On the Approximation of the Entire Pareto Front of a Constrained Multi-objective Optimization Problem

Angel E. Rodriguez-Fernandez, Carlos Ignacio Hernández Castellanos, Oliver Schütze

Abstract: So far, many constraint-handling techniques (CHTs) exist that allow specialized multi-objective evolutionary algorithms (MOEAs) to deal with constrained multi-objective optimization problems (CMOPs). In contrast, all existing external archivers that yield certain approximation qualities in the limit still assume the feasibility of each incoming candidate solution. While this is acceptable for unconstrained or lightly constrained MOPs, this assumption is inadequate for the consideration of problems with complex domains. In this study, we make a first effort to investigate how these external archivers can be prepared for CMOPs. To this end, we discuss if and how existing CHTs can be leveraged. In this study, we consider the problem of capturing the entire Pareto front (ideally in the mathematical sense). As the base algorithm we will take \(ArchiveUpdateP_Q\) that stores all non-dominated solutions found during the run of the algorithm. Our discussion and results indicate that while existing CHTs work adequately, they come with certain issues, such as introducing additional parameters that need adjustment, lacking theoretical results, or incurring a certain computational overhead. Finally, we performe a numerical analysis, integrating several MOEAs with the investigated CHTs and comparing the performance of all methods using HV and \(\varDelta _p\) as indicators.