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A Dissection of the Duality Gap of Set Covering Problems

In: Operations Research Proceedings 2019

Author

Listed:
  • Uledi Ngulo

    (Linköping University)

  • Torbjörn Larsson

    (Linköping University)

  • Nils-Hassan Quttineh

    (Linköping University)

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.

Suggested Citation

  • Uledi Ngulo & Torbjörn Larsson & Nils-Hassan Quttineh, 2020. "A Dissection of the Duality Gap of Set Covering Problems," Operations Research Proceedings, in: Janis S. Neufeld & Udo Buscher & Rainer Lasch & Dominik Möst & Jörn Schönberger (ed.), Operations Research Proceedings 2019, pages 175-181, Springer.
    • Handle: RePEc:spr:oprchp:978-3-030-48439-2_21
    DOI: 10.1007/978-3-030-48439-2_21
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