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Many real optimisation problems lead to multimodal domains and so require theidentification of multiple optima. Niching methods have been developed tomaintain the population diversity, to investigate many peaks in parallel and toreduce the effect of genetic drift. Using rigorous runtime analysis, we analysefor the first time two well known niching methods: probabilistic crowding andrestricted tournament selection (RTS). We incorporate both methods into a$(\mu+1)~EA$ on the bimodal function Twomax where the goal is to find twooptima at opposite ends of the search space. In probabilistic crowding, theoffspring compete with their parents and the survivor is chosen proportionallyto its fitness. On Twomax probabilistic crowding fails to find any reasonablesolution quality even in exponential time. In RTS the offspring compete againstthe closest individual amongst $w$ (window size) individuals. We prove that RTSfails if $w$ is too small, leading to exponential times with high probability.However, if w is chosen large enough, it finds both optima for Twomax in time$O(\mu n \log{n})$ with high probability. Our theoretical results areaccompanied by experimental studies that match the theoretical results and alsoshed light on parameters not covered by the theoretical results.

Runtime Analysis of Probabilistic Crowding and Restricted Tournament Selection for Bimodal Optimisation