Schema analysis of average fitness in multiplicative landscape

Abstract

By applying the schema theorem, we study the effects of crossover in Genetic Algorithms with the multiplicative fitness function. On this landscape, the analytical expression of the exact schema theorem can be obtained, and this makes it possible to carry out the mathematical investigation of genetic operators. We consider the average fitness under the action of selection, mutation and crossover. To do this, we give the expressions for the average and variance of fitness in terms of schema frequencies. The theoretical results are compared with numerical experiments. © Springer-Verlag Berlin Heidelberg 2003.