Guaranteeing Coevolutionary Objective Measures

The task of understanding the dynamics of coevolutionary algorithms or comparing performance between such algorithms is complicated by the fact the internal fitness measures are subjective. Though several techniques have been proposed to use external or objective measures to help in analysis, there are clearly properties of fitness payoff, like intransitivity, for which these techniques are ineffective. We feel that a principled approach to this problem is to first establish the theoretical bounds to guarantee objective measures in one CEA model; from there one can later examine the effects of deviating from the assumptions made by these bounds. To this end, we present a model of competitive fitness assessment with a single population and non-parametric selection (such as tournament selection), and show minimum conditions and examples under which an objective measure exists, and when the dynamics of the coevolutionary algorithm are identical to those of a traditional EA.