Hyperbolicity of the fixed point set for the simple genetic algorithm |
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Authors: | Christina Hayes,Tomá &scaron Gedeon |
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Affiliation: | Department of Mathematical Sciences, Montana State University, Bozeman, MT 59715, United States |
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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. |
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Keywords: | Genetic algorithm Generic property Hyperbolic fixed point |
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