Variable and Value Ordering Decision Matrix Hyper-heuristics: A Local Improvement Approach

  • José Carlos Ortiz-Bayliss
  • Hugo Terashima-Marín
  • Ender Özcan
  • Andrew J. Parkes
  • Santiago Enrique Conant-Pablos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7094)


Constraint Satisfaction Problems (CSP) represent an important topic of study because of their many applications in different areas of artificial intelligence and operational research. When solving a CSP, the order in which the variables are selected to be instantiated and the order of the corresponding values to be tried affect the complexity of the search. Hyper-heuristics are flexible methods that provide generality when solving different problems and, within CSP, they can be used to determine the next variable and value to try. They select from a set of low-level heuristics and decide which one to apply at each decision point according to the problem state. This study explores a hyper-heuristic model for variable and value ordering within CSP based on a decision matrix hyper-heuristic that is constructed by going into a local improvement method that changes small portions of the matrix. The results suggest that the approach is able to combine the strengths of different low-level heuristics to perform well on a wide range of instances and compensate for their weaknesses on specific instances.


Constraint Satisfaction Hyper-heuristics Variable and Value Ordering 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bittle, S.A., Fox, M.S.: Learning and using hyper-heuristics for variable and value ordering in constraint satisfaction problems. In: Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers, GECCO 2009, pp. 2209–2212. ACM, New York (2009)Google Scholar
  2. 2.
    Brelaz, D.: New methods to colour the vertices of a graph. Communications of the ACM 22 (1979)Google Scholar
  3. 3.
    Burke, E., Hyde, M., Kendall, G., Ochoa, G., Özcan, E., Rong, Q.: A survey of hyper-heuristics. Tech. Rep. NOTTCS-TR-SUB-0906241418-2747, School of Computer Science, University of Nottingham (2009)Google Scholar
  4. 4.
    Burke, E., Hyde, M., Kendall, G., Ochoa, G., Özcan, E., Woodward, J.R.: A classification of hyper-heuristic approaches. Tech. Rep. NOTTCS-TR-SUB-0907061259-5808, School of Computer Science, University of Nottingham (2009)Google Scholar
  5. 5.
    Chakhlevitch, K., Cowling, P.: Hyperheuristics: Recent developments. In: Cotta, C., Sevaux, M., Sörensen, K. (eds.) Adaptive and Multilevel Metaheuristics. SCI, vol. 136, pp. 3–29. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Cheeseman, P., Kanefsky, B., Taylor, W.M.: Where the really hard problems are. In: Proceedings of IJCAI 1991, pp. 331–337 (1991)Google Scholar
  7. 7.
    Denzinger, J., Fuchs, M., Fuchs, M., Informatik, F.F., Munchen, T.: High performance atp systems by combining several ai methods. In: Proc. Fifteenth International Joint Conference on Artificial Intelligence, IJCAI 1997, pp. 102–107. Morgan Kaufmann (1997)Google Scholar
  8. 8.
    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
  9. 9.
    Fukunaga, A.S.: Automated discovery of local search heuristics for satisfiability testing. Evolutionary Computation 16, 31–61 (2008)CrossRefGoogle Scholar
  10. 10.
    Gent, I.P., MacIntyre, E., Prosser, P., Smith, B.M., 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)Google Scholar
  11. 11.
    Mackworth, A.K.: Consistency in networks of relations. Artificial Intelligence 8(1), 99–118 (1977)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Minton, S., Johnston, M.D., Phillips, A., Laird, P.: Minimizing conflicts: A heuristic repair method for csp and scheduling problems. Artificial Intellgence 58, 161–205 (1992)CrossRefzbMATHGoogle Scholar
  13. 13.
    Ortiz-Bayliss, J.C., Terashima-Marín, H., Özcan, E., Parkes, A.J.: Mapping the performance of heuristics for constraint satisfaction. In: IEEE Congress on Evolutionary Computation (CEC), pp. 1–8 (July 2010)Google Scholar
  14. 14.
    Ortiz-Bayliss, J.C., Terashima-Marín, H., Özcan, E., Parkes, A.J.: On the idea of evolving decision matrix hyper-heuristics for solving constraint satisfaction problems. In: Proceedings of the 13th Annual Conference Companion on Genetic and Evolutionary Computation, GECCO 2011, pp. 255–256. ACM, New York (2011)Google Scholar
  15. 15.
    Prosser, P.: Binary constraint satisfaction problems: Some are harder than others. In: Proceedings of the European Conference in Artificial Intelligence, Amsterdam, Holland, pp. 95–99 (1994)Google Scholar
  16. 16.
    Smith, B.M.: Locating the phase transition in binary constraint satisfaction problems. Artificial Intelligence 81, 155–181 (1996)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Terashima-Marín, H., Ortiz-Bayliss, J.C., Ross, P., Valenzuela-Rendón, M.: Hyper-heuristics for the dynamic variable ordering in constraint satisfaction problems. In: GECCO 2008: Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation. ACM (2008)Google Scholar
  18. 18.
    Tsang, E., Kwan, A.: Mapping constraint satisfaction problems to algorithms and heuristics. Tech. Rep. CSM-198, Department of Computer Sciences, University of Essex (1993)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • José Carlos Ortiz-Bayliss
    • 1
  • Hugo Terashima-Marín
    • 1
  • Ender Özcan
    • 2
  • Andrew J. Parkes
    • 2
  • Santiago Enrique Conant-Pablos
    • 1
  1. 1.Tecnológico de MonterreyMonterreyMexico
  2. 2.University of NottinghamNottinghamUnited Kingdom

Personalised recommendations