Abstract
This paper presents a Markov model for the convergence of multi-parent genetic algorithms (MPGAs). The proposed model formulates the variation of gene frequency caused by selection, multi-parent crossover, and mutation. In addition, it reveals the pairwise equivalence phenomenon in the number of parents and identifies the correlation between this number and the mean fitness in the OneMax problem. The good fit between theoretical and experimental results demonstrate the capability of this model. Moreover, the superiority of multi-parent crossover in convergence fitness over 2-parent crossover is validated theoretically as well as empirically. © 2005 IEEE.