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The integral basis method for integer programming

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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.

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Authors and Affiliations

  1. Otto-von-Guericke-Universität Magdeburg, Department of Mathematics/IMO, Universitätsplatz 2, 39106 Magdeburg, Germany (e-mail: {haus,mkoeppe,weismant}@imo.math.uni-magdeburg.de), , , , , , DE

    Utz-Uwe Haus, Matthias Köppe & Robert Weismantel

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  1. Utz-Uwe Haus
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  2. Matthias Köppe
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  3. Robert Weismantel
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Manuscript received: February 2001

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Haus, UU., Köppe, M. & Weismantel, R. The integral basis method for integer programming. Mathematical Methods of OR 53, 353–361 (2001). https://doi.org/10.1007/s001860100124

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  • DOI: https://doi.org/10.1007/s001860100124

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