Luus-Jaakola algorithm to design optical th in-film systems by optimizing the thickness of the layers as well as the number of layers. We show that the optimization model can improve the results using fewer layers of material with the Luus-Jaakola method for the design of x-ray multilayer mirrors in both the angular and spectral domains. Numerical results indicate that the proposed approach performs very competitively with other approaches. It has become possible to design optical coatings with fewer layers. This opens a new opportunity for the design of high quality optical coatings. We then apply this technique to help in the design of multilayer mirrors for a target application, such as an astronomical grazing-incidence hard X-ray telescope. These designs are compared with other author's results. Further, we present a computational study of a modification of the Luus-Jaakola method that could be used in multilayer mirrors with more than two components. Then we apply this method to determine the optical constants, thickness and root mean square roughens of the layers. Finally, in the last part of the thesis we present optimization results of phase-only sampled fiber Bragg gratings by using the modified Luus-Jaakola method. We show that it is able to produce a high number of channels with less refractive-index modulation, high reflectivity, as well as requiring fewer segments.

Al-Marzoug, Saeed M.

425

Optimal power allocation for multiuser transmit beamforming via regularized channel inversion  

Microsoft Academic Search

In this paper, we consider an optimal power allocation problem that maximizes the sum-rate of a single-cell MISO broadcast channel with regularized channel inversion (RCI) beamforming at the base station (BS). Unlike the channel inversion or zero forcing beamforming, the optimal power allocation with RCI precoding at the base station is a nonlinear non-convex optimization problem with many local optima.

Rusdha Muharar; Jamie Evans

2011-01-01

426

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

427

Application of particle swarm optimization algorithm in the heating system planning problem.  

PubMed

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. PMID:23935429

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

2013-07-01

428

Use of Generalized Network Flow Programming in Solving the Optimal Power Flow Problem.  

National Technical Information Service (NTIS)

The Optimal Power Flow problem is important in both system planning and operating environments. Due to the complexity in implementation and extensive execution times of existing OPF computer programs, there exists the need for a faster, simpler solution t...

R. E. Rice

1986-01-01

429

Enhancing GJK: computing minimum and penetration distances between convex polyhedra  

Microsoft Academic Search

The problem of tracking the distance between two convex polyhedra is finding applications in many areas of robotics, including intersection detection, collision detection, and path planning. We present new results that confirm an almost-constant time complexity for an enhanced version of Gilbert, Johnson and Keerthi's (GJK) algorithm, and also describe modifications to the algorithm to compute measures of penetration distance

Stephen Cameron

1997-01-01

430

Clustering of non-convex patterns for medical imaging  

Microsoft Academic Search

The study treats the problem of partitional clustering of non-convex patterns of arbitrary shape, with no definite analytical description of the data. A new method for calculating the distance is defined, according to a data induced metric principle. Calculation of the distance is carried out using weighted graphs. The new distance is introduced in the fuzzy k-means algorithm, and the

Isak Gath; Anna Smolyak Iskoz

1995-01-01

431

Optimum Shape of a Cooling Fin on a Convex Cylinder.  

National Technical Information Service (NTIS)

The problem considered is that of maximizing the heat dissipation of a cooling fin of fixed weight attached to a cylinder with a convex cross-section by properly tapering the fin. It is assumed that Newton's law of cooling holds and that the boundary of t...

R. J. Duffin D. K. McLain

1968-01-01

432

Designing Multi-Link Robot Arms in a Convex Polygon.  

National Technical Information Service (NTIS)

The problem of designing a k-link robot arm confined in a convex polygon that can reach any point in the polygon starting from a fixed initial configuration is considered. The links of an arm are assumed to be all of the same length. We present a necessar...

I. Suzuki M. Yamashita

1994-01-01

433

On constrained infinite-time linear quadratic optimal control  

Microsoft Academic Search

This work presents a solution to the infinite-time linear quadratic optimal control (ITLQOC) problem with state and control constraints. It is shown that a single, finite dimensional, convex program of known size can yield this solution. Properties of the resulting value function, with respect to initial conditions, are also established and are shoen to be useful in determining the aforementioned

D. Chmielewski; V. Manousiouthakis

1996-01-01

434

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

2013-05-31

435

Partially and Fully Constrained Ant Algorithms for the Optimal Solution of Large Scale Reservoir Operation Problems  

Microsoft Academic Search

This paper presents a constrained formulation of the ant colony optimization algorithm (ACOA) for the optimization of large\\u000a scale reservoir operation problems. ACO algorithms enjoy a unique feature namely incremental solution building capability.\\u000a In ACO algorithms, each ant is required to make a decision at some points of the search space called decision points. If the\\u000a constraints of the problem

M. H. Afshar; R. Moeini

2008-01-01

436

A computationally efficient iterative solution of the multidestination optimal dynamic routing problem  

Microsoft Academic Search

The dynamic routing problem for multiple destination networks is considered. The minimum time rather than total delay cost functional is employed. The problem is solved through an iterative link-by-link optimization. Each link capacity is optimally partitioned by examining the upper bounds for the evacuation time imposed through different capacity allocations for each origin\\/destination pair traffic. The computational complexity per iteration

G. I. Stassinopoulos; M. G. Kazantzakis

1991-01-01

437

Numerical Methods Based on Gaussian Quadrature and Continuous Runge-Kutta Integration for Optimal Control Problems  

Microsoft Academic Search

\\u000a This paper provides a numerical approach for solving optimal control problems governed by ordinary differential equations.\\u000a Continuous extension of an explicit, fixed step-size Runge-Kutta scheme is used in order to approximate state variables; moreover,\\u000a the objective function is discretized by means of Gaussian quadrature rules. The resulting scheme represents a nonlinear programming\\u000a problem, which can be solved by optimization algorithms.

