Abstract
Nonlinear constraint satisfaction or optimisation models need to be reduced to equivalent linear forms before they can be solved by (Integer) Linear Programming solvers. A choice of linearisation methods exist. There are generic linearisations and constraint-specific, user-defined linearisations. Hence a model reformulation system needs to be flexible and open to allow complex and novel linearisations to be specified. In this paper we show how the declarative model reformulation system Cadmium can be used to effectively transform constraint problems to different linearisations, allowing easy exploration of linearisation possibilities.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
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.
References
Flener, P., Pearson, J., Ågren, M.: Introducing ESRA, a relational language for modelling combinatorial problems. In: LOPSTR’03, 214–232 (2003)
Frisch, A.M., Grum, M., Jefferson, C., Hernandez, B.M., Miguel, I.: The design of ESSENCE: A constraint language for specifying combinatorial problems. In: IJCAI 2007 (2007)
Garcia de la Banda, M.J., Marriott, K., Rafeh, R., Wallace, M.: The modelling language Zinc. [19], 700–705
Nethercote, N., Stuckey, P.J., Becket, R., Brand, S., Duck, G.J., Tack, G.: MiniZinc: Towards a standard CP modelling language. [20], 529–543
Duck, G.J., Stuckey, P.J., Brand, S.: ACD term rewriting. In: Etalle, S., Truszczyński, M. (eds.) ICLP 2006. LNCS, vol. 4079, pp. 117–131. Springer, Heidelberg (2006)
McKinnon, K., Williams, H.: Constructing integer programming models by the predicate calculus. Annals of Operations Research 21, 227–246 (1989)
Refalo, P.: Linear formulation of constraint programming models and hybrid solvers. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 369–383. Springer, Heidelberg (2000)
Rafeh, R., et al.: From Zinc to design model. In: Hanus, M. (ed.) PADL 2007. LNCS, vol. 4354, pp. 215–229. Springer, Heidelberg (2006)
Frühwirth, T.: Theory and practice of Constraint Handling Rules. Journal of Logic Programming 37(1-3), 95–138 (1998)
Clavel, M., et al.: The Maude 2.0 system. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 76–87. Springer, Heidelberg (2003)
Li, Q., Guo, Y., Ida, T.: Modelling integer programming with logic: Language and implementation. IEICE Transactions of Fundamentals of Electronics, Communications and Computer Sciences E83-A(8), 1673–1680 (2000)
Balas, E.: Disjunctive programming: Properties of the convex hull of feasible points. Discrete Applied Mathematics 89(1-3), 3–44 (1998)
Tseitin, G.: On the complexity of derivation in propositional calculus. In: Studies in Constructive Mathematics and Mathematical Logic, pp. 115–125 (1968); Reprinted in Siekmann, J., Wrightson, G.(eds.) Automation of Reasoning, vol. 2, pp. 466–483, Springer, Heidelberg (1983)
Hooker, J.: Integrated Methods for Optimization. Springer, Heidelberg (2007)
Baatar, D., et al.: Minimum cardinality matrix decomposition into consecutive-ones matrices: CP and IP approaches. In: Van Hentenryck, P., Wolsey, L.A. (eds.) CPAIOR 2007. LNCS, vol. 4510, pp. 1–15. Springer, Heidelberg (2007)
Frisch, A.M., Jefferson, C., Hernández, B.M., Miguel, I.: The rules of constraint modelling. In: Kaelbling, L.P., Saffiotti, A. (eds.) 19th International Joint Conference on Artificial Intelligence (IJCAI 2005), pp. 109–116 (2005)
Tamura, N., Taga, A., Kitagawa, S., Banbara, M.: Compiling finite linear CSP into SAT. [19], 590–603
Ohrimenko, O., Stuckey, P., Codish, M.: Propagation = lazy clause generation. [20], 544–558
Benhamou, F. (ed.): CP 2006. LNCS, vol. 4204. Springer, Heidelberg (2006)
Bessière, C. (ed.): CP 2007. LNCS, vol. 4741. Springer, Heidelberg (2007)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Brand, S., Duck, G.J., Puchinger, J., Stuckey, P.J. (2007). Flexible, Rule-Based Constraint Model Linearisation. In: Hudak, P., Warren, D.S. (eds) Practical Aspects of Declarative Languages. PADL 2008. Lecture Notes in Computer Science, vol 4902. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77442-6_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-77442-6_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77441-9
Online ISBN: 978-3-540-77442-6
eBook Packages: Computer ScienceComputer Science (R0)