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Disjunctive Programming and Cooperating Solvers

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Advances in Computational and Stochastic Optimization, Logic Programming, and Heuristic Search

Part of the book series: Operations Research/Computer Science Interfaces Series ((ORCS,volume 9))

Abstract

There are two fundamental themes in constraint programming. One is discrete or finite domain constraint programming based on the constraint satisfaction model. The other is continuous constraint programming based on linear programming and its extensions. In this paper we propose techniques for making constraint solvers of these different types cooperate: we present a scheduling application of the Dutch Railways and a new kind of algorithm for solving disjunctive programming problems, one which could not be developed without cooperating solvers. What emerges is that cooperating solvers, which have old roots in special purpose operations research methods, constitute a basic technology with potentially wide applicability.

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References

  1. Balas, E.: Disjunctive Programming and a Hierarchy of Relaxations for Discrete Optimization Problems. SIAM Journal Algebraic and Discrete Methods 6 (1985), 149–156

    Google Scholar 

  2. Balas, E.; Ceria, S.; Cornuéjols, G.: A Lift-and-project Cutting Plane Algorithm for Mixed 0–1 Programs. Mathematical Programming 58 (1993) 245–324.

    Google Scholar 

  3. Baptiste, P.;Le Pape, C.: Constraint Propagation and Decomposition Techniques for Highly Disjunctive and Highly Cumulative Project Scheduling Problems. Submitted to CP97.

    Google Scholar 

  4. Barth, P.: Logic Based 0–1 Constraint Programming, Kluwer 1996

    Google Scholar 

  5. Bertsekas, D.: Linear Network Optimization: Algorithms and Codes. MIT Press 1991

    Google Scholar 

  6. Beaumont, N.: An algorithm for disjunctive programming European Journal of Operational Research 48 (1990), 362–371

    Article  Google Scholar 

  7. Bollapragada, S.; Ghattas, O.; Hooker, J. N.: Optimal Design of Truss Structures by Logic-Based Branch and Cut, to appear

    Google Scholar 

  8. Carlier, J.; Pinson, E.: An algorithm for solving the job shop problem. Annals of Operations Research 26 (1990), 269–287

    Google Scholar 

  9. Caseau, Y.; Laburthe, E: Improved CLP Scheduling with Task Intervals. In: Van Hentenryck, P. (ed.): Proc. of the Il t h Int. Conf. on Logic Programming, 369–383, MIT Press 1994

    Google Scholar 

  10. Colmerauer, A.: Opening the Prolog III Universe. BYTE Magazine,8/1987

    Google Scholar 

  11. DeBacker, B.; Beringer, H.: Combinatorial Problem Solving in Constraint Logic Programming with Cooperating Solvers. In: Beierle, C.; Plumer, L (eds.): Logic Programming: Formal Methods and Practical Applications, Elsevier 1995

    Google Scholar 

  12. DeBacker, B.; Beringer, H.: Cooperative solvers and global constraints: the case of linear arithmetic constraints, ILPS’95 Workshop, 1995

    Google Scholar 

  13. Dincbas, M.; van Hentenryck, P.; Simonis, H.; Aggoun, A.; Graf, T.; Berthier, F.: The Constraint Logic Programming Language CHIP. FGCS’88 Proceedings (1988) 693–702

    Google Scholar 

  14. Glover, F: A Bound Escalation Method for the Solution of Integer Linear Programs. Carnegie-Mellon University, 1965

    Google Scholar 

  15. Gomory, R. E.: An Algorithm for Integer Solutions to Linear Programs. In: Graves, R. L.; Wolfe, P.: Recent Advances in Mathematical Programming. McGraw-Hill (1963) 269–302

    Google Scholar 

  16. Greenberg, H.: A Branch-and-Bound Solution to the General Scheduling Problem. Operations Research 8 (1968), 353–361

    Article  Google Scholar 

  17. Groot, R Minimum Circulation of Railway Stock — An Integer Programming Problem. MS Thesis, University of Amsterdam, 1996

    Google Scholar 

  18. Haken, A.: The Intractability of Resolution. Theoretical Computer Science 39 (1985) 297–308

    Article  Google Scholar 

  19. Hooker, J. N.; Yan, H.; Grossmann, I. E.; Raman, R.: Logic Cuts for Processing Networks with Fixed Charges. Computers Ops. Res. 21 (1994) 265–279

