Document Type

Article

Publication Title

Evolutionary Computation

Publisher

Massachusetts Institute of Technology Press

Publication Date

1995

Volume

3

Issue

4

Disciplines

Computer Sciences

Abstract

The infinite population simple genetic algorithm is a discrete dynamical system model of a genetic algorithm. It is conjectured that trajectories in the model 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 fimess preserves the finiteness of the fixed point set. These results allow 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.

Keywords

Genetic algorithms, fixed point, transversality, infinite population model, dynamical system

DOI

10.1162/evco.1995.3.3.299

Comments

Finiteness of the Fixed Point Set for the Simple Genetic Algorithm, (with Michael D. Vose), Evolutionary Computation, vol. 3, number 4 (1995). View original published article at 10.1162/evco.1995.3.3.299.

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