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18
Global optimization by multilevel coordinate search
 J. Global Optimization
, 1999
"... Abstract. Inspired by a method by Jones et al. (1993), we present a global optimization algorithm based on multilevel coordinate search. It is guaranteed to converge if the function is continuous in the neighborhood of a global minimizer. By starting a local search from certain good points, an impro ..."
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Cited by 73 (11 self)
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Abstract. Inspired by a method by Jones et al. (1993), we present a global optimization algorithm based on multilevel coordinate search. It is guaranteed to converge if the function is continuous in the neighborhood of a global minimizer. By starting a local search from certain good points, an improved convergence result is obtained. We discuss implementation details and give some numerical results.
A LocallyBiased Form Of The Direct Algorithm
 Journal of Global Optimization
, 2001
"... . In this paper we propose a form of the DIRECT algorithm that is strongly biased toward local search. This form should do well for small problems with a single global minimizer and only a few local minimizers. We motivate our formulation with some results on how the original formulation of the DIRE ..."
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Cited by 27 (4 self)
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. In this paper we propose a form of the DIRECT algorithm that is strongly biased toward local search. This form should do well for small problems with a single global minimizer and only a few local minimizers. We motivate our formulation with some results on how the original formulation of the DIRECT algorithm clusters its search near a global minimizer. We report on the performance of our algorithm on a suite of test problems and observe that the algorithm performs particularly well when termination is based on a budget of function evaluations. Key words. DIRECT, local clustering, local bias 1. Introduction. The DIRECT (DIviding RECTangles) algorithm [13, 14] is a pattern search method (in the sense of [17]) that balances local and global search in a attempt to efficiently find a global optimizer. Other deterministic sampling methods, such as implicit filtering [9, 15], MDS [6], HookeJeeves [10], or NelderMead [16], drive an approximate gradient to zero and are not designed for g...
Extensions to the Taguchi Method of Product Design
, 1991
"... The Taguchi method of product design is an experimental approximation to minimizing the expected value of target variance for certain classes of problems. Taguchi’s method is extended to designs which involve variables each of which has a range of values all of which must be satisfied (necessity), a ..."
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Cited by 20 (6 self)
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The Taguchi method of product design is an experimental approximation to minimizing the expected value of target variance for certain classes of problems. Taguchi’s method is extended to designs which involve variables each of which has a range of values all of which must be satisfied (necessity), and designs which involve variables each of which has a range of values any of which might be used (possibility). Tuning parameters, as a part of the design process, are also demonstrated within Taguchi’s method. The method is also extended to solve design problems with constraints, invoking the methods of constrained optimization. Finally, the Taguchi method uses a factorial method to search the design space, with a confined definition of an optimal solution. This is compared with other methods of searching the design space and their definitions of an optimal solution.
The TOMLAB NLPLIB Toolbox for Nonlinear Programming. Advanced Modeling and Optimization
, 1999
"... The paper presents the toolbox NLPLIB TB 1.0 (NonLinear Programming LIBrary) � a set of Matlab solvers, test problems, graphical and computational utilities for unconstrained and constrained optimization, quadratic programming, unconstrained and constrained nonlinear least squares, boxbounded globa ..."
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Cited by 9 (7 self)
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The paper presents the toolbox NLPLIB TB 1.0 (NonLinear Programming LIBrary) � a set of Matlab solvers, test problems, graphical and computational utilities for unconstrained and constrained optimization, quadratic programming, unconstrained and constrained nonlinear least squares, boxbounded global optimization, global mixedinteger nonlinear programming, and exponential sum model tting. NLPLIB TB, like the toolbox OPERA TB for linear and discrete optimization, is a part of TOMLAB � an environment in Matlab for research and teaching in optimization. TOMLAB currently solves small and medium size dense problems. Presently, NLPLIB TB implements more than 25 solver algorithms, and it is possible to call solvers in the Matlab Optimization Toolbox. MEX le interfaces are prepared for seven Fortran and C solvers, and others are easily added using the same type of interface routines. Currently, MEX le interfaces have beendeveloped for MINOS, NPSOL, NPOPT, NLSSOL, LPOPT, QPOPT and LSSOL. There are four ways to solve a problem: by a direct call to the solver routine or a call to amultisolver driver routine, or interactively, using the Graphical
Reformulation and Convex Relaxation Techniques for Global Optimization
 4OR
, 2004
"... Many engineering optimization problems can be formulated as nonconvex nonlinear programming problems (NLPs) involving a nonlinear objective function subject to nonlinear constraints. Such problems may exhibit more than one locally optimal point. However, one is often solely or primarily interested i ..."