Fasma Diele; Carmela Marangi; Stefania Ragni

2004-01-01

438

Many-Objective Optimization for Knapsack Problems Using Correlation-Based Weighted Sum Approach  

Microsoft Academic Search

In this paper, we examine the effectiveness of an EMO (Evolutionary Multi-criterion Optimization) algorithm using a correlation\\u000a based weighted sum for many objective optimization problems. Recently many EMO algorithms are proposed for various multi-objective\\u000a problems. However, it is known that the convergence performance to the Pareto-frontier becomes weak in approaches using archives\\u000a for non-dominated solutions since the size of archives

Tadahiko Murata; Akinori Taki

2009-01-01

439

A Domain Decomposition Method for the Helmholtz equation and related Optimal Control Problems  

Microsoft Academic Search

: We present an iterative domain decomposition method to solve the Helmholtzequation and related optimal control problems. The proof of convergence of this methodrelies on energy techniques. This method leads to efficient algorithms for the numerical resolutionof harmonic wave propagation problems in heterogeneous media and their control.Keywords : Domain decomposition, Helmholtz equation, Harmonic waves, Optimal control,Waveguide, Absorbing boundary conditionsAMS(MOS) subject...

Jean-david Benamou

1996-01-01

440

Grid-Based Topology Optimization of Rigid Body Mechanisms Using Different Problem Formulations  

Microsoft Academic Search

In the design process of rigid body mechanisms two main development steps can be distinguished, namely type (topology) and\\u000a dimensional synthesis. Whereas much work has already been done on solving the problem of dimensional synthesis, optimization\\u000a based approaches to topology design of rigid body mechanisms are rare.\\u000a \\u000a Unlike solving the discrete combinatorial problem of optimal mechanism topology by means of

Kai Sedlaczek; Peter Eberhard

441

Equivalence of second order optimality conditions for bang–bang control problems. Part 1: Main results  

Microsoft Academic Search

Abstract: Second order optimality conditions have been derived in the literature in two different forms. Osmolovskii (1988a, 1995, 2000, 2004) obtained second order necessary and sufficient conditions requiring that a certain quadratic form be positive (semi)-definite on a critical cone. Agrachev, Stefani, Zezza (2002) first reduced the bang-bang control problem to finite-dimensional optimization and then show that well-known sufficient optimality

N. p. Osmolovskii; H. Maurer

442

Second Order Sufficient Optimality Conditions for Some State-constrained Control Problems of Semilinear Elliptic Equations  

Microsoft Academic Search

. This paper deals with a class of optimal control problems governed by elliptic equationswith nonlinear boundary condition. The case of boundary control is studied. Pointwise constraintson the control and certain equality and set--constraints on the state are considered. Secondorder sufficient conditions for local optimality of controls are established.Key words. Boundary control, semilinear elliptic equations, sufficient optimality conditions,state constraintsAMS subject...

Eduardo Casas; Fredi Tröltzsch; Andreas Unger

2000-01-01

443

Numerical solution of optimal control problems for loaded lumped parameter systems  

NASA Astrophysics Data System (ADS)

An optimal control problem for the system of linear (with respect to phase variables) loaded ordinary differential equations with initial (local) and nonseparated multipoint (nonlocal) conditions is investigated. Necessary optimality conditions are obtained, numerical schemes of their solution are proposed, and results of numerical experiments are presented.

Abdullaev, V. M.; Aida-Zade, K. R.

2006-09-01

444

An Integer Programming Approach to the Optimal Product Line Selection Problem  

Microsoft Academic Search

A zero-one integer mathematical programming formulation is proposed to solve the optimal product line selection problem. Based on individual consumer measurements from conjoint analysis, the formulation seeks to find an optimal subset of products that is drawn from a proposed set of product alternatives with specified product characteristics. In addition to its inherent flexibility in incorporating various realistic constraints, a

Richard D. McBride; Fred S. Zufryden

1988-01-01

445

On the optimal and suboptimal nonlinear filtering problem for discrete-time systems  

Microsoft Academic Search

This paper examines optimal and suboptimal algorithms for the state filtering problem in discrete-time nonlinear systems. The optimal equations of sequential filtering are analyzed and conditions are obtained which ensure a multimodal character for the a posteriori densities. This analysis is utilized in the discussion of the performance of suboptimal linearized filters, and suggestions are made for their improvement in

M. L. ANDRADE NETTO; L. Gimeno; M. J. MENDES

1978-01-01

446

CT-ACO - hybridizing ant colony optimization with cyclic transfer search for the vehicle routing problem  

