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Table Constraints for Integer Programming

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

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Subject Classification

ACM Subject Classification
  • Software and its engineering → Constraint and logic languages
  • Mathematics of computing → Solvers
  • Applied computing → Operations research
Keywords
  • Table constraints
  • integer programming
  • cut generation
  • modelling

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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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.CP.2026.6

Author Details

Hendrik Bierlee
  • KU Leuven, Belgium
Wout Piessens
  • KU Leuven, Belgium
Tias Guns
  • KU Leuven, Belgium
Peter J. Stuckey
  • Monash University, Melbourne, Australia
  • OPTIMA ITTC, Melbourne, Australia

Funding

  • Bierlee, Hendrik: funded by the European Research Council (ERC) under the EU Horizon 2020 research and innovation programme (Grant No 101002802, CHAT-Opt)
  • Piessens, Wout: funded by the Research Foundation-Flanders (FWO-Vlaanderen, G020525N)
  • Guns, Tias: funded by the European Research Council (ERC) under the EU Horizon 2020 research and innovation programme (Grant No 101002802, CHAT-Opt)
  • Stuckey, Peter J.: funded by the Australian Government through the Australian Research Council Industrial Transformation Training Centre in Optimisation Technologies, Integrated Methodologies, and Applications (OPTIMA), Project ID IC200100009

Supplementary Materials

References

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