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Automatic Generation and Selection of Streamlined Constraint Models via Monte Carlo Search on a Model Lattice

  • Patrick Spracklen
  • Özgür AkgünEmail author
  • Ian Miguel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11008)

Abstract

Streamlined constraint reasoning is the addition of uninferred constraints to a constraint model to reduce the search space, while retaining at least one solution. Previously it has been established that it is possible to generate streamliners automatically from abstract constraint specifications in Essence and that effective combinations of streamliners can allow instances of much larger scale to be solved. A shortcoming of the previous approach was the crude exploration of the power set of all combinations using depth and breadth first search. We present a new approach based on Monte Carlo search over the lattice of streamlined models, which efficiently identifies effective streamliner combinations.

Notes

Acknowledgements

This work was supported via EPSRC EP/P015638/1. We thank our anonymous reviewers for helpful comments.

References

  1. 1.
    Akgün, Ö.: Extensible automated constraint modelling via refinement of abstract problem specifications. Ph.D. thesis, University of St Andrews (2014)Google Scholar
  2. 2.
    Akgun, O., Frisch, A.M., Gent, I.P., Hussain, B.S., Jefferson, C., Kotthoff, L., Miguel, I., Nightingale, P.: Automated symmetry breaking and model selection in Conjure. In: Schulte, C. (ed.) CP 2013. LNCS, vol. 8124, pp. 107–116. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40627-0_11CrossRefGoogle Scholar
  3. 3.
    Akgün, Ö., Gent, I.P., Jefferson, C., Miguel, I., Nightingale, P.: Breaking conditional symmetry in automated constraint modelling with Conjure. In: ECAI, pp. 3–8 (2014)Google Scholar
  4. 4.
    Akgün, Ö., Miguel, I., Jefferson, C., Frisch, A.M., Hnich, B.: Extensible automated constraint modelling. In: Proceedings of the Twenty-Fifth AAAI Conference on Artificial Intelligence, pp. 4–11. AAAI Press (2011)Google Scholar
  5. 5.
    Auer, P., Cesa-Bianchi, N., Fischer, P.: Finite-time analysis of the multiarmed bandit problem. Mach. Learn. 47(2), 235–256 (2002).  https://doi.org/10.1023/A:1013689704352CrossRefzbMATHGoogle Scholar
  6. 6.
    Ayel, J., Favaron, O.: Helms are graceful. In: Progress in Graph Theory (Waterloo, Ont., 1982), pp. 89–92. Academic Press, Toronto (1984)Google Scholar
  7. 7.
    Bellman, R.: Dynamic Programming and Markov Processes. JSTOR (1961)Google Scholar
  8. 8.
    Browne, C., Powley, E., Whitehouse, D., Lucas, S., Cowling, P.I., Tavener, S., Perez, D., Samothrakis, S., Colton, S., et al.: A survey of Monte Carlo tree search methods. IEEE Trans. Comput. Intell. AI 4(1), 1–43 (2012)CrossRefGoogle Scholar
  9. 9.
    Čagalj, M., Hubaux, J.P., Enz, C.: Minimum-energy broadcast in all-wireless networks: Np-completeness and distribution issues. In: Proceedings of the 8th Annual International Conference on Mobile Computing and Networking, pp. 172–182. ACM (2002)Google Scholar
  10. 10.
    Charnley, J., Colton, S., Miguel, I.: Automatic generation of implied constraints. ECAI 141, 73–77 (2006)Google Scholar
  11. 11.
    Colton, S., Miguel, I.: Constraint generation via automated theory formation. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 575–579. Springer, Heidelberg (2001).  https://doi.org/10.1007/3-540-45578-7_42CrossRefGoogle Scholar
  12. 12.
    Flener, P., Frisch, A., Hnich, B., Kiziltan, Z., Miguel, I., Walsh, T.: Matrix modelling. In: Proceedings of the CP-01 Workshop on Modelling and Problem Formulation, p. 223 (2001)Google Scholar
  13. 13.
    Flener, P., Frisch, A.M., Hnich, B., Kiziltan, Z., Miguel, I., Walsh, T.: Matrix modelling: exploiting common patterns in constraint programming. In: Proceedings of the International Workshop on Reformulating Constraint Satisfaction Problems, pp. 27–41 (2002)Google Scholar
  14. 14.
    Frisch, A.M., Grum, M., Jefferson, C., Hernández, B.M., Miguel, I.: The essence of essence. In: Modelling and Reformulating Constraint Satisfaction Problems, p. 73 (2005)Google Scholar
  15. 15.
    Frisch, A.M., Grum, M., Jefferson, C., Hernández, B.M., Miguel, I.: The design of essence: a constraint language for specifying combinatorial problems. IJCAI 7, 80–87 (2007)Google Scholar
  16. 16.
    Frisch, A.M., Harvey, W., Jefferson, C., Martínez-Hernández, B., Miguel, I.: Essence: a constraint language for specifying combinatorial problems. Constraints 13(3), 268–306 (2008)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Frisch, A.M., Jefferson, C., Miguel, I.: Symmetry breaking as a prelude to implied constraints: a constraint modelling pattern. In: ECAI, vol. 16, p. 171 (2004)Google Scholar
  18. 18.
    Frisch, A.M., Miguel, I., Walsh, T.: Symmetry and implied constraints in the steel mill slab design problem. In: Proceedings of CP01 Workshop on Modelling and Problem Formulation (2001)Google Scholar
