An Improved Riesz s-Energy-Based Archive to Handle Dominance Resistant Solutions

Abstract

Recently, the potential energy functions, which come from physics, have been successfully applied to increase the performance of multi-objective evolutionary algorithms (MOEAs). The increase in performance is notable in terms of the generation of evenly distributed Pareto front approximations regardless of the associated manifold geometry. A remarkable potential energy function is the Riesz s-energy which has been employed to assess Pareto front approximations and to promote the design of selection mechanisms of MOEAs, such as archiving strategies. However, an important issue of the Riesz s-energy and some other potential energy functions is that they reward the existence of dominance resistant solutions (DRSs) in a Pareto front approximation even though DRSs are harmful solutions. In this paper, we propose a mechanism to improve the performance of a Riesz s-energy-based archive which is embedded into the MOEA based on decomposition (MOEA/D). Our proposed mechanism incorporates the density-based clustering of applications with noise (DBSCAN) and a penalization function into the Riesz s-energy-based archive to let it handle DRSs. Our experimental results show that this improved archive allows MOEA/D to generate, with a higher probability, DRS-free Pareto front approximations when tackling especially multi-frontal multi-objective optimization problems.