When is non-deteriorating population update in MOEAs beneficial?

Population update in multi-objective evolutionary algorithms (MOEAs) can be seen as an archiving process, namely, updating the population by comparing it with new solutions and deciding which ones to keep and which ones to discard. It thus may be useful for a population update mechanism to have some desirable archiving properties; for example, non-deteriorating, i.e., the population does not accept solutions that are inferior to solutions eliminated in the past. Unfortunately, none of mainstream MOEAs hold such a property. On the other hand, different from the archiving process which focuses on how to choose the best solutions from a set of candidate solutions, population update in MOEAs also cares about where these candidate solutions come from and what they are used for. It has been reported recently that allowing some dominated solutions in the population may help the search jump out of local optima. In this paper, we investigate the above seemingly “contradictory” observations, and aim to answer the question of whether holding the property non-deteriorating is beneficial or detrimental to MOEAs. We examine three representative MOEAs and modify their population update rules to make them non-deteriorating. We find that holding it is not necessarily beneficial for all the algorithms, but is generally useful, particularly for those whose population update mechanism does not hold any other desirable properties (e.g., set-monotone and limit-stable) like NSGA-II.