Generic properties of the infinite population genetic algorithm

Abstract

The infinite population model for the genetic algorithm, where the iteration of the genetic algorithm corresponds to an iteration of a map G, is a discrete dynamical system. The map G is a composition of a selection operator and a mixing operator, where the latter models the effects of both mutation and crossover. This dissertation examines the finiteness and hyperbolicity of fixed points of this model. For a typical mixing operator, the fixed point set of G is finite and all fixed points are hyperbolic.