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Genetic algorithms in random environments: two examples
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  • Published: 06 June 2005

Genetic algorithms in random environments: two examples

  • Jean Bérard1 

Probability Theory and Related Fields volume 133, pages 123–140 (2005)Cite this article

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Abstract

We study the asymptotic behavior of two mutation-selection genetic algorithms in random environments. First, the state space is a supercritical Galton-Watson tree conditioned upon non-extinction and the objective function is the distance from the root. In the second case, the state space is a regular tree and the objective function is a sample of a tree-indexed random walk. We prove that, after n steps, the algorithms find the maximum possible value of the objective function up to a finite random constant.

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Authors and Affiliations

  1. Ex-Laboratoire de Probabilités, Combinatoire and Statistique; Université Claude Bernard, Lyon I, France

    Jean Bérard

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  1. Jean Bérard
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Correspondence to Jean Bérard.

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Bérard, J. Genetic algorithms in random environments: two examples. Probab. Theory Relat. Fields 133, 123–140 (2005). https://doi.org/10.1007/s00440-004-0419-y

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  • Received: 12 June 2001

  • Revised: 08 November 2004

  • Published: 06 June 2005

  • Issue Date: September 2005

  • DOI: https://doi.org/10.1007/s00440-004-0419-y

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Keywords

  • Objective Function
  • Genetic Algorithm
  • State Space
  • Stochastic Process
  • Asymptotic Behavior
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