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