Table of Contents
ISRN Operations Research
Volume 2013 (2013), Article ID 203032, 10 pages
http://dx.doi.org/10.1155/2013/203032
Research Article

A New Formulation of the Set Covering Problem for Metaheuristic Approaches

École Polytechnique de Montréal, C.P. 6079, Succ. Centre-Ville, Montréal, QC, Canada H3C 3A7

Received 18 February 2013; Accepted 4 April 2013

Academic Editors: L. Buzna, P. Ekel, C. Mohan, and M. Wang

Copyright © 2013 Nehme Bilal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Two difficulties arise when solving the set covering problem (SCP) with metaheuristic approaches: solution infeasibility and set redundancy. In this paper, we first present a review and analysis of the heuristic approaches that have been used in the literature to address these difficulties. We then present a new formulation that can be used to solve the SCP as an unconstrained optimization problem and that eliminates the need to address the infeasibility and set redundancy issues. We show that all local optimums with respect to the new formulation and a 1-flip neighbourhood structure are feasible and free of redundant sets. In addition, we adapt an existing greedy heuristic for the SCP to the new formulation and compare the adapted heuristic to the original heuristic using 88 known test problems for the SCP. Computational results show that the adapted heuristic finds better results than the original heuristic on most of the test problems in shorter computation times.