An alternative hypervolume-based selection mechanism for multi-objective evolutionary algorithms

Abstract

In this paper, we are interested in selection mechanisms based on the hypervolume indicator with a particular emphasis on the mechanism used in an improved version of the S metric selection evolutionary multi-objective algorithm (SMS-EMOA) called iSMS-EMOA, which exploits the locality property of the hypervolume. Here, we propose a new selection scheme which approximates the contribution of solutions to the hypervolume and it is designed to preserve the locality property exploited by iSMS-EMOA. This approach is proposed as an alternative to the use of exact hypervolume calculations and is aimed for solving many-objective optimization problems. The proposed approach is called "approximate version of the improved SMS-EMOA (aviSMS-EMOA)" and is validated using standard test problems (with three or more objectives) and performance indicators taken from the specialized literature. Our preliminary results indicate that our proposed approach is a good alternative to solve many-objective optimization problems, if we consider both quality in the solutions and running time required to obtain them because it outperforms two versions of the original SMS-EMOA that approximate the contributions to the hypervolume, it outperforms MOEA/D using penalty boundary intersection and it is competitive with respect to the original SMS-EMOA in several of the test problems adopted. Also, its computational cost is reasonable (it is slower than MOEA/D, but faster than SMS-EMOA).