The Domination Game: Dilating Bubbles to Fill Up Pareto Fronts

Vasco Coelho, Daniele M. Papetti, Andrea Tangherloni, Paolo Cazzaniga, Daniela Besozzi, Marco S. Nobile

Abstract:

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.