The Domination Game: Dilating Bubbles to Fill Up Pareto Fronts

Multi-objective optimization algorithms might struggle in finding optimal dominating solutions, especially in real-case scenarios where problems are generally characterized by non-separability, non-differentiability, and multi-modality issues. An effective strategy that already showed to improve the outcome of optimization algorithms consists in manipulating the search space, in order to explore its most promising areas. In this work, starting from a Pareto front identified by an optimization strategy, we exploit Local Bubble Dilation Functions (LBDFs) to manipulate a locally bounded region of the search space containing non-dominated solutions. We tested our approach on the benchmark functions included in the DTLZ and WFG suites, showing that the Pareto front obtained after the application of LBDFs is most of the time characterized by an increased hyper-volume value. Our results confirm that LBDFs are an effective means to identify additional non-dominated solutions that can improve the quality of the Pareto front.