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

Hypervolume contribution is an important concept in evolutionary multi-objective optimization (EMO). It involves hypervolume-based EMO algorithms and hypervolume subset selection algorithms. Its main drawback that it computationally expensive high-dimensional spaces, which limits its applicability to many-objective optimization. Recently, R2 indicator variant (i.e., R2HVC indicator) proposed approximate the contribution. The uses line segments along a number of direction vectors for approximation. has been shown different vector sets lead approximation quality. In this paper, we propose Learning Approximate (LtA), set generation method indicator. automatically learned from training data. can then be used improve usefulness LtA examined by comparing with other commonly-used methods Experimental results suggest superiority over generating high quality sets.