Modeling crossover-induced linkage in genetic algorithms

The dynamics of a genetic algorithm undergoing ranking selection, mutation, and two-point crossover for the ones-counting problem is studied using a statistical mechanics approach. This approach has been used previously to study this problem, but with uniform crossover. Two-point crossover induces additional linkage between nearby loci which changes the dynamics significantly. To account for this linkage, the evolution of the auto-correlation function is incorporated into a model of the dynamics. This complicates the analysis and requires several additional approximations to be made. Nevertheless, the model we derive is shown to capture the main features of the dynamics and is in good agreement with simulations.