Microsoft Academic Search

Ant colony optimization (ACO) is a meta-heuristic approach to tackle hard combinatorial optimization problems. The basic component of ACO is a solution construction mechanism, which simulates the decision-making processes of ant colonies as they forage for food and find the most efficient routes from their nests to food sources. Due to its constructive nature, we hybridize the solution construction mechanism

Xiaoxia Zhang; Lixin Tang

2005-01-01

447

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

448

Evolutionary computation system for problem-tailored genetic optimization of catalytic materials  

Microsoft Academic Search

The paper addresses key problems pertaining to the commonly used evolutionary approach to optimization of catalytic materials. These are on the one hand the narrow scope of genetic algorithms developed specifically for searching optimal catalyst, on the other hand the insufficient dealing in existing implementations of genetic algorithms with mixed opti- mization. The paper outlines a program generator automatically generating

Martin Holena; David Linke; Uwe Rodemerck

2010-01-01

449

A Novel Approach to Dynamic Optimization of ODE and DAE Systems as High-Index Problems  

Microsoft Academic Search

Solution of many problems in plant operations requires determination of optimal control profi les subject to state constraints for systems modeled by ordinary differential equations (ODEs) or dif ferential-alge- braic equations (DAEs). For example, optimal temperature and\\/or feed rate profiles are important for the oper - ation of many batch reactions. Similar observations apply to reflux policies for batch distillation,

William F. Feehery; Julio R. Banga; Paul I. Barton

450

Recent developments in evolutionary computation for manufacturing optimization: problems, solutions, and comparisons  

Microsoft Academic Search

The use of intelligent techniques in the manufacturing field has been growing the last decades due to the fact that most manufacturing optimization problems are combinatorial and NP hard. This paper examines recent developments in the field of evolutionary computation for manufacturing optimization. Significant papers in various areas are highlighted, and comparisons of results are given wherever data are available.

Christos Dimopoulos; Ali M. S. Zalzala

2000-01-01

451

Ordinal Hill Climbing Algorithms for Discrete Manufacturing Process Design Optimization Problems  

Microsoft Academic Search

Thispaper introduces ordinal hill climbing algorithms for addressingdiscrete manufacturing process design optimization problems usingcomputer simulation models. Ordinal hill climbing algorithmscombine the search space reduction feature of ordinal optimizationwith the global search feature of generalized hill climbing algorithms.By iteratively applying the ordinal optimization strategy withinthe generalized hill climbing algorithm framework, the resultinghybrid algorithm can be applied to intractable discrete optimizationproblems. Computational

Kelly A. Sullivan; Sheldon H. Jacobson

2000-01-01

452

An Improved Particle Swarm Optimization for the Multi-Depot Vehicle Routing Problem  

Microsoft Academic Search

This paper proposes a formulation of the multi-depot vehicle routing problem (MDVRP) that is solved by the particle swarm optimization (PSO) algorithm. PSO is one of the evolutionary computation technique, motivated by the group organism behavior such as bird flocking or fish schooling. Compared with other search methods, such as genetic algorithm, ant colony optimization and simulated annealing algorithm, PSO

Zhang Wenjing; Jianzhong Ye

2010-01-01

453

Necessary optimality conditions in an abnormal optimization problem with equality constraints  

Microsoft Academic Search

An abnormal minimization problem with equality constraints and a finite-dimensional image is examined. Second-order necessary\\u000a conditions for this problem are given that strengthen previously known results.

A. V. Arutyunov; D. Yu. Karamzin

2006-01-01

454

DEA on Relaxed Convexity Assumptions  

Microsoft Academic Search

In a recent paper, Petersen (Petersen, N. C. 1990. Data envelopment analysis on a relaxed set of assumptions. Management Sci. 36 305--314.) proposed to relax the convexity assumptions invoked in traditional Data Envelopment Analysis (DEA). Unfortunately, the new approach is not consistent with the relaxed assumptions. Also, the efficiency evaluations in input and output spaces are based on different technologies

Peter Bogetoft

1996-01-01

455

Stability of Vector Problems of Integer Optimization: Relationship with the Stability of Sets of Optimal and Nonoptimal Solutions  

Microsoft Academic Search

Several types of stability against perturbations of vector criterion coefficients are analyzed from the same point of view for a vector integer optimization problem with quadratic criterion functions. The concept of stability is defined. Necessary and sufficient conditions are formulated and analyzed for each type of stability. The topological structure of the sets of initial data on which some solution

T. T. Lebedeva; N. V. Semenova; T. I. Sergienko

2005-01-01

456

Particle swarm and ant colony algorithms hybridized for improved continuous optimization  

Microsoft Academic Search

This paper proposes PSACO (particle swarm ant colony optimization) algorithm for highly non-convex optimization problems. Both particle swarm optimization (PSO) and ant colony optimization (ACO) are co-operative, population-based global search swarm intelligence metaheuristics. PSO is inspired by social behavior of bird flocking or fish schooling, while ACO imitates foraging behavior of real life ants. In this study, we explore a

