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Improving branch-and-cut performance by random sampling

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Abstract

We discuss the variability in the performance of multiple runs of branch-and-cut mixed integer linear programming solvers, and we concentrate on the one deriving from the use of different optimal bases of the linear programming relaxations. We propose a new algorithm exploiting more than one of those bases and we show that different versions of the algorithm can be used to stabilize and improve the performance of the solver.

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Notes

  1. Note that even a parallel implementation of the sampling phase would introduce some unavoidable overhead in the method. Such overhead is disregarded in the results reported in this section, but is instead taken into account in Sect. 5, where a real parallel implementation of the sampling phase is evaluated.

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Acknowledgments

This research was partially supported by MiUR, Italy (PRIN project “Mixed-Integer Nonlinear Optimization: Approaches and Applications”) and by the University of Padova (Progetto di Ateneo “Exploiting randomness in Mixed-Integer Linear Programming”). Thanks are due to two anonymous referees for their helpful comments; we also thank Hans D. Mittelmann for the use of the cluster at Arizona State University.

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Authors and Affiliations

  1. DEI, University of Padova, Padua, Italy

    Matteo Fischetti, Michele Monaci & Domenico Salvagnin

  2. DEI, University of Bologna, Bologna, Italy

    Andrea Lodi

  3. CPLEX Optimization, IBM, Bologna, Italy

    Andrea Tramontani

Authors
  1. Matteo Fischetti
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  2. Andrea Lodi
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  3. Michele Monaci
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  4. Domenico Salvagnin
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  5. Andrea Tramontani
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Corresponding author

Correspondence to Andrea Lodi.

Appendix: detailed results

Appendix: detailed results

See Table 8.

Table 8 Cross-solver performance variability
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Fischetti, M., Lodi, A., Monaci, M. et al. Improving branch-and-cut performance by random sampling. Math. Prog. Comp. 8, 113–132 (2016). https://doi.org/10.1007/s12532-015-0096-0

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