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Introduction to Combinatorial Optimisation in Numberjack

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Data Mining and Constraint Programming

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10101))

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Abstract

This chapter presents an introduction to combinatorial optimisation in the context of the high-level modelling platform, Numberjack. The process of developing an effective model for a combinatorial problem is presented, along with details on how such problems can be solved using three of the most prominent solution paradigms.

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Notes

  1. 1.

    http://numberjack.ucc.ie/.

References

  1. Tourbier, Y., Oplobedu, A., Marcovitch, J., CHARME: un langage industriel de programmation par contraintes, illustr par une application chez Renault. In: Proceedings of the Ninth International Workshop on Expert Systems and their Applications, pp. 55–70 (1989)

    Google Scholar 

  2. Aggoun, A., Beldiceanu, N.: Extending CHIP in order to solve complex scheduling and placement problems. In: JFPL 1992, 1éres Journées Francophones de Programmation Logique, p. 51 (1992)

    Google Scholar 

  3. Amadini, R., Gabbrielli, M., Mauro, J.: A multicore tool for constraint solving. In: Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, pp. 232–238 (2015)

    Google Scholar 

  4. Ansótegui, C., Sellmann, M., Tierney, K.: A gender-based genetic algorithm for the automatic configuration of algorithms. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 142–157. Springer, Heidelberg (2009). doi:10.1007/978-3-642-04244-7_14

    Chapter  Google Scholar 

  5. Babai, L.: Monte-carlo algorithms in graph isomorphism testing. Technical report DMS 79–10, Université de Montréal (1979)

    Google Scholar 

  6. Beldiceanu, N., Carlsson, M., Rampon, J.-X.: Global constraint catalog. Technical report SICS-T 2005/08-SE (2005)

    Google Scholar 

  7. 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). doi:10.1007/978-3-642-23786-7_4

    Chapter  Google Scholar 

  8. Beldiceanu, N., Simonis, H.: A model seeker: extracting global constraint models from positive examples. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 141–157. Springer, Heidelberg (2012). doi:10.1007/978-3-642-33558-7_13

    Chapter  Google Scholar 

  9. Bessiere, C.: Constraint propagation. In: Handbook of Constraint Programming, pp. 29–83 (2006)

    Google Scholar 

  10. Biere, A., Heule, M.J.H., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press, Amsterdam (2009)

    MATH  Google Scholar 

  11. Boussemart, F., Hemery, F., Lecoutre, C., Sais, L.: Boosting systematic search by weighting constraints. In: Proceedings of the 16th Eureopean Conference on Artificial Intelligence, ECAI 2004, pp. 146–150 (2004)

    Google Scholar 

  12. Chu, G., Stuckey, P.J.: Learning value heuristics for constraint programming. In: Michel, L. (ed.) CPAIOR 2015. LNCS, vol. 9075, pp. 108–123. Springer, Heidelberg (2015). doi:10.1007/978-3-319-18008-3_8

    Google Scholar 

  13. Coletta, R., Bessiére, C., O’Sullivan, B., Freuder, E.C., O’Connell, S., Quinqueton, J.: Semi-automatic modeling by constraint acquisition. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 812–816. Springer, Heidelberg (2003). doi:10.1007/978-3-540-45193-8_58

    Chapter  Google Scholar 

  14. Cook, S.A.: The complexity of theorem-proving procedures. In: Proceedings of the 3rd Annual ACM Symposium on Theory of Computing, pp. 151–158 (1971)

    Google Scholar 

  15. Costas, J.P.: A study of a class of detection waveforms having nearly ideal range - doppler ambiguity properties. Proc. IEEE 72(8), 996–1009 (1984)

    Article  Google Scholar 

  16. Dooms, G.: The CP(Graph) computation domain in constraint programming. Ph.D. thesis, Université catholique de Louvain, Faculté des sciences appliquées (2006)

    Google Scholar 

  17. Fages, J.-G.: Exploitation de structures de graphe en programmation par contraintes. (On the use of graphs within constraint-programming). Ph.D. thesis, École des mines de Nantes, France (2014)

    Google Scholar 

  18. Fitzgerald, T., Malitsky, Y., O’Sullivan, B., Tierney, K.: ReACT: real-time algorithm configuration through tournaments. In: Proceedings of the Seventh Annual Symposium on Combinatorial Search, SOCS 2014 (2014)

