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Just MIP it!

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Matheuristics

Part of the book series: Annals of Information Systems ((AOIS,volume 10))

Abstract

Modern Mixed-Integer Programming (MIP) solvers exploit a rich arsenal of tools to attack hard problems. It is idely accepted by the OR community that the solution of very hard MIPs can take advantage from the solution of a series of time-consuming auxiliary Linear Programs (LPs) intended to enhance the performance of the overall MIP solver. For instance, auxiliary LPs may be solved to generate powerful disjunctive cuts, or to implement a strong branching policy. Also well established is the fact that finding good-quality heuristic MIP solutions often requires a computing time that is just comparable to that needed to solve the LP relaxations. So, it makes sense to think of a new generation of MIP solvers where auxiliary MIPs (as opposed to LPs) are heuristically solved on the fly, with the aim of bringing the MIP technology under the chest of the MIP solver itself. This leads to the idea of “translating into a MIP model” (MIPping) some crucial decisions to be taken within a MIP algorithm (How to cut? How to improve the incumbent solution? Is the current node dominated?). In this paper we survey a number of successful applications of the above approach.

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Acknowledgment

This work was supported by the Future and Emerging Technologies unit of the EC (IST priority), under contract no. FP6-021235-2 (project “ARRIVAL”) and by MiUR, Italy.

Author information

Authors and Affiliations

  1. DEI, Università di Padova, Padua, Italy

    Matteo Fischetti

  2. DEIS, Università di Bologna, Bologna, Italy

    Andrea Lodi

  3. DMPA, Università di Padova, Padua, Italy

    Domenico Salvagnin

Authors
  1. Matteo Fischetti
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  2. Andrea Lodi
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  3. Domenico Salvagnin
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Corresponding author

Correspondence to Matteo Fischetti .

Editor information

Editors and Affiliations

  1. Dipto. Scienze dell‘Informazione, Universitá di Bologna, Contrada Sacchi 3, Cesena, 47023, Italy

    Vittorio Maniezzo

  2. Avenue Franklin Roosevelt 50, Bruxelles, 1050, Belgium

    Thomas Stützle

  3. Dept. Wirtschaftswissenschaften, Inst. Wirtschaftsinformatik, Universität Hamburg, Von-Melle-Park 5, Hamburg, 20146, Germany

    Stefan Voß

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Fischetti, M., Lodi, A., Salvagnin, D. (2009). Just MIP it!. In: Maniezzo, V., Stützle, T., Voß, S. (eds) Matheuristics. Annals of Information Systems, vol 10. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1306-7_2

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