Advertisement

Abstract

In recent years, the Constraint Programming (CP) and Operations Research (OR) communities have explored the advantages of combining CP and OR techniques to formulate and solve combinatorial optimization problems. These advantages include a more versatile modeling framework and the ability to combine complementary strengths of the two solution technologies. This research has reached a stage at which further development would benefit from a general-purpose modeling and solution system. We introduce here a system for integrated modeling and solution called SIMPL. Our approach is to view CP and OR techniques as special cases of a single method rather than as separate methods to be combined. This overarching method consists of an infer-relax-restrict cycle in which CP and OR techniques may interact at any stage. We describe the main features of SIMPL and illustrate its usage with examples.

Keywords

Operation Research Constraint Programming Master Problem Global Constraint Problem Restriction 
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.
    Balas, E.: Disjunctive programming: Properties of the convex hull of feasible points. Discrete Applied Mathematics 89, 3–44 (1998)CrossRefMathSciNetzbMATHGoogle Scholar
  2. 2.
    Baptiste, P., Le Pape, C., Nuijten, W.: Constraint-Based Scheduling. Kluwer, Dordrecht (2001)zbMATHGoogle Scholar
  3. 3.
    Benders, J.F.: Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4, 238–252 (1962)CrossRefMathSciNetzbMATHGoogle Scholar
  4. 4.
    Beringer, H., de Backer, B.: Combinatorial problem solving in constraint logic programming with cooperating solvers. In: Beierle, C., Plümer, L. (eds.) Logic Programming: Formal Methods and Practical Applications, Elsevier Science, Amsterdam (1995)Google Scholar
  5. 5.
    Berkelaar, M.: LP_SOLVE, Available from ftp://ftp.ics.ele.tue.nl/pub/lp_solve/
  6. 6.
    Bockmayr, A., Eisenbrand, F.: Combining logic and optimization in cutting plane theory. In: Kirchner, H., Ringeissen, C. (eds.) FroCos 2000. LNCS (LNAI), vol. 1794, pp. 1–17. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  7. 7.
    Bockmayr, A., Kasper, T.: Branch and infer: A unifying framework for integer and finite domain constraint programming. INFORMS Journal on Computing 10(3), 287–300 (1998)CrossRefMathSciNetzbMATHGoogle Scholar
  8. 8.
    Colombani, Y., Heipcke, S.: Mosel: An Overview. Dash Optimization (2002)Google Scholar
  9. 9.
    Dash Optimization. XPRESS-MP, http://www.dashoptimization.com
  10. 10.
    Eremin, A., Wallace, M.: Hybrid Benders decomposition algorithms in constraint logic programming. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 1–15. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  11. 11.
    Focacci, F., Lodi, A., Milano, M.: Cost-based domain filtering. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 189–203. Springer, Heidelberg (1999)Google Scholar
  12. 12.
    Focacci, F., Lodi, A., Milano, M.: Cutting planes in constraint programming: A hybrid approach. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 187–201. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  13. 13.
    Gutin, G., Punnen, A.P. (eds.): Traveling Salesman Problem and Its Variations. Kluwer, Dordrecht (2002)zbMATHGoogle Scholar
  14. 14.
    Hooker, J.N.: Logic-Based Methods for Optimization. In: Wiley-Interscience Series in Discrete Mathematics and Optimization (2000)Google Scholar
  15. 15.
    Hooker, J.N.: Logic, optimization and constraint programming. INFORMS Journal on Computing 14(4), 295–321 (2002)CrossRefMathSciNetGoogle Scholar
  16. 16.
    Hooker, J.N.: A framework for integrating solution methods. In: Bhargava, H.K., Ye, M. (eds.) Computational Modeling and Problem Solving in the Networked World, pp. 3–30. Kluwer, Dordrecht (2003); Plenary talk at the Eighth INFORMS Computing Society Conference (ICS)Google Scholar
  17. 17.
    Hooker, J.N.: Logic-based benders decomposition for planning and scheduling. GSIA, Carnegie Mellon University (2003) (manuscript)Google Scholar
  18. 18.
    Hooker, J.N., Osorio, M.A.: Mixed logical/linear programming. Discrete Applied Mathematics 96-97(1-3), 395–442 (1999)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Hooker, J.N., Ottosson, G.: Logic-based benders decomposition. Mathematical Programming 96, 33–60 (2003)MathSciNetzbMATHGoogle Scholar