  19. 19.
    Frisch, A.M., Miguel, I., Walsh, T.: CGRASS: a system for transforming constraint satisfaction problems. In: O’Sullivan, B. (ed.) CologNet 2002. LNCS, vol. 2627, pp. 15–30. Springer, Heidelberg (2003).  https://doi.org/10.1007/3-540-36607-5_2CrossRefGoogle Scholar
  20. 20.
    Frucht, R.: Graceful numbering of wheels and related graphs. Ann. N. Y. Acad. Sci. 319(1), 219–229 (1979)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Gent, I.P., Jefferson, C., Miguel, I.: Minion: a fast scalable constraint solver. ECAI 141, 98–102 (2006)Google Scholar
  22. 22.
    Gomes, C., Sellmann, M.: Streamlined constraint reasoning. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 274–289. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-30201-8_22CrossRefzbMATHGoogle Scholar
  23. 23.
    Huczynska, S., McKay, P., Miguel, I., Nightingale, P.: Modelling equidistant frequency permutation arrays: an application of constraints to mathematics. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 50–64. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-642-04244-7_7CrossRefGoogle Scholar
  24. 24.
    Kouril, M., Franco, J.: Resolution tunnels for improved SAT solver performance. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 143–157. Springer, Heidelberg (2005).  https://doi.org/10.1007/11499107_11CrossRefGoogle Scholar
  25. 25.
    Le Bras, R., Gomes, C.P., Selman, B.: Double-wheel graphs are graceful. In: Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence, IJCAI 2013, pp. 587–593. AAAI Press (2013). http://dl.acm.org/citation.cfm?id=2540128.2540214
  26. 26.
    Le Bras, R., Gomes, C.P., Selman, B.: On the Erdős discrepancy problem. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 440–448. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-10428-7_33CrossRefGoogle Scholar
  27. 27.
    LeBras, R., Gomes, C.P., Selman, B.: Double-wheel graphs are graceful. In: IJCAI, pp. 587–593 (2013)Google Scholar
  28. 28.
    Lee, Y., Sherali, H.D., Han, J., Kim, S.I.: A branch-and-cut algorithm for solving an intraring synchronous optical network design problem. Networks 35(3), 223–232 (2000)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Ma, K., Feng, C.: On the gracefulness of gear graphs. Math. Pract. Theor. 4, 72–73 (1984)MathSciNetGoogle Scholar
  30. 30.
    Nethercote, N., Stuckey, P.J., Becket, R., Brand, S., Duck, G.J., Tack, G.: MiniZinc: towards a standard CP modelling language. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 529–543. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-74970-7_38CrossRefGoogle Scholar
  31. 31.
    Nightingale, P., Akgün, Ö., Gent, I.P., Jefferson, C., Miguel, I.: Automatically improving constraint models in Savile Row through associative-commutative common subexpression elimination. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 590–605. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-10428-7_43CrossRefGoogle Scholar
  32. 32.
    Nightingale, P., Akgün, O., Gent, I.P., Jefferson, C., Miguel, I., Spracklen, P.: Automatically improving constraint models in Savile Row. Artif. Intell. 251, 35–61 (2017).  https://doi.org/10.1016/j.artint.2017.07.001MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Nightingale, P., Spracklen, P., Miguel, I.: Automatically improving SAT encoding of constraint problems through common subexpression elimination in Savile Row. In: Pesant, G. (ed.) CP 2015. LNCS, vol. 9255, pp. 330–340. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-23219-5_23CrossRefGoogle Scholar
  34. 34.
    Parrello, B.D., Kabat, W.C., Wos, L.: Job-shop scheduling using automated reasoning: a case study of the car-sequencing problem. J. Autom. Reason. 2(1), 1–42 (1986)MathSciNetCrossRefGoogle Scholar
  35. 35.
    Slaney, J., Fujita, M., Stickel, M.: Automated reasoning and exhaustive search: quasigroup existence problems. Comput. Math. Appl. 29(2), 115–132 (1995)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Smith, B.M., Brailsford, S.C., Hubbard, P.M., Williams, H.P.: The progressive party problem: integer linear programming and constraint programming compared. Constraints 1(1–2), 119–138 (1996)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Toth, P., Vigo, D.: The vehicle routing problem. In: SIAM (2002)Google Scholar
  38. 38.
    van der Waerden, B.: Beweis einer Baudetschen Vermutung. Nieuw Arch. Wisk. 19, 212–216 (1927)zbMATHGoogle Scholar
  39. 39.
    Walsh, T.: CSPLib problem 015: Schur’s lemma. http://www.csplib.org/Problems/prob015
  40. 40.
    Wetter, J., Akgün, Ö., Miguel, I.: Automatically generating streamlined constraint models with Essence and Conjure. In: Pesant, G. (ed.) CP 2015. LNCS, vol. 9255, pp. 480–496. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-23219-5_34CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.School of Computer ScienceUniversity of St AndrewsSt AndrewsUK

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