Quantifying the Severity of the Permutation Problem in Neuroevolution

  • Stefan Haflidason
  • Richard Neville
Conference paper
Part of the Proceedings in Information and Communications Technology book series (PICT, volume 2)


In this paper we investigate the likely severity of the Permutation Problem on a standard Genetic Algorithm used for the evolutionary optimisation of Neural Networks. We present a method for calculating the expected number of permutations in an initial population given a particular representation and show that typically this number is very low. This low expectation coupled with the empirical evidence suggests that the severity of the Permutation Problem is low in general, and so not a common cause of poor performance in Neuroevolutionary algorithms.


Genetic Algorithm Hide Neuron Radial Basis Function Neural Network String Length Standard Genetic Algorithm 
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.
    Angeline, P., Saunders, G., Pollack, J.: An evolutionary algorithm that constructs recurrent neural networks. Neural Networks (1994)Google Scholar
  2. 2.
    Yao, X.: Evolving artificial neural networks. Proceedings of the IEEE (1999)Google Scholar
  3. 3.
    Yao, X., Islam, M.: Evolving artificial neural network ensembles. Computational Intelligence Magazine (2008)Google Scholar
  4. 4.
    Belew, R., McInerney, J., Schraudolph, N.: Evolving networks: Using the genetic algorithm with connectionist learning. Tech. rept. CSE TR90-174 UCSD (1990)Google Scholar
  5. 5.
    Branke, J.: Evolutionary algorithms for neural network design and training. In: Proceedings of the 1st Nordic Workshop on Genetic Algorithms (1995)Google Scholar
  6. 6.
    Carse, B., Fogarty, T.C.: Fast evolutionary learning of minimal radial basis function neural networks using a genetic algorithm. Selected Papers from AISB Workshop on Evolutionary Computing (1996)Google Scholar
  7. 7.
    García-Pedrajas, N., Ortiz-Boyer, D., Hervás-Martínez, C.: An alternative approach for neural network evolution with a genetic algorithm: Crossover by combinatorial optimization. Neural Networks (2006)Google Scholar
  8. 8.
    Montana, D., Davis, L.: Training feedforward neural networks using genetic algorithms. In: Proceedings of the Eleventh International Joint Conference on Artificial Intelligence (1989)Google Scholar
  9. 9.
    Stanley, K.: Efficient evolution of neural networks through complexification. PhD Thesis, The University of Texas at Austin (2004)Google Scholar
  10. 10.
    Thierens, D.: Non-redundant genetic coding of neural networks. In: Proceedings of IEEE International Conference on Evolutionary Computation (1996)Google Scholar
  11. 11.
    Schaffer, J., Whitley, D., Eshelman, L.: Combinations of genetic algorithms and neural networks: a survey ofthe state of the art. Combinations of Genetic Algorithms and Neural Networks (1992)Google Scholar
  12. 12.
    Hancock, P.: Genetic algorithms and permutation problems: a comparison of recombination operators for neural net structure specification. In: Proceedings of the International Workshop on Combinations of Genetic Algorithms and Neural Networks (1992)Google Scholar
  13. 13.
    Froese, T., Spier, E.: Convergence and crossover: The permutation problem revisited. University of Sussex Cognitive Science Research Paper CSRP 596 (2008)Google Scholar
  14. 14.
    Haflidason, S., Neville, R.: On the significance of the permutation problem in neuroevolution. In: Proceedings of the 11th Annual conference on Genetic and Evolutionary Computation, GECCO (2009)Google Scholar
  15. 15.
    Yao, X., Liu, Y.: A new evolutionary system for evolving artificial neural networks. IEEE Transactions on Neural Networks (1997)Google Scholar

Copyright information

© Springer Tokyo 2010

Authors and Affiliations

  • Stefan Haflidason
    • 1
  • Richard Neville
    • 1
  1. 1.School of Computer ScienceUniversity of ManchesterUK

Personalised recommendations