A visual demonstration of convergence properties of cooperative coevolution

Abstract

We introduce a model for cooperative coevolutionary algorithms (CCEAs) using partial mixing, which allows us to compute the expected long-run convergence of such algorithms when individuals' fitness is based on the maximum payoff of some N evaluations with partners chosen at random from the other population. Using this model, we devise novel visualization mechanisms to attempt to qualitatively explain a difficult-to-conceptualize pathology in CCEAs: the tendency for them to converge to suboptimal Nash equilibria. We further demonstrate visually how increasing the size of N, or biasing the fitness to include an ideal-collaboration factor, both improve the likelihood of optimal convergence, and under which initial population configurations they are not much help. © Springer-Verlag 2004.