Lazy Greedy Hypervolume Subset Selection from Large Candidate Solution Sets

TL;DR

This paper introduces a lazy greedy algorithm for hypervolume subset selection that significantly reduces computation time by exploiting submodularity, making it feasible for large candidate sets.

Contribution

The paper presents a novel lazy greedy algorithm that accelerates hypervolume subset selection by avoiding unnecessary calculations, outperforming existing methods on large datasets.

Findings

Algorithm is hundreds of times faster than the original greedy method.

Significant speedup over the fastest known greedy algorithms.

Effective on large candidate solution sets.

Abstract

Subset selection is a popular topic in recent years and a number of subset selection methods have been proposed. Among those methods, hypervolume subset selection is widely used. Greedy hypervolume subset selection algorithms can achieve good approximations to the optimal subset. However, when the candidate set is large (e.g., an unbounded external archive with a large number of solutions), the algorithm is very time-consuming. In this paper, we propose a new lazy greedy algorithm exploiting the submodular property of the hypervolume indicator. The core idea is to avoid unnecessary hypervolume contribution calculation when finding the solution with the largest contribution. Experimental results show that the proposed algorithm is hundreds of times faster than the original greedy inclusion algorithm and several times faster than the fastest known greedy inclusion algorithm on many test problems.