An experimental investigation of variation operators in reference-point based many-objective optimization

Reference-point based multi-objective evolutionary algorithms (MOEAs) have shown promising performance in manyobjective optimization. However, most of existing research within this area focused on improving the environmental selection procedure, and little work has been done on the effect of variation operators. In this paper, we conduct an experimental investigation of variation operators in a typical reference-point based MOEA, i.e., NSGA-III. First, we provide a new NSGA-III variant, i.e., NSGA-III-DE, which introduces differential evolution (DE) operator into NSGA-III, and we further examine the effect of two main control parameters in NSGA-III-DE. Second, we have an experimental analysis of the search behavior of NSGA-III-DE and NSGA-III. We observe that NSGA-III-DE is generally better at exploration whereas NSGA-III normally has advantages in exploitation. Third, based on this observation, we present two other NSGA-III variants, where DE operator and genetic operators are simply combined to reproduce solutions. Experimental results on several benchmark problems show that very encouraging performance can be achieved by three suggested new NSGA-III variants. Our work also indicates that the performance of NSGA-III is significantly bottlenecked by its variation operators, providing opportunities for the study of the other alternative ones.