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Search combinators

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Abstract

The ability to model search in a constraint solver can be an essential asset for solving combinatorial problems. However, existing infrastructure for defining search heuristics is often inadequate. Either modeling capabilities are extremely limited or users are faced with a general-purpose programming language whose features are not tailored towards writing search heuristics. As a result, major improvements in performance may remain unexplored. This article introduces search combinators, a lightweight and solver-independent method that bridges the gap between a conceptually simple modeling language for search (high-level, functional and naturally compositional) and an efficient implementation (low-level, imperative and highly non-modular). By allowing the user to define application-tailored search strategies from a small set of primitives, search combinators effectively provide a rich domain-specific language (DSL) for modeling search to the user. Remarkably, this DSL comes at a low implementation cost to the developer of a constraint solver. The article discusses two modular implementation approaches and shows, by empirical evaluation, that search combinators can be implemented without overhead compared to a native, direct implementation in a constraint solver.

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References

  1. Baatar, D., Boland, N., Brand, S., Stuckey, P.J. (2011). CP and IP approaches to cancer radiotherapy delivery optimization. Constraints, 16(2), 173–194.

    Article  MathSciNet  MATH  Google Scholar 

  2. Boussemart, F., Hemery, F., Lecoutre, C., Sais, L. (2004). Boosting systematic search by weighting constraints. In R.L. de Mántaras, & L. Saitta (Eds.), Proceedings of the 16th Eureopean conference on artificial intelligence, ECAI’2004 (pp. 146–150). IOS Press.

  3. Choi, C.W., Henz, M., Ng, K.B. (2001). A compositional framework for search. In Proceedings of CICLOPS: C olloquium on implementation of constraint and logic p rogramming systems, appeared as technical report TR-CS-003/2001. New Mexico State University.

  4. Cook, W.R. (1989). A denotational semantics of inheritance. Ph.D. thesis, Brown University.

  5. Cremet, V., Garillot, F., Lenglet, S., Odersky, M. (2006). A core calculus for scala type checking. In R. Kralovic, & P. Urzyczyn (Eds.), Mathematical foundations of computer science 2006, 31st international symposium, MFCS 2006. LNCS (Vol. 4162, pp. 1–23). Springer.

  6. Desouter, B. (2012). Modular search heuristics in scala. Master’s thesis, Ghent University (in Dutch).

  7. Hamadi, Y., Monfroy, E., Saubion, F. (Eds.) (2012). Autonomous search. Springer.

  8. Harvey, W.D., & Ginsberg, M.L. (1995). Limited discrepancy search. In Proceedings of the fourteenth international joint conference on artificial intelligence, IJCAI 95 (pp. 607–613). Morgan Kauufmann.

  9. IBM Corporation (2011). IBM ILOG CP optimizer. http://www-01.ibm.com/software/integration/optimization/cplex-cp-optimizer/. Accessed November 2012

  10. Kiczales, G., Lamping, J., Menhdhekar, A., Maeda, C., Lopes, C., Loingtier, J., Irwin, J. (1997). Aspect-oriented programming. In ECOOP’97 - object-oriented programming, 11th European conference. LNCS (Vol. 1241, pp. 220–242). Springer.

  11. Korf, R.E. (1985). Depth-first iterative-deepening: an optimal admissible tree search. Artificial Intelligence, 27, 97–109.

    Article  MathSciNet  MATH  Google Scholar 

  12. Kuchcinski, K., & Szymanek, R. (2012). JaCoP - Java constraint programming solver. http://www.jacop.eu/. Accessed November 2012

  13. Laburthe, F., & Caseau, Y. (2002). SALSA: a language for search algorithms. Constraints, 7(3), 255–288.

    Article  MathSciNet  MATH  Google Scholar 

  14. Marriott, K., Nethercote, N., Rafeh, R., Stuckey, P., Garcia de la Banda, M., Wallace, M. (2008). The design of the zinc modelling language. Constraints, 13(3), 229–267.

    Article  MathSciNet  MATH  Google Scholar 

  15. Nethercote, N., Stuckey, P., Becket, R., Brand, S., Duck, G., Tack, G. (2007). Minizinc: towards a standard CP modelling language. In C. Bessiere (Ed.), Thirteenth international conference on principles and practice of constraint programming. LNCS (Vol. 4741, pp. 529–543). Springer.

  16. Perron, L. (1999). Search procedures and parallelism in constraint programming. In J. Jaffar (Ed.), Fifth international conference on principles and practice of constraint programming. LNCS (Vol. 1713, pp. 346–360). Springer.

  17. Rafeh, R., Marriott, K., de la Banda, M.G., Nethercote, N., Wallace, M. (2008). Adding search to zinc. In P.J. Stuckey (Ed.), Fourteenth international conference on principles and practice of constraint programming. LNCS (Vol. 5202, pp. 624–629). Springer.

  18. Refalo, P. (2004). Impact-based search strategies for constraint programming. In M. Wallace (Ed.), Tenth international conference on principles and practice of constraint programming. LNCS (Vol. 3258, pp. 557–571). Springer.

  19. Samulowitz, H., Tack, G., Fischer, J., Wallace, M., Stuckey, P. (2010). Towards a lightweight standard search language. In The 9th international workshop on constraint modelling and reformulation (ModRef). http://www.it.uu.se/research/group/astra/ModRef10/programme.html. Accessed November 2012

  20. Schimpf, J., & Shen, K. (2012). ECLiPSe – from LP to CLP. Theory and Practice of Logic Programming, 12(1–2), 127–156.

    Article  MathSciNet  MATH  Google Scholar 

  21. Schrijvers, T., Stuckey, P.J., Wadler, P. (2009). Monadic constraint programming. Journal of Functional Programming, 19(6), 663–697.

    Article  MathSciNet  MATH  Google Scholar 

  22. Schrijvers, T., Tack, G., Wuille, P., Samulowitz, H., Stuckey, P. (2011). Search combinators. In J. Lee (Ed.), Seventeenth international conference on principles and practice of constraint programming. LNCS (Vol. 6876, pp. 774–788). Springer.

  23. Schrijvers, T., Triska, M., Demoen, B. (2012). Tor: extensible search with hookable disjunction. In Principles and practice of declarative programming (PPDP’12). ACM.

  24. Schulte, C. (1997). Programming constraint inference engines. In G. Smolka (Ed.), Third international conference on principles and practice of constraint programming. LNCS (Vol. 1330, pp. 519–533). Springer

  25. Schulte, C., et al. (2009). Gecode, the generic constraint development environment. http://www.gecode.org/. Accessed November 2012

  26. Sellmann, M., & Kadioglu, S. (2008). Dichotomic search protocols for constrained optimization. In P.J. Stuckey (Ed.), Fourteenth international conference on principles and practice of constraint programming. LNCS (Vol. 5202, pp. 251–265). Springer.

  27. Smolka, G. (1995). The Oz programming model. In J. van Leeuwen (Ed.), Computer science today. LNCS (Vol. 1000, pp. 324–343). Springer.

  28. Swedish Institute of Computer Science (2008). SICStus prolog. http://www.sics.se/isl/sicstuswww/site/. Accessed November 2012

  29. Van Hentenryck, P., & Michel, L. (2005). Constraint-based local search. MIT Press.

  30. Van Hentenryck, P., & Michel, L. (2006). Nondeterministic control for hybrid search. Constraints, 11(4), 353–373.

    Article  MathSciNet  MATH  Google Scholar 

  31. Van Hentenryck, P., Perron, L., Puget, J.F. (2000). Search and strategies in OPL. ACM Transactions on Computational Logic, 1(2), 285–315.

    Article  MathSciNet  Google Scholar 

  32. Wielemaker, J., Schrijvers, T., Triska, M., Lager, T. (2012). SWI-Prolog. Theory and Practice of Logic Programming, 12(1–2), 67–96.

    Article  MathSciNet  MATH  Google Scholar 

  33. Zhou, N.F. (2012). The language features and architecture of B-Prolog. Theory and Practice of Logic Programming, 12(1–2), 189–218.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Universiteit Gent, Gent, Belgium

    Tom Schrijvers & Pieter Wuille

  2. National ICT Australia (NICTA), Victoria, Australia

    Guido Tack & Peter J. Stuckey

  3. Monash University, Victoria, Australia

    Guido Tack

  4. Katholieke Universiteit Leuven, Leuven, Belgium

    Pieter Wuille

  5. IBM Research, New York, USA

    Horst Samulowitz

  6. University of Melbourne, Victoria, Australia

    Peter J. Stuckey

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  1. Tom Schrijvers
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  2. Guido Tack
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  4. Horst Samulowitz
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  5. Peter J. Stuckey
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Correspondence to Tom Schrijvers.

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Schrijvers, T., Tack, G., Wuille, P. et al. Search combinators. Constraints 18, 269–305 (2013). https://doi.org/10.1007/s10601-012-9137-8

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