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Local Branching Relaxation Heuristics for Integer Linear Programs

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13884))

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Abstract

Large Neighborhood Search (LNS) is a popular heuristic algorithm for solving combinatorial optimization problems (COP). It starts with an initial solution to the problem and iteratively improves it by searching a large neighborhood around the current best solution. LNS relies on heuristics to select neighborhoods to search in. In this paper, we focus on designing effective and efficient heuristics in LNS for integer linear programs (ILP) since a wide range of COPs can be represented as ILPs. Local Branching (LB) is a heuristic that selects the neighborhood that leads to the largest improvement over the current solution in each iteration of LNS. LB is often slow since it needs to solve an ILP of the same size as input. Our proposed heuristics, LB-RELAX and its variants, use the linear programming relaxation of LB to select neighborhoods. Empirically, LB-RELAX and its variants compute as effective neighborhoods as LB but run faster. They achieve state-of-the-art anytime performance on several ILP benchmarks.

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Notes

  1. 1.

    Appendix is available in the full version of the paper: https://arxiv.org/abs/2212.08183.

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Acknowledgements

This paper reports on research done while Taoan Huang and Aaron Ferber were interns at Meta AI (FAIR). The research at the University of Southern California was supported by the National Science Foundation (NSF) under grant number 2112533.

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Authors and Affiliations

  1. University of Southern California, Los Angeles, USA

    Taoan Huang, Aaron Ferber & Bistra Dilkina

  2. Meta AI (FAIR), Menlo Park, USA

    Yuandong Tian & Benoit Steiner

Authors
  1. Taoan Huang
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  2. Aaron Ferber
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  3. Yuandong Tian
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  4. Bistra Dilkina
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  5. Benoit Steiner
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Correspondence to Taoan Huang .

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  1. Department of Management, University of Toronto Scarborough and Rotman School of Management, University of Toronto, Toronto, ON, Canada

    Andre A. Cire

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Huang, T., Ferber, A., Tian, Y., Dilkina, B., Steiner, B. (2023). Local Branching Relaxation Heuristics for Integer Linear Programs. In: Cire, A.A. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2023. Lecture Notes in Computer Science, vol 13884. Springer, Cham. https://doi.org/10.1007/978-3-031-33271-5_7

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  • DOI: https://doi.org/10.1007/978-3-031-33271-5_7

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