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.
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References
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)
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
Balas, E., Saltzman, M.J.: Facets of the three-index assignment polytope. Discrete Applied Mathematics 23, 201–229 (1989)
Christoff, T., Löbel, A.: Polyhedral Representation Transformation Algorithm v.1.4.0 (2003), URL: http://www.zib.de/Optimization/Software/Porta
Dénes, J., Keedwell, A.D.: Latin Squares: New developments in the Theory and Applications. North-Holland, Amsterdam (1991)
Hooker, J.N.: Logic Based Methods for Optimization. Wiley, NY (2000)
Pierskalla, W.P.: The multidimensional assignment problem. Operations Research 16, 422–431 (1968)
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)
Yan, H., Hooker, J.N.: Tight Representation of Logic Constraints as Cardinality Rules. Mathematical Programming 85(2), 363–377 (1999)
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)
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Appa, G., Magos, D., Mourtos, I. (2004). LP Relaxations of Multiple all_different Predicates. In: Régin, JC., Rueher, M. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2004. Lecture Notes in Computer Science, vol 3011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24664-0_25
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DOI: https://doi.org/10.1007/978-3-540-24664-0_25
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