P. S. Shelokar; Patrick Siarry; Valadi K. Jayaraman; Bhaskar D. Kulkarni

2007-01-01

457

Analytical and numerical analysis of inverse optimization problems: conditions of uniqueness and computational methods  

PubMed Central

One of the key problems of motor control is the redundancy problem, in particular how the central nervous system (CNS) chooses an action out of infinitely many possible. A promising way to address this question is to assume that the choice is made based on optimization of a certain cost function. A number of cost functions have been proposed in the literature to explain performance in different motor tasks: from force sharing in grasping to path planning in walking. However, the problem of uniqueness of the cost function(s) was not addressed until recently. In this article, we analyze two methods of finding additive cost functions in inverse optimization problems with linear constraints, so-called linear-additive inverse optimization problems. These methods are based on the Uniqueness Theorem for inverse optimization problems that we proved recently (Terekhov et al., J Math Biol 61(3):423–453, 2010). Using synthetic data, we show that both methods allow for determining the cost function. We analyze the influence of noise on the both methods. Finally, we show how a violation of the conditions of the Uniqueness Theorem may lead to incorrect solutions of the inverse optimization problem.

Zatsiorsky, Vladimir M.

2011-01-01

458

The travelling salesman problem with neighbourhoods: MINLP solution  

Microsoft Academic Search

The travelling salesman problem (TSP) with neighbourhoods extends the TSP to the case where each vertex of the tour is allowed to move in a given region. This NP-hard optimization problem has recently received increasing attention in several technical fields such as robotics, unmanned aerial vehicles, or utility management. In this paper, the problem is formulated as a non-convex mixed-integer

Iacopo Gentilini; François Margot; Kenji Shimada

2012-01-01

459

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

460

A multi-objective Artificial Bee Colony for optimizing multi-objective problems  

Microsoft Academic Search

This work proposes a multi-objective artificial bee colony (MOABC) for optimizing problems with multiple objectives. We have adapted the original Artificial Bee Colony (ABC) algorithm to multi objective problems with a grid-based approach for maintaining and adaptively assessing the Pareto front. The Pareto set is used to control the flying behaviours of the individuals and structuring the bee colony. The

Ramin Hedayatzadeh; Bahareh Hasanizadeh; Reza Akbari; Koorush Ziarati

2010-01-01

461

A new ant colony optimization algorithm for the multidimensional Knapsack problem  

Microsoft Academic Search

The paper proposes a new ant colony optimization (ACO) approach, called binary ant system (BAS), to multidimensional Knapsack problem (MKP). Different from other ACO-based algorithms applied to MKP, BAS uses a pheromone laying method specially designed for the binary solution structure, and allows the generation of infeasible solutions in the solution construction procedure. A problem specific repair operator is incorporated

Min Kong; Peng Tian; Yucheng Kao

2008-01-01

462

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

463

An extremal optimization search method for the protein folding problem: the go-model example  

Microsoft Academic Search

The protein folding problem consists of predicting the functional (native)structure of the protein given its linear sequence of amino acids. Despite extensive progress made in understanding the process of protein folding, this problem still remains extremely challenging. In this paper we introduce, implement and evaluate the Extremal Optimization method - a biologically inspired approach which has been applied very successfully

Alena Shmygelska

2007-01-01

464

A hybrid particle swarm optimization approach for distribution network reconfiguration problem  

Microsoft Academic Search

A hybrid particle swarm optimization (PSO) approach is proposed here to solve the distribution network reconfiguration (DNR) problem. This approach is a combination of the binary PSO algorithm and the discrete PSO algorithm. In the problem-solving process, the distribution network is simplified through grouping the branches, and then each group of branches is represented by one dimensional coding. Based on

Zhenkun Li; Xingying Chen; Kun Yu; Yi Sun; Haoming Liu

2008-01-01

465

Ant Colony Optimization Approaches for the Dynamic Load-Balanced Clustering Problem in Ad Hoc Networks  

Microsoft Academic Search

This paper presents three ant colony optimization (ACO) approaches for a difficult graph theoretic problem formulated from the task of computing load-balanced clusters in ad hoc networks. These three approaches contain novel strategies for adapting the search process to the new problem structure whenever an environment change occurs. An environment change occurs when nodes in the network move. Dynamic changes

Chin K. Ho; Hong T. Ewe

2007-01-01

466

Superlinearly convergent quasi-newton algorithms for nonlinearly constrained optimization problems  

Microsoft Academic Search

A class of algorithms for nonlinearly constrained optimization problems is proposed. The subproblems of the algorithms are linearly constrained quadratic minimization problems which contain an updated estimate of the Hessian of the Lagrangian. Under suitable conditions and updating schemes local convergence and a superlinear rate of convergence are established. The convergence proofs require among other things twice differentiable objective and

U. M. Garcia Palomares; O. L. Mangasarian

1976-01-01

467

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

468

An infeasible interior-point algorithm for optimal power-flow problems  

Microsoft Academic Search

This paper deals with the application of an infeasible interior point method to optimal power flow problems. Besides discussing the problem formulation, the paper offers a detailed description of the infeasible interior point algorithm; it also addresses some important implementation issues such as the determination of the barrier parameter, the choice of the initial point, and the efficient solution of

Xihui Yan; Victor H. Quintana

1996-01-01

469

A Domain Decomposition Method for the Helmholtz Equation and Related Optimal Control Problems  

Microsoft Academic Search

We present an iterative domain decomposition method to solve the Helmholtz equation and related optimal control problems. The proof of convergence of this method relies on energy techniques. This method leads to efficient algorithms for the numerical resolution of harmonic wave propagation problems in homogeneous and heterogeneous media.

