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 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.
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