Fast Greedy Subset Selection from Large Candidate Solution Sets in Evolutionary Multi-objective Optimization

TL;DR

This paper introduces efficient greedy algorithms for subset selection in evolutionary multi-objective optimization, leveraging submodularity of hypervolume, IGD, and IGD+ indicators to significantly reduce computation time.

Contribution

It proves IGD and IGD+ are submodular and develops faster greedy algorithms for subset selection based on this property.

Findings

Proposed algorithms are significantly faster than standard greedy methods.

Validated efficiency through computational experiments.

Demonstrated applicability to large solution sets in EMO.

Abstract

Subset selection is an interesting and important topic in the field of evolutionary multi-objective optimization (EMO). Especially, in an EMO algorithm with an unbounded external archive, subset selection is an essential post-processing procedure to select a pre-specified number of solutions as the final result. In this paper, we discuss the efficiency of greedy subset selection for the hypervolume, IGD and IGD+ indicators. Greedy algorithms usually efficiently handle subset selection. However, when a large number of solutions are given (e.g., subset selection from tens of thousands of solutions in an unbounded external archive), they often become time-consuming. Our idea is to use the submodular property, which is known for the hypervolume indicator, to improve their efficiency. First, we prove that the IGD and IGD+ indicators are also submodular. Next, based on the submodular property, we propose an efficient greedy inclusion algorithm for each indicator. Then, we demonstrate through computational experiments that the proposed algorithms are much faster than the standard greedy subset selection algorithms.