Skip to main content

A Model Seeker: Extracting Global Constraint Models from Positive Examples

  • Conference paper
Principles and Practice of Constraint Programming (CP 2012)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7514))

Abstract

We describe a system which generates finite domain constraint models from positive example solutions, for highly structured problems. The system is based on the global constraint catalog, providing the library of constraints that can be used in modeling, and the Constraint Seeker tool, which finds a ranked list of matching constraints given one or more sample call patterns.

We have tested the modeler with 230 examples, ranging from 4 to 6,500 variables, using between 1 and 7,000 samples. These examples come from a variety of domains, including puzzles, sports-scheduling, packing & placement, and design theory. When comparing against manually specified “canonical” models for the examples, we achieve a hit rate of 50%, processing the complete benchmark set in less than one hour on a laptop. Surprisingly, in many cases the system finds usable candidate lists even when working with a single, positive example.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Beldiceanu, N., Carlsson, M., Flener, P., Pearson, J.: On the reification of global constraints. Technical Report T2012:02, SICS (2012)

    Google Scholar 

  2. Beldiceanu, N., Carlsson, M., Rampon, J.: Global constraint catalog, 2nd edn. (revision a). Technical Report T2012:03, SICS (2012)

    Google Scholar 

  3. Beldiceanu, N., Simonis, H.: A Constraint Seeker: Finding and Ranking Global Constraints from Examples. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 12–26. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  4. Beldiceanu, N., Simonis, H.: Using the global constraint seeker for learning structured constraint models: a first attempt. In: The 10th International Workshop on Constraint Modelling and Reformulation (ModRef 2011), Perugia, Italy, pp. 20–34 (September 2011)

    Google Scholar 

  5. Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning ways for your mathematical plays, 2nd edn., vol. 4. A K Peters/CRC Press (2004)

    Google Scholar 

  6. Bessière, C., Coletta, R., Freuder, E.C., O’Sullivan, B.: Leveraging the Learning Power of Examples in Automated Constraint Acquisition. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 123–137. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  7. Bessière, C., Coletta, R., Koriche, F., O’Sullivan, B.: A SAT-Based Version Space Algorithm for Acquiring Constraint Satisfaction Problems. In: Gama, J., Camacho, R., Brazdil, P.B., Jorge, A.M., Torgo, L. (eds.) ECML 2005. LNCS (LNAI), vol. 3720, pp. 23–34. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  8. Bessière, C., Coletta, R., Petit, T.: Acquiring Parameters of Implied Global Constraints. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 747–751. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  9. Bose, R.C., Shrikhande, S.S., Parker, E.T.: Further results on the construction of mutually orthogonal latin squares and the falsity of Euler’s conjecture. Canadian Journal of Mathematics 12, 189–203 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  10. Carlier, J., Pinson, E.: An algorithm for solving the job shop problem. Management Science 35, 164–176 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  11. Charnley, J., Colton, S., Miguel, I.: Automatic generation of implied constraints. In: Brewka, G., Coradeschi, S., Perini, A., Traverso, P. (eds.) ECAI. Frontiers in Artificial Intelligence and Applications, vol. 141, pp. 73–77. IOS Press (2006)

    Google Scholar 

  12. Drakakis, K.: A review of Costas arrays. Journal of Applied Mathematics, 1–32 (2006)

    Google Scholar 

  13. Dudeney, H.E.: Amusements in Mathematics. Dover, New York (1917)

    Google Scholar 

  14. Flener, P., Frisch, A., Hnich, B., Kiziltan, Z., Miguel, I., Walsh, T.: Matrix modelling. Technical Report 2001-023, Department of Information Technology, Uppsala University (September 2001)

    Google Scholar 

  15. Haynes, T.W., Hedetniemi, S.T., Slater, P.J.: Fundamentals of Domination in Graphs. Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker (1998)

    Google Scholar 

  16. Van Hentenryck, P., Michel, L.: Constraint-Based Local Search. MIT Press, Boston (2005)

    Google Scholar 

  17. Henz, M.: Scheduling a major college basketball conference - revisited. Operations Research 49, 163–168 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  18. Henz, M., Müller, T., Thiel, S.: Global constraints for round robin tournament scheduling. European Journal of Operational Research 153(1), 92–101 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  19. Hernández, B.M.: The Systematic Generation of Channelled Models in Constraint Satisfaction. PhD thesis, University of York, York, YO10 5DD, UK, Department of Computer Science (2007)

    Google Scholar 

  20. Hooker, J.N.: Integrated Methods for Optimization. Springer Science + Business Media, LLC, New York (2007)

    MATH  Google Scholar 

  21. Lallouet, A., Lopez, M., Martin, L., Vrain, C.: On learning constraint problems. In: ICTAI (1), pp. 45–52. IEEE Computer Society (2010)

    Google Scholar 

  22. Maher, M.J.: Open Constraints in a Boundable World. In: van Hoeve, W.-J., Hooker, J.N. (eds.) CPAIOR 2009. LNCS, vol. 5547, pp. 163–177. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  23. Marriott, K., Nethercote, N., Rafeh, R., Stuckey, P.J., de la Banda, M.G., Wallace, M.: The design of the Zinc modelling language. Constraints 13(3), 229–267 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  24. Nemhauser, G., Trick, M.: Scheduling a major college basketball conference. Operations Research 46, 1–8 (1998)

    Article  Google Scholar 

  25. O’Sullivan, B.: Automated modelling and solving in constraint programming. In: Fox, M., Poole, D. (eds.) AAAI, pp. 1493–1497. AAAI Press (2010)

    Google Scholar 

  26. Petkovic, M.S.: Famous Puzzles of Great Mathematicians. American Mathematical Society, Providence (2009)

    MATH  Google Scholar 

  27. Roussel, O., Lecoutre, C.: XML representation of constraint networks format XCSP 2.1. Technical Report arXiv:0902.2362v1, Universite Lille-Nord de France, Artois (2009)

    Google Scholar 

  28. Schreuder, J.A.M.: Combinatorial aspects of construction of competition Dutch professional football leagues. Discrete Applied Mathematics 35(3), 301–312 (1992)

    Article  MATH  Google Scholar 

  29. Smith, B.M., Brailsford, S.C., Hubbard, P.M., Paul Williams, H.: The progressive party problem: Integer linear programming and constraint programming compared. Constraints 1(1/2), 119–138 (1996)

    Article  MathSciNet  Google Scholar 

  30. Walser, J.P.: Domain-Independent Local Search for Linear Integer Optimization. PhD thesis, Technical Faculty of the University des Saarlandes, Saarbruecken, Germany (October 1998)

    Google Scholar 

  31. Watkins, J.J.: Across the Board: The Mathematics of Chessboard Problems. Princeton University Press, Princeton (2004)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Beldiceanu, N., Simonis, H. (2012). A Model Seeker: Extracting Global Constraint Models from Positive Examples. In: Milano, M. (eds) Principles and Practice of Constraint Programming. CP 2012. Lecture Notes in Computer Science, vol 7514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33558-7_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-33558-7_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33557-0

  • Online ISBN: 978-3-642-33558-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics