Robust min-max regret covering problems

Amadeu A. Coco (), Andréa Cynthia Santos and Thiago F. Noronha
Additional contact information
Amadeu A. Coco: Normandie Université
Andréa Cynthia Santos: Normandie Université
Thiago F. Noronha: Federal University of Minas Gerais

Computational Optimization and Applications, 2022, vol. 83, issue 1, No 4, 141 pages

Abstract: Abstract This article deals with two min-max regret covering problems: the min-max regret Weighted Set Covering Problem (min-max regret WSCP) and the min-max regret Maximum Benefit Set Covering Problem (min-max regret MSCP). These problems are the robust optimization counterparts, respectively, of the Weighted Set Covering Problem and of the Maximum Benefit Set Covering Problem. In both problems, uncertainty in data is modeled by using an interval of continuous values, representing all the infinite values every uncertain parameter can assume. This study has the following major contributions: (i) a proof that MSCP is $$\varSigma _p^2$$ Σ p 2 -Hard, (ii) a mathematical formulation for the min-max regret MSCP, (iii) exact and (iv) heuristic algorithms for the min-max regret WSCP and the min-max regret MSCP. We reproduce the main exact algorithms for the min-max regret WSCP found in the literature: a Logic-based Benders decomposition, an extended Benders decomposition and a branch-and-cut. In addition, such algorithms have been adapted for the min-max regret MSCP. Moreover, five heuristics are applied for both problems: two scenario-based heuristics, a path relinking, a pilot method and a linear programming-based heuristic. The goal is to analyze the impact of such methods on handling robust covering problems in terms of solution quality and performance.

Keywords: Robust optimization; Covering problems; Heuristics; Exact methods; Uncertainties (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-022-00391-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:83:y:2022:i:1:d:10.1007_s10589-022-00391-x

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-022-00391-x

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().