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The integral basis method for integer programming

Author

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  • Utz-Uwe Haus
  • Matthias Köppe
  • Robert Weismantel

Abstract

This paper introduces an exact algorithm for solving integer programs, neither using cutting planes nor enumeration techniques. It is a primal augmentation algorithm that relies on iteratively substituting one column by columns that correspond to irreducible solutions of certain linear diophantine inequalities. We demonstrate the algorithm's potential by testing it on some instances of the MIPLIB with up to 6000 variables. Copyright Springer-Verlag Berlin Heidelberg 2001

Suggested Citation

  • Utz-Uwe Haus & Matthias Köppe & Robert Weismantel, 2001. "The integral basis method for integer programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(3), pages 353-361, July.
    • Handle: RePEc:spr:mathme:v:53:y:2001:i:3:p:353-361
    DOI: 10.1007/s001860100124
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    Cited by:

    1. Abdelouahab Zaghrouti & François Soumis & Issmail El Hallaoui, 2014. "Integral Simplex Using Decomposition for the Set Partitioning Problem," Operations Research, INFORMS, vol. 62(2), pages 435-449, April.
    2. Abdelouahab Zaghrouti & Issmail El Hallaoui & François Soumis, 2018. "Improved integral simplex using decomposition for the set partitioning problem," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(2), pages 185-206, June.
    3. Abdelouahab Zaghrouti & Issmail El Hallaoui & François Soumis, 2020. "Improving set partitioning problem solutions by zooming around an improving direction," Annals of Operations Research, Springer, vol. 284(2), pages 645-671, January.

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