Jean-David Benamou; Bruno Desprès

1997-01-01

470

Decomposition based and branch and bound global optimization approaches for the phase equilibrium problem  

Microsoft Academic Search

An increasingly popular approach when solving the phase and chemical equilibrium problem is to pose it as an optimization problem. However, difficulties are encountered due to the highly nonlinear nature of the models used to represent the behavior of the fluids, and because of the existence of multiple local solutions. This work shows how it is possible to guarantee e-global

Conor M. McDonald; Christodoulos A. Floudas

1994-01-01

471

Surrogate-Assisted Evolutionary Optimization Frameworks for High-Fidelity Engineering Design Problems  

Microsoft Academic Search

Abstract: Over the last decade, Evolutionary Algorithms (EAs) have emerged as a powerful paradigm for global optimization of multimodal functions. More recently, there has been significant interest in applying EAs to engineering design problems. However, in many complex engineering design problems where high-fidelity analysis models are used, each function evaluation may require a Computational Structural Mechanics (CSM), Computational Fluid Dynamics

Y. S. Ong; P. B. Nair; A. J. Keane; K. W. Wong

2004-01-01

472

The theoretical analysis and algorithm on a class of optimal curve fitting problems  

Microsoft Academic Search

In this paper, the theory and algorithm on a class of optimal curve fitting problems which can be extensively applied to the engineering are established and completed. With regard to the curve fitting problems, the available theories and methods are largely concerned with the spline interpolation and linear or nonlinear least squares methods, and there are lots of ripe results.

Fusheng Wang; Kecun Zhang

2006-01-01

473

A class of stochastic optimization problems with application to selective data editing  

Microsoft Academic Search

We present a class of stochastic optimization problems with constraints expressed in terms of expectation and with partial knowledge of the outcome in advance to the decision. The constraints imply that the problem cannot be reduced to a deterministic one. Since the knowledge of the outcome is relevant to the decision, it is necessary to seek the solution in a

Ignacio Arbués; Margarita González; Pedro Revilla

2012-01-01

474

A class of stochastic optimization problems with application to selective data editing  

Microsoft Academic Search

We present a class of stochastic optimization problems with constraints expressed in terms of expectation and with partial knowledge of the outcome in advance to the decision. The constraints imply that the problem cannot be reduced to a deterministic one. Since the knowledge of the outcome is relevant to the decision, it is necessary to seek the solution in a

Ignacio Arbués; Margarita González; Pedro Revilla

2010-01-01

475

Study on parameter optimization for support vector regression in solving the inverse ECG problem.  

PubMed

The typical inverse ECG problem is to noninvasively reconstruct the transmembrane potentials (TMPs) from body surface potentials (BSPs). In the study, the inverse ECG problem can be treated as a regression problem with multi-inputs (body surface potentials) and multi-outputs (transmembrane potentials), which can be solved by the support vector regression (SVR) method. In order to obtain an effective SVR model with optimal regression accuracy and generalization performance, the hyperparameters of SVR must be set carefully. Three different optimization methods, that is, genetic algorithm (GA), differential evolution (DE) algorithm, and particle swarm optimization (PSO), are proposed to determine optimal hyperparameters of the SVR model. In this paper, we attempt to investigate which one is the most effective way in reconstructing the cardiac TMPs from BSPs, and a full comparison of their performances is also provided. The experimental results show that these three optimization methods are well performed in finding the proper parameters of SVR and can yield good generalization performance in solving the inverse ECG problem. Moreover, compared with DE and GA, PSO algorithm is more efficient in parameters optimization and performs better in solving the inverse ECG problem, leading to a more accurate reconstruction of the TMPs. PMID:23983808

Jiang, Mingfeng; Jiang, Shanshan; Zhu, Lingyan; Wang, Yaming; Huang, Wenqing; Zhang, Heng

2013-07-25

476

Optimal control of a convective boundary condition in a thermistor problem  

SciTech Connect

We consider the optimal control of a two-dimensional steady-state thermistor. The problem is described by a system of two nonlinear elliptic partial differential equations with appropriate boundary conditions which model the coupling of the thermistor to its surroundings. Based on physical considerations, an objective functional to be minimized is introduced and the convective boundary coefficient is taken as the control. Existence and uniqueness of the optimal control are proven. To characterize this optimal control, the optimality system consisting of the state and adjoint equations is derived.

