On the role of population size and niche radius in fitness sharing

In this paper, we propose a characterization of the dynamic behavior of an evolutionary algorithm (EA) with fitness sharing as a function of both the niche radius and the population size. Such a characterization, given in terms of the mean and the standard deviation of the number of niches found during the evolution, can be applied to any EA employing a proportional selection mechanism and does not make any assumption on either the fitness landscape or the internal parameters of the EA itself. On the basis of the proposed characterization, a method for estimating the optimal values for the population size and the niche radius without any a priori information on the fitness landscape is presented and tested on a standard set of functions. The proposed method also provides the best solution for the problem at hand, i.e., the solution obtained in correspondence of such optimal values, at no additional cost.