Gradient-Guided Local Search for Large-Scale Hypervolume Subset Selection

Yang Nan, Tianye Shu, Hisao Ishibuchi, Ke Shang

Abstract: The use of an unbounded archive (UA) has attracted much attention in the filed of evolutionary multiobjective optimization (EMO) since a solution set selected from the UA is often better than the final population. The size of the UA is very large (e.g., 1 000 000) since it is unbounded and it stores all the examined nondominated solutions during the execution of an EMO algorithm. Thus, an algorithm which can efficiently select a high-quality subset from a large-scale candidate set (e.g., UA) is needed. In this article, we propose a gradient-guided local search hypervolume subset selection (GL-HSS) algorithm to efficiently select a high-quality subset from a large-scale candidate set. In each iteration of GL-HSS, the gradient of the hypervolume (HV) contribution of each selected solution is used to guide the local search. As a result, the proposed algorithm can quickly improve the HV of the selected subset. Experimental results show that, compared to the existing subset selection algorithms, the proposed GL-HSS algorithm can efficiently select high-quality subsets from various large-scale candidate sets.