Genotype-Fitness Correlation Analysis for Evolutionary Design of Self-assembly Wang Tiles

  • Germán Terrazas
  • Natalio Krasnogor
Part of the Studies in Computational Intelligence book series (SCI, volume 387)


In a previous work we have reported on the evolutionary design optimisation of self-assembling Wang tiles. Apart from the achieved findings [11], nothing has been yet said about the effectiveness by which individuals were evaluated. In particular when the mapping from genotype to phenotype and from this to fitness is an intricate relationship. In this paper we aim to report whether our genetic algorithm, using morphological image analyses as fitness function, is an effective methodology. Thus, we present here fitness distance correlation to measure how effectively the fitness of an individual correlates to its genotypic distance to a known optimum when the genotype-phenotype-fitness mapping is a complex, stochastic and non-linear relationship.


Evolutionary Design Intricate Relationship Minkowski Functional Ridge Function Genotypic Distance 
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.
    Altenberg, L.: Fitness Distance Correlation Analysis: An Instructive Counter example. In: 7th International Conference on Genetic Algorithms, pp. 57–64. Morgan Kaufmann, San Francisco (1997)Google Scholar
  2. 2.
    Jones, T.: Evolutionary algorithms, fitness landscapes and search. PhD thesis, University of New Mexico (1995)Google Scholar
  3. 3.
    Jones, T., Forrest, S.: Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms. In: 6th International Conference on Genetic Algorithms, pp. 184–192. Morgan Kaufmann Publishers Inc., San Francisco (1995)Google Scholar
  4. 4.
    Koljonen, J.: On fitness distance distributions and correlations, GA performance, and population size of fitness functions with translated optima. In: Honkela, T., Kortela, J., Raiko, T., Valpola, H. (eds.) 9th Scandinavian Conference on Artificial Intelligence, Finnish Artificial Intelligence Society, Espoo, Finland, pp. 68–74 (2006)Google Scholar
  5. 5.
    Li, L., Siepmann, P., Smaldon, J., Terrazas, G., Krasnogor, N.: Automated Self-Assembling Programming. In: Krasnogor, N., Gustafson, S., Pelta, D., Verdegay, J.L. (eds.) Systems Self-Assembly: Multidisciplinary Snapshots. Elsevier, Amsterdam (2008)Google Scholar
  6. 6.
    Michielsen, K., Raedt, H.D.: Morphological image analysis. Computer Physics Communications 1, 94–103 (2000)CrossRefGoogle Scholar
  7. 7.
    Michielsen, K., Raedt, H.D.: Integral-geometry morphological image analysis. Physics Reports 347, 461–538 (2001), doi:10.1016/S0370-1573(00)00106-XMathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Quick, R.J., Rayward-Smith, V.J., Smith, G.D.: Fitness distance correlation and ridge functions. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 77–86. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  9. 9.
    Rothemund, P.W.K., Winfree, E.: The program-size complexity of self-assembled squares (extended abstract). In: 32nd ACM Symposium on Theory of computing, pp. 459–468. ACM, New York (2000), doi: Google Scholar
  10. 10.
    Terrazas, G., Krasnogor, N., Kendall, G., Gheorghe, M.: Automated Tile Design for Self-Assembly Conformations. In: IEEE Congress on Evolutionary Computation, vol. 2, pp. 1808–1814. IEEE Press, Los Alamitos (2005)CrossRefGoogle Scholar
  11. 11.
    Terrazas, G., Gheorghe, M., Kendall, G., Krasnogor, N.: Evolving Tiles for Automated Self-Assembly Design. In: IEEE Congress on Evolutionary Computation, pp. 2001–2008. IEEE Press, Los Alamitos (2007)CrossRefGoogle Scholar
  12. 12.
    Tomassini, M., Vanneschi, L., Collard, P., Clergue, M.: A Study of Fitness Distance Correlation as a Difficulty Measure in Genetic Programming. Evolutionary Computation 13(2), 213–239 (2005), doi: Scholar
  13. 13.
    Vanneschi, L., Tomassini, M.: Pros and Cons of Fitness Distance Correlation in Genetic Programming. In: Barry, A.M. (ed.) Bird of a Feather Workshops, Genetic and Evolutionary Computation Conference, pp. 284–287. AAAI, Chigaco (2003)Google Scholar
  14. 14.
    Vanneschi, L., Tomassini, M., Collard, P., Clergue, M.: Fitness Distance Correlation in Structural Mutation Genetic Programming. In: Ryan, C., Soule, T., Keijzer, M., Tsang, E.P.K., Poli, R., Costa, E. (eds.) EuroGP 2003. LNCS, vol. 2610, pp. 455–464. Springer, Heidelberg (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Germán Terrazas
    • 1
  • Natalio Krasnogor
    • 1
  1. 1.ASAP Group, School of Computer ScienceUniversity of NottinghamUK

Personalised recommendations