Skip to main content
SpringerLink
Log in
Book cover

Nature Inspired Cooperative Strategies for Optimization (NICSO 2013) pp 329–342Cite as

Branching Schemes and Variable Ordering Heuristics for Constraint Satisfaction Problems: Is There Something to Learn?

  • Chapter

  • 1167 Accesses

Part of the book series: Studies in Computational Intelligence ((SCI,volume 512))

Abstract

When solving a constraint satisfaction problem by using systematic algorithms it is needed to expand and explore a search tree to find a solution. In this work we study both binary and k-way branching schemes while they interact with various variable ordering heuristics, and how those interactions affect the cost of finding a solution to different instances. Both branching schemes have been used in previous investigations and it is not straight forward to determine the conditions that make one branching scheme better than the other. But we provide evidence that, in order to decide, variable ordering heuristics play a major role in the performance of these branching schemes. This study is intended to work as a preliminary study to develop hyper-heuristics for branching schemes in combination with variable ordering heuristics. The final part of the analysis presents a very simple naive hyper-heuristic that randomly applies binary and k-way branching as the search progresses in combination with some well known variable ordering heuristics. The scope of this paper is to explore the interactions between different variable ordering heuristics and these two branching schemes, in order to produce some relations between their performance. We expect these relations to be used in further studies as the basis for more robust hyper-heuristics that take into consideration the information gathered in this investigation.

This is a preview of subscription content, 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   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Balafoutis, T., Stergiou, K.: Adaptive branching for constraint satisfaction problems. In: Proceedings of the 2010 Conference on ECAI 2010, pp. 855–860. IOS Press, Amsterdam (2010)

    Google Scholar 

  2. Balafoutis, T., Paparrizou, A., Stergiou, K.: Experimental evaluation of branching schemes for the csp. CoRR abs/1009.0407 (2010)

    Google Scholar 

  3. Berlier, J., McCollum, J.: A constraint satisfaction algorithm for microcontroller selection and pin assignment. In: Proceedings of the IEEE SoutheastCon 2010 (SoutheastCon), pp. 348–351 (2010)

    Google Scholar 

  4. Bessière, C., Régin, J.C.: Mac and combined heuristics: Two reasons to forsake FC (and CBJ) on hard problems. In: Freuder, E.C. (ed.) CP 1996. LNCS, vol. 1118, Springer, Heidelberg (1996)

    Google Scholar 

  5. Bitner, J.R., Reingold, E.M.: Backtrack programming techniques. Communications of the ACM 18(11), 651–656 (1975)

    Article  MATH  Google Scholar 

  6. Burke, E., Hart, E., Kendall, G., Newall, J., Ross, P., Shulenburg, S.: Hyper-heuristics: an emerging direction in modern research technology. In: Handbook of Metaheuristics, pp. 457–474. Kluwer Academic Publishers (2003)

    Google Scholar 

  7. Burke, E.K., Hyde, M.R., Kendall, G., Ochoa, G., Ozcan, E., Woodward, J.R.: Exploring hyper-heuristic methodologies with genetic programming. In: Mumford, C.L., Jain, L.C. (eds.) Computational Intelligence. ISRL, vol. 1, pp. 177–201. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  8. Burke, E.K., Hyde, M., Kendall, G., Ochoa, G., Ozcan, E., Woodward, J.R.: A classification of hyper-heuristic approaches. In: Gendreau, M., Potvin, J.Y. (eds.) Handbook of Metaheuristics. International Series in Operations Research & Management Science, vol. 146, pp. 449–468. Springer, US (2010)

    Chapter  Google Scholar 

  9. Cheeseman, P., Kanefsky, B., Taylor, W.M.: Where the really hard problems are. In: Proceedings of International Joint Conferences on Artificial Intelligence (IJCAI 1991), pp. 331–337 (1991)

