Advertisement

Objective as a Feature for Robust Search Strategies

  • Anthony Palmieri
  • Guillaume PerezEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11008)

Abstract

In constraint programming the search strategy entirely guides the solving process, and drastically affects the running time for solving particular problem instances. Many features have been defined so far for the design of efficient and robust search strategies, such as variables’ domains, constraint graph, or even the constraints triggering fails. In this paper, we propose to use the objective functions of constraint optimization problems as a feature to guide search strategies. We define an objective-based function, to monitor the objective bounds modifications and to extract information. This function is the main feature to design a new variable selection heuristic, whose results validate human intuitions about the objective modifications. Finally, we introduce a simple but efficient combination of features, to incorporate the objective in the state-of-the-art search strategies. We illustrate this new method by testing it on several classic optimization problems, showing that the new feature often yields to a better running time and finds better solutions in the given time.

References

  1. 1.
    Boussemart, F., Hemery, F., Lecoutre, C., Sais, L.: Boosting systematic search by weighting constraints. In: ECAI, vol. 16, p. 146 (2004)Google Scholar
  2. 2.
    Chu, G., Stuckey, P.J.: Learning value heuristics for constraint programming. In: Michel, L. (ed.) CPAIOR 2015. LNCS, vol. 9075, pp. 108–123. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-18008-3_8CrossRefGoogle Scholar
  3. 3.
    Fages, J.-G., Prud’Homme, C.: Making the first solution good! In: ICTAI 2017 29th IEEE International Conference on Tools with Artificial Intelligence (2017)Google Scholar
  4. 4.
    Gauthier, J.-M., Ribière, G.: Experiments in mixed-integer linear programming using pseudo-costs. Math. Program. 12(1), 26–47 (1977)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Gay, S., Hartert, R., Lecoutre, C., Schaus, P.: Conflict ordering search for scheduling problems. In: Pesant, G. (ed.) CP 2015. LNCS, vol. 9255, pp. 140–148. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-23219-5_10CrossRefGoogle Scholar
  6. 6.
    Gent, I.P., Walsh, T.: CSPlib: a benchmark library for constraints. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 480–481. Springer, Heidelberg (1999).  https://doi.org/10.1007/978-3-540-48085-3_36CrossRefGoogle Scholar
  7. 7.
    Haralick, R.M., Elliott, G.L.: Increasing tree search efficiency for constraint satisfaction problems. Artif. Intell. 14(3), 263–313 (1980)CrossRefGoogle Scholar
  8. 8.
    Heras, F., Larrosa, J.: New inference rules for efficient max-sat solving. In: AAAI, pp. 68–73 (2006)Google Scholar
  9. 9.
    Hutter, F., Hoos, H., Leyton-Brown, K.: An evaluation of sequential model-based optimization for expensive blackbox functions. In: Proceedings of the 15th Annual Conference Companion on Genetic and Evolutionary Computation, pp. 1209–1216. ACM (2013)Google Scholar
  10. 10.
    Larrosa, J., Schiex, T.: Solving weighted CSP by maintaining arc consistency. Artif. Intell. 159(1–2), 1–26 (2004)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Lecoutre, C., Saïs, L., Tabary, S., Vidal, V.: Reasoning from last conflict(s) in constraint programming. Artif. Intell. 173(18), 1592–1614 (2009)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Levasseur, N., Boizumault, P., Loudni, S.: A value ordering heuristic for weighted CSP. In: 19th IEEE International Conference on Tools with Artificial Intelligence, ICTAI 2007, vol. 1, pp. 259–262. IEEE (2007)Google Scholar
  13. 13.
    Lombardi, M., Schaus, P.: Cost impact guided LNS. In: Simonis, H. (ed.) CPAIOR 2014. LNCS, vol. 8451, pp. 293–300. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-07046-9_21CrossRefGoogle Scholar
  14. 14.
    Michel, L., Van Hentenryck, P.: Activity-based search for black-box constraint programming solvers. In: Beldiceanu, N., Jussien, N., Pinson, É. (eds.) CPAIOR 2012. LNCS, vol. 7298, pp. 228–243. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-29828-8_15CrossRefGoogle Scholar
  15. 15.
    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
  16. 16.
    Palmieri, A., Régin, J.-C., Schaus, P.: Parallel strategies selection. In: Rueher, M. (ed.) CP 2016. LNCS, vol. 9892, pp. 388–404. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-44953-1_25CrossRefGoogle Scholar
  17. 17.
    Pesant, G.: Counting-based search for constraint optimization problems. In: Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, Phoenix, Arizona, 12–17 February 2016, USA, pp. 3441–3448 (2016)Google Scholar
  18. 18.
    Pesant, G., Quimper, C.-G., Zanarini, A.: Counting-based search: branching heuristics for constraint satisfaction problems. J. Artif. Intell. Res. (JAIR) 43, 173–210 (2012)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Prud’homme, C., Fages, J.-G., Lorca, X.: Choco Documentation. TASC, INRIA Rennes, LINA CNRS UMR 6241, COSLING S.A.S (2016)Google Scholar
  20. 20.
    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_41CrossRefzbMATHGoogle Scholar
  21. 21.
    Régin, J.-C.: A Filtering algorithm for constraints of difference in CSPS. In: AAAI, vol. 94, pp. 362–367 (1994)Google Scholar
  22. 22.
    Schaus, P., Van Hentenryck, P., Régin, J.-C.: Scalable load balancing in nurse to patient assignment problems. In: van Hoeve, W.-J., Hooker, J.N. (eds.) CPAIOR 2009. LNCS, vol. 5547, pp. 248–262. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-642-01929-6_19CrossRefGoogle Scholar
  23. 23.
    Simonis, H., O’Sullivan, B.: Search strategies for rectangle packing. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 52–66. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-85958-1_4CrossRefGoogle Scholar
  24. 24.
    Smith, B.M., Grant, S.A.: Trying harder to fail first. Research Report Series-University of Leeds School of Computer Studies LU SCS RR (1997)Google Scholar
  25. 25.
    Vilím, P., Laborie, P., Shaw, P.: Failure-directed search for constraint-based scheduling. In: Michel, L. (ed.) CPAIOR 2015. LNCS, vol. 9075, pp. 437–453. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-18008-3_30CrossRefzbMATHGoogle Scholar
  26. 26.
    Wallace, M.: Practical applications of constraint programming. Constraints 1(1–2), 139–168 (1996)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Xia, W., Yap, RH.C.: Learning robust search strategies using a bandit-based approach. In: AAAI Conference on Artificial Intelligence (2018)Google Scholar
  28. 28.
    Zitoun, H., Michel, C., Rueher, M., Michel, L.: Search strategies for floating point constraint systems. In: Beck, J.C. (ed.) CP 2017. LNCS, vol. 10416, pp. 707–722. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-66158-2_45CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Huawei Technologies Ltd., French Research CenterParisFrance
  2. 2.Université de Caen - Normandie, GREYCCaenFrance
  3. 3.Department of Computer ScienceCornell UniversityIthacaUSA

Personalised recommendations