# Maximizing Submodular or Monotone Functions under Partition Matroid Constraints by Multi-objective Evolutionary Algorithms

arXiv: https://arxiv.org/abs/2006.12773 · HTML: https://mlsanity.com/paper/2006.12773/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2020.

## Built on by (most cited first, 4 of 4)

- [Effective and Imperceptible Adversarial Textual Attack via Multi-objectivization](https://mlsanity.com/paper/2111.01528/) (2021)
- [Multi-objective Evolutionary Algorithms are Generally Good: Maximizing Monotone Submodular Functions over Sequences](https://mlsanity.com/paper/2104.09884/) (2021)
- [Benchmarking Algorithms for Submodular Optimization Problems Using IOHProfiler](https://mlsanity.com/paper/2302.01464/) (2023)
- [Rigorous Runtime Analysis of MOEA/D for Solving Multi-Objective Minimum Weight Base Problems](https://mlsanity.com/paper/2306.03409/) (2023)

## Abstract (arXiv)

Many important problems can be regarded as maximizing submodular functions under some constraints. A simple multi-objective evolutionary algorithm called GSEMO has been shown to achieve good approximation for submodular functions efficiently. While there have been many studies on the subject, most of existing run-time analyses for GSEMO assume a single cardinality constraint. In this work, we extend the theoretical results to partition matroid constraints which generalize cardinality constraints, and show that GSEMO can generally guarantee good approximation performance within polynomial expected run time. Furthermore, we conducted experimental comparison against a baseline GREEDY algorithm in maximizing undirected graph cuts on random graphs, under various partition matroid constraints. The results show GSEMO tends to outperform GREEDY in quadratic run time.