Effects of dominance resistant solutions on the performance of evolutionary multi-objective and many-objective algorithms

Dominance resistant solutions (DRSs) in multi-objective problems have very good values for some objectives and very bad values for other objectives. Whereas DRSs are far away from the Pareto front, they are hardly dominated by other solutions due to some very good objective values. It is well known that the existence of DRSs severely degrades the search ability of Pareto dominance-based algorithms such as NSGA-II and SPEA2. In this paper, we examine the effect of DRSs on the search ability of NSGA-II on the DTLZ test problems with many objectives. We slightly change their problem formulation to increase the size of the DRS region. Through computational experiments, we show that DRSs have a strong negative effect on the search ability of NSGA-II whereas they have almost no effect on MOEA/D with the PBI function. We also show that a slightly modified NSGA-II for decreasing the negative effect of DRSs works well on many-objective DTLZ test problems (its performance is similar to NSGA-III and MOEA/D). These results suggest that DTLZ is not an appropriate test suite for evaluating many-objective evolutionary algorithms. This issue is further addressed through computational experiments on newly formulated test problems with no distance function.