论文标题
学会近似：高量贡献近似的自动方向矢量设置生成
Learning to Approximate: Auto Direction Vector Set Generation for Hypervolume Contribution Approximation
论文作者
论文摘要
超量贡献是进化多目标优化（EMO）中的重要概念。它涉及基于高频的EMO算法和高量卷子集选择算法。它的主要缺点是它在高维空间中的计算昂贵，这将其适用性限制在多个目标优化中。最近，提出了一个R2指示器变体（即$ r_2^{\ text {hvc}} $指示器）以近似于超量贡献。 $ r_2^{\ text {hvc}} $指示器使用沿多个方向向量的线段进行超量贡献近似。已经显示出不同的方向向量集导致不同的近似质量。在本文中，我们建议\ textit {学习近似（LTA）}，这是$ r_2^{\ text {hvc}} $ indodator的方向向量设置生成方法。方向向量集自动从训练数据中学习。然后可以在$ r_2^{\ text {hvc}} $指示器中使用学习方向向量集以提高其近似质量。通过将$ r_2^{\ text {hvc}} $指示器的其他常用方向矢量设置方法进行比较，可以检查提出的LTA方法的有用性。实验结果表明，LTA优于生成高质量方向矢量集的其他方法。
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., $R_2^{\text{HVC}}$ indicator) is proposed to approximate the hypervolume contribution. The $R_2^{\text{HVC}}$ 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 $R_2^{\text{HVC}}$ indicator. The direction vector set is automatically learned from training data. The learned direction vector set can then be used in the $R_2^{\text{HVC}}$ 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 $R_2^{\text{HVC}}$ indicator. Experimental results suggest the superiority of LtA over the other methods for generating high quality direction vector sets.
