Riesz s-energy-based Reference Sets for Multi-Objective optimization

Jesús Guillermo Falcón-Cardona, Hisao Ishibuchi, Carlos A. Coello Coello

Abstract: Currently, reference sets, which are a collection of feasible or infeasible points in objective space, are the backbone of several multi-objective evolutionary algorithms (MOEAs) and quality indicators (QIs). For both MOEAs and QIs, an important question is how to construct the reference set regardless of the dimensionality of the objective space, preserving well-diversified solutions. The Simplex-Lattice-Design method (SLD) that constructs a set of convex weights in a simplex, has been usually used to define reference sets. However, it is not a good option since Pareto fronts with irregular geometries cannot be completely intersected by the weight vectors. In this paper, we propose a tool based on the Riesz s-energy to generate reference sets exhibiting good diversity properties. Our experimental results support the Riesz s-energy-based reference sets as a better option due to their invariance to the Pareto front shape and the objective space dimensionality.