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Exploiting Entropy in Constraint Programming

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13884))

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Abstract

The introduction of Belief Propagation in Constraint Programming through the CP-BP framework makes possible the computation of an estimation of the probability that a given variable-value combination belongs to a solution. The availability of such marginal probability distributions, effectively ranking domain values, allows us to develop branching heuristics but also more generally to apply the concept of entropy to Constraint Programming. We explore how variable and problem entropy can improve how we solve combinatorial problems in the CP-BP framework. We evaluate our proposal on an extensive set of benchmark instances.

A. Burlats—Most of this work was carried out while the first author was at Polytechnique Montréal.

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Notes

  1. 1.

    We will generally omit superscript P for ease of notation.

  2. 2.

    http://www.xcsp.org/instances/.

  3. 3.

    Availables at http://www.xcsp.org/instances/.

  4. 4.

    Available at https://www.minizinc.org/challenge2022/mznc2022_probs.tar.gz.

  5. 5.

    Solver and used instances are available at https://github.com/PesantGilles/MiniCPBP.

References

  1. Babaki, B., Omrani, B., Pesant, G.: Combinatorial search in CP-based iterated belief propagation. In: Simonis, H. (ed.) CP 2020. LNCS, vol. 12333, pp. 21–36. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-58475-7_2

    Chapter  Google Scholar 

  2. Boussemart, F., Hemery, F., Lecoutre, C., Sais, L.: Boosting systematic search by weighting constraints. In: de Mántaras, R.L., Saitta, L. (eds.) Proceedings of the 16th European Conference on Artificial Intelligence, ECAI 2004, Including Prestigious Applicants of Intelligent Systems, PAIS 2004, Valencia, Spain, 22–27 August 2004, pp. 146–150. IOS Press (2004)

    Google Scholar 

  3. Gagnon, S., Pesant, G.: Accelerating counting-based search. In: van Hoeve, W.-J. (ed.) CPAIOR 2018. LNCS, vol. 10848, pp. 245–253. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93031-2_17

    Chapter  Google Scholar 

  4. Michel, L., Schaus, P., Van Hentenryck, P.: MiniCP: a lightweight solver for constraint programming. Math. Program. Comput. 13(1), 133–184 (2021). https://doi.org/10.1007/s12532-020-00190-7

  5. Pearl, J.: Reverend Bayes on inference engines: a distributed hierarchical approach. In: Proceedings of the National Conference on Artificial Intelligence, Pittsburgh, PA, 18–20 August 1982, pp. 133–136 (1982). http://www.aaai.org/Library/AAAI/1982/aaai82-032.php

  6. Pesant, G.: From support propagation to belief propagation in constraint programming. J. Artif. Intell. Res. 66, 123–150 (2019). https://doi.org/10.1613/jair.1.11487

    Article  MathSciNet  MATH  Google Scholar 

  7. Refalo, P.: Impact-based search strategies for constraint programming. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 557–571. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30201-8_41

    Chapter  MATH  Google Scholar 

  8. Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27(3), 379–423 (1948). https://doi.org/10.1002/j.1538-7305.1948.tb01338.x

    Article  MathSciNet  MATH  Google Scholar 

  9. Vavrille, M., Truchet, C., Prud’homme, C.: Solution sampling with random table constraints. In: Michel, L.D. (ed.) 27th International Conference on Principles and Practice of Constraint Programming, CP 2021, Montpellier, France (Virtual Conference), 25–29 October 2021. LIPIcs, vol. 210, pp. 56:1–56:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021). https://doi.org/10.4230/LIPIcs.CP.2021.56

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Author information

Authors and Affiliations

  1. UCLouvain, Ottignies-Louvain-la-Neuve, Belgium

    Auguste Burlats

  2. Polytechnique Montréal, Montreal, Canada

    Gilles Pesant

Authors
  1. Auguste Burlats
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  2. Gilles Pesant
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Corresponding authors

Correspondence to Auguste Burlats or Gilles Pesant .

Editor information

Editors and Affiliations

  1. Department of Management, University of Toronto Scarborough and Rotman School of Management, University of Toronto, Toronto, ON, Canada

    Andre A. Cire

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Burlats, A., Pesant, G. (2023). Exploiting Entropy in Constraint Programming. In: Cire, A.A. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2023. Lecture Notes in Computer Science, vol 13884. Springer, Cham. https://doi.org/10.1007/978-3-031-33271-5_21

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  • DOI: https://doi.org/10.1007/978-3-031-33271-5_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-33270-8

  • Online ISBN: 978-3-031-33271-5

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