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Boosting the feasibility pump

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Abstract

The feasibility pump (FP) has proved to be an effective method for finding feasible solutions to mixed integer programming problems. FP iterates between a rounding procedure and a projection procedure, which together provide a sequence of points alternating between LP feasible but fractional solutions, and integer but LP infeasible solutions. The process attempts to minimize the distance between consecutive iterates, producing an integer feasible solution when closing the distance between them. We investigate the benefits of enhancing the rounding procedure with a clever integer line search that efficiently explores a large set of integer points. An extensive computational study on benchmark instances demonstrates the efficacy of the proposed approach.

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Notes

  1. http://miplib.zib.de/miplib2003/.

  2. http://miplib.zib.de/miplib2010/.

  3. http://coral.ie.lehigh.edu/~mip-instances/instances/.

  4. http://people.brunel.ac.uk/~mastjjb/jeb/orlib/mipinfo.html.

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Acknowledgments

We thank Domenico Salvagnin for providing the source code of his implementation of the feasibility pump with constraint propagation and for answering all of our questions promptly, elaborately, and clearly. The research of the fourth author was partially supported by the Progetto di Ateneo on “Computational Integer Programming” of the University of Padova, and by MiUR, Italy (PRIN project “Integrated Approaches to Discrete and Nonlinear Optimization”).

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Authors and Affiliations

  1. The University of Newcastle, Callaghan, Australia

    Natashia L. Boland & Martin W. P. Savelsbergh

  2. Royal Melbourne Institute of Technology, Melbourne, Australia

    Andrew C. Eberhard & Angelos Tsoukalas

  3. SK Innovation, Seoul, Korea

    Faramroze G. Engineer

  4. University of Padova, Padova, Italy

    Matteo Fischetti

Authors
  1. Natashia L. Boland
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  2. Andrew C. Eberhard
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  3. Faramroze G. Engineer
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  4. Matteo Fischetti
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  5. Martin W. P. Savelsbergh
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  6. Angelos Tsoukalas
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Corresponding author

Correspondence to Martin W. P. Savelsbergh.

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Boland, N.L., Eberhard, A.C., Engineer, F.G. et al. Boosting the feasibility pump. Math. Prog. Comp. 6, 255–279 (2014). https://doi.org/10.1007/s12532-014-0068-9

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  • DOI: https://doi.org/10.1007/s12532-014-0068-9

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