An empirical study on the handling of overlapping solutions in evolutionary multiobjective optimization

Abstract

We focus on the handling of overlapping solutions in evolutionary multiobjective optimization (EMO) algorithms. First we show that there exist a large number of overlapping solutions in each population when EMO algorithms are applied to multiobjective combinatorial optimization problems with only a few objectives. Next we implement three strategies to handle overlapping solutions. One strategy is the removal of overlapping solutions in the objective space. In this strategy, overlapping solutions in the objective space are removed during the generation update phase except for only a single solution among them. As a result, each solution in the current population has a different location in the objective space. Another strategy is to remove overlapping solutions so that each solution in the current population has a different location in the decision space. The other strategy is the modification of Pareto ranking where overlapping solutions in the objective space are allocated to different fronts. As a result, each solution in each front has a different location in the objective space. Effects of each strategy on the performance of the NSGA-II algorithm are examined through computational experiments on multiobjective 0/1 knapsack problems, multiobjective flowshop scheduling problems, and multiobjective fuzzy rule selection problems.