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Integrating Constraint and Integer Programming for the Orthogonal Latin Squares Problem

  • Gautam Appa
  • Ioannis Mourtos
  • Dimitris Magos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2470)

Abstract

We consider the problem of Mutually Orthogonal Latin Squares and propose two algorithms which integrate Integer Programming (IP) and Constraint Programming (CP). Their behaviour is examined and compared to traditional CP and IP algorithms. The results assess the quality of inference achieved by the CP and IP, mainly in terms of early identification of infeasible subproblems. It is clearly illustrated that the integration of CP and IP is beneficial and that one hybrid algorithm exhibits the best performance as the problem size grows. An approach for reducing the search by excluding isomorphic cases is also presented.

Keywords

Search Tree Hybrid Algorithm Combinatorial Optimisation Problem Constraint Programming Valid Inequality 
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.

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References

  1. [1]
    Appa G., Magos D., Mourtos I., Janssen J. C. M.: On the Orthogonal Latin Squares polytope. Submitted to Discrete Mathematics (2001). (URL: http://www.cdam.lse.ac.uk/Reports/reports2001.html)
  2. [2]
    Bockmayr A., Casper T.: Branch and infer: a unifying framework for integer and finite domain constraint programming. INFORMS Journal on Computing, 10 (1998) 187–200.CrossRefGoogle Scholar
  3. [3]
    Chandru V., Hooker J. N.: Optimization methods for logical inference. J.Wiley (1999).Google Scholar
  4. [4]
    Dantzig G. B.: Linear Programming and extensions. Princeton Univ. Press (1963).Google Scholar
  5. [5]
    Dénes J., Keedwell A. D.: Latin squares and their applications. Acad. Press (1974).Google Scholar
  6. [6]
    Freuder E. C., Wallace R. J. (ed.): Constraint Programming and Large Scale Discrete Optimization. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 57, Amer. Math. Soc (1998).Google Scholar
  7. [7]
    Gomes C., Shmoys D.: The Promise of LP to Boost CSP Techniques for Combinatorial Problems, CP-AI-OR’02, 291-305, Le Croisic, France (2002).Google Scholar
  8. [8]
    Hooker J. N., Osorio M. A.: Mixed logical/linear programming. Discrete Applied Mathematics, 9697 (1994) 395–442.MathSciNetGoogle Scholar
  9. [9]
    Hooker J. N.: Logic-Based Methods for Optimization: Combining Optimization and Constraint Satisfaction. J.Wiley (2000).Google Scholar
  10. [10]
    Laywine C. F., Mullen G. L.: Discrete Mathematics using Latin squares. J.Wiley (1998).Google Scholar
  11. [11]
    Magos D., Miliotis P.: An algorithm for the planar three-index assignment problem. European Journal of Operational Research 77 (1994) 141–153.zbMATHCrossRefGoogle Scholar
  12. [12]
    Nemhauser G. L., Wolsey L. A.: Integer and Combinatorial Optimization. J.Wiley (1988).Google Scholar
  13. [13]
    Regin J. C.: A filtering algorithm for constraints of difference in CSPs. Proceedings of National Conference on Artificial Intelligence (1994), 362–367.Google Scholar
  14. [14]
    Savelsbergh M. W. P.: Preprocessing and Probing for Mixed Integer Programming Problems. ORSA J. on Computing, 6 (1994) 445–454.MathSciNetzbMATHCrossRefGoogle Scholar
  15. [15]
    Tsang E.: Foundations of Constraint Satisfaction, Acad. Press (1993).Google Scholar
  16. [16]
    Dash Associates: XPRESS-MP Version 12, Reference Manual (2001).Google Scholar
  17. [17]
    Zhang H., Hsiang J.: Solving open quasigroup problems by propositional reasoning, Proc. of International Computer Symposium, Hsinchu, Taiwan (1994).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Gautam Appa
    • 1
  • Ioannis Mourtos
    • 1
  • Dimitris Magos
    • 2
  1. 1.London School of EconomicsLondonUK
  2. 2.Technological Educational Institute of AthensAthensGreece

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