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Mathematical Programming

, Volume 170, Issue 1, pp 207–236 | Cite as

Binary extended formulations of polyhedral mixed-integer sets

  • Sanjeeb Dash
  • Oktay Günlük
  • Robert Hildebrand
Full Length Paper Series B

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.

Keywords

Mixed-integer programming Binarization Extended formulations Cutting planes Branch-and-bound 

Mathematics Subject Classification

90C11 90C57 

Notes

Acknowledgements

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

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2018

Authors and Affiliations

  1. 1.IBM T. J. Watson Research CenterYorktown HeightsUSA
  2. 2.Grado Department of Industrial and Systems EngineeringVirginia TechBlacksburgUSA

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