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Constraints

, Volume 20, Issue 3, pp 325–345 | Cite as

A constraint-based local search backend for MiniZinc

  • Gustav Björdal
  • Jean-Noël MonetteEmail author
  • Pierre Flener
  • Justin Pearson
Article

Abstract

MiniZinc is a modelling language for combinatorial problems, which can then be solved by a solver provided in a backend. There are many backends, based on technologies such as constraint programming, integer programming, or Boolean satisfiability solving. However, to the best of our knowledge, there is currently no constraint-based local search (CBLS) backend. We discuss the challenges to develop such a backend and give an overview of the design of a CBLS backend for MiniZinc. Experimental results show that for some MiniZinc models, our CBLS backend, based on the OscaR/CBLS solver, is able to give good-quality results in competitive time.

Keywords

Constraint-based local search MiniZinc 

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References

  1. 1.
    Achterberg, T. (2009). SCIP: Solving constraint integer programs. Mathematical Programming Computation, 1(1), 1–41.CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Akgün, O., Frisch, A.M., Gent, I.P., Hussain, B.S., Jefferson, C., Kotthoff, L., Miguel, I., & Nightingale, P. (2013). Automated symmetry breaking and model selection in CONJURE. In C. Schulte (Ed.) CP 2013, LNCS, (Vol. 8124 pp. 107–116): Springer.Google Scholar
  3. 3.
    Amadini, R., Gabbrielli, M., & Mauro, J. (2014). Sunny: a lazy portfolio approach for constraint solving. Theory and Practice of Logic Programming, 14, 509–524.CrossRefzbMATHGoogle Scholar
  4. 4.
    Beldiceanu, N., Carlsson, M., Demassey, S., & Petit, T. (2007). Global constraint catalogue: Past, present, and future. Constraints, 12(1), 21–62. The catalogue is at http://sofdem.github.io/gccat.CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Benoist, T., Estellon, B., Gardi, F., Megel, R., & Nouioua, K. (2011). LocalSolver 1.x: a black-box local-search solver for 0-1 programming. 4OR. A Quarterly Journal of Operations Research, 9(3), 299–316.zbMATHMathSciNetGoogle Scholar
  6. 6.
    Björdal, G. (2014). The first constraint-based local search backend for MiniZinc. Bachelor Thesis in Computer Science, Report IT 14 066, Faculty of Science and Technology, Uppsala University, Sweden. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-234847.
  7. 7.
    Bofill, M., Palahí, M., Suy, J., & Villaret, M. fzn2smt, a compiler from the FlatZinc language to the standard SMT-LIB language. http://ima.udg.edu/Recerca/lap/fzn2smt/.
  8. 8.
    Codognet, P., & Diaz, D. (2001). Yet another local search method for constraint solving. In K. Steinhöfel (Ed.) SAGA 2001, First International Symposium on Stochastic Algorithms: Foundations and Applications, LNCS, (Vol. 2264 pp. 73–90): Springer.Google Scholar
  9. 9.
    De Landtsheer, R. (2012). Oscar.cbls: a constraint-based local search engine. https://bitbucket.org/oscarlib/oscar/downloads/Oscar.cbls.pdf.
  10. 10.
    Dotú, I., & Van Hentenryck, P. (2005). Scheduling social golfers locally. In R. Barták, & M. Milano (Eds.) CP-AI-OR 2005, LNCS, (Vol. 3524 pp. 155–167): Springer.Google Scholar
  11. 11.
    Elsayed, S.A.M., & Michel, L. (2011). Synthesis of search algorithms from high-level CP models. In J. Lee (Ed.) CP 2011, LNCS, (Vol. 6876 pp. 256–270): Springer.Google Scholar
  12. 12.
    Feydy, T., Somogyi, Z., & Stuckey, P. (2011). Half-reification and flattening. In J. Lee (Ed.) CP 2011, LNCS, (Vol. 6876 pp. 286–301): Springer.Google Scholar
  13. 13.
    Fontaine, D., Michel, L., & Van Hentenryck, P. (2013). Model combinators for hybrid optimization. In C. Schulte (Ed.) CP 2013, LNCS, (Vol. 8124 pp. 299–314): Springer.Google Scholar
  14. 14.
    Frisch, A.M., Grum, M., Jefferson, C., Martinez Hernandez, B., & Miguel, I. (2007). The design of ESSENCE: A constraint language for specifying combinatorial problems. In M. Veloso (Ed.), IJCAI 2007 (pp. 80–87). AAAI Press.Google Scholar
  15. 15.
    Fujiwara, T. (2014). iZ based solver for MiniZinc Challenge. http://www.minizinc.org/challenge2014/description_izplus.txt.
  16. 16.
    Gecode Team. Gecode/FlatZinc. http://www.gecode.org/flatzinc.html.
  17. 17.
    Glover, F. (1989). Tabu Search Part I. ORSA Journal on Computing, 1(3), 190–206.Google Scholar
  18. 18.
    Y. Hamadi, E. Monfroy, & F. Saubion (Eds.) (2012). Autonomous Search: Springer.Google Scholar
  19. 19.
    He, J., Flener, P., & Pearson, J. (2012). Solution neighbourhoods for constraint-directed local search. In S. Bistarelli, E. Monfroy, & B. O’Sullivan (Eds.) SAC/CSP 2012. (pp. 74–79): ACM Press.Google Scholar
  20. 20.
    Hoos, H.H. (2012). Automated algorithm configuration and parameter tuning. In Y. Hamadi, E. Monfroy, & F. Saubion (Eds.) Autonomous Search. (pp. 37–71): Springer.Google Scholar
  21. 21.
    Hoos, H.H., & Stützle, T. (2004). Stochastic Local Search: Foundations & Applications: Elsevier/Morgan Kaufmann.Google Scholar
  22. 22.
    Karp, R.M. (1972). Reducibility among combinatorial problems. In R.E. Miller, & J.W. Thatcher (Eds.) Complexity of Computer Computations. (pp. 85–103): Plenum Press.Google Scholar
  23. 23.
    Monette, J.N., Deville, Y., & Van Hentenryck, P. (2009). Aeon: Synthesizing scheduling algorithms from high-level models. In J.W. Chinneck, B. Kristjansson, & M.J. Saltzman (Eds.) Operations Research and Cyber-Infrastructure, Operations Research/Computer Science Interfaces, (Vol. 47 pp. 43–59): Springer.Google Scholar
  24. 24.
    Nethercote, N. Converting MiniZinc to FlatZinc. http://www.minizinc.org/downloads/doc-1.6/mzn2fzn.pdf .
  25. 25.
    Nethercote, N., Stuckey, P.J., Becket, R., Brand, S., Duck, G.J., & Tack, G. (2007). MiniZinc: Towards a standard CP modelling language. In C. Bessière (Ed.), CP 2007, LNCS (Vol. 4741, pp. 529–543). Springer. http://www.minizinc.org/.
  26. 26.
    Newton, M.H., Pham, D.N., Sattar, A., & Maher, M. (2011). Kangaroo: An efficient constraint-based local search system using lazy propagation. In J. Lee (Ed.) CP 2011, LNCS, (Vol. 6876 pp. 645–659): Springer.Google Scholar
  27. 27.
    Nightingale, P., Akgün, O., Gent, I.P., Jefferson, C., & Miguel, I. (2014). Automatically improving constraint models in Savile Row through associative-commutative common subexpression elimination. In B. O’Sullivan (Ed.) CP 2014, LNCS, (Vol. 8656 pp. 590–605): Springer.Google Scholar
  28. 28.
    Nowicki, E., & Smutnicki, C. (1996). A fast taboo search algorithm for the job shop problem. Management Science, 42(6), 797–813.CrossRefzbMATHGoogle Scholar
  29. 29.
    Opturion Pty Ltd. Opturion CPX. http://www.opturion.com/cpx.
  30. 30.
    OR Team at Google. OR-Tools. https://code.google.com/p/or-tools/.
  31. 31.
    OscaR Team (2012). OscaR: Scala in OR. https://bitbucket.org/oscarlib/oscar.
  32. 32.
    Parr, T.J. (2007). The Definitive ANTLR Reference: Building Domain-Specific Languages: The Pragmatic Bookshelf.Google Scholar
  33. 33.
    Prestwich, S.D. (2002). Supersymmetric modeling for local search. In P. Flener, & J. Pearson (Eds.) SymCon 2002. http://www.it.uu.se/research/group/astra/SymCon02.
  34. 34.
    Stuckey, P.J., Becket, R., & Fischer, J. (2010). Philosophy of the MiniZinc challenge. Constraints, 15(3), 307–316.CrossRefzbMATHGoogle Scholar
  35. 35.
    Stuckey, P.J., Feydy, T., Schutt, A., Tack, G., & Fischer, J. (2014). The MiniZinc challenge 2008–2013. AI Magazine, 35(2), 55–60.Google Scholar
  36. 36.
    Van Hentenryck, P. (1999). The OPL Optimization Programming Language: The MIT Press.Google Scholar
  37. 37.
    Van Hentenryck, P., & Michel, L. (2003) In F. Rossi (Ed.), Control abstractions for local search (Vol. 2833, pp. 65–80): Springer.Google Scholar
  38. 38.
    Van Hentenryck, P., & Michel, L. (2004). Scheduling abstractions for local search. In J.C. Régin, & M. Rueher (Eds.) CP-AI-OR 2004, LNCS, (Vol. 3011 pp. 319–334): Springer.Google Scholar
  39. 39.
    Van Hentenryck, P., & Michel, L. (2007). Synthesis of constraint-based local search algorithms from high-level models. In A. Howe, & R.C. Holte (Eds.) AAAI 2007. (pp. 273–278): AAAI Press.Google Scholar
  40. 40.
    Van Hentenryck, P., & Michel, L. (2009). Constraint-Based Local Search: The MIT Press.Google Scholar
  41. 41.
    Van Hentenryck, P., Michel, L., & Liu, L. (2004). Constraint-based combinators for local search. In M. Wallace (Ed.) CP 2004, LNCS, (Vol. 3258 pp. 47–61): Springer.Google Scholar
  42. 42.
    Yunes, T.H., Aron, I.D., & Hooker, J.N. (2010). An integrated solver for optimization problems. Operations Research, 58(2), 342–356.CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Information TechnologyUppsala UniversityUppsalaSweden

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