A Parametric Study of Crossover Operators in Multi-objective Evolutionary Algorithm

The performance of Multi-Objective Evolutionary Algorithms (MOEAs) depends on the various parameter settings such as population size, generation size, crossover, mutation and so on. It is often difficult to know the appropriate parameter setting for a real-world optimization problem in advance. Besides, the optimal parameter values might depend on each optimization problem and MOEA itself. However, there are few studies for investigating the effect of parameters even in benchmark problems. Therefore, in this study, the effects on performance due to the crossover operators and MOEAs are widely investigated by using eight benchmark problems, including DTLZ and WFG benchmark problems. The number of objectives is set to three and six. We consider five major crossover operators: Simulated Binary crossover (SBX), Simplex crossover (SPX), Differential Evolution operator (DE), Parent Centric crossover (PCX), and Unimodal Normal Distribution crossover (UNDX). As MOEAs, we adopt Non-dominated sorting genetic algorithm-II (NSGAII), Non-dominated sorting genetic algorithm-III (NSGA-III),-Dominance-based Evolutionary Algorithm (-MOEA), Indicator-Based Evolutionary Algorithm (IBEA) and Multi-Objective Evolutionary Algorithm with decomposition (MOEA/D) in this study. The experimental results on benchmark problems show that the effect of the crossover operator on each MOEA is almost the same in both three and six objectives. This indicates that the knowledge has been obtained so far could adapt to the other MOEAs and more than three objectives. In addition, parameters of some crossover operators such as SBX have little impact on the performance. This indicates that these crossover operators can be set to a value used so far without the need of tuning.