Study on Improving Efficiency of Multi-Objective Evolutionary Algorithm with Large Population by M2M Decomposition and Elitist Mate Selection Scheme

Multi-objective evolutionary algorithms (MOEAs) are an active research topic for multi-objective design problems. MOEAs are population-based global optimization algorithms and it is said that the performance of the MOEAs depends on the population size. It is well-known that the population size should be large enough to guarantee the diversity of the solution while the large population size makes the convergence slow. This study is on the trade-off of the convergence speed and the diversity of the solutions and the trade-off is visualized from the view point of the efficiency of the algorithms against the population size. It is clearly shown that there is an optimal population size with regard to the efficiency for each problem and for a target quality of the solutions. To shift the optimal population size toward larger, i.e, to make the convergence fast with good diversity property, two methods are employed. First method is the multi-objective-to-multi-objective (M2M) decomposition and the other is a newly proposed elitist mate selection based on binary tournament (termed EBT). Experimental studies on MOP test instances show that NSGA-II incorporated with the M2M decomposition and the EBT (NSGA-II-EM2M in short) shows the highest and fastest performance with better efficiency over NSGA-II and NSGA-II-M2M with different mate selection schemes.