Advertisement

Search Space Extraction

  • Deepak Mehta
  • Barry O’Sullivan
  • Luis Quesada
  • Nic Wilson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5732)

Abstract

Systematic tree search is often used in conjunction with inference and restarts when solving challenging Constraint Satisfaction Problems (csps). In order to improve the efficiency of constraint solving, techniques that learn during search, such as constraint weighting and nogood learning, have been proposed. Constraint weights can be used to guide heuristic choices. Nogood assignments can be avoided by adding additional constraints. Both of these techniques can be used in either one-shot systematic search, or in a setting in which we frequently restart the search procedure. In this paper we propose a third way of learning during search, generalising previous work by Freuder and Hubbe. Specifically, we show how, in a restart context, we can guarantee that we avoid revisiting a previously visited region of the search space by extracting it from the problem. Likewise, we can avoid revisiting inconsistent regions of the search space by extracting inconsistent subproblems, based on a significant improvement upon Freuder and Hubbe’s approach. A major empirical result of this paper is that our approach significantly outperforms \(\mbox{\sc mac}\) combined with weighted degree heuristics and restarts on challenging constraint problems. Our approach can be regarded as an efficient form of learning that does not rely on constraint propagation. Instead, we rely on a reformulation of a csp into an equivalent set of csps, none of which contain any of the search space we wish to avoid.

Keywords

Search Space Search Tree Constraint Satisfaction Problem Constraint Network Solver Competition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Sabin, D., Freuder, E.C.: Contradicting conventional wisdom in constraint satisfaction. In: ECAI, pp. 125–129 (1994)Google Scholar
  2. 2.
    Boussemart, F., Hemery, F., Lecoutre, C., Saïs, L.: Boosting systematic search by weighting constraints. In: Proceedings of the Thirteenth European Conference on Artificial Intelligence (2004)Google Scholar
  3. 3.
    Grimes, D., Wallace, R.J.: Learning to identify global bottlenecks in constraint satisfaction search. In: FLAIRS Conference, pp. 592–597 (2007)Google Scholar
  4. 4.
    Schiex, T., Verfaillie, G.: Nogood recording for static and dynamic constraint satisfaction problems. In: ICTAI, pp. 48–55 (1993)Google Scholar
  5. 5.
    Lecoutre, C., Sais, L., Tabary, S., Vidal, V.: Nogood recording from restarts. In: IJCAI, pp. 131–136 (2007)Google Scholar
  6. 6.
    Freuder, E.C., Hubbe, P.D.: Extracting constraint satisfaction subproblems. In: IJCAI, pp. 548–557 (1995)Google Scholar
  7. 7.
    Rossi, F., van Beek, P., Walsh, T.: Handbook of Constraint Programming. Elsevier Science Inc., Amsterdam (2006)zbMATHGoogle Scholar
  8. 8.
    Gomes, C.P., Selman, B., Kautz, H.A.: Boosting combinatorial search through randomization. In: AAAI/IAAI, pp. 431–437 (1998)Google Scholar
  9. 9.
    Hemery, F., Lecoutre, C., Sais, L., Boussemart, F.: Extracting mucs from constraint networks. In: ECAI, pp. 113–117 (2006)Google Scholar
  10. 10.
    Boussemart, F., Hemery, F., Lecoutre, C.: Description and representation of the problems selected for the first international constraint satisfaction solver competition. In: van Dongen, M. (ed.) Proceedings of the Second International Workshop on Constraint Propagation and Implementation. Solver Competition, vol. 2, pp. 7–26 (2005)Google Scholar
  11. 11.
    Cabon, B., De Givry, S., Lobjois, L., Schiex, T., Warners, J.: Radio link frequency assignment. Journal of Constraints 4, 79–89 (1999)CrossRefzbMATHGoogle Scholar
  12. 12.
    Bessière, C., Chmeiss, A., Saïs, L.: Neighborhood-based variable ordering heuristics for the constraint satisfaction problem. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 565–569. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  13. 13.
    Gent, I., MacIntyre, E., Prosser, P., Smith, B., Walsh, T.: Random constraint satisfaction: Flaws and structure. Journal of Constraints 6(4), 345–372 (2001)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Deepak Mehta
    • 1
  • Barry O’Sullivan
    • 1
  • Luis Quesada
    • 1
  • Nic Wilson
    • 1
  1. 1.Cork Constraint Computation Centre Department of Computer ScienceUniversity College CorkIreland

Personalised recommendations