CRI-EMOA: A Pareto-Front Shape Invariant Evolutionary Multi-objective Algorithm

Abstract

The use of multi-objective evolutionary algorithms (MOEAs) that employ a set of convex weight vectors as search directions, as a reference set or as part of a quality indicator has been widely extended. However, a recent study indicates that these MOEAs do not perform very well when tackling multi-objective optimization problem (MOPs), having different Pareto front geometries. Hence, it is necessary to propose MOEAs whose good performance is not strongly depending on certain Pareto front shapes. In this paper, we propose a Pareto-front shape invariant MOEA that combines the individual effect of two indicator-based density estimators. We selected the weakly Pareto-compliant IGD\(^+\) indicator to promote convergence and the Riesz s-energy indicator that leads to uniformly distributed point sets for the large class of rectifiable d-dimensional manifolds. Our proposed approach, called CRI-EMOA, is compared with respect to MOEAs that adopt convex weight vectors (NSGA-III, MOEA/D and MOMBI2) as well as to MOEAs not using this set of vectors (\(\varDelta _p\)-MOEA and GDE-MOEA) on MOPs belonging to the test suites DTLZ, DTLZ\(^{-1}\), WFG and WFG\(^{-1}\). Our experimental results show that CRI-EMOA outperforms the considered MOEAs, regarding the hypervolume indicator and the Solow-Polasky indicator, on most of the test problems and that its performance does not depend on the Pareto front shape of the problems.