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Hybrid Solving Techniques

  • Tobias Achterberg
  • Andrea Lodi
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 45)

Abstract

Hybrid methods have always been one of the most intriguing directions in these 10–15 years spent in creating and enhancing the relationship between constraint programming and operations research. Three main hybridization contexts have been explored: hybrid modeling, hybrid solving (algorithmic methods) and hybrid software tools. In this chapter we concentrate on the algorithmic side of the hybridization.

Keywords

Travel Salesman Problem Constraint Programming Domain Propagation Global Constraint Constraint Handler 
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.

Notes

Acknowledgments

We are grateful to the editors Michela Milano and Pascal Van Hentenryck for their support and patience. We are indebted to an anonymous referee for a very careful reading and useful suggestions.

References

  1. 1.
    Achterberg T (2007) Constraint integer programming. PhD thesis, Technische Universität Berlin. http://opus.kobv.de/tuberlin/volltexte/2007/1611/
  2. 2.
    Achterberg T (2009) SCIP: solving constraint integer programs. Math Program Comput 1(1):1–41MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Achterberg T, Koch T, Martin A (2005) Branching rules revisited. Oper Res Lett 33:42–54MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Berthold T (2006) Primal heuristics for mixed integer programs. Master’s thesis, Technische Universität BerlinGoogle Scholar
  5. 5.
    Crowder H, Johnson EL, Padberg MW (1983) Solving large scale zero-one linear programming problems. Oper Res 31:803–834MATHCrossRefGoogle Scholar
  6. 6.
    Danna E, Rothberg E, Le Pape C (2005) Exploring relaxation induced neighborhoods to improve MIP solutions. Math Program 102(1):71–90MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Fischetti M, Toth P (1989) An additive bounding procedure for combinatorial optimization problems. Oper Res 37:319–328MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Focacci F, Lodi A, Milano M (1999) Cost-based domain filtering. In: Jaffar J (ed) Principles and practice of constraint programming – CP99. Lecture notes in computer science, vol 1713. Springer, New York, pp 189–203Google Scholar
  9. 9.
    Focacci F, Lodi A, Milano M (2000) Cutting planes in constraint programming: an hybrid approach. In: Dechter R (ed) Principles and practice of constraint programming – CP00. Lecture notes in computer science, vol 1894. Springer, Berlin, pp 187–201Google Scholar
  10. 10.
    Focacci F, Lodi A, Milano M (2002) A hybrid exact algorithm for the TSPTW. INFORMS J Comput 14:403–417CrossRefMathSciNetGoogle Scholar
  11. 11.
    Focacci F, Lodi A, Milano M (2002) Optimization-oriented global constraints. Constraints 7:351–365MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Gomes C, Selman B, Kautz H (1998) Boosting combinatorial search through randomization. In: Proceedings of the fifteenth national conference on artificial intelligence (AAAI-98)Google Scholar
  13. 13.
    Harvey W, Ginsberg M (1995) Limited discrepancy search. In: Proceedings of the 14th IJCAI. San Francisco, CA, Morgan Kaufmann, pp 607–615Google Scholar
  14. 14.
    Hooker JN (2007) Integrated methods for optimization. Springer, BerlinMATHGoogle Scholar
  15. 15.
    Jain V, Grossmann IE (2001) Algorithms for hybrid MILP/CP models for a class of optimization problems. INFORMS J Comput 13:258–276CrossRefMathSciNetGoogle Scholar
  16. 16.
    Klar A (2006) Cutting planes in mixed integer programming. Master’s thesis, Technische Universität BerlinGoogle Scholar
  17. 17.
    Lodi A, Milano M, Rousseau L-M (2006) Discrepancy-based additive bounding procedures. INFORMS J Comput 18:480–493CrossRefMathSciNetGoogle Scholar
  18. 18.
    Marchand H (1998) A polyhedral study of the mixed knapsack set and its use to solve mixed integer programs. PhD thesis, Faculté des Sciences Appliquées, Université catholique de LouvainGoogle Scholar
  19. 19.
    Marchand H, Wolsey LA (2001) Aggregation and mixed integer rounding to solve MIPs. Oper Res 49(3):363–371MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Marques-Silva JP, Sakallah KA (1999) GRASP: a search algorithm for propositional satisfiability. IEEE Trans Comput 48:506–521CrossRefMathSciNetGoogle Scholar
  21. 21.
    Milano M, Ottosson G, Refalo P, Thorsteinsson ES (2002) The role of integer programming techniques in constraint programming’s global constraints. INFORMS J Comput 14:387–402CrossRefMathSciNetGoogle Scholar
  22. 22.
    Milano M, van Hoeve WJ (2002) Reduced cost-based ranking for generating promising subproblems. In: van Hentenryck P (ed) Principles and practice of constraint programming – CP02. Lecture notes in computer science, vol 2470. Springer, Berlin, pp 1–16Google Scholar
  23. 23.
    Milano M, Wallace M (2006) Integrating operations research in constraint programming. 4OR 4:175–219Google Scholar
  24. 24.
    Moskewicz MW, Madigan CF, Zhao Y, Zhang L, Malik S (2001) Chaff: engineering an efficient SAT solver. In: Proceedings of the design automation conferenceGoogle Scholar
  25. 25.
    Nemhauser GL, Wolsey LA (1988) Integer and combinatorial optimization. Wiley, New YorkMATHGoogle Scholar
  26. 26.
    Refalo P (2000) Linear formulation of constraint programming models and hybrid solvers. In: Dechter R (ed) Principles and practice of constraint programming – CP00. Lecture notes in computer science, vol 1894. Springer, London, pp 369–383Google Scholar
  27. 27.
    Régin JC (1994) A filtering algorithm for constraints of difference in CSPs. In: Hayes-Roth B, Korf R (eds) Proceedings of the national conference on artificial intelligence – AAAI94, pp 362–367Google Scholar
  28. 28.
    Rodo\check{s}ek R, Wallace M (1998) A generic model and hybrid algorithm for hoist scheduling problems. In: Maher MJ, Puget J-F (eds) Principles and practice of constraint programming – CP98. Lecture notes in computer science, vol 1520. Springer, London, pp 385–399Google Scholar
  29. 29.
    Rodo\check{s}ek R, Wallace MG, Hajian MT (1999) A new approach to integrating mixed integer programming with constraint logic programming. Ann Oper Res 86:63–87Google Scholar
  30. 30.
    Sadykov R, Wolsey LA (2006) Integer programming and constraint programming in solving a multi-machine assignment scheduling problem with deadlines and release dates. INFORMS J Comput 18:209–217CrossRefMathSciNetGoogle Scholar
  31. 31.
    Thienel S (1995) ABACUS – A Branch-and-Cut System. PhD thesis, Institut für Informatik, Universität zu KölnGoogle Scholar
  32. 32.
    Wolter K (2006) Implementation of cutting plane separators for mixed integer programs. Master’s thesis, Technische Universität BerlinGoogle Scholar

Copyright information

© Springer Science+Business Media LLC 2011

Authors and Affiliations

  1. 1.IBMCPLEX OptimizationBoeblingenGermany
  2. 2.DEISUniversity of BolognaBolognaItaly

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