On the Runtime Analysis of the Clearing Diversity-Preserving Mechanism

Clearing is a niching method inspired by the principle of assigning the available resources among a niche to a single individual. The clearing procedure supplies these resources only to the best individual of each niche: the winner. So far, its analysis has been focused on experimental approaches that have shown that clearing is a powerful diversity-preserving mechanism. Using rigorous runtime analysis to explain how and why it is a powerful method, we prove that a mutation-based evolutionary algorithm with a large enough population size, and a phenotypic distance function always succeeds in optimising all functions of unitation for small niches in polynomial time, while a genotypic distance function requires exponential time. Finally, we prove that with phenotypic and genotypic distances clearing is able to find both optima for Twomax and several general classes of bimodal functions in polynomial expected time. We use empirical analysis to highlight some of the characteristics that makes it a useful mechanism and to support the theoretical results

Empirical analysis of diversity-preserving mechanisms on example landscapes for multimodal optimisation

Many diversity-preserving mechanisms have been developed to reduce the risk of premature convergence in evolutionary algorithms and it is not clear which mechanism is best. Most multimodal optimisation problems studied empirically are restricted to real-parameter problems and are not accessible to theoretical analysis, while theoreticians analyse the simple bimodal function TwoMax. This paper looks to narrow the gap between both approaches. We perform an extensive empirical study involving 9 common diversity mechanisms on Jansen-Zarges multimodal function classes (Jansen and Zarges, PPSN 2016) that allow to control important problem features while still being amenable to theoretical analysis. This allows us to study functions with various degrees of multimodality and to explain the results in the light of previous theoretical works. We show which mechanisms are able to find and maintain a large number of distant optima, escape from local optima, and which fail to locate even a single peak