Population Sizing for Sharing Methods

Sharing methods promote the formation and maintenance of stable subpopulations or niches in genetic algorithms. This paper derives, for various models of sharing, lower bounds on the population size required to maintain, with probability , a xed number of niches. The rst model assumes all niches are equivalent with respect to tness and that crossover is minimally disruptive. The next two models allow niches to diier with respect to tness. The nal model takes into account the disruptive eeects of crossover. GAs with sharing are run on seven test problems in optimization and classiication, using population sizes derived from the models.