Skip to main content
SpringerLink
Log in

Randomness as a Constraint

  • Conference paper
  • First Online:
Principles and Practice of Constraint Programming (CP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9255))

Abstract

Some optimisation problems require a random-looking solution with no apparent patterns, for reasons of fairness, anonymity, undetectability or unpredictability. Randomised search is not a good general approach because problem constraints and objective functions may lead to solutions that are far from random. We propose a constraint-based approach to finding pseudo-random solutions, inspired by the Kolmogorov complexity definition of randomness and by data compression methods. Our “entropy constraints” can be implemented in constraint programming systems using well-known global constraints. We apply them to a problem from experimental psychology and to a factory inspection problem.

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

Access this chapter

Log in via an institution
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. Apt, K.R., Wallace, M.: Constraint Logic Programming Using Eclipse. Cambridge University Press (2007)

    Google Scholar 

  2. Beltrami, E.: What Is Random? Chance and Order in Mathematics and Life. Copernicus (1999)

    Google Scholar 

  3. van Casteren, M., Davis, M.H.: Mix, a Program for Pseudorandomization. Behaviour Research Methods 38(4), 584–589 (2006)

    Article  Google Scholar 

  4. Cilibrasi, R., Vitányi, P.M.B.: Clustering by Compression. IEEE Transactions on Information Theory 51(4), 1523–1545 (2005)

    Article  MATH  Google Scholar 

  5. Chaitin, G.J.: Algorithmic Information Theory. Cambridge University Press (1987)

    Google Scholar 

  6. Claessen, K., Duregård, J., Pałka, M.H.: Generating constrained random data with uniform distribution. In: Codish, M., Sumii, E. (eds.) FLOPS 2014. LNCS, vol. 8475, pp. 18–34. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  7. Cutler, C.C.: Differential Quantization for Television Signals. U. S. Patent 2, 605, 361, July 1952

    Google Scholar 

  8. Dechter, R., Kask, K., Bin, E., Emek, R.: Generating random solutions for constraint satisfaction problems. In: Proceedings of the 18th National Conference on Artificial Intelligence, pp. 15–21 (2002)

    Google Scholar 

  9. Ermon, S., Gomes, C.P., Selman, B.: Uniform solution sampling using a constraint solver as an oracle. In: Proceedings of the Twenty-Eighth Conference on Uncertainty in Artificial Intelligence, pp. 255–264. AUAI Press (2012)

    Google Scholar 

  10. French, R.M., Perruchet, P.: Generating Constrained Randomized Sequences: Item Frequency Matters. Behaviour Research Methods 41(4), 1233–1241 (2009)

    Article  Google Scholar 

  11. Hebrard, E., Hnich, B., O’Sullivan, B., Walsh, T.: Finding diverse and similar solutions in constraint programming. In: Proceedings of the 20th National Conference on Artificial Intelligence (2005)

    Google Scholar 

  12. Van Hentenryck, P., Coffrin, C., Gutkovich, B.: Constraint-based local search for the automatic generation of architectural tests. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 787–801. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  13. Hinkelmann, K., Kempthorne, O.: Design and Analysis of Experiments I and II. Wiley (2008)

    Google Scholar 

  14. Housworth, E.A., Martins, E.P.: Random Sampling of Constrained Phylogenies: Conducting Phylogenetic Analyses When the Philogeny is Partially Known. Syst. Biol. 50(5), 628–639 (2001)

    Article  Google Scholar 

  15. Huffman, D.A.: A Method for the Construction of Minimum Redundancy Codes. Proceedings of the IRE 40, 1098–1101 (1951)

    Article  Google Scholar 

  16. Kitchen, N., Kuehlmann, A.: Stimulus generation for constrained random simulation. In: Proceedings of the 2007 IEEE/ACM International Conference on Computer-Aided Design, pp. 258–265. IEEE Press (2007)

    Google Scholar 

  17. Knuth, D.E.: The Art of Computer Programming. Seminumerical Algorithms, 2nd edn., vol. 2, p. 89. Addison-Wesley (1981)

    Google Scholar 

  18. Marsaglia, G., Tsang, W.W.: Some Difficult-to-pass Tests of Randomness. Journal of Statistical Software 7(3) (2002)

    Google Scholar 

  19. Naveh, R., Metodi, A.: Beyond feasibility: CP usage in constrained-random functional hardware verification. In: Schulte, C. (ed.) CP 2013. LNCS, vol. 8124, pp. 823–831. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  20. Ouellet, P., Quimper, C.-G.: The multi-inter-distance constraint. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence, pp. 629–634 (2011)

    Google Scholar 

  21. Pachet, F., Roy, P.: Markov Constraints: Steerable Generation of Markov Sequences. Constraints 16(2), 148–172 (2011)

    Article  MathSciNet  Google Scholar 

  22. Pesant, G., Régin, J.-C.: SPREAD: a balancing constraint based on statistics. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 460–474. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  23. Pincus, S.M., Gladstone, I.M., Ehrenkranz, R.A.: A Regularity Statistic for Medical Data Analysis. Journal of Clinical Monitoring and Computing 7(4), 335–345 (1991)

    Article  Google Scholar 

  24. Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes in C, 2nd edn. Cambridge University Press, UK (1992)

    MATH  Google Scholar 

  25. Ramsey, F.P.: On a Problem of Formal Logic. Proceedings London Mathematical Society s2 30(1), 264–286 (1930)

    Article  MathSciNet  Google Scholar 

  26. 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 

  27. Régin, J.-C.: Generalized Arc Consistency for Global Cardinality Constraint. In: 14th National Conference on Artificial Intelligence, pp. 209–215 (1996)

    Google Scholar 

  28. Régin, J.-C.: A filtering algorithm for constraints of difference in CSPs. In: Proceedings of the 12th National Conference on Artificial Intelligence, Vol. 1, pp. 362–367 (1994)

    Google Scholar 

  29. Rissanen, J.J., Langdon, G.G.: Arithmetic Coding. IBM Journal of Research and Development 23(2), 149–162 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  30. Rossi, R., Prestwich, S., Tarim, S.A.: Statistical constraints. In: 21st European Conference on Artificial Intelligence (2014)

    Google Scholar 

  31. Sayood, K.: Introduction to Data Compression. Morgan Kaufmann (2012)

    Google Scholar 

  32. Shannon, C.E.: A Mathematical Theory of Communication. Bell System Technical Journal 27(3), 379–423 (1948)

    Article  MATH  MathSciNet  Google Scholar 

  33. Wallace, G.K.: The JPEG Still Picture Compression Standard. Communications of the ACM 34, 31–44 (1991)

    Article  Google Scholar 

  34. Welch, T.A.: A Technique for High-Performance Data Compression. IEEE Computer, 8–19, June 1984

    Google Scholar 

  35. Ziv, J., Lempel, A.: A Universal Algorithm for Data Compression. IEEE Transactions on Information Theory IT 23(3), 337–343 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  36. Ziv, J., Lempel, A.: Compression of Individual Sequences via Variable-Rate Coding. IEEE Transactions on Information Theory IT 24(5), 530–536 (1978)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Insight Centre for Data Analytics, University College Cork, Cork, Ireland

    Steven D. Prestwich

  2. University of Edinburgh Business School, Edinburgh, UK

    Roberto Rossi

  3. Department of Management, Cankaya University, Ankara, Turkey

    S. Armagan Tarim

Authors
  1. Steven D. Prestwich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roberto Rossi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Armagan Tarim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Steven D. Prestwich .

Editor information

Editors and Affiliations

  1. École Polytechnique de Montréal, Montréal, Québec, Canada

    Gilles Pesant

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Prestwich, S.D., Rossi, R., Tarim, S.A. (2015). Randomness as a Constraint. In: Pesant, G. (eds) Principles and Practice of Constraint Programming. CP 2015. Lecture Notes in Computer Science(), vol 9255. Springer, Cham. https://doi.org/10.1007/978-3-319-23219-5_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-23219-5_25

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23218-8

  • Online ISBN: 978-3-319-23219-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation