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Fitness Clouds and Problem Hardness in Genetic Programming

  • Leonardo Vanneschi
  • Manuel Clergue
  • Philippe Collard
  • Marco Tomassini
  • Sébastien Vérel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3103)

Abstract

This paper presents an investigation of genetic programming fitness landscapes. We propose a new indicator of problem hardness for tree-based genetic programming, called negative slope coefficient, based on the concept of fitness cloud. The negative slope coefficient is a predictive measure, i.e. it can be calculated without prior knowledge of the global optima. The fitness cloud is generated via a sampling of individuals obtained with the Metropolis-Hastings method. The reliability of the negative slope coefficient is tested on a set of well known and representative genetic programming benchmarks, comprising the binomial-3 problem, the even parity problem and the artificial ant on the Santa Fe trail.

Keywords

Genetic Algorithm Genetic Programming Negative Slope Genetic Operator Problem Hardness 
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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References

  1. 1.
    Altenberg, L.: The evolution of evolvability in genetic programming. In: Kinnear, K. (ed.) Advances in Genetic Programming, pