Difficulties in Evolutionary Multiobjective Optimization for Many-Objective Optimization Problems and Their Scalability Improvement Techniques

Abstract

In this paper, we examine the behavior of evolutionary multiobjective optimization (EMO) algorithms to clarify the difficulties in their scalability to many-objective optimization problems. Whereas EMO algorithms usually work well on two-objective problems, it has also been reported that they do not work well on many-objective problems. First, we examine the behavior of the most well-known and frequently-used Pareto-based EMO algorithm (i.e., NSGA-II) on many-objective 0/1 knapsack problems. Experimental results show that the search ability of NSGA-II is severely deteriorated by the increase in the number of objectives. This is because the selection pressure toward the Pareto front is severely weakened by the increase in the number of non-dominated solutions. Next we briefly review some approaches to the scalability improvement of EMO algorithms to many-objective problems. Then we examine their effects on the search ability of NSGA-II. Experimental results show that the improvement in the convergence of solutions to the Pareto front often leads to the decrease in their diversity.