The Tunneling Algorithm for the Global Minimization of Functions

Levy, A. V.; Montalvo, Antonio

doi:10.1137/0906002

Cited by 409 publications

(160 citation statements)

References 5 publications

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“…Otherwise, we keep trying for this value of m until an imposed CPU time limit is reached. This strategy lies in two facts: (a) a stochastic global optimization method based on multistart strategies is used for the process of looking for a global minimizer of (20), and (b) we have the ability of recognizing that a global minimizer was found only if the global minimum of the instance being solved is zero. The whole procedure is described by Algorithm 4.1.…”

Section: Methodsmentioning

confidence: 99%

“…If, for a given m, a minimizer of (20) with null objective function is found, the value of m is increased by one and the process continues. Otherwise, we keep trying for this value of m until an imposed CPU time limit is reached.…”

Section: Methodsmentioning

confidence: 99%

“…In this subsection, we describe different simple alternatives for generating initial guesses to find a stationary point of (20) at Step 4 of Algorithm 4.1. We considered trivial initial random guesses that do not make use of any previously obtained solution.…”

Section: Plain Alternatives For Multistart Initial Guessesmentioning

confidence: 99%

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Packing circles within ellipses

Birgin

Bustamante

Callisaya

et al. 2013

Int Trans Operational Res

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. AbstractThe problem of packing circles within ellipses is considered in the present paper. A new ellipse-based system of coordinates is introduced by means of which a closed formula to compute the distance of an arbitrary point to the boundary of an ellipse exists. Nonlinear programming models for some variants of 2D and 3D packing problems involving circular items and elliptical objects are given. The resulting models are medium-sized highly nonlinear challenging nonlinear programming problems for which a global solution is sought. For this purpose, multistart strategies are carefully and thoroughly explored. Numerical experiments are exhibited.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Packing circles within ellipses

Birgin

Bustamante

Callisaya

et al. 2013

Int Trans Operational Res

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show abstract

“…The Schubert function ( f 16 ) has multiple local and global optima [2,14]. The number of local optima increases exponentially with the dimension.…”

Section: Schubert Functionmentioning

confidence: 99%

Self-adaptive randomized and rank-based differential evolution for multimodal problems

Urfalıoḡlu

Arıkan

2011

J Glob Optim

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Differential Evolution (DE) is a widely used successful evolutionary algorithm (EA) based on a population of individuals, which is especially well suited to solve problems that have non-linear, multimodal cost functions. However, for a given population, the set of possible new populations is finite and a true subset of the cost function domain. Furthermore, the update formula of DE does not use any information about the fitness of the population. This paper presents a novel extension of DE called Randomized and Rank-based Differential Evolution (R2DE) and its self-adaptive version SAR2DE to improve robustness and global convergence speed on multimodal problems by introducing two multiplicative terms in the DE update formula. The first term is based on a random variate of a Cauchy distribution, which leads to a randomization. The second term is based on ranking of individuals, so that R2DE exploits additional information provided by the population fitness. In extensive experiments conducted with a wide range of complexity settings, we show that the proposed heuristics lead to an overall improvement in robustness and speed of convergence compared to several global optimization techniques, including DE, Opposition based Differential Evolution (ODE), DE with Random Scale Factor (DERSF) and the self-adaptive Cauchy distribution based DE (NSDE).

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“…The Tunneling Algorithm (TA) that is a gradient-based optimization technique is one of the deterministic global optimizations [2] . On the other hand, the GA which is population-based optimization technique belongs to the stochastic global optimization technique [3] .…”

Section: Introductionmentioning

confidence: 99%

Differential evolution as the global optimization technique and its application to structural optimization

Kitayama

Arakawa

Yamazaki

2011

Applied Soft Computing

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In this paper, the basic characteristics of the Differential Evolution (DE) are examined. Thus, one is the meta-heuristics, and the other is the global optimization technique. It is said that DE is the global optimization technique, and also belongs to the meta-huristics. Indeed, DE can find the global minimum through numerical experiments. However, there are no proofs and useful investigations with regard to such comments. In this paper, the DE is compared with the Generalized Random Tunneling Algorithm (GRTA) and the Particle Swarm Optimization (PSO) that are the global optimization techniques for continuous design variables. Through the examinations, some common characteristics as the global optimization technique are clarified in this paper. Through benchmark test problems including structural optimization problems, the search ability of DE as the global optimization technique is examined.

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The Tunneling Algorithm for the Global Minimization of Functions

Cited by 409 publications

References 5 publications

Packing circles within ellipses

Packing circles within ellipses

Self-adaptive randomized and rank-based differential evolution for multimodal problems

Differential evolution as the global optimization technique and its application to structural optimization

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