Learning to Approximate: Auto Direction Vector Set Generation for Hypervolume Contribution Approximation

by   Ke Shang, et al.

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., R_2^HVC indicator) is proposed to approximate the hypervolume contribution. The R_2^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 Learning to Approximate (LtA), a direction vector set generation method for the R_2^HVC indicator. The direction vector set is automatically learned from training data. The learned direction vector set can then be used in the R_2^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 R_2^HVC indicator. Experimental results suggest the superiority of LtA over the other methods for generating high quality direction vector sets.


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