RBSS: A fast subset selection strategy for multi-objective optimization

Abstract

Multi-objective optimization problems (MOPs) aim to obtain a set of Pareto-optimal solutions, and as the number of objectives increases, the quantity of these optimal solutions grows exponentially. However, a plethora of optimal solutions can impose significant decision stress on decision-makers. Subset selection, as the extension of a model, can extract a representative set of solutions, thereby alleviating the decision-makers’ choice pressure. In addition, extending a model undoubtedly incurs additional time costs. To cope with the foregoing issues, a fast subset selection method named ranking-based subset selection (RBSS) is proposed in this paper. It can efficiently select a small number of optimal solutions within an unbounded external archive and can be directly applied to any multi-objective evolutionary algorithm. This allows it to maintain good distribution and diversity with very little time investment. We employed a ranking-based approach to map the objective space to a ranking space (an integer space) defined by us and then selected the corresponding subset in the ranking space. The well-behaved mathematical properties of the ranking space and the advantages of using integer calculations accelerated the subset selection process. Experimental results indicate that compared to several state-of-the-art subset selection methods, RBSS is capable of selecting a set of representative and diverse solutions across different types of MOPs, while consuming significantly less time. Specifically, for problems where the Pareto front is a two-dimensional manifold and a one-dimensional manifold, the time consumption of RBSS is approximately only 0.028% to 27.5% and 4.6e−4% to 0.15% of that required by other algorithms, respectively.