When Coevolutionary Algorithms Exhibit Evolutionary Dynamics

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 a variety of techniques have been proposed to use external or objective measures to help in analysis, there are clearly properties of fitness payoff (e.g., intransitivity) which call such methods into question in certain contexts. 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. We also discuss terminological difficulties in the coevolution literature, and present a detailed description of external measures presently in use in the literature.