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February 2002 Global Optimization with Exploration/Selection Algorithms and Simulated Annealing
Olivier François
Ann. Appl. Probab. 12(1): 248-271 (February 2002). DOI: 10.1214/aoap/1015961163


This article studies a stochastic model of an evolutionary algorithm that evolves a “population” of potential solutions to a minimization problem. The minimization process is based on two operators. First, each solution is regarded as an individual that attempts a random search on a graph, involving a probabilistic operator called exploration. The second operator is called selection. This deterministic operator creates interaction between individuals. The convergence of the evolutionary process is described within the framework of simulated annealing. It can be quantified by means of two quantities called the critical height and the optimal convergence exponent, which both measure the difficulty of the algorithm to deal with the minimization problem. This work describes the critical height for large enough population sizes. Explicit bounds are given for the optimal convergence exponent, using a few geometric quantities. As an application, this work allows comparisons of the evolutionary strategy with independent parallel runs of the simulated annealing algorithm, and it helps deciding when one method should be preferred to the other.


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Olivier François. "Global Optimization with Exploration/Selection Algorithms and Simulated Annealing." Ann. Appl. Probab. 12 (1) 248 - 271, February 2002.


Published: February 2002
First available in Project Euclid: 12 March 2002

zbMATH: 1012.60066
MathSciNet: MR1890064
Digital Object Identifier: 10.1214/aoap/1015961163

Primary: 60J10 , 92D15

Keywords: Evolutionary algorithms , generalized simulated annealing

Rights: Copyright © 2002 Institute of Mathematical Statistics


Vol.12 • No. 1 • February 2002
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