Genericity of the Fixed Point Set for the Infinite Population Genetic Algorithm

摘要

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 paper shows that for a typical mixing operator, the fixed point set of G is finite. That is, an arbitrarily small perturbation of the mixing operator will result in a map G with finitely many fixed points. Further, any sufficiently small perturbation of the mixing operator preserves the finiteness of the fixed point set.