Hrynkiv, Volodymyr [Worcester Polytechnic Institute; Lenhart, Suzanne M [ORNL; Protopopescu, Vladimir A [ORNL

2008-01-01

477

An ant colony optimization approach to the multiple-choice multidimensional knapsack problem  

Microsoft Academic Search

In this paper, we present an ant colony optimization (ACO) approach to solve the multiple-choice multidimensional knapsack problem (MMKP). This problem concerns many real life problems, and is hard to solve due to its strong constraints and NP-hard property. The ACO approach given in this paper follows the algorithmic scheme of max-min ant system, but has some new features with

Zhigang Ren; Zuren Feng

2010-01-01

478

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

479

An approach to solving discrete vector optimization problems over a combinatorial set of permutations  

Microsoft Academic Search

Complex discrete multicriteria problems over a combinatorial set of permutations are analyzed. Some properties of an admissible\\u000a domain for a combinatorial multicriteria problem embedded into an arithmetic Euclidian space are considered. Optimality conditions\\u000a are obtained for different types of effective solutions. A new approach to solving the problems formulated is constructed\\u000a and substantiated.

N. V. Semenova; L. N. Kolechkina; A. N. Nagirna

2008-01-01

480

On the cellular convexity of complexes.  

PubMed

In this paper we discuss cellular convexity of complexes. A new definition of cellular convexity is given in terms of a geometric property. Then it is proven that a regular complex is celiularly convex if and only if there is a convex plane figure of which it is the cellular image. Hence, the definition of cellular convexity by Sklansky [7] is equivalent to the new definition for the case of regular complexes. The definition of Minsky and Papert [4] is shown to be equivalent to our definition. Therefore, aU definitions are virtually equivalent. It is shown that a regular complex is cellularly convex if and only if its minimum-perimeter polygon does not meet the boundary of the complex. A 0(n) time algorithm is presented to determine the cellular convexity of a complex when it resides in n × m cells and is represented by the run length code. PMID:21868981

Kim, C E

1981-06-01

481

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

482

Pareto optimality and Walrasian equilibria  

NASA Astrophysics Data System (ADS)

The paper concerns the study of a class of convex, constrained multiobjective optimization problems from the viewpoint of the existence issues. The main feature of the presented approach is that the classical qualification condition requiring the existence of interior points in the effective domains of functions under consideration does not hold. A variant of duality theory for multiobjective optimization problems based on the Fenchel theorem is formulated. Next, by using very recent results on the Walrasian general equilibrium model of economy obtained in Naniewicz [Z. Naniewicz, Pseudo-monotonicity and economic equilibrium problem in reflexive Banach space, MathE Oper. Res. 32 (2007) 436-466] the conditions ensuring the existence of Pareto optimal solutions for the class of multiobjective optimization problems are established. The concept of the proper efficiency is used as the solution notion. Finally, a new version of the second fundamental theorem of welfare economics is presented.

Naniewicz, Zdzislaw

2008-05-01

483

An Approximation Algorithm for MINIMUM CONVEX COVER with Logarithmic Performance Guarantee  

Microsoft Academic Search

The problem Minimum Convex Cover of covering a given polygon with a minimum number of (possibly overlapping) convex poly- gons is known to be NP-hard, even for polygons without holes (3). We propose a polynomial-time approximation algorithm for this problem for polygons with or without holes that achieves an approximation ratio of O(log n), where n is the number of

Stephan Eidenbenz; Peter Widmayer

2001-01-01

484

Convex profiles from asteroid lightcurves  

NASA Astrophysics Data System (ADS)

A lightcurve inversion method that yields a two-dimensional convex profile is introduced. The number of parameters that characterize the profile is limited only by the number of Fourier harmonics used to represent the parent lightcurve. The implementation of the method is outlined by a recursive quadratic programming algorithm, and its application to photoelectric lightcurves and radar measurements is discussed. Special properties of the lightcurves of geometrically scattering ellipsoids are pointed out, and those properties are used to test the inversion method and obtain a criterion for judging whether any lightcurve could actually be due to such an object. Convex profiles for several asteroids are shown, and the method's validity is discussed from a physical as well as purely statistical point of view.

Ostro, S. J.; Connelly, R.

1984-03-01

485

Compatibility of subsystem states and convex geometry  

SciTech Connect

The subsystem compatibility problem, which concerns the question of whether a set of subsystem states are compatible with a state of the entire system, has received much study. Here we attack the problem from a new angle, utilizing the ideas of convexity that have been successfully employed against the separability problem. Analogously to an entanglement witness, we introduce the idea of a compatibility witness, and prove a number of properties about these objects. We show that the subsystem compatibility problem can be solved numerically and efficiently using semidefinite programming, and that the numerical results from this solution can be used to extract exact analytic results, an idea which we use to disprove a conjecture about the subsystem problem made by Butterley et al. [Found. Phys. 36, 83 (2006)]. Finally, we consider how the ideas can be used to tackle some important variants of the compatibility problem; in particular, the case of identical particles (known as N-representability in the case of fermions) is considered.

