Adaptive Bisection of Numerical CSPs | SpringerLink
Skip to main content

Adaptive Bisection of Numerical CSPs

  • Conference paper
Principles and Practice of Constraint Programming (CP 2012)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7514))

Abstract

Bisection is a search algorithm for numerical CSPs. The main principle is to select one variable at every node of the search tree and to bisect its interval domain. In this paper, we introduce a new adaptive variable selection strategy following an intensification diversification approach. Intensification is implemented by the maximum smear heuristic. Diversification is obtained by a round-robin ordering on the variables. The balance is automatically adapted during the search according to the solving state. Experimental results from a set of standard benchmarks show that this new strategy is more robust. Moreover, it is particularly efficient for solving the well-known Transistor problem, illustrating the benefits of an adaptive search.

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

Access this chapter

Subscribe and save

Springer+ Basic
¥17,985 /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
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 11439
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 14299
Price includes VAT (Japan)
  • 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. Benhamou, F., McAllester, D., Van Hentenryck, P.: CLP(Intervals) Revisited. In: Proc. ILPS, pp. 124–138 (1994)

    Google Scholar 

  2. Csendes, T., Ratz, D.: Subdivision Direction Selection in Interval Methods for Global Optimization. SIAM J. Numerical Analysis 34, 922–938 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  3. Feo, T.A., Resende, M.G.C.: Greedy Randomized Adaptive Search Procedures. Journal of Global Optimization 6, 109–133 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  4. Granvilliers, L., Benhamou, F.: Algorithm 852: Realpaver: an Interval Solver using Constraint Satisfaction Techniques. ACM Trans. Mathematical Software 32(1), 138–156 (2006)

    Article  MathSciNet  Google Scholar 

  5. Hamadi, Y., Monfroy, E., Saubion, F. (eds.): Autonomous Search. Springer (2012)

    Google Scholar 

  6. Van Hentenryck, P., Mcallester, D., Kapur, D.: Solving Polynomial Systems Using a Branch and Prune Approach. SIAM J. Numerical Analysis 34, 797–827 (1997)

    Article  MATH  Google Scholar 

  7. Kearfott, R.B.: Some Tests of Generalized Bisection. ACM Trans. Mathematical Software 13(3), 197–220 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kearfott, R.B., Novoa, M.: Algorithm 681: INTBIS, a portable interval Newton/bisection package. ACM Trans. Mathematical Software 16(2), 152–157 (1990)

    Article  MATH  Google Scholar 

  9. Lhomme, O.: Consistency Techniques for Numeric CSPs. In: Proc. IJCAI, pp. 232–238 (1993)

    Google Scholar 

  10. Refalo, P.: Impact-Based Search Strategies for Constraint Programming. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 557–571. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  11. Trombettoni, G., Araya, I., Neveu, B., Chabert, G.: Inner Regions and Interval Linearizations for Global Optimization. In: Proc. AAAI, pp. 99–104 (2011)

    Google Scholar 

  12. Trombettoni, G., Chabert, G.: Constructive Interval Disjunction. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 635–650. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Granvilliers, L. (2012). Adaptive Bisection of Numerical CSPs. In: Milano, M. (eds) Principles and Practice of Constraint Programming. CP 2012. Lecture Notes in Computer Science, vol 7514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33558-7_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-33558-7_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33557-0

  • Online ISBN: 978-3-642-33558-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics