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Alternating criteria search: a parallel large neighborhood search algorithm for mixed integer programs

Author

Listed:
  • Lluís-Miquel Munguía

    (Georgia Institute of Technology)

  • Shabbir Ahmed

    (Georgia Institute of Technology)

  • David A. Bader

    (Georgia Institute of Technology)

  • George L. Nemhauser

    (Georgia Institute of Technology)

  • Yufen Shao

    (ExxonMobil Upstream Research Company)

Abstract

We present a parallel large neighborhood search framework for finding high quality primal solutions for general mixed-integer programs (MIPs). The approach simultaneously solves a large number of sub-MIPs with the dual objective of reducing infeasibility and optimizing with respect to the original objective. Both goals are achieved by solving restricted versions of two auxiliary MIPs, where subsets of the variables are fixed. In contrast to prior approaches, ours does not require a feasible starting solution. We leverage parallelism to perform multiple searches simultaneously, with the objective of increasing the effectiveness of our heuristic. We computationally compare the proposed framework with a state-of-the-art MIP solver in terms of solution quality, scalability, reproducibility, and parallel efficiency. Results show the efficacy of our approach in finding high quality solutions quickly both as a standalone primal heuristic and when used in conjunction with an exact algorithm.

Suggested Citation

  • Lluís-Miquel Munguía & Shabbir Ahmed & David A. Bader & George L. Nemhauser & Yufen Shao, 2018. "Alternating criteria search: a parallel large neighborhood search algorithm for mixed integer programs," Computational Optimization and Applications, Springer, vol. 69(1), pages 1-24, January.
    • Handle: RePEc:spr:coopap:v:69:y:2018:i:1:d:10.1007_s10589-017-9934-5
    DOI: 10.1007/s10589-017-9934-5
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    References listed on IDEAS

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    1. Edward Rothberg, 2007. "An Evolutionary Algorithm for Polishing Mixed Integer Programming Solutions," INFORMS Journal on Computing, INFORMS, vol. 19(4), pages 534-541, November.
    2. Thorsten Koch & Ted Ralphs & Yuji Shinano, 2012. "Could we use a million cores to solve an integer program?," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(1), pages 67-93, August.
    3. Egon Balas & Sebastián Ceria & Milind Dawande & Francois Margot & Gábor Pataki, 2001. "Octane: A New Heuristic for Pure 0--1 Programs," Operations Research, INFORMS, vol. 49(2), pages 207-225, April.
    4. David A. Bader & William E. Hart & Cynthia A. Phillips, 2005. "Parallel Algorithm Design for Branch and Bound," International Series in Operations Research & Management Science, in: H J. G (ed.), Tutorials on Emerging Methodologies and Applications in Operations Research, chapter 0, pages 5-1-5-44, Springer.
    5. Merce, C. & Fontan, G., 2003. "MIP-based heuristics for capacitated lotsizing problems," International Journal of Production Economics, Elsevier, vol. 85(1), pages 97-111, July.
    6. Tobias Achterberg & Timo Berthold & Gregor Hendel, 2012. "Rounding and Propagation Heuristics for Mixed Integer Programming," Operations Research Proceedings, in: Diethard Klatte & Hans-Jakob Lüthi & Karl Schmedders (ed.), Operations Research Proceedings 2011, edition 127, pages 71-76, Springer.
    7. Mike Hewitt & George L. Nemhauser & Martin W. P. Savelsbergh, 2010. "Combining Exact and Heuristic Approaches for the Capacitated Fixed-Charge Network Flow Problem," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 314-325, May.
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    Cited by:

    1. Tonbari, Mohamed El & Ahmed, Shabbir, 2023. "Consensus-based Dantzig-Wolfe decomposition," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1441-1456.

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