Finiteness of the Fixed Point Set for the Simple Genetic Algorithm Alden H. Wright Computer Science Dept. The University of Montana Missoula, MT 59812-1008 wright@cs.umt.edu Michael D. Vose Computer Science Dept. The University of Tennessee Knoxville, TN 37996-1301 vose@cs.utk.edu ABSTRACT The Infinite Population Simple Genetic Algorithm is a discrete dynamical system model of a genetic algorithm. Trajectories in the model are conjectured to always converge to fixed points. This paper shows that an arbitrarily small perturbation of the fitness will result in a model with a finite number of fixed points. Moreover, every sufficiently small perturbation of fitness preserves finiteness of the fixed point set. These results enable proofs and constructions that require finiteness of the fixed point set. For example, applying the stable manifold theorem to a fixed point requires the hyperbolicity of the differential of the transition map of the genetic algorithm, which requires (among other things) that the fixed point be isolated.