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Table Constraints for Integer Programming

Authors: Hendrik Bierlee, Wout Piessens, Tias Guns, and Peter J. Stuckey

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Hendrik Bierlee, Wout Piessens, Tias Guns, Peter J. Stuckey. Table Constraints for Integer Programming (Software, Source Code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@misc{dagstuhl-artifact-26917,
   title = {{Table Constraints for Integer Programming}}, 
   author = {Bierlee, Hendrik and Piessens, Wout and Guns, Tias and Stuckey, Peter J.},
   note = {Software, https://wms.cs.kuleuven.be/chat-opt, https://www.fwo.be/, https://optima.org.au/, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:1b22a434c54cd6bb28794cf6c9771f6a002e07f0;origin=https://github.com/ML-KULeuven/table-constraints-for-integer-programming;visit=swh:1:snp:993c9810181126cd29c2384d17d88d3c58cbdc58;anchor=swh:1:rev:3a9a6ff8e84d1d4ea474c2da6cf466a6be923128}{\texttt{swh:1:dir:1b22a434c54cd6bb28794cf6c9771f6a002e07f0}} (visited on 2026-07-13)},
   url = {https://github.com/ML-KULeuven/table-constraints-for-integer-programming},
   doi = {10.4230/artifacts.26917},
}

Document

DOI: 10.4230/LIPIcs.CP.2026.6

Table Constraints for Integer Programming

Authors: Hendrik Bierlee, Wout Piessens, Tias Guns, and Peter J. Stuckey

Published in: LIPIcs, Volume 379, 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026)

Abstract

Global constraints are a central concept in Constraint Programming (CP), which allow modellers to compactly express complex relations, and which allow solvers to efficiently handle them. Table constraints have especially been well-studied as they can express arbitrary finite relations, and are extensively used in CP benchmarks. In this paper we study how to best deal with table constraints when using Integer Linear Programming (ILP) solvers. We study two paradigms: linear encodings, and a lazy cut generation approach. For the encoding we propose a novel MDD-based flow encoding. For the cut generation, in which lazy constraints are generated on-demand during branch-and-cut search, we investigate different ways of generating such integer and fractional cuts as well as how to strengthen them through shrinking and cut lifting. We experimentally compare the different approaches on CP competition instances with a wide variety of table constraints, showing clear benefits over the standard integer encoding.

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Hendrik Bierlee, Wout Piessens, Tias Guns, and Peter J. Stuckey. Table Constraints for Integer Programming. In 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 379, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bierlee_et_al:LIPIcs.CP.2026.6,
  author =	{Bierlee, Hendrik and Piessens, Wout and Guns, Tias and Stuckey, Peter J.},
  title =	{{Table Constraints for Integer Programming}},
  booktitle =	{32nd International Conference on Principles and Practice of Constraint Programming (CP 2026)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-432-1},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{379},
  editor =	{Beldiceanu, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2026.6},
  URN =		{urn:nbn:de:0030-drops-266397},
  doi =		{10.4230/LIPIcs.CP.2026.6},
  annote =	{Keywords: Table constraints, integer programming, cut generation, modelling}
}

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Table Constraints for Integer Programming

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Table Constraints for Integer Programming

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