    Article  Google Scholar 

  20. ILOG Planner Reference Manual, ILOG 1996.

    Google Scholar 

  21. Jaffar, J.; Michaylov, S.: Methodology and Implementation of a CLP System. In: Lassez, J.-L. (ed.): ICLP’87 Proceedings. MIT Press 1987

    Google Scholar 

  22. Land, A. H.; Doig, A. G.: An Automatic Method of Solving Discrete Programming Problems. Econometrica 28 (1960) 497–520

    Article  Google Scholar 

  23. Lovâcs, A.; Schrijver, A.: Cones of matrices and set-functions and 0–1 optimization. SIAM Journal of Optimization 1 (1991) 166–190

    Article  Google Scholar 

  24. Mackworth, A. K.; Freuder, E. C.: The complexity of constraint satisfaction revisited. Artificial Intelligence 25 (1993) 65–74

    Article  Google Scholar 

  25. McAloon, K.; Tretkoff, C.: Optimization and Computational Logic. John Wiley & Sons 1996

    Google Scholar 

  26. McAloon, K.; Tretkoff, C.: Logic, Modeling, and Programming. Annals of Operations Research,to appear

    Google Scholar 

  27. Nuijten, W.; Aarts, E: A computational study of constraint satisfaction for multiple capacitated job shop scheduling, European Journal of Operational Research (1995)

    Google Scholar 

  28. Puget, J-F; Leconte, M: Beyond the Glass Box: Constraints as Objects, ILPS ‘85,MIT Press.

    Google Scholar 

  29. Raman, R.; Grossmann, I. E.: Modeling and Computational Techniques for Logic-Based Integer Programming Computers and Chemical Engineering 18 (1994), 563–578

    Article  Google Scholar 

  30. Rodo“sek, R.; Wallace, M.; Hajian, M. T.: A New Approach to Integrate Mixed Integer Programming with CLP, Technical Report, Imperial College

    Google Scholar 

  31. Savelsbergh, M.: Preprocessing and probing techniques for mixed integer programming problems. ORSA Journal on Computing 6, 445–454

    Google Scholar 

  32. Schimpf, J.; Novello, S.: IC-Parc ECLiPSe Library Manual, Imperial College

    Google Scholar 

  33. Smith, S. F.; Cheng, C.-C.: Slack-Based Heuristics for Constraint Satisfaction Scheduling. In: Proceedings of the Eleventh National Conference on Artificial Intelligence, 1993

    Google Scholar 

  34. Solnon, C.: Coopération de solveurs linéaires sur les réels pour la résolution de problèmes linéaires sur les entiers. To appear in Journées Francophones 97

    Google Scholar 

  35. Schrijver, A.: Theory of Linear and Integer Programming, John Wiley & Sons 1986

    Google Scholar 

  36. Schrijver, A.: Minimum Circulation of Railway Stock, CWI Quarterly 1996

    Google Scholar 

  37. Van Hentenryck, P.: Constraint Satisfaction in Logic Programming. MIT Press 1989

    Google Scholar 

  38. Van Hentenryck, P.; Delville, Y.; Teng, Choh-Man: A generic arc consistency algorithm and its specializations, Artificial Intelligence 57 1992. MIT Press 1989

    Google Scholar 

  39. Wetzel, G.: Abductive and Constraint Logic Programming PhD Thesis, Imperial College

    Google Scholar 

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Author information

Authors and Affiliations

  1. Logic Based Systems Lab, Brooklyn College and CUNY Graduate Center, Brooklyn, NY, 11210, USA

    Ken McAloon, Carol Tretkoff & Gerhard Wetzel

Authors
  1. Ken McAloon
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  2. Carol Tretkoff
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  3. Gerhard Wetzel
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Editor information

Editors and Affiliations

  1. University of California, Davis, USA

    David L. Woodruff

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© 1998 Springer Science+Business Media New York

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McAloon, K., Tretkoff, C., Wetzel, G. (1998). Disjunctive Programming and Cooperating Solvers. In: Woodruff, D.L. (eds) Advances in Computational and Stochastic Optimization, Logic Programming, and Heuristic Search. Operations Research/Computer Science Interfaces Series, vol 9. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2807-1_3

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  • DOI: https://doi.org/10.1007/978-1-4757-2807-1_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-5023-9

  • Online ISBN: 978-1-4757-2807-1

  • eBook Packages: Springer Book Archive

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