A tri-phase multimodal evolutionary search performance profile on the 'Hierarchical if and only if' problem.
Martin John Oates, David Corne, Roger J. Loader · 2000
Previous work by the authors has explored performance profiles of simple evolutionary algorithms over a range of problems. These studies have revealed a consistent bimodal feature, where the optimal mutation rate occurs at the trough between two peaks in convergence time. However, careful examination revealed anomalies suggesting higher modality features in the performance profile under certain conditions. Here we report on a detailed examination of the performance profile of Watson et al's H-IFF problem, aimed at further exploring and understanding this multimodal performance profile. We find that the series of troughs correspond to a series of mutation rates which each seem tuned towards increasingly better suboptima. Further, by examining the curves of mean fitness, convergence time, and the variance of convergence time, we can identify a three-phase nature to the profile; i.e.: search behaviour cycles through three distinct phases, which repeat in synchronisation with peaks and troughs. These findings seem important in relation to the need for robust and reliable parameter tuning.