Papers › Learning to Approximate: Auto Direction Vector Set Generation for Hypervolume...
Learning to Approximate: Auto Direction Vector Set Generation for Hypervolume Contribution Approximation
Ke Shang, Tianye Shu, Hisao Ishibuchi
Hypervolume contribution is an important concept in evolutionary multi-objective optimization (EMO). It involves in hypervolume-based EMO algorithms and hypervolume subset selection algorithms. Its main drawback is that it is computationally expensive in high-dimensional spaces, which limits its applicability to many-objective optimization. Recently, an R2 indicator variant (i.e., R₂^(HVC) indicator) is proposed to approximate the hypervolume contribution. The R₂^(HVC) indicator uses line segments along a number of direction vectors for hypervolume contribution approximation. It has been shown that different direction vector sets lead to different approximation quality. In this paper, we propose \textit{Learning to Approximate (LtA)}, a direction vector set generation method for the R₂^(HVC) indicator. The direction vector set is automatically learned from training data. The learned direction vector set can then be used in the R₂^(HVC) indicator to improve its approximation quality. The usefulness of the proposed LtA method is examined by comparing it with other commonly-used direction vector set generation methods for the R₂^(HVC) indicator. Experimental results suggest the superiority of LtA over the other methods for generating high quality direction vector sets.
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