A Dissection of the Duality Gap of Set Covering Problems

Uledi Ngulo (), Torbjörn Larsson and Nils-Hassan Quttineh ()
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Uledi Ngulo: Linköping University
Torbjörn Larsson: Linköping University
Nils-Hassan Quttineh: Linköping University

A chapter in Operations Research Proceedings 2019, 2020, pp 175-181 from Springer

Abstract: Abstract Set covering problems are well-studied and have many applications. Sometimes the duality gap is significant and the problem is computationally challenging. We dissect the duality gap with the purpose of better understanding its relationship to problem characteristics, such as problem shape and density. The means for doing this is a set of global optimality conditions for discrete optimization problems. These decompose the duality gap into two terms: near-optimality in a Lagrangian relaxation and near-complementarity in the relaxed constraints. We analyse these terms for numerous instances of large size, including some real-life instances. We conclude that when the duality gap is large, typically the near-complementarity term is large and the near-optimality term is small. The large violation of complementarity is due to extensive over-coverage. Our observations should have implications for the design of solution methods, and especially for the design of core problems.

Keywords: Discrete optimization; Set covering problem; Duality gap (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:oprchp:978-3-030-48439-2_21

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DOI: 10.1007/978-3-030-48439-2_21

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