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Cited by 9 (7 self)
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Many engineering optimization problems can be formulated as nonconvex nonlinear programming problems (NLPs) involving a nonlinear objective function subject to nonlinear constraints. Such problems may exhibit more than one locally optimal point. However, one is often solely or primarily interested in determining the globally optimal point. This thesis is concerned with techniques for establishing such global optima using spatial BranchandBound (sBB) algorithms.
Offline handwritten Chinese character recognition by radical decomposition
 ACM Trans. Asian Lang. Inform. Process
, 2003
"... Offline handwritten Chinese character recognition is a very hard patternrecognition problem of considerable practical importance. Two popular approaches are to extract features holistically from the character image or to decompose characters structurally into component parts—usually strokes. Here w ..."
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Cited by 7 (0 self)
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Offline handwritten Chinese character recognition is a very hard patternrecognition problem of considerable practical importance. Two popular approaches are to extract features holistically from the character image or to decompose characters structurally into component parts—usually strokes. Here we take a novel approach, that of decomposing into radicals on the basis of image information (i.e., without first decomposing into strokes). During training, 60 examples of each radical were represented by “landmark ” points, labeled semiautomatically, with radicals in different characteristic positions treated as distinctly different radicals. Kernel principalcomponent analysis then captured the main (nonlinear) variations around the mean radical. During the recognition, the dynamic tunneling algorithm was used to search for optimal shape parameters in terms of chamfer distance minimization. Considering character composition as a Markov process in which up to four radicals are combined in some assumed sequential order, we can recognize complete, hierarchicallycomposed characters by using the Viterbi algorithm. This gave a character recognition rate of 93.5 % characters correct (writerindependent) on a test set of 430,800 characters from 2,154 character classes composed of 200 radical categories, which is comparable to the best reported results in the literature. Although the initial semiautomatic landmark labeling is time consuming,
An adaptive restart implementation of DIRECT
 In International Conference on Continuous Optimization
, 2004
"... Abstract. This paper is concerned with the algorithmic behavior of the DIRECT (DIviding RECTangles) algorithm. We show that DIRECT is sensitive to additive scaling, and this sensitivity can affect convergence. We present a modified version of the algorithm, and illustrate the effectiveness of our mo ..."
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Cited by 7 (0 self)
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Abstract. This paper is concerned with the algorithmic behavior of the DIRECT (DIviding RECTangles) algorithm. We show that DIRECT is sensitive to additive scaling, and this sensitivity can affect convergence. We present a modified version of the algorithm, and illustrate the effectiveness of our modification with numerical results.
Global Optimization with the DIRECT Algorithm
, 2005
"... der the direction of C.T. Kelley.) This work describes theoretical results, and practical improvements to the DIRECT Algorithm, a direct search global optimization algorithm for boundconstrained problems. We rigorously show that a subsequence of the points sampled by the algorithm satisfy first o ..."
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Cited by 6 (1 self)
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der the direction of C.T. Kelley.) This work describes theoretical results, and practical improvements to the DIRECT Algorithm, a direct search global optimization algorithm for boundconstrained problems. We rigorously show that a subsequence of the points sampled by the algorithm satisfy first order necessary conditions for both smooth and nonsmooth problems. We show linear convergence of the algorithm for linear problems, and demonstrate why our analysis cannot be extended to more general problems. We analyze a parameter of DIRECT, and show that it negatively affects the performance of the algorithm. A modified version of the DIRECT is introduced. Test examples are used to demonstrate the effectiveness of the modified algorithm. We apply DIRECT to six wellfield optimization problems from the literature. We collect data on the problems with DIRECT, and utilize statistical methods to glean information from the data about the wellfield problems.
Combinatorial Problem Solving Using Randomized Dynamic Tunneling on A Production System
, 1995
"... Levy and Montalvo, Yao, and Shima individually proposed tunneling algorithms. The tunneling algorithms employ analogy to tunnel effect in physics, and are used to optimize continuous systems. The present paper proposes a method of solving combinatorial problems using a type of randomized dynamic tun ..."
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Cited by 5 (0 self)
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Levy and Montalvo, Yao, and Shima individually proposed tunneling algorithms. The tunneling algorithms employ analogy to tunnel effect in physics, and are used to optimize continuous systems. The present paper proposes a method of solving combinatorial problems using a type of randomized dynamic tunneling technique. This method is based on a computational model called CCM*. CCM* is an extended version of the Chemical Casting Model (CCM). CCM was proposed by the author toward developing a method of solving open and incompletelyspecified problems that may change while being solved, using selforganizing computation. The 01 integer programming problem is solved using CCM* with a very simple rule and an evaluation function. CCM* allows us to escape from local maxima by composing the rule dynamically and randomly. This cannot be done by using the original production rule as is. Our experiments show that approximate solutions can be found more rapidly by CCM* than by using a branchandb...