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Just MIP it!

  • Matteo Fischetti
  • Andrea Lodi
  • Domenico Salvagnin
Chapter
Part of the Annals of Information Systems book series (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.

Keywords

Mixed Integer Mixed Integer Linear Program Valid Inequality Incumbent Solution Dominance Test 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

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.

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Matteo Fischetti
    • 1
  • Andrea Lodi
    • 2
  • Domenico Salvagnin
    • 3
  1. 1.DEI, Università di PadovaPaduaItaly
  2. 2.DEIS, Università di BolognaBolognaItaly
  3. 3.DMPA, Università di PadovaPaduaItaly

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