Distance-based subset selection revisited

In this paper, we revisit the distance-based subset selection (DSS) algorithm in evolutionary multi-objective optimization. First, we show one drawback of the DSS algorithm, i.e., a uniformly distributed solution set cannot always be selected. Then, we show that this drawback can be overcome by maximizing the uniformity level of the selected solution set, which is defined by the minimum distance between two solutions in the solution set. Furthermore, we prove that the DSS algorithm is a greedy inclusion algorithm with respect to the maximization of the uniformity level. Based on this conclusion, we generalize DSS as a subset selection problem where the objective is to maximize the uniformity level of the subset. In addition to the greedy inclusion DSS algorithm, a greedy removal algorithm and an iterative algorithm are proposed for the generalized DSS problem. We also extend the Euclidean distance in the original DSS to other widely-used and user-defined distances. We conduct extensive experiments on solution sets over different types of Pareto fronts to compare the three DSS algorithms with different distances. Our results suggest the usefulness of the generalized DSS for selecting a uniform subset. The effect of using different distances on the selected subsets is also analyzed.