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Branch-and-cut for linear programs with overlapping SOS1 constraints

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Abstract

SOS1 constraints require that at most one of a given set of variables is nonzero. In this article, we investigate a branch-and-cut algorithm to solve linear programs with SOS1 constraints. We focus on the case in which the SOS1 constraints overlap. The corresponding conflict graph can algorithmically be exploited, for instance, for improved branching rules, preprocessing, primal heuristics, and cutting planes. In an extensive computational study, we evaluate the components of our implementation on instances for three different applications. We also demonstrate the effectiveness of this approach by comparing it to the solution of a mixed-integer programming formulation, if the variables appearing in SOS1 constraints ar bounded.

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Acknowledgements

We are grateful to the referees for their detailed comments, which helped us to improve the paper. Furthermore, we thank Norbert Fabritius for the implementation of test instance generators. The work of Tobias Fischer is supported by the Excellence Initiative of the German Federal and State Governments and the Graduate School of Computational Engineering at Technische Universität Darmstadt.

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Authors and Affiliations

  1. Graduate School of Computational Engineering, TU Darmstadt, Dolivostraße 15, 64293, Darmstadt, Germany

    Tobias Fischer

  2. Department of Mathematics, Research Group Optimization, TU Darmstadt, Dolivostraße 15, 64293, Darmstadt, Germany

    Marc E. Pfetsch

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  1. Tobias Fischer
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Correspondence to Tobias Fischer.

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Fischer, T., Pfetsch, M.E. Branch-and-cut for linear programs with overlapping SOS1 constraints. Math. Prog. Comp. 10, 33–68 (2018). https://doi.org/10.1007/s12532-017-0122-5

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