A Dissection of the Duality Gap of Set Covering Problems

Ngulo, Uledi,1983-Linköpings universitet,Tillämpad matematik,Tekniska fakulteten (author)

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.

Larsson, Torbjörn,1957-Linköpings universitet,Tillämpad matematik,Tekniska fakulteten(Swepub:liu)torla64 (author)
Quttineh, Nils-Hassan,1979-Linköpings universitet,Tillämpad matematik,Tekniska fakulteten(Swepub:liu)nilqu94 (author)
Linköpings universitetTillämpad matematik (creator_code:org_t)

In:Operations Research Proceedings 2019Cham, Switzerland : Springer, s. 175-18197830304843859783030484392

By the author/editor: Ngulo, Uledi, 19 ...; Larsson, Torbjör ...; Quttineh, Nils-H ...

About the subject

NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Computational Ma ...

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