  Many real optimisation problems lead to multimodal domains and so require the
identification of multiple optima. Niching methods have been developed to
maintain the population diversity, to investigate many peaks in parallel and to
reduce the effect of genetic drift. Using rigorous runtime analysis, we analyse
for the first time two well known niching methods: probabilistic crowding and
restricted tournament selection (RTS). We incorporate both methods into a
$(\mu+1)~EA$ on the bimodal function Twomax where the goal is to find two
optima at opposite ends of the search space. In probabilistic crowding, the
offspring compete with their parents and the survivor is chosen proportionally
to its fitness. On Twomax probabilistic crowding fails to find any reasonable
solution quality even in exponential time. In RTS the offspring compete against
the closest individual amongst $w$ (window size) individuals. We prove that RTS
fails 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 are
accompanied by experimental studies that match the theoretical results and also
shed light on parameters not covered by the theoretical results.

Neural and Evolutionary Computing