Selecting a small number of representative non-dominated solutions by a hypervolume-based solution selection approach

A large number of non-dominated solutions are often obtained by a single run of an evolutionary multiobjective optimization (EMO) algorithm. In the EMO research area, it is usually assumed that a single solution is to be chosen from the obtained non-dominated solutions by the decision maker. It is, however, time-consuming and not easy for the decision maker to examine a large number of obtained non-dominated solutions. Motivated by these discussions, we proposed single-objective and multiobjective formulations of solution selection problems to present only a small number of representative non-dominated solutions to the decision maker in our former study. The basic idea is to minimize the number of solutions to be presented while maximizing their hypervolume. A number of single-objective formulations can be derived from such a two-objective solution selection problem. In this paper, single-objective rule selection is performed as a post-processing procedure of EMO algorithms to select a prespecified number of non-dominated solutions (e.g., 10 or 20 solutions). Through computational experiments on multiobjective 0/1 knapsack problems, we examine the characteristic features of selected non-dominated solutions. We also examine the effect of the choice of a reference point for hypervolume calculation on the distribution of selected non-dominated solutions.