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Abstract

This paper examines sets of all_different predicates that appear in multidimensional assignment problems. It proposes the study of certain LP relaxations as a prerequisite of integrating CP with IP on these problems. The convex hull of vectors satisfying simultaneously two predicates is analysed and a separation algorithm for facet-defining inequalities is proposed.

Keywords

Convex Hull Assignment Problem Constraint Programming Linear Programming Relaxation Integer Program Model 
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., Mourtos, I., Magos, D.: Integrating Constraint and Integer Programming for the Orthogonal Latin Squares Problem. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 17–32. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Appa, G., Magos, D., Mourtos, I.: Polyhedral resuls for assignment problems. LSE CDAM Workin Paper Series, URL: http://www.cdam.lse.ac.uk/Reports/Files/cdam-2002-01.pdf
  3. 3.
    Balas, E., Saltzman, M.J.: Facets of the three-index assignment polytope. Discrete Applied Mathematics 23, 201–229 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Christoff, T., Löbel, A.: Polyhedral Representation Transformation Algorithm v.1.4.0 (2003), URL: http://www.zib.de/Optimization/Software/Porta
  5. 5.
    Dénes, J., Keedwell, A.D.: Latin Squares: New developments in the Theory and Applications. North-Holland, Amsterdam (1991)zbMATHGoogle Scholar
  6. 6.
    Hooker, J.N.: Logic Based Methods for Optimization. Wiley, NY (2000)zbMATHGoogle Scholar
  7. 7.
    Pierskalla, W.P.: The multidimensional assignment problem. Operations Research 16, 422–431 (1968)zbMATHCrossRefGoogle Scholar
  8. 8.
    Spieksma, F.C.R.: Multi-index assignment problems: complexity, approximation, applications. In: Pitsoulis, L., Pardalos, P. (eds.) Nonlinear Assignment Problems, Algorithms and Applications, pp. 1–12. Kluwer Academic Publishers, Dordrecht (2000)Google Scholar
  9. 9.
    Yan, H., Hooker, J.N.: Tight Representation of Logic Constraints as Cardinality Rules. Mathematical Programming 85(2), 363–377 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Williams, H.P., Yang, H.: Representations of the all-different Predicate of Constraint Satisfaction in Integer Programming. INFORMS Journal on Computing 13, 96–103 (2001)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

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

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