A heuristic for the non-unicost set covering problem using local branching

TL;DR

This paper introduces a general heuristic using local branching for the non-unicost set covering problem, demonstrating competitive performance across multiple test instances and highlighting the potential of local branching as a standalone matheuristic.

Contribution

It presents a novel application of local branching to the non-unicost set covering problem, avoiding problem-specific neighborhood definitions.

Findings

Outperforms six of eight existing heuristics

Slightly worse than one heuristic, but overall competitive

Shows potential of local branching as a standalone approach

Abstract

In this paper we present a heuristic for the non-unicost set covering problem using local branching. Local branching eliminates the need to define a problem specific search neighbourhood for any particular (zero-one) optimisation problem. It does this by incorporating a generalised Hamming distance neighbourhood into the problem, and this leads naturally to an appropriate neighbourhood search procedure. We apply our approach to the non-unicost set covering problem. Computational results are presented for 65 test problems that have been widely considered in the literature. Our results indicate that our heuristic is better than six of the eight other heuristics we examined, slightly worse than that of one heuristic, but that there is a single heuristic that out-performs all others. We believe that the work described here illustrates that the potential for using local branching, operating as a stand-alone matheuristic, has not been fully exploited in the literature.