ICML 2025

Improved Theoretically-Grounded Evolutionary Algorithms
for Subset Selection with a Linear Cost Constraint
Dan-Xuan Liu 1 2 Chao Qian 1 2
Abstract
The subset selection problem with a monotone
and submodular objective function under a lin-
ear cost constraint has wide applications, such
as maximum coverage, influence maximization,
and feature selection, just to name a few. Various
greedy algorithms have been proposed with good
performance both theoretically and empirically.
Recently, evolutionary algorithms (EAs), inspired
by Darwin’s evolution theory, have emerged
as a prominent methodology, offering both em-
pirical advantages and theoretical guarantees.
Among these, the multi-objective EA, POMC, has
demonstrated the best empirical performance to
date, achieving an approximation guarantee of
(1/2)(1 −1/e). However, there remains a gap
in the approximation bounds of EAs compared
to greedy algorithms, and their full theoretical
potential is yet to be realized. In this paper, we re-
analyze the approximation performance of POMC
theoretically, and derive an improved guarantee of
1/2, which thus provides theoretical justification
for its encouraging empirical performance. Fur-
thermore, we propose a novel multi-objective EA,
EPOL, which not only achieves the best-known
practical approximation guarantee of 0.6174, but
also delivers superior empirical performance in
applications of maximum coverage and influence
maximization. We hope this work can help bet-
ter solving the subset selection problem, but also
enhance our theoretical understanding of EAs.
1. Introduction
The subset selection problem aims to select a subset X
from a given ground set V that maximizes a specific func-
1National Key Laboratory for Novel Software Technology,
Nanjing University, Nanjing 210023, China 2School of Artificial
Intelligence, Nanjing University, Nanjing 210023, China. Corre-
spondence to: Chao Qian <qianc@nju.edu.cn>.
Proceedings of the 42 nd International Conference on Machine
Learning,...