Evolutionary many-objective optimization by NSGA-II and MOEA/D with large populations

Evolutionary multiobjective optimization (EMO) is an active research area in the field of evolutionary computation. EMO algorithms are designed to find a non-dominated solution set that approximates the entire Pareto front of a multiobjective optimization problem. Whereas EMO algorithms usually work well on two-objective and three-objective problems, their search ability is degraded by the increase in the number of objectives. One difficulty in the handling of many-objective problems is the exponential increase in the number of non-dominated solutions necessary for approximating the entire Pareto front. A simple countermeasure to this difficulty is to use large populations in EMO algorithms. In this paper, we examine the behavior of EMO algorithms with large populations (e.g., with 10,000 individuals) through computational experiments on multiobjective and many-objective knapsack problems with two, four, six, eight and ten objectives. We examine two totally different algorithms: NSGA-II and MOEA/D. NSGA-II is a Pareto dominance-based algorithm while MOEA/D uses scalarizing functions. Their search ability is examined for various specifications of the population size under the fixed computation load. That is, we use the total number of examined solutions as the stopping condition of each algorithm. Thus the use of a very large population leads to the termination at an early generation (e.g., 20th generation). It is demonstrated through computational experiments that the use of too large populations makes NSGA-II very slow and inefficient. On the other hand, MOEA/D works well even when it is executed with a very large population. We also discuss why MOEA/D works well even when the population size is unusually large.