Behavior of EMO algorithms on many-objective optimization problems with correlated objectives

Recently it has been pointed out in many studies that evolutionary multi-objective optimization (EMO) algorithms with Pareto dominance-based fitness evaluation do not work well on many-objective problems with four or more objectives. In this paper, we examine the behavior of well-known and frequently used EMO algorithms such as NSGA-II, SPEA2 and MOEA/D on many-objective problems with correlated or dependent objectives. First we show that good results on many-objective 0/1 knapsack problems with randomly generated objectives are not obtained by Pareto dominance-based EMO algorithms (i.e., NSGA-II and SPEA2). Next we show that the search ability of NSGA-II and SPEA2 is not degraded by the increase in the number of objectives when they are highly correlated or dependent. In this case, the performance of MOEA/D is deteriorated. As a result, NSGA-II and SPEA2 outperform MOEA/D with respect to the convergence of solutions toward the Pareto front for some many objective problems. Finally we show that the addition of highly correlated or dependent objectives can improve the performance of EMO algorithms on two-objective problems in some cases.