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Local Rapid Learning for Integer Programs

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11494))

Abstract

Conflict learning algorithms are an important component of modern MIP and CP solvers. But strong conflict information is typically gained by depth-first search. While this is the natural mode for CP solving, it is not for MIP solving. Rapid Learning is a hybrid CP/MIP approach where CP search is appliedat the root to learn information to support the remaining MIP solve. This has been demonstrated to be beneficial for binary programs. In this paper, we extend the idea of Rapid Learning to integer programs, where not all variables are restricted to the domain \(\{0,1\}\), and rather than just running a rapid CP search at the root, we will apply it repeatedly at local search nodes within the MIP search tree. To do so efficiently, we present six heuristic criteria to predict the chance for local Rapid Learning to be successful. Our computational experiments indicate that our extended Rapid Learning algorithm significantly speeds up MIP search and is particularly beneficial on highly dual degenerate problems.

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Notes

  1. 1.

    For disambiguation, we will use the term vertex for elements of the conflict graph, as opposed to nodes of the search tree.

  2. 2.

    By CP search we mean applying a depth-first search using only propagation for reasoning, no LP relaxation is solved during the search.

  3. 3.

    In SCIP, emphasis settings correspond to a group of individual parameters being changed.

  4. 4.

    An instance is called affected when the solving path changes.

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Acknowledgments

The work for this article has been partly conducted within the Research Campus MODAL funded by the German Federal Ministry of Education and Research (BMBF grant number 05M14ZAM). We thank the anonymous reviewers for their valuable suggestions and helpful comments.

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Authors and Affiliations

  1. Fair Isaac Germany GmbH, Takustr. 7, 14195, Berlin, Germany

    Timo Berthold

  2. Monash University and Data61, Melbourne, Australia

    Peter J. Stuckey

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

    Jakob Witzig

Authors
  1. Timo Berthold
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  2. Peter J. Stuckey
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  3. Jakob Witzig
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Correspondence to Timo Berthold .

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Editors and Affiliations

  1. Ecole Polytechnique de Montréal, Montréal, QC, Canada

    Louis-Martin Rousseau

  2. University of Western Macedonia, Kozani, Greece

    Kostas Stergiou

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Berthold, T., Stuckey, P.J., Witzig, J. (2019). Local Rapid Learning for Integer Programs. In: Rousseau, LM., Stergiou, K. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2019. Lecture Notes in Computer Science(), vol 11494. Springer, Cham. https://doi.org/10.1007/978-3-030-19212-9_5

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  • DOI: https://doi.org/10.1007/978-3-030-19212-9_5

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