Intransitivity in Coevolution

We review and investigate the current status of intransitivity as a potential obstacle in coevolution. Pareto-Coevolution avoids intransitivity by translating any standard superiority relation into a transitive Pareto-dominance relation. Even for transitive problems though, cycling is possible. Recently however, algorithms that provide monotonic progress for Pareto-Coevolution have become available. The use of such algorithms avoids cycling, whether caused by intransitivity or not. We investigate this in experiments with two intransitive test problems, and find that the IPCA and LAPCA archive methods establish monotonic progress on both test problems, thereby substantially outperforming the same method without an archive.