On the Robustness of Lexicase Selection to Contradictory Objectives

Lexicase and epsilon-lexicase selection are state of the art parent selection techniques for problems featuring multiple selection criteria. Originally, lexicase selection was developed for cases where these selection criteria are unlikely to be in conflict with each other, but preliminary work suggests it is also a highly effective many-objective optimization algorithm. However, to predict whether these results generalize, we must understand lexicase selection's performance on contradictory objectives. Prior work has shown mixed results on this question. Here, we develop theory identifying circumstances under which lexicase selection will succeed or fail to find a Pareto-optimal solution. To make this analysis tractable, we restrict our investigation to a theoretical problem with maximally contradictory objectives. Ultimately, we find that lexicase and epsilon-lexicase selection each have a region of parameter space where they are incapable of optimizing contradictory objectives. Outside of this region, however, they perform well despite the presence of contradictory objectives. Based on these findings, we propose theoretically-backed guidelines for parameter choice. Additionally, we identify other properties that may affect whether a many-objective optimization problem is a good fit for lexicase or epsilon-lexicase selection.