On the Effect of Populations in Evolutionary Multi-Objective Optimisation

Multi-objective evolutionary algorithms (MOEAs) have become increasingly popular as multi-objective problem solving techniques. An important open problem is to understand the role of populations in MOEAs. We present two simple bi-objective problems which emphasise when populations are needed. Rigorous runtime analysis points out an exponential runtime gap between the population-based algorithm Simple Evolutionary Multi-objective Optimiser (SEMO) and several single individual-based algorithms on this problem. This means that among the algorithms considered, only the population-based MOEA is successful and all other algorithms fail.