On the runtime analysis of fitness sharing mechanisms

Fitness sharing is a popular diversity mechanism implementing the idea that similar individuals in the population have to share resources and thus, share their fitnesses. Previous runtime analyses of fitness sharing studied a variant where selection was based on populations instead of individuals. We use runtime analysis to highlight the benefits and dangers of the original fitness sharing mechanism on the well-known test problem TwoMax, where diversity is crucial for finding both optima. In contrast to population-based sharing, a (2+1) EA in the original setting does not guarantee finding both optima in polynomial time; however, a (μ+1) EA with μ ≥ 3 always succeeds in expected polynomial time. We further show theoretically and empirically that large offspring populations in (μ+λ) EAs can be detrimental as overpopulation can make clusters of search points go extinct.