Archive-based Single-Objective Evolutionary Algorithms for Submodular Optimization

TL;DR

This paper introduces novel single-objective evolutionary algorithms that incrementally expand the feasible search space, effectively solving constrained submodular maximization problems which were previously challenging for such methods.

Contribution

It presents the first provably successful single-objective algorithms for constrained submodular maximization, using variants of the $(1+\lambda)$-EA and $(1+1)$-EA that incrementally increase the feasible region.

Findings

Algorithms are provably successful for various classes of submodular problems.

Incremental feasible region expansion improves optimization performance.

First single-objective algorithms with theoretical guarantees for constrained submodular maximization.

Abstract

Constrained submodular optimization problems play a key role in the area of combinatorial optimization as they capture many NP-hard optimization problems. So far, Pareto optimization approaches using multi-objective formulations have been shown to be successful to tackle these problems while single-objective formulations lead to difficulties for algorithms such as the $(1+1)$-EA due to the presence of local optima. We introduce for the first time single-objective algorithms that are provably successful for different classes of constrained submodular maximization problems. Our algorithms are variants of the $(1+\lambda)$-EA and $(1+1)$-EA and increase the feasible region of the search space incrementally in order to deal with the considered submodular problems.