Theoretical and Empirical Properties of the Genetic Algorithm as a Numerical Optimizer

Abstract

We investigate the basic form of the genetic algorithm as an optimization technique. Its failure to maximize a simple function of a string of 50 binary variables prompts a closer study of Holland's “schema theorem” and we find the implications of this result to be much weaker than are often claimed. Further theoretical results and exact calculations for simple problems provide an understanding of how the genetic algorithm works and why it failed in our original application. We show that the algorithm can be fine tuned to succeed in that problem but only by introducing features that could cause serious difficulties in harder problems.