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Binary extended formulations of polyhedral mixed-integer sets

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Abstract

We analyze different ways of constructing binary extended formulations of polyhedral mixed-integer sets with bounded integer variables and compare their relative strength with respect to split cuts. We show that among all binary extended formulations where each bounded integer variable is represented by a distinct collection of binary variables, what we call “unimodular” extended formulations are the strongest. We also compare the strength of some binary extended formulations from the literature. Finally, we study the behavior of branch-and-bound on such extended formulations and show that branching on the new binary variables leads to significantly smaller enumeration trees in some cases.

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Acknowledgements

We would like to thank Andrea Lodi for pointing out the importance of binarization techniques and for fruitful discussions.

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Authors and Affiliations

  1. IBM T. J. Watson Research Center, Yorktown Heights, New York, USA

    Sanjeeb Dash & Oktay Günlük

  2. Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, VA, USA

    Robert Hildebrand

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  1. Sanjeeb Dash
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  2. Oktay Günlük
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  3. Robert Hildebrand
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Correspondence to Oktay Günlük.

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Dash, S., Günlük, O. & Hildebrand, R. Binary extended formulations of polyhedral mixed-integer sets. Math. Program. 170, 207–236 (2018). https://doi.org/10.1007/s10107-018-1294-0

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  • DOI: https://doi.org/10.1007/s10107-018-1294-0

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