HVC-Net: Deep Learning Based Hypervolume Contribution Approximation

Abstract

AbstractIn this paper, we propose HVC-Net, a deep learning based hypervolume contribution approximation method for evolutionary multi-objective optimization. The basic idea of HVC-Net is to use a deep neural network to approximate the hypervolume contribution of each solution in a non-dominated solution set. HVC-Net has two characteristics: (1) It is permutation equivalent to the order of solutions in the input solution set, and (2) a single HVC-Net can handle solution sets of various size (e.g., solution sets with 20, 50 and 100 solutions). The performance of HVC-Net is evaluated through computational experiments by comparing it with two commonly-used hypervolume contribution approximation methods (i.e., point-based method and line-based method). Our experimental results show that HVC-Net outperforms the other two methods in terms of both the runtime and the ability to identify the smallest (largest) hypervolume contributor in a solution set, which shows the superiority of HVC-Net for hypervolume contribution approximation.KeywordsHypervolume contributionApproximationEvolutionary multi-objective optimizationDeep learning