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Conflict-Free Learning for Mixed Integer Programming

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12296))

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Abstract

Conflict learning plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. A major step for MIP conflict learning is to aggregate the LP relaxation of an infeasible subproblem to a single globally valid constraint, the dual proof, that proves infeasibility within the local bounds. Among others, one way of learning is to add these constraints to the problem formulation for the remainder of the search.

We suggest to not restrict this procedure to infeasible subproblems, but to also use global proof constraints from subproblems that are not (yet) infeasible, but can be expected to be pruned soon. As a special case, we also consider learning from integer feasible LP solutions. First experiments of this conflict-free learning strategy show promising results on the MIPLIB2017 benchmark set.

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Acknowledgments

The work for this article has been conducted within the Research Campus Modal funded by the German Federal Ministry of Education and Research (fund number 05M14ZAM).

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Authors and Affiliations

  1. Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany

    Jakob Witzig

  2. Fair Isaac Germany GmbH, Stubenwald-Allee 19, 64625, Bensheim, Germany

    Timo Berthold

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  1. Jakob Witzig
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  2. Timo Berthold
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Correspondence to Jakob Witzig .

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Editors and Affiliations

  1. LAAS - CNRS, Toulouse, France

    Emmanuel Hebrard

  2. TU Wien, Vienna, Wien, Austria

    Nysret Musliu

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Witzig, J., Berthold, T. (2020). Conflict-Free Learning for Mixed Integer Programming. In: Hebrard, E., Musliu, N. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2020. Lecture Notes in Computer Science(), vol 12296. Springer, Cham. https://doi.org/10.1007/978-3-030-58942-4_34

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  • DOI: https://doi.org/10.1007/978-3-030-58942-4_34

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  • Print ISBN: 978-3-030-58941-7

  • Online ISBN: 978-3-030-58942-4

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