Title: A novel decomposition approach to set covering problems by exploiting special structures

Authors: Maryam Radman; Kourosh Eshghi

Addresses: Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran ' Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran

Abstract: The set covering problem (SCP) has quite a large coefficient matrix in practical problems, but due to its low density, most of its entries are zero. Drawing on this observation, some methods can be developed to exploit special structures of the coefficient matrix of an SCP in such a way that they contain smaller dense subproblems. Against this backdrop, in this paper, three structures, namely 'partitioned', 'semi-block angular', and 'block angular', are proposed. To begin with, some heuristic methods are presented to exploit these structures of the coefficient matrices of SCPs; then, by optimally solving the smaller subproblems of these structures, their solutions are used to solve the whole problem based on the proposed theorem. Our approach has been tested using well-known instances from OR-Library and shown to be comparable with some of the recently-developed methods to solve SCPs.

Keywords: set covering problem; SCP; constraint partitioning; decomposition techniques; special structures; clustering methods.

DOI: 10.1504/IJMOR.2022.121115

International Journal of Mathematics in Operational Research, 2022 Vol.21 No.2, pp.254 - 279

Received: 01 Jul 2020
Accepted: 04 Jan 2021
Published online: 25 Feb 2022 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article