    Google Scholar 

  19. Freuder, E.C.: In pursuit of the holy grail. Constraints 2(1), 57–61 (1997)

    Article  MATH  Google Scholar 

  20. Freuder, E.C., O’Sullivan, B.: Grand challenges for constraint programming. Constraints 19(2), 150–162 (2014)

    Article  Google Scholar 

  21. 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)

    Article  MathSciNet  MATH  Google Scholar 

  22. Geelen, P.A.: Dual viewpoint heuristics for binary constraint satisfaction problems. In: Proceedings of the 10th European Conference on Artificial Intelligence, ECAI 1992, pp. 31–35. Wiley (1992)

    Google Scholar 

  23. Gent, I.P., Jefferson, C., Kotthoff, L., Miguel, I., Moore, N.C.A., Nightingale, P., Petrie, K.E.: Learning when to use lazy learning in constraint solving. In: Proceedings of the 19th European Conference on Artificial Intelligence, ECAI 2010, pp. 873–878 (2010)

    Google Scholar 

  24. Gervet, C.: Set intervals in constraint-logic programming: definition and implementation of a language. Ph.D. thesis, Université de France-Compté (1995)

    Google Scholar 

  25. Gomes, C.P., Sabharwal, A.: Exploiting runtime variation in complete solvers. In: Handbook of Satisfiability, pp. 271–288 (2009)

    Google Scholar 

  26. Gomes, C.P., Selman, B., Crato, N., Kautz, H.: Heavy-tailed phenomena in satisfiability and constraint satisfaction problems. J. Autom. Reason. 24(1–2), 67–100 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  27. Gomes, C.P., Selman, B., Kautz, H.A.: Boosting combinatorial search through randomization. In: Proceedings of the 15th National Conference on Artificial Intelligence, AAAI 1998, pp. 431–437 (1998)

    Google Scholar 

  28. Haralick, R.M., Elliott, G.L.: Increasing tree search efficiency for constraint satisfaction problems. Artif. Intell. 14(3), 263–313 (1980)

    Article  Google Scholar 

  29. Hebrard, E., O’Mahony, E., O’Sullivan, B.: Constraint programming and combinatorial optimisation in numberjack. In: Lodi, A., Milano, M., Toth, P. (eds.) CPAIOR 2010. LNCS, vol. 6140, pp. 181–185. Springer, Heidelberg (2010). doi:10.1007/978-3-642-13520-0_22

    Chapter  Google Scholar 

  30. Van Hentenryck, P., Carillon, J.-P., Generality versus specificity: an experience with AI and OR techniques. In: Proceedings of the 7th National Conference on Artificial Intelligence, AAAI 1988, pp. 660–664 (1988)

    Google Scholar 

  31. Hnich, B.: CSPLib problem 034: Warehouse location problem. http://www.csplib.org/Problems/prob034

  32. Hulubei, T., O’Sullivan, B.: The impact of search heuristics on heavy-tailed behaviour. Constraints 11(2–3), 159–178 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  33. Hurley, B., Kotthoff, L., Malitsky, Y., O’Sullivan, B.: Proteus: a hierarchical portfolio of solvers and transformations. In: Simonis, H. (ed.) CPAIOR 2014. LNCS, vol. 8451, pp. 301–317. Springer, Heidelberg (2014). doi:10.1007/978-3-319-07046-9_22

    Chapter  Google Scholar 

  34. Hutter, F., Hoos, H.H., Leyton-Brown, K.: Sequential model-based optimization for general algorithm configuration. In: Coello, C.A.C. (ed.) LION 2011. LNCS, vol. 6683, pp. 507–523. Springer, Heidelberg (2011). doi:10.1007/978-3-642-25566-3_40

    Chapter  Google Scholar 

  35. Kotthoff, L., Gent, I.P., Miguel. I.: A preliminary evaluation of machine learning in algorithm selection for search problems. In: Proceedings of the 4th Annual Symposium on Combinatorial Search, SOCS 2011 (2011)

    Google Scholar 

  36. Laurière, J.-L.: A language and a program for stating and solving combinatorial problems. Artif. Intell. 10(1), 29–127 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  37. Luby, M., Sinclair, A., Zuckerman, D.: Optimal speedup of las vegas algorithms. Inf. Process. Lett. 47(4), 173–180 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  38. Mackworth, A.K.: Consistency in networks of relations. Artif. Intell. 8(1), 99–118 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  39. Mehta, D., O’Sullivan, B., Kotthoff, L., Malitsky, Y.: Lazy branching for constraint satisfaction. In: Proceedings of the 25th International Conference on Tools with Artificial Intelligence, ICTAI 2013, pp. 1012–1019 (2013)

