Department of Mathematics
A Generic Property of the Infinite Population Genetic
Algorithm
Christina Hayes
Montana State University
Genetic Algorithms (GAs) are a class of stochastic search algorithms based on the idea of natural selection. I will give a brief introduction to GAs, as well as a dynamical systems model of GAs acting on an infinite population. We will then study an infinite population model for genetic algorithms, where the iteration of the algorithm corresponds to an iteration of a map G. The map G is a composition of a selection operator and a mixing operator, where the latter models effects of both mutation and crossover. We examine the hyperbolicity of fixed points of this model. We show that for a typical (generic) mixing operator all the fixed points are hyperbolic.
All interested persons are welcome.