Analyzing Cooperative Coevolution with Evolutionary Game Theory

The task of understanding coevolutionary algorithms is a very difficult one. These algorithms search landscapes which are in some sense adaptive. As a result, the dynamical behaviors of coevolutionary systems can frequently be even more complex than traditional evolutionary algorithms (EAs). Moreover, traditional EA theory tells us little about coevolutionary algorithms. One major question that has yet to be clearly addressed is whether or not coevolutionary algorithms are well–suited for optimization tasks. Although this question is equally applicable to competitive, as well as cooperative approaches, answering the question for cooperative coevolutionary algorithms is perhaps more attainable. Recently, evolutionary game theoretic (EGT) models have begun to be used to help analyze the dynamical behaviors of coevolutionary algorithms. One type of EGT model which is already reasonably well understood are multi–population symmetric games. We believe these games can be used to analytically model cooperative coevolutionary algorithms. This paper introduces our analysis framework, explaining how and why such models may be generated. It includes some examples illustrating specific theoretical and empirical analyses. We demonstrate that using our framework, a better understanding for the degree to which cooperative coevolutionary algorithms can be used for optimization can be achieved.