Nothing Special   »   [go: up one dir, main page]

Skip to main content

A Relaxation of the Cumulative Constraint

  • Conference paper
  • First Online:
Principles and Practice of Constraint Programming - CP 2002 (CP 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2470))

  • 1007 Accesses

Abstract

Hybrid methods that combine constraint programming with mathematical programming make essential use of continuous relaxations for global constraints. We state a relaxation for the cumulative constraint. In particular we identify facet-defining inequalities for problems in which some jobs have the same duration, release time, and resource consumption rate. We also identify a much larger class of valid inequalities that exist in all problems.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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.

Similar content being viewed by others

References

  1. Aggoun, A., and N. Beldiceanu, Extending CHIP in order to solve complex scheduling and placement problems, Mathematical and Computer Modelling 17 (1993) 57–73.

    Article  MathSciNet  Google Scholar 

  2. Baptiste, P., and C. Le Pape, Constraint propagation and decomposition techniques for highly disjunctive and highly cumulative project scheduling problems. Principles and Practice of Constraint Programming (CP 97), Springer-Verlag (Berlin, 1997) 375–89.

    Google Scholar 

  3. Bockmayr, A., and T. Kasper. 1998. Branch and infer: A unifying framework for integer and finite domain constraint programming, INFORMS Journal on Computing 10 287–300.

    Article  MathSciNet  MATH  Google Scholar 

  4. Demassey, S., C. Artigues and P. Michelon, A hybrid constraint propagation-cutting plane algorithm for the RCPSP, 4th International Workshop on Integration of AI and OR techniques in Constraint Programming for Combinatorial Optimisation Problems (CPAIOR’02), Le Croisic, France (2002) 321–331.

    Google Scholar 

  5. Heipcke, S. 1999. Combined Modelling and Problem Solving in Mathematical Programming and Constraint Programming, Ph.D. Thesis, University of Buckingham.

    Google Scholar 

  6. Hooker, J. N. 1995. Logic-based Benders decomposition, presented at INFORMS 1995.

    Google Scholar 

  7. Hooker, J. N. 1997. Constraint satisfaction methods for generating valid cuts, in D. L. Woodruff, ed., Advances in Computational and Stochasic Optimization, Logic Programming and Heuristic Search, Kluwer (Dordrecht) 1–30.

    Google Scholar 

  8. Hooker, J. N. 2000. Logic-Based Methods for Optimization: Combining Optimization and Constraint Satisfaction, Wiley (New York).

    Book  MATH  Google Scholar 

  9. Hooker, J. N. 2001. Logic, optimization and constraint programming, to appear in INFORMS Journal on Computing.

    Google Scholar 

  10. Hooker, J. N., and M. A. Osorio. 1999. Mixed logical/linear programming, Discrete Applied Mathematics 96-97 395–442.

    Google Scholar 

  11. Hooker, J. N., and G. Ottosson, Logic-based Benders decomposition, to appear in Mathematical Programming.

    Google Scholar 

  12. Jain, V., and I. E. Grossmann. 1999. Algorithms for hybrid MILP/CLP models for a class of optimization problems, INFORMS Journal on Computing, to appear.

    Google Scholar 

  13. Ottosson, G., and E. Thorsteinsson. 2000. Linear relaxations and reduced-cost based propagation of continuous variable subscripts, CP’AI’OR’00.

    Google Scholar 

  14. Ottosson, G., E. Thorsteinsson, and J. N. Hooker. 1999. Mixed global constraints and inference in hybrid CLP-IP solvers, CP99 Post-Conference Workshop on Large Scale Combinatorial Optimization and Constraints, http://www.dash.co.uk/wscp99, 57–78.

  15. Réfalo, P. 1999. Tight cooperation and its application in piecewise linear optimization, in J. Jaffar, ed., Principles and Practice of Constraint Programming, Lecture Notes in Computer Science 1713, Springer (Berlin), 373–389.

    Google Scholar 

  16. Thorsteinsson, E. S. 2001. Branch-and-check: A hybrid framework integrating mixed integer programming and constraint logic programming, CP01.

    Google Scholar 

  17. Williams, H. P., and J. M. Wilson. 1998. Connections between integer linear programming and constraint logic programming-An overview and introduction to the cluster of articles, INFORMS Journal on Computing 10 261–264.

    Article  MathSciNet  MATH  Google Scholar 

  18. Williams, H. P., and Hong Yan. 2001. Representations of the all-different predicate, INFORMS Journal on Computing, to appear.

    Google Scholar 

  19. Yan, H., and J. N. Hooker. 1999. Tight representation of logical constraints as cardinality rules, Mathematical Programming 85 363–377.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hooker, J.N., Yan, H. (2002). A Relaxation of the Cumulative Constraint. In: Van Hentenryck, P. (eds) Principles and Practice of Constraint Programming - CP 2002. CP 2002. Lecture Notes in Computer Science, vol 2470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46135-3_46

Download citation

  • DOI: https://doi.org/10.1007/3-540-46135-3_46

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44120-5

  • Online ISBN: 978-3-540-46135-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics