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Hyperbolicity of the fixed point set for the simple genetic algorithm

Authors
Journal
Theoretical Computer Science
0304-3975
Publisher
Elsevier
Publication Date
Volume
411
Issue
25
Identifiers
DOI: 10.1016/j.tcs.2010.02.009
Keywords
  • Genetic Algorithm
  • Generic Property
  • Hyperbolic Fixed Point
Disciplines
  • Computer Science
  • Mathematics

Abstract

Abstract We study an infinite population model for the genetic algorithm, where the iteration of the algorithm corresponds to an iteration of a map G . The map G is a composition of a selection operator and a mixing operator, where the latter models effects of both mutation and crossover. We examine the hyperbolicity of fixed points of this model. We show that for a typical mixing operator all the fixed points are hyperbolic.

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