Direction Vector Selection for R2-Based Hypervolume Contribution Approximation

Abstract

AbstractRecently, an R2-based hypervolume contribution approximation (i.e., \(R_2^{HVC}\) indicator) has been proposed and applied to evolutionary multi-objective algorithms and subset selection. The \(R_2^{HVC}\) indicator approximates the hypervolume contribution using a set of line segments determined by a direction vector set. Although the \(R_2^{HVC}\) indicator is computationally efficient compared with the exact hypervolume contribution calculation, its approximation error is large if an inappropriate direction vector set is used. In this paper, we propose a method to generate a direction vector set for reducing the approximation error of the \(R_2^{HVC}\) indicator. The method generates a set of direction vectors by selecting a small direction vector set from a large candidate direction vector set in a greedy manner. Experimental results show that the proposed method outperforms six existing direction vector set generation methods. The direction vector set generated by the proposed method can be further used to improve the performance of hypervolume-based algorithms which rely on the \(R_2^{HVC}\) indicator.KeywordsEvolutionary multi-objective optimizationHypervolume contributionHypervolume contribution approximation