Modeling the Dynamics of a Changing Range Genetic Algorithm

The paper extends an approach of modeling the dynamics of the genetic algorithm that based on the methods from statistical physics. These methods are applied to describe the effect of an adjustment of a search space size of GA according to a power law on the macroscopic statistical properties of population such as the average fitness and the variance fitness of population. An interaction of the various genetic algorithm operators and how these interactions give rise to optimal parameters values is studied. The equations of motion are derived for the one-max problem that expressed the macroscopic statistical properties of population after reproductive genetic operators and an adjustment of a search space size in terms of those prior to the operation. Predictions of the theory are compared with experiments and are shown to predict the average fitness and the variance fitness of the final population accurately.