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

Radman, M ; Sharif University of Technology | 2022

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  1. Type of Document: Article
  2. DOI: 10.1504/IJMOR.2022.121115
  3. Publisher: Inderscience Publishers , 2022
  4. Abstract:
  5. 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. Copyright © 2022 Inderscience Enterprises Ltd
  6. Keywords:
  7. Clustering methods ; Constraint partitioning ; Decomposition techniques ; SCP ; Set covering problem ; Special structures
  8. Source: International Journal of Mathematics in Operational Research ; Volume 21, Issue 2 , 2022 , Pages 254-279 ; 17575850 (ISSN)
  9. URL: https://www.inderscienceonline.com/doi/abs/10.1504/IJMOR.2022.121115