    Google Scholar 

  10. Cowling, P.I., Kendall, G., Soubeiga, E.: A hyperheuristic approach to scheduling a sales summit. In: Burke, E., Erben, W. (eds.) PATAT 2000. LNCS, vol. 2079, pp. 176–190. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  11. Crawford, B., Soto, R., Castro, C., Monfroy, E.: A hyperheuristic approach for dynamic enumeration strategy selection in constraint satisfaction. In: Ferrández, J.M., Álvarez Sánchez, J.R., de la Paz, F., Toledo, F.J. (eds.) IWINAC 2011, Part II. LNCS, vol. 6687, pp. 295–304. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  12. Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Communications of ACM 5(7), 394–397 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  13. Dunkin, N., Allen, S.: Frequency assignment problems: Representations and solutions. Tech. Rep. CSD-TR-97-14, University of London (1997)

    Google Scholar 

  14. Epstein, S.L., Freuder, E.C., Wallace, R.J.: Learning to support constraint programmers. Computational Intelligence 21(4), 336–371 (2005)

    Article  MathSciNet  Google Scholar 

  15. Fisher, H., Thompson, G.L.: Probabilistic learning combinations of local job-shop scheduling rules. In: Factory Scheduling Conference, Carnegie Institute of Technology (1961)

    Google Scholar 

  16. Freuder, E.C.: A sufficient condition for backtrack-free search. Journal of the ACM 29(1), 24–32 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  17. Freuder, E.C., Mackworth, A.K.: Constraint-Based Reasoning. MIT/Elsevier (1994)

    Google Scholar 

  18. Garey, M.R., Johnson, D.S.: Computers and Intractability; A Guide to the Theory of NP-Completeness. W.H. Freeman (1979)

    Google Scholar 

  19. Geelen, P.A.: Dual viewpoint heuristics for binary constraint satisfaction problems. In: Proceedings of the 10th European Conference on Artificial Intelligence (ECAI 1992), pp. 31–35. John Wiley & Sons (1992)

    Google Scholar 

  20. Gent, I., MacIntyre, E., Prosser, P., Smith, B., Walsh, T.: An empirical study of dynamic variable ordering heuristics for the constraint satisfaction problem. In: Freuder, E.C. (ed.) CP 1996. LNCS, vol. 1118, pp. 179–193. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  21. Haralick, R.M., Elliott, G.L.: Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence 14, 263–313 (1980)

    Article  Google Scholar 

  22. Hwang, J., Mitchell, D.G.: 2 -way vs. d -way branching for CSP. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 343–357. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  23. Kumar, V.: Algorithms for constraint satisfaction: a survey. AI Magazine 13(1), 32–44 (1992)

    Google Scholar 

  24. Lagoudakis, M.G., Littman, M.L.: Learning to select branching rules in the dpll procedure for satisfiability. Electronic Notes in Discrete Mathematics 9, 344–359 (2001)

    Article  Google Scholar 

  25. Mackworth, A.K.: Consistency in networks of relations. Artificial Intelligence 8(1), 99–118 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  26. Minton, S., Johnston, M.D., Phillips, A., Laird, P.: Minimizing conflicts: A heuristic repair method for CSP and scheduling problems. Artificial Intelligence 58, 161–205 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  27. Montanari, U.: Networks of constraints: fundamentals properties and applications to picture processing. Information Sciences 7, 95–132 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  28. O’Mahony, E., Hebrard, E., Holland, A., Nugent, C., O’Sullivan, B.: Using case-based reasoning in an algorithm portfolio for constraint solving. In: Proceedings of the 19th Irish Conference on Artificial Intelligence and Cognitive Science (2008)

    Google Scholar 

  29. Ortiz-Bayliss, J.C., Terashima-Marín, H., Conant-Pablos, S.E.: Learning vector quantization for variable ordering in constraint satisfaction problems. Pattern Recogn. Lett. 34(4), 423–432 (2013)

    Article  Google Scholar 

  30. Park, V.: An empirical study of different branching strategies for constraint satisfaction problems. PhD thesis, University of Waterloo (2004)