  20. 20.
    Hooker, J.N., Ottosson, G., Thorsteinsson, E., Kim, H.-J.: On integrating constraint propagation and linear programming for combinatorial optimization. In: Proceedings of the 16th National Conference on Artificial Intelligence, pp. 136–141. MIT Press, Cambridge (1999)Google Scholar
  21. 21.
    Hooker, J.N., Yan, H.: Logic circuit verification by Benders decomposition. In: Saraswat, V., Van Hentenryck, P. (eds.) Principles and Practice of Constraint Programming: The Newport Papers, pp. 267–288. MIT Press, Cambridge (1995)Google Scholar
  22. 22.
    Hooker, J.N., Yan, H.: A relaxation for the cumulative constraint. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 686–690. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  23. 23.
    ILOG S.A. The CPLEX mixed integer linear programming and barrier optimizer, http://www.ilog.com/products/cplex/
  24. 24.
    Jain, V., Grossmann, I.E.: Algorithms for hybrid MILP/CP models for a class of optimization problems. INFORMS Journal on Computing 13(4), 258–276 (2001)CrossRefMathSciNetGoogle Scholar
  25. 25.
    Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B.: The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization. John Wiley & Sons, Chichester (1985)zbMATHGoogle Scholar
  26. 26.
    Leipert, S.: The tree interface version 1.0: A tool for drawing trees, Available at http://www.informatik.uni-koeln.de/old-ls_juenger/projects/vbctool.html
  27. 27.
    Milano, M., Ottosson, G., Refalo, P., Thorsteinsson, E.S.: The role of integer programming techniques in constraint programming’s global constraints. INFORMS Journal on Computing 14(4), 387–402 (2002)CrossRefMathSciNetGoogle Scholar
  28. 28.
    Ottosson, G., Thorsteinsson, E.S., Hooker, J.N.: Mixed global constraints and inference in hybrid CLP-IP solvers. In: CP 1999 Post Conference Workshop on Large Scale Combinatorial Optimization and Constraints, pp. 57–78 (1999)Google Scholar
  29. 29.
    Refalo, P.: Tight cooperation and its application in piecewise linear optimization. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 375–389. Springer, Heidelberg (1999)Google Scholar
  30. 30.
    Refalo, P.: Linear formulation of constraint programming models and hybrid solvers. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 369–383. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  31. 31.
    Régin, J.-C.: A filtering algorithm for constraints of difference in CSPs. In: Proceedings of the National Conference on Artificial Intelligence, pp. 362–367 (1994)Google Scholar
  32. 32.
    Rodošek, R., Wallace, M., Hajian, M.T.: A new approach to integrating mixed integer programming and constraint logic programming. Annals of Operations Research 86, 63–87 (1999)CrossRefMathSciNetzbMATHGoogle Scholar
  33. 33.
    Thorsteinsson, E.S.: Branch-and-Check: A hybrid framework integrating mixed integer programming and constraint logic programming. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 16–30. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  34. 34.
    Van Hentenryck, P.: The OPL Optimization Programming Language. MIT Press, Cambridge (1999)Google Scholar
  35. 35.
    Wallace, M., Novello, S., Schimpf, J.: ECLiPSe: A platform for constraint logic programming. ICL Systems Journal 12, 159–200 (1997)Google Scholar
  36. 36.
    Williams, H.P., Yan, H.: Representations of the all different predicate of constraint satisfaction in integer programming. INFORMS Journal on Computing 13(2), 96–103 (2001)CrossRefMathSciNetGoogle Scholar
  37. 37.
    Yan, H., Hooker, J.N.: Tight representations of logical constraints as cardinality rules. Mathematical Programming 85, 363–377 (1999)CrossRefMathSciNetzbMATHGoogle Scholar
  38. 38.
    Yunes, T.H.: On the sum constraint: Relaxation and applications. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 80–92. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Ionuţ Aron
    • 1
  • John N. Hooker
    • 1
  • Tallys H. Yunes
    • 1
  1. 1.Graduate School of Industrial AdministrationCarnegie Mellon UniversityPittsburghUSA

Personalised recommendations