2 research outputs found
Runtime Analysis of Probabilistic Crowding and Restricted Tournament Selection for Bimodal Optimisation
Many real optimisation problems lead to multimodal domains and so require the identifi-
cation 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 (µ+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(µn 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