The dynamics of a changing range genetic algorithm

The formalism is presented for modelling of a genetic algorithm (GA) with an adjustment of a search space size, which assumes that the environment and the population form a unique system; it establishes a dynamic balance and convergence towards an optimal solution. The paper describes the effect of an adjustment of a search space size of GA on the macroscopic statistical properties of population such as the average fitness and the variance fitness of Population. The equations of motion were 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. Copyright (C) 2009 John Wiley & Sons, Ltd.