Analysis of diversity mechanisms for optimisation in dynamic environments with low frequencies of change

Abstract

Evolutionary dynamic optimisation has become one of the most active research areas in evolutionary computation. We consider the BALANCE function for which the poor performance of the (1+1) EA at low frequencies of change has been shown in the literature. We analyse the impact of populations and diversity mechanisms towards the robustness of evolutionary algorithms with respect to frequencies of change. We rigorously prove that for each population size mu, there exists a sufficiently low frequency of change such that the (μ+1) EA without diversity requires expected exponential time. Furthermore we prove that a crowding as well as a genotype diversity mechanism do not help the (μ+1) EA. On the positive side we prove that, independent of the frequency of change, a fitness-diversity mechanism turns the runtime from exponential to polynomial. Finally, we show how a careful use of fitness-sharing together with a crowding mechanism is effective already with a population of size 2.