Mathematical Programming

, Volume 170, Issue 1, pp 237–266 | Cite as

Theoretical challenges towards cutting-plane selection

  • Santanu S. DeyEmail author
  • Marco Molinaro
Full Length Paper Series B


While many classes of cutting-planes are at the disposal of integer programming solvers, our scientific understanding is far from complete with regards to cutting-plane selection, i.e., the task of selecting a portfolio of cutting-planes to be added to the LP relaxation at a given node of the branch-and-bound tree. In this paper we review the different classes of cutting-planes available, known theoretical results about their relative strength, important issues pertaining to cut selection, and discuss some possible new directions to be pursued in order to accomplish cutting-plane selection in a more principled manner. Finally, we review some lines of work that we undertook to provide a preliminary theoretical underpinning for some of the issues related to cut selection.

Mathematics Subject Classification

90C11 90C57 



We would like to thank Tobias Achterberg, Domenico Salvagnin and Roland Wunderling for their help with preparing this manuscript. We would also like to thank anonymous reviewers for their feedback that greatly improved the presentation of this manuscript. Santanu S. Dey would like to acknowledge the support of NSF CMMI Grant # 1562578. Marco Molinaro would like to acknowledge the support of CNPq grants Universal #431480/2016-8 and Bolsa de Produtividade em Pesquisa #310516/2017-0.


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

Authors and Affiliations

  1. 1.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Computer Science DepartmentPUC-RioRio de JaneiroBrazil

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