Hyperbolic fixed points are typical in the space of mixing operators for the infinite population genetic algorithm

Authors:
Christina Hayes;Tomáš Gedeon
Affiliations:
Montana State University, Bozeman, Montana;Montana State University, Bozeman, Montana
Venue:
GECCO '05 Proceedings of the 7th annual workshop on Genetic and evolutionary computation
Year:
2005

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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.