Hall, William [Department of Mathematics, University of York, Heslington, York YO10 5DD (United Kingdom)

2007-03-15

486

Probability-based least square support vector regression metamodeling technique for crashworthiness optimization problems  

NASA Astrophysics Data System (ADS)

This paper presents a crashworthiness design optimization method based on a metamodeling technique. The crashworthiness optimization is a highly nonlinear and large scale problem, which is composed various nonlinearities, such as geometry, material and contact and needs a large number expensive evaluations. In order to obtain a robust approximation efficiently, a probability-based least square support vector regression is suggested to construct metamodels by considering structure risk minimization. Further, to save the computational cost, an intelligent sampling strategy is applied to generate sample points at the stage of design of experiment (DOE). In this paper, a cylinder, a full vehicle frontal collision is involved. The results demonstrate that the proposed metamodel-based optimization is efficient and effective in solving crashworthiness, design optimization problems.

Wang, Hu; Li, Enying; Li, G. Y.

2011-03-01

487

A deterministic annealing algorithm for a combinatorial optimization problem using replicator equations  

NASA Astrophysics Data System (ADS)

We have proposed an optimization method for a combinatorial optimization problem using replicator equations. To improve the solution further, a deterministic annealing algorithm may be applied. During the annealing process, bifurcations of equilibrium solutions will occur and affect the performance of the deterministic annealing algorithm. In this paper, the bifurcation structure of the proposed model is analyzed in detail. It is shown that only pitchfork bifurcations occur in the annealing process, and the solution obtained by the annealing is the branch uniquely connected with the uniform solution. It is also shown experimentally that in many cases, this solution corresponds to a good approximate solution of the optimization problem. Based on the results, a deterministic annealing algorithm is proposed and applied to the quadratic assignment problem to verify its performance.

Tsuchiya, K.; Nishiyama, T.; Tsujita, K.

2001-02-01

488

Implementation and comparison of PSO-based algorithms for multi-modal optimization problems  

NASA Astrophysics Data System (ADS)

This paper aims to compare the global search capability and overall performance of a number of Particle Swarm Optimization (PSO) based algorithms in the context solving the Dynamic Economic Dispatch (DED) problem which takes into account the operation limitations of generation units such as valve-point loading effect as well as ramp rate limits. The comparative study uses six PSO-based algorithms including the basic PSO and hybrid PSO algorithms using a popular benchmark test IEEE power system which is 10-unit 24-hour system with non-smooth cost functions. The experimental results show that one of the hybrid algorithms that combines the PSO with both inertia weight and constriction factor, and the Gaussian mutation operator (CBPSO-GM) is promising in achieving the near global optimal of a non-linear multi-modal optimization problem, such as the DED problem under the consideration.

Sriyanyong, Pichet; Lu, Haiyan

2013-10-01

489

Simulation-based multi-objective optimization of a real-world scheduling problem  

Microsoft Academic Search

This paper presents a successful application of sim ulation- based multi-objective optimization of a complex rea l-world scheduling problem. Concepts of the implemented simula- tion-based optimization architecture are described, as well as how different components of the architecture are im- plemented. Multiple objectives are handled in the o ptimi- zation process by considering the decision makers' prefer- ences using both

Anna Persson; Henrik Grimm; Ng Amos; Thomas Lezama; Jonas Ekberg; Stephan Falk; Peter Stablum

2006-01-01

490

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

491

Hybridizing the harmony search algorithm with a spreadsheet ‘Solver’ for solving continuous engineering optimization problems  

Microsoft Academic Search

In this article, a hybrid global–local optimization algorithm is proposed to solve continuous engineering optimization problems. In the proposed algorithm, the harmony search (HS) algorithm is used as a global-search method and hybridized with a spreadsheet ‘Solver’ to improve the results of the HS algorithm. With this purpose, the hybrid HS–Solver algorithm has been proposed. In order to test the

M. Tamer Ayvaz; Ali Haydar Kayhan; Huseyin Ceylan; Gurhan Gurarslan

2009-01-01

492

A new relaxation algorithm for the time optimal control problem of step motors  

Microsoft Academic Search

The free end-velocity time-optimal control of a bifilar-wound hybrid step motor is considered. The necessary conditions for the optimal control are derived from motor, load, and driver circuit models using Pontryagin's minimum principle. A reduced-order relaxation method, involving forward\\/backward integrations, is presented for finding the solution to the nonlinear two-point boundary value problem specified by the necessary conditions, including generation

R. H. Brown; Y. Zhu; X. Feng

1989-01-01

493

Study on Multi-Depots Vehicle Scheduling Problem and Its Two-Phase Particle Swarm Optimization  

Microsoft Academic Search

\\u000a To get global solution in multi-depots vehicle scheduling problem (MDVSP), MDVSP models are established. Two-phase particle\\u000a swarm optimization (TPPSO) is established to solve MDVSP. The optimization course are as follow: first phase, set up goods\\u000a number dimension particle position vector, vector’s every column corresponds to goods, vector elements are random vehicle\\u000a serial number, thus we can assign goods to vehicles.

Suxin Wang; Leizhen Wang; Huilin Yuan; Meng Ge; Ben Niu; Weihong Pang; Yuchuan Liu

2009-01-01

494

Nonconvex variational problem with recursive integral functionals in Sobolev spaces: Existence and representation  

NASA Astrophysics Data System (ADS)

The purpose of this paper is twofold. First, we present the existence theorem of an optimal trajectory in a nonconvex variational problem with recursive integral functionals by employing the norm-topology of a weighted Sobolev space. We show the continuity of the integral functional and the compactness of the set of admissible trajectories. Second, we show that a recursive integrand is represented by a normal integrand under the conditions guaranteeing the existence of optimal trajectories. We also demonstrate that if the recursive integrand satisfies the convexity conditions, then the normal integrand is a convex function. These results are achieved by the application of the representation theorem in Lp-spaces.

Sagara, Nobusumi

2007-03-01

495

Optimization of the time-dependent traveling salesman problem with Monte Carlo methods  

NASA Astrophysics Data System (ADS)

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.

Bentner, Johannes; Bauer, Günter; Obermair, Gustav M.; Morgenstern, Ingo; Schneider, Johannes

2001-09-01

496

Solution of the optimal plant location and sizing problem using simulated annealing and genetic algorithms  

SciTech Connect

In the optimal plant location and sizing problem it is desired to optimize cost function involving plant sizes, locations, and production schedules in the face of supply-demand and plant capacity constraints. We will use simulated annealing (SA) and a genetic algorithm (GA) to solve this problem. We will compare these techniques with respect to computational expenses, constraint handling capabilities, and the quality of the solution obtained in general. Simulated Annealing is a combinatorial stochastic optimization technique which has been shown to be effective in obtaining fast suboptimal solutions for computationally, hard problems. The technique is especially attractive since solutions are obtained in polynomial time for problems where an exhaustive search for the global optimum would require exponential time. We propose a synergy between the cluster analysis technique, popular in classical stochastic global optimization, and the GA to accomplish global optimization. This synergy minimizes redundant searches around local optima and enhances the capable it of the GA to explore new areas in the search space.

Rao, R.; Buescher, K.L.; Hanagandi, V.

1995-12-31

497

Positive Schemes for Air Pollution Problems, Optimal Location of Industrial Enterprises and Optimization of their Emissions  

Microsoft Academic Search

Environmental problems are becoming more and more important for our world and their importance will even increase in the future. High pollution of air, water and soil may cause damage to plants, animals and humans. Therefore, the development of industry must be coupled with the protection of the environment, especially in fast-growing countries like Vietnam. In this talk we deal

Matthias Ehrhardt

498

Global Minimization for Continuous Multiphase Partitioning Problems Using a Dual Approach  

Microsoft Academic Search

This paper is devoted to the optimization problem of continuous multi-partitioning, or multi-labeling, which is based on a\\u000a convex relaxation of the continuous Potts model. In contrast to previous efforts, which are tackling the optimal labeling\\u000a problem in a direct manner, we first propose a novel dual model and then build up a corresponding duality-based approach.\\u000a By analyzing the dual

Egil Bae; Jing Yuan; Xue-Cheng Tai

2011-01-01

499

The Hamilton-Jacobi theory for solving optimal feedback control problems with general boundary conditions  

NASA Astrophysics Data System (ADS)

This dissertation presents a general methodology for solving the optimal feedback control problem in the context of Hamiltonian system theory. It is first formulated as a two point boundary value problem for a standard Hamiltonian system, and the associated phase flow is viewed as a canonical transformation. Then relying on the Hamilton-Jacobi theory, we employ generating functions to develop a unified methodology for solving a variety of optimal feedback control formulations with general types of boundary conditions. The major accomplishment is to establish a theoretical connection between the optimal cost function and a special kind of generating function. Guided by this recognition, we are ultimately led to a new flexible representation of the optimal feedback control law for a given system, which is adjustable to various types of boundary conditions by algebraic conversions and partial differentiations. This adaptive property provides a substantial advantage over the classical dynamic programming method in the sense that we do not need to solve the Hamilton-Jacobi-Bellman equation repetitively for varying types of boundary conditions. Furthermore for a special type of boundary condition, it also enables us to work around an inherent singularity of the Hamilton-Jacobi-Bellman equation by a special algebraic transformation. Taking full advantage of these theoretical insights, we develop a systematic algorithm for solving a class of optimal feedback control problems represented by smooth analytic Hamiltonians, and apply it to problems with different characteristics. Then, broadening the practical utility of generating functions for problems where the relevant Hamiltonian is non-smooth, we construct a pair of Cauchy problems from the associated Hamilton-Jacobi equations. This alternative formulation is justified by solving problems with control constraints which usually feature non-smoothness in the control logic. The main result of this research establishes that the optimal feedback control problem can be solved by the generating functions of the canonical solution flow corresponding to the necessary conditions. This result demonstrates the power of analyzing the optimal feedback control problem within the comprehensive field of classical Hamiltonian system theory.

Park, Chandeok

500

On-line time-optimal path tracking for robots  

Microsoft Academic Search

This paper focuses on time-optimal path tracking, which involves planning of robot motions along prescribed geo- metric paths. Starting from a discretized convex reformulation of time-optimal path tracking problems, a log-barrier based batch solution method is presented which allows to rapidly obtain an approximate solution with smooth actuator torques. Based on this batch method, a recursive variant is derived for

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

2009-01-01