Effects of removing overlapping solutions on the performance of the NSGA-II algorithm

The focus of this paper is the handling of overlapping solutions in evolutionary multiobjective optimization (EMO) algorithms. In the application of EMO algorithms to some multiobjective combinatorial optimization problems, there exit a large number of overlapping solutions in each generation. We examine the effect of removing overlapping solutions on the performance of EMO algorithms. In this paper, overlapping solutions are removed from the current population except for a single solution. We implement two removal strategies of overlapping solutions. One is the removal of overlapping solutions in the objective space. In this strategy, one solution is randomly chosen among the overlapping solutions with the same objective vector and left in the current population. The other overlapping solutions with the same objective vector are removed from the current population. As a result, each solution in the current population has a different location in the objective space. It should be noted that the overlapping solutions in the objective space are not necessary the same solution in the decision space. Thus we also examine the other strategy where the overlapping solutions in the decision space are removed from the current population except for a single solution. As a result, each solution in the current population has a different location in the decision space. The effect of removing overlapping solutions is examined through computational experiments where each removal strategy is combined into the NSGA-II algorithm.