    Google Scholar 

  40. Mehta, D., O’Sullivan, B., Quesada, L., Ruffini, M., Payne, D.B., Doyle, L.: Designing resilient long-reach passive optical networks. In: Proceedings of the 23rd Conference on Innovative Applications of Artificial Intelligence, IAAI 2011 (2011)

    Google Scholar 

  41. Murty, K.G.: Linear Programming. Wiley, Hoboken (1983)

    MATH  Google Scholar 

  42. 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). doi:10.1007/978-3-540-74970-7_38

    Chapter  Google Scholar 

  43. O’Mahony, E., Hebrard, E., Holland, A., Nugent, C., O’Sullivan, B.: Using case-based reasoning in an algorithm portfolio for constraint solving. In: Irish Conference on Artificial Intelligence and Cognitive Science (2008)

    Google Scholar 

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

    Chapter  Google Scholar 

  45. Régin, J.-C.: A filtering algorithm for constraints of difference in csps. In: Proceedings of the 12th National Conference on Artificial Intelligence, AAAI 1994, pp. 362–367 (1994)

    Google Scholar 

  46. Régin, J.-C.: Generalized arc consistency for global cardinality constraint. In: Proceedings of the 8th Innovative Applications of Artificial Intelligence Conference, IAAI 1996, pp. 209–215 (1996)

    Google Scholar 

  47. Rossi, F., van Beek, P., Walsh, T.: Handbook of Constraint Programming. Foundations of Artificial Intelligence. Elsevier, New York (2006)

    MATH  Google Scholar 

  48. Sabin, D., Freuder, E.C.: Contradicting conventional wisdom in constraint satisfaction. In: Proceedings of the 11th European Conference on Artificial Intelligence, ECAI 1994, pp. 125–129. Springer, Heidelberg (1994)

    Google Scholar 

  49. Simonin, G., Artigues, C., Hebrard, E., Lopez, P.: Scheduling scientific experiments on the rosetta/philae mission. In: Milano, M. (ed.) Principles and Practice of Constraint Programming. LNCS, vol. 7514, pp. 23–37. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  50. Simonis, H.: Constraint applications in networks. In: Handbook of Constraint Programming, pp. 875–903 (2006)

    Google Scholar 

  51. Simonis, H.: Models for global constraint applications. Constraints 12(1), 63–92 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  52. van Beek, P.: CSPLib problem 006: Golomb rulers. http://www.csplib.org/Problems/prob006

  53. van Hoeve, W.-J., Katriel, I.: Global constraints. In: Handbook of Constraint Programming. Foundations of Artificial Intelligence, vol. 2, pp. 169–208. Elsevier (2006)

    Google Scholar 

  54. Wallace, M.: Practical applications of constraint programming. Constraints 1(1/2), 139–168 (1996)

    Article  MathSciNet  Google Scholar 

  55. Walsh, T.: Search in a small world. In: Proceedings of the 16th International Joint Conference on Artificial Intelligence, IJCAI 1999, pp. 1172–1177 (1999)

    Google Scholar 

  56. Wolsey, L.A.: Integer Programming. Wiley-Interscience, New York (1998)

    MATH  Google Scholar 

  57. Xu, L., Hutter, F., Hoos, H.H., Leyton-Brown, K.: SATzilla: portfolio-based algorithm selection for SAT. J. Artif. Intell. Res. 32, 565–606 (2008)

    MATH  Google Scholar 

  58. Yip, Y.K.J.: The length-lex representation for constraint programming over sets. Ph.D. thesis, Brown University (2011)

    Google Scholar 

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Hurley, B., O’Sullivan, B. (2016). Introduction to Combinatorial Optimisation in Numberjack. In: Bessiere, C., De Raedt, L., Kotthoff, L., Nijssen, S., O'Sullivan, B., Pedreschi, D. (eds) Data Mining and Constraint Programming. Lecture Notes in Computer Science(), vol 10101. Springer, Cham. https://doi.org/10.1007/978-3-319-50137-6_1

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  • DOI: https://doi.org/10.1007/978-3-319-50137-6_1

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