Landscapes and the Maximal Constraint Satisfaction Problem

  • Meriema Belaidouni
  • Jin-Kao Hao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1829)


Landscape is an important notion in studying the difficulty of a combinatorial problem and the behavior of heuristics. In this paper, two new measures for analyzing landscapes are introduced, each of them based on the Hamming distance of iso-cost levels. Sampling techniques based on neighborhood search are defined in order to effect an approximation of these measures. These measures and techniques are used to analyze and characterize the properties of Maximal Constraint Satisfaction Problem random landscapes.


Simulated Annealing Tabu Search Constraint Satisfaction Problem Cost Level Random Instance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Asselmeyer, E., Rosé, H., Korst, J.: Smoothing representation of fitness landscape - The genotype phenotype map of evolution. Biol. Systems (1995)Google Scholar
  2. 2.
    Barnett, L.: Evolutionary dynamics on fitness landscapes with neutrality. MSc Dissertation (1997),
  3. 3.
    Belaidouni, M., Hao, J.K.: A measure of combinatorial landscape difficulty for the Metropolis algorithm (1999) (submitted)Google Scholar
  4. 4.
    Belaidouni, M., Hao, J.K.: Search space analysis of the maximal constraint satisfaction problem. In: Proc. Of 5th French Workshop on Practical Solving of NP Complete Problems, pp. 58–71 (1999) (in French)Google Scholar
  5. 5.
    Catoni, O.: Rough large estimates for simulated annealing: application to exponential schedules. The Annals of Probability 20(3), 196–208 (1997)Google Scholar
  6. 6.
    Freuder, E.C., Wallace, R.J.: Partial Constraint Satisfaction. Artificial Intelligence 58(1-3), 21–70 (1992)Google Scholar
  7. 7.
    Galinier, P., Hao, J.K.: Tabu search for maximal constraint satisfaction problems. In: Smolka, G. (ed.) CP 1997. LNCS, vol. 1330, pp. 196–208. Springer, Heidelberg (1997)Google Scholar
  8. 8.
    Gent, I.P., MacIntyre, E., Prosser, P., Walsh, T.: Scaling effects in the CSP phase transition. In: Montanari, U., Rossi, F. (eds.) CP 1995. LNCS, vol. 976, pp. 70–87. Springer, Heidelberg (1995)Google Scholar
  9. 9.
    Hao, J.K., Pannier, J.: Simulated annealing and Tabu search for constraint solving. Artificial Intelligence and Mathematics IV (1998)Google Scholar
  10. 10.
    Hertz, A., Jaumard, B., De Aragao, M.P.: Local optima topology for the k-coloring problem. Discrete Applied Mathematics 49, 257–280 (1994)Google Scholar
  11. 11.
    Jones, T., Forrest, S.: Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In: Proc. of the 6th International Conference on Genetic Algorithms, pp. 184–192 (1995)Google Scholar
  12. 12.
    Kauffman, S.A.: Adaptation on rugged fitness landscapes. Lectures in the Sciences of Complexity. In: Stein, D. (ed.) SFI Studies in the Sciences of Complexity, pp. 527–618. Addison- Wesley Longman, Amsterdam (1989)Google Scholar
  13. 13.
    Kirkpatrick, S., Toulouse, G.: Configuration space analysis of travelling salesman problem. J. Physics 46, 1277–1292 (1985)Google Scholar
  14. 14.
    Manderick, B., de Weger, B., Spiessens, P.: The genetic algorithm and the structure of the fitness landscape. In: PPSN III (1994)Google Scholar
  15. 15.
    Smith, B.M.: Phase transition and the mushy region in constraint satisfaction problems. In: Proc of ECAI 1994, pp. 100–104 (1994)Google Scholar
  16. 16.
    Weinberger, E.: Correlated and uncorrelated fitness landscapes and how to tell the difference. Biol. Cybern. 63, 325–336 (1990)Google Scholar
  17. 17.
    Wright, S.: The roles of mutation, inbreeding, and selection in evolution. In: Proc. of the Sixth Congress on Genetics, vol. 1, p. 365 (1932)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Meriema Belaidouni
    • 1
  • Jin-Kao Hao
    • 2
  1. 1.LGI2P, EMA-EERIE, Parc Scientifique Georges BesseNîmes
  2. 2.LERIAUniversité d’AngersAngers Cedex 01

Personalised recommendations