Local Optima Networks, Landscape Autocorrelation and Heuristic Search Performance

  • Francisco Chicano
  • Fabio Daolio
  • Gabriela Ochoa
  • Sébastien Vérel
  • Marco Tomassini
  • Enrique Alba
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7492)


Recent developments in fitness landscape analysis include the study of Local Optima Networks (LON) and applications of the Elementary Landscapes theory. This paper represents a first step at combining these two tools to explore their ability to forecast the performance of search algorithms. We base our analysis on the Quadratic Assignment Problem (QAP) and conduct a large statistical study over 600 generated instances of different types. Our results reveal interesting links between the network measures, the autocorrelation measures and the performance of heuristic search algorithms.


Genetic Algorithm Simulated Anneal Local Optimum Landscape Metrics Quadratic Assignment Problem 
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.


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  1. 1.
    Angel, E., Zissimopoulos, V.: On the landscape ruggedness of the quadratic assignment problem. Theoretical Computer Sciences 263, 159–172 (2000)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bäck, T., Fogel, D.B., Michalewicz, Z. (eds.): Evolutionary Computation 1. Basic Algorithms and Operators. IOP Publishing Lt. (2000)Google Scholar
  3. 3.
    Barnes, J.W., Dokov, S.P., Acevedo, R., Solomon, A.: A note on distance matrices yielding elementary landscapes for the TSP. Journal of Mathematical Chemistry 31(2), 233–235 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Barrat, A., Barthélemy, M., Vespignani, A.: Dynamical processes on complex networks. Cambridge University Press (2008)Google Scholar
  5. 5.
    Burkard, R.E., Karisch, S.E., Rendl, F.: QAPLIB - a quadratic assignment problem library. Journal of Global Optimization 10, 391–403 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Chicano, F., Luque, G., Alba, E.: Elementary landscape decomposition of the quadratic assignment problem. In: Proceedings of GECCO, pp. 1425–1432. ACM, New York (2010)Google Scholar
  7. 7.
    Chicano, F., Luque, G., Alba, E.: Autocorrelation measures for the quadratic assignment problem. Applied Mathematics Letters 25(4), 698–705 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Daolio, F., Tomassini, M., Vérel, S., Ochoa, G.: Communities of minima in local optima networks of combinatorial spaces. Physica A: Statistical Mechanics and its Applications 390(9), 1684–1694 (2011)CrossRefGoogle Scholar
  9. 9.
    Daolio, F., Vérel, S., Ochoa, G., Tomassini, M.: Local optima networks of the quadratic assignment problem. In: IEEE Congress on Evolutionary Computation, CEC 2010, pp. 3145–3152. IEEE Press (2010)Google Scholar
  10. 10.
    Enright, A.J., Van Dongen, S., Ouzounis, C.A.: An efficient algorithm for large-scale detection of protein families. Nucleic Acids Research 30(7), 1575–1584 (2002)CrossRefGoogle Scholar
  11. 11.
    García-Pelayo, R., Stadler, P.: Correlation length, isotropy and meta-stable states. Physica D: Nonlinear Phenomena 107(2-4), 240–254 (1997)CrossRefGoogle Scholar
  12. 12.
    Knowles, J.D., Corne, D.W.: Instance Generators and Test Suites for the Multiobjective Quadratic Assignment Problem. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 295–310. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Stadler, P.F.: Fitness Landscapes. In: Biological Evolution and Statistical Physics, pp. 183–204. Springer (2002)Google Scholar
  14. 14.
    Taillard, E.D.: Comparison of iterative searches for the quadratic assignment problem. Location Science 3, 87–105 (1995)zbMATHCrossRefGoogle Scholar
  15. 15.
    Tomassini, M., Vérel, S., Ochoa, G.: Complex-network analysis of combinatorial spaces: The NK landscape case. Phys. Rev. E 78(6), 066114 (2008)CrossRefGoogle Scholar
  16. 16.
    Verel, S., Ochoa, G., Tomassini, M.: Local optima networks of NK landscapes with neutrality. IEEE Trans. on Evolutionary Computation 15(6), 783–797 (2011)CrossRefGoogle Scholar
  17. 17.
    Weinberger, E.: Correlated and uncorrelated fitness landscapes and how to tell the difference. Biological Cybernetics 63(5), 325–336 (1990)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Francisco Chicano
    • 1
  • Fabio Daolio
    • 2
  • Gabriela Ochoa
    • 3
  • Sébastien Vérel
    • 4
  • Marco Tomassini
    • 2
  • Enrique Alba
    • 1
  1. 1.E.T.S. Ingeniería InformáticaUniversity of MálagaSpain
  2. 2.Information Systems DepartmentUniversity of LausanneLausanneSwitzerland
  3. 3.Inst. of Computing Sciences and MathematicsUniversity of StirlingScotland, UK
  4. 4.INRIA Lille - Nord Europe and University of Nice Sophia-AntipolisFrance

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