SCIL — Symbolic Constraints in Integer Linear Programming

  • Ernst Althaus
  • Alexander Bockmayr
  • Matthias Elf
  • Michael Jünger
  • Thomas Kasper
  • Kurt Mehlhorn
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2461)


We describe a new software system SCIL that introduces symbolic constraints into branch-and-cut-and-price algorithms for integer linear programs. Symbolic constraints are known from constraint programming and contribute signi.cantly to the expressive power, ease of use, and e.ciency of constraint programming systems.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [ABCC99]
    D. Applegate, R. Bixby, V. Chvátal, and W. Cook. Tsp-solver “concorde”., 1999.
  2. [AJR00]
    N. Ascheuer, M. Jünger, and G. Reinelt. A branch amp; cut algorithm for the asymmetric traveling salesman problem with precedence constraints. Computational Optimization and Applications, 17(1):61–84, 2000.MATHCrossRefMathSciNetGoogle Scholar
  3. [AKLM]
    E. Althaus, O. Kohlbacher, H.-P. Lenhof, and P. Müller. A combinatorial approach to protein docking with flexible side-chains. In Proceedings of the 4th Annual International Conference on Computational Molecular Biology (RECOMB-00).Google Scholar
  4. [AM01]
    E. Althaus and K. Mehlhorn. Traveling salesman-based curve reconstruction in polynomial time. SIAM Journal on Computing, 31(1):27–66, 2001.MATHCrossRefMathSciNetGoogle Scholar
  5. [BC94]
    N. Beldiceanu and E. Contejean. Introducing global constraints in CHIP. Mathl. Comput. Modelling, 20(12):97–123, 1994.MATHCrossRefGoogle Scholar
  6. [BFP95]
    E. Balas, M. Fischetti, and W. R. Pulleyblank. The precedenceconstrained asymmetric traveling salesman polytope. Mathematical Programming, 68:241–265, 1995.MathSciNetGoogle Scholar
  7. [BJN+98]
    C. Barnhart, E. Johnson, G. Nemhauser, M. Savelsbergh, and P. Vance. Branch-and-price: column generation for solving huge integer programs. Operations Research, 46:316–329, 1998.MATHMathSciNetGoogle Scholar
  8. [BK98]
    A. Bockmayr and T. Kasper. Branch and infer: a unifying framework for integer and finite domain constraint programming. INFORMS Journal on Computing, 10:287–300, 1998.MATHMathSciNetGoogle Scholar
  9. [CF97]
    A. Caprara and M. Fischetti. Annotated bibliographies in combinatorial optimization, chapter Branch-and-cut algorithms, pages 45–64. Wiley, 1997.Google Scholar
  10. [Cor02]
    GAMS Development Corporation. Gams: General algebraic modeling system, 2002.Google Scholar
  11. [CPL]
  12. [Das00]
    Dash Associates. XPRESS 12 Reference Manual: XPRESS-MP Optimizer Subroutine Library XOSL, 2000.Google Scholar
  13. [DFJ54]
    G. B. Dantzig, D.R. Fulkerson, and S.M. Johnson. Solution of a large scale traveling salesman problem. Operations Research, 2:393–410, 1954.MathSciNetCrossRefGoogle Scholar
  14. [DvHS+88]
    M. Dincbas, P. van Hentenryck, H. Simonis, A. Aggoun, and T. Graf. The constraint logic programming language CHIP. In Fifth Generation Computer Systems, Tokyo, 1988. Springer, 1988.Google Scholar
  15. [EGJR01]
    M. Elf, C. Gutwenger, M. Jünger, and G. Rinaldi. Computational Combinatorial Optimization, volume 2241 of Lecture Notes in Computer Science, chapter Branch-and-cut algorithms for combinatorial optimization and their implementation in ABACUS, pages 157–222. Springer, 2001.CrossRefGoogle Scholar
  16. [FGK92]
    R. Fourer, D.M. Gay, and B. W. Kernighan. AMPL: A modeling language for Mathematical Programming. Duxbury Press/Wadsworth Publishing, 1992.Google Scholar
  17. [GJR84]
    M. Grötschel, M. Jünger, and G. Reinelt. A cutting plane algorithm for the linear ordering problem. Operations Research, 32:1195–1220, 1984.MATHMathSciNetGoogle Scholar
  18. [ILO]
  19. [JT00]
    M. Jünger and S. Thienel. The abacus system for branch and cut and price algorithms in integer programming and combinatorial optimization. Software Practice and Experience, 30:1325–1352, 2000.MATHCrossRefGoogle Scholar
  20. [Kas98]
    T. Kasper. A Unifying Logical Framework for Integer Linear Programming and Finite Domain Constraint Programming. PhD thesis, Fachbereich Informatik, Universität des Saarlandes, 1998.Google Scholar
  21. [LED]
    LEDA (Library of Efficient Data Types and Algorithms).
  22. [MN99]
    K. Mehlhorn and S. Näher. The LEDA Platform for Combinatorial and Geometric Computing. Cambridge University Press, 1999. 1018 pages.Google Scholar
  23. [Nad02]
    D. Naddef. The Traveling Salesman Problem and its Variations, chapter Polyhedral theory, branch and cut algorithms for the symmetric traveling salesman problem. Kluwer Academic Publishing, 2002.Google Scholar
  24. [NW88]
    G. L. Nemhauser and L.A. Wolsey. Integer and Combinatorial Optimization. John Wiley amp; Sons, 1988.Google Scholar
  25. [PR91]
    M. Padberg and G. Rinaldi. A branch and cut algorithm for the resolution of large scale symmetric traveling salesman problems. SIAM Review, 33(60–10), 1991.MATHCrossRefMathSciNetGoogle Scholar
  26. [SDJ+96]
    C. Simone, M. Diehl, M. Jünger, P. Mutzel, and G. Rinaldi. Exact ground states of two-dimensional +-Jising spin glasses. Journal of Statistical Physics, 84:1363–1371, 1996.CrossRefGoogle Scholar
  27. [Smo96]
    G. Smolka. Constraints in OZ. ACM Computing Surveys, 28(4es):75, December 1996.CrossRefMathSciNetGoogle Scholar
  28. [VBJN94]
    P. H. Vance, C. Barnhart, E. L. Johnson, and G. Nemhauser. Solving binary cutting stock problems by column generation and branch-and-bound. Computational Optimization and Applications, 3:111–130, 1994.MATHCrossRefMathSciNetGoogle Scholar
  29. [vHS96]
    P. van Hentenryck and V. Saraswat. Strategic directions in constraint programming. ACM Computing Surveys, 28(4):701–726, 1996.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Ernst Althaus
    • 1
  • Alexander Bockmayr
    • 2
  • Matthias Elf
    • 3
  • Michael Jünger
    • 3
  • Thomas Kasper
    • 4
  • Kurt Mehlhorn
    • 5
  1. 1.International Computer Science InstituteBerkeleyUSA
  2. 2.LORIAUniversité Henri PoincaréVand-uvre-lès-NancyFrance
  3. 3.Universität zu KölnInstitut für InformatikKölnGermany
  4. 4.SAP AGGBU Supply Chain ManagementWalldorfGermany
  5. 5.Max-Planck-Institute für InformatikSaarbrückenGermany

Personalised recommendations