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A note on linearized reformulations for a class of bilevel linear integer problems

Author

Listed:
  • M. Hosein Zare

    (University of Pittsburgh)

  • Juan S. Borrero

    (Oklahoma State University)

  • Bo Zeng

    (University of Pittsburgh)

  • Oleg A. Prokopyev

    (University of Pittsburgh
    Laboratory of Algorithms and Technologies for Networks Analysis, National Research University Higher School of Economics)

Abstract

We consider reformulations of a class of bilevel linear integer programs as equivalent linear mixed-integer programs (linear MIPs). The most common technique to reformulate such programs as a single-level problem is to replace the lower-level linear optimization problem by Karush–Kuhn–Tucker (KKT) optimality conditions. Employing the strong duality (SD) property of linear programs is an alternative method to perform such transformations. In this note, we describe two SD-based reformulations where the key idea is to exploit the binary expansion of upper-level integer variables. We compare the performance of an off-the-shelf MIP solver with the SD-based reformulations against the KKT-based one and show that the SD-based approaches can lead to orders of magnitude reduction in computational times for certain classes of instances.

Suggested Citation

  • M. Hosein Zare & Juan S. Borrero & Bo Zeng & Oleg A. Prokopyev, 2019. "A note on linearized reformulations for a class of bilevel linear integer problems," Annals of Operations Research, Springer, vol. 272(1), pages 99-117, January.
    • Handle: RePEc:spr:annopr:v:272:y:2019:i:1:d:10.1007_s10479-017-2694-x
    DOI: 10.1007/s10479-017-2694-x
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