Skip to main content

Flexible, Rule-Based Constraint Model Linearisation

  • Conference paper
Practical Aspects of Declarative Languages (PADL 2008)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 4902))

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Flener, P., Pearson, J., Ågren, M.: Introducing ESRA, a relational language for modelling combinatorial problems. In: LOPSTR’03, 214–232 (2003)

    Google Scholar 

  2. 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)

    Google Scholar 

  3. Garcia de la Banda, M.J., Marriott, K., Rafeh, R., Wallace, M.: The modelling language Zinc. [19], 700–705

    Google Scholar 

  4. Nethercote, N., Stuckey, P.J., Becket, R., Brand, S., Duck, G.J., Tack, G.: MiniZinc: Towards a standard CP modelling language. [20], 529–543

    Google Scholar 

  5. 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)

    Chapter  Google Scholar 

  6. McKinnon, K., Williams, H.: Constructing integer programming models by the predicate calculus. Annals of Operations Research 21, 227–246 (1989)

    Article  MATH  Google Scholar 

  7. 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)

    Chapter  Google Scholar 

  8. Rafeh, R., et al.: From Zinc to design model. In: Hanus, M. (ed.) PADL 2007. LNCS, vol. 4354, pp. 215–229. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. Frühwirth, T.: Theory and practice of Constraint Handling Rules. Journal of Logic Programming 37(1-3), 95–138 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  10. Clavel, M., et al.: The Maude 2.0 system. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 76–87. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  11. 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)

    Google Scholar 

  12. Balas, E.: Disjunctive programming: Properties of the convex hull of feasible points. Discrete Applied Mathematics 89(1-3), 3–44 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  13. 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)

    Google Scholar 

  14. Hooker, J.: Integrated Methods for Optimization. Springer, Heidelberg (2007)

    MATH  Google Scholar 

  15. 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)

    Chapter  Google Scholar 

  16. 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)

    Google Scholar 

  17. Tamura, N., Taga, A., Kitagawa, S., Banbara, M.: Compiling finite linear CSP into SAT. [19], 590–603

    Google Scholar 

  18. Ohrimenko, O., Stuckey, P., Codish, M.: Propagation = lazy clause generation. [20], 544–558

    Google Scholar 

  19. Benhamou, F. (ed.): CP 2006. LNCS, vol. 4204. Springer, Heidelberg (2006)

    Google Scholar 

  20. Bessière, C. (ed.): CP 2007. LNCS, vol. 4741. Springer, Heidelberg (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Paul Hudak David S. Warren

Rights and permissions

Reprints 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)

Publish with us

Policies and ethics