Study of evolution in genetic algorithms by eigen's theory including crossover operator

A theory representing the dynamics of infinite population genetic algorithms (GAs) is given by using Eigen's (1971) evolution model. The effect of crossover, which was neglected in Eigen's original theory of molecular evolution, is included to study the evolution of infinite population GAs. In this paper, we present a theory of GA dynamics, in which we give a coupled form of discrete time equations for GA evolution including the crossover process. It is shown that the Walsh analysis of allele frequencies provides a very powerful tool for studying evolutionary processes by mutation and crossover. A new theory is applied to the GA on the multiplicative landscape, for which we have an analytical solution. The theoretical result is compared with numerical GA experiments.