    Google Scholar 

  31. Petrovic, S., Qu, R.: Case-based reasoning as a heuristic selector in a hyper-heuristic for course timetabling problems. In: Proceedings of the 6th International Conference on Knowledge-Based Intelligent Information Engineering Systems and Applied Technologies (KES 2002), vol. 82, pp. 336–340 (2002)

    Google Scholar 

  32. Purdom, P.W.: Search rearrangement backtracking and polynomial average time. Artificial Intelligence 21, 117–133 (1983)

    Article  Google Scholar 

  33. Smith, B.M.: Locating the phase transition in binary constraint satisfaction problems. Artificial Intelligence 81, 155–181 (1996)

    Article  MathSciNet  Google Scholar 

  34. Smith, B.M.: Value ordering for finding all solutions. In: International Joint Conference on Artificial Intelligence (IJCAI 2005), pp. 311–316 (2005)

    Google Scholar 

  35. Smith, B.M., Grant, S.A.: Sparse constraint graphs and exceptionally hard problems. In: Proceedings of the International Joint Conferences on Artificial Intelligence (IJCAI 1995), pp. 646–651 (1995)

    Google Scholar 

  36. Smith, B.M., Sturdy, P.: An empirical investigation of value ordering for finding all solutions. In: Workshop on Modelling and Solving Problems with Constraints (2004)

    Google Scholar 

  37. Soto, R., Crawford, B., Monfroy, E., Bustos, V.: Using autonomous search for generating good enumeration strategy blends in constraint programming. In: Murgante, B., Gervasi, O., Misra, S., Nedjah, N., Rocha, A.M.A.C., Taniar, D., Apduhan, B.O. (eds.) ICCSA 2012, Part III. LNCS, vol. 7335, pp. 607–617. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  38. Wallace, R.J.: Analysis of heuristic synergies. In: Hnich, B., Carlsson, M., Fages, F., Rossi, F. (eds.) CSCLP 2005. LNCS (LNAI), vol. 3978, pp. 73–87. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  39. Williams, C.P., Hogg, T.: Using deep structure to locate hard problems. In: Proceedings of AAAI 1992, pp. 472–477 (1992)

    Google Scholar 

  40. Xu, K., Boussemart, F., Hemery, F., Lecoutre, C.: Random constraint satisfaction: Easy generation of hard (satisfiable) instances. Artificial Intelligence 171(8-9), 514–534 (2007)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Automated Scheduling, Optimisation and Planning (ASAP) School of Computer Science, University of Nottingham, Nottingham, UK

    José Carlos Ortiz-Bayliss

  2. Tecnológico de Monterrey, Campus Monterrey, Mexico, Monterrey

    Hugo Terashima-Marín & Santiago Enrique Conant-Pablos

Authors
  1. José Carlos Ortiz-Bayliss
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hugo Terashima-Marín
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Santiago Enrique Conant-Pablos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to José Carlos Ortiz-Bayliss .

Editor information

Editors and Affiliations

  1. School of Computer Science, University of Nottingham, Nottingham, United Kingdom

    German Terrazas

  2. School of Computing, University of Kent, Canterbury, Kent, United Kingdom

    Fernando E. B. Otero

  3. Center for Research on ICT, University of Granada, Granada, Spain

    Antonio D. Masegosa

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Ortiz-Bayliss, J.C., Terashima-Marín, H., Conant-Pablos, S.E. (2014). Branching Schemes and Variable Ordering Heuristics for Constraint Satisfaction Problems: Is There Something to Learn?. In: Terrazas, G., Otero, F., Masegosa, A. (eds) Nature Inspired Cooperative Strategies for Optimization (NICSO 2013). Studies in Computational Intelligence, vol 512. Springer, Cham. https://doi.org/10.1007/978-3-319-01692-4_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-01692-4_25

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-01691-7

  • Online ISBN: 978-3-319-01692-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation