Linear Formulation of Constraint Programming Models and Hybrid Solvers

  • Philippe Refalo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1894)


Constraint programming offers a variety of modeling objects such as logical and global constraints, that lead to concise and clear models for expressing combinatorial optimization problems. We propose a way to provide a linear formulation of such a model and detail, in particular, the transformation of some global constraints. An automatic procedure for producing and updating formulations has been implemented and we illustrate it on combinatorial optimization problems.


linear formulation global constraints hybrid solvers 


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  1. 1.
    W. Adams and T. Johnson. Improved linear programming based lower bounds for the quadratic assignment problem. In P. Pardalos and H. Wolkowicz, editors, Quadratic Assignment and Related Problems, number 16, pages 49–72. AMS, Providence, Rhode Island, 1994.Google Scholar
  2. 2.
    B. De Backer and H. Beringer. Cooperative solvers and global constraints: The case of linear arithmetic constraints. In Proceedings of the Post Conference Workshop on Constraint, Databases and Logic Programming, ILPS’95, 1995.Google Scholar
  3. 3.
    E. Balas. Disjunctive programming and a hierarchy of relaxations for discrete optimization problems. SIAM Journal Alg. Disc. Meth., 6(3):466–486, 1985.zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    N. Beldiceanu and E. Contejean. Introducing global constraints in CHIP. Mathl. Comput. Modelling, 20(12), 1994.Google Scholar
  5. 5.
    A. Bockmayr and T. Kasper. Branch and infer: A unifying framework for integer and finite domain constraint programming. INFORMS Journal on Computing, 10(3):287–300, 1998.zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    F. Focacci, A. Lodi, and M. Milano. Cost-based domain filtering. In Proceedings of 5th International Conference CP 99, Alexandria, Virginia, October 1999. Springer-Verlag.Google Scholar
  7. 7.
    F. Focacci, A. Lodi, M. Milano, and D. Vigo. Solving tsp through the integration of cp and or methods. In Proceedings of the CP 98 Workshop on Large Scale Combinatorial Optimization and Constraints, 1998.Google Scholar
  8. 8.
    J. N. Hooker and M. A. Osorio. Mixed logical / linear programming. Discrete Applied Mathematics, 1996. to appear.Google Scholar
  9. 9.
    J. N. Hooker, G. Ottosson, E. S. Thornsteinsson, and Hak-Jin Kim. A scheme for unifying optimization and constraint satisfaction methods. Knowledge Engineering Review, 2000. to appear.Google Scholar
  10. 10.
    R. Jeroslow. Logic based decision support: Mixed integer model formulation. Annals of Discrete Mathematics, (40), 1989.Google Scholar
  11. 11.
    G. Mitra, C. Lucas, S. Moody, and E. Hadjiconstantinou. Tools for reformulating logical forms into zero-one mixed integer programs. European Journal of Operational Research, (72):262–276, 1994.zbMATHCrossRefGoogle Scholar
  12. 12.
    ILOG Planner 3.3. User Manual. ILOG, S. A., Gentilly, France, December 1999.Google Scholar
  13. 13.
    P. Refalo. Tight cooperation and its application in piecewise linear optimization. In Proceedings of 5th International Conference CP 99, Alexandria, Virginia, October 1999. Springer-Verlag.Google Scholar
  14. 14.
    J. C. Regin. A filtering algorithm for constraints of difference in csps. In Proceedings of AAAI-94, pages 362–367, Seattle, Washington, 1994.Google Scholar
  15. 15.
    R. Rodosek and M. Wallace. A generic model and hybrid algorithm for hoist scheduling problems. In Proceedings of the 4th International Conference on Principles and Practice of Constraint Programming-CP’98, pages 385–399, Pisa, Italy, 1998. Also in LNCS 1520.CrossRefGoogle Scholar
  16. 16.
    R. Rodosek, M. Wallace, and M. T. Hajian. A new approach to integrate mixed integer programming with CLP. In Proceedings of the CP’96 Workshop on Constraint Programming Applications, Boston, MA, USA, 1996.Google Scholar
  17. 17.
    M. Rueher and C. Solnon. Concurrent cooperating solvers over the reals. Reliable Computing, 3(3):325–333, 1997.zbMATHCrossRefGoogle Scholar
  18. 18.
    ILOG Solver 4.4. User Manual. ILOG, S. A., Gentilly, France, June 1999.Google Scholar
  19. 19.
    P. van Hentenryck. Constraint Satisfaction in Logic Programming. MIT Press, Cambridge, Mass., 1989.Google Scholar
  20. 20.
    P. van Hentenryck, H. Simonis, and M. Dincbas. Constraint satisfaction using constraint logic programming. Artificial Intelligence, 58(1–3):113–159, 1992.zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    H. P. Williams. Model Building in Mathematical Programming. Wiley, 1999.Google Scholar
  22. 22.
    L. A. Wolsey. Integer Programming. Wiley, 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Philippe Refalo
    • 1
  1. 1.ILOG, Les TaissounieresSophia AntipolisFrance

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