THE DYNAMICS OF A CHANGING RANGE GENETIC ALGORITHM UNDER STABILIZING SELECTION

The formalism is presented for modeling of a genetic algorithm (GA) with an adjustment of a search space size. The formalism for modeling of GA with an adjustment of a search space size assumes that the environment and the population form a unique system. In this paper, the formalism is applied to a problem which exhibits an interesting dynamics reminiscent of stabilizing selection in population biology. The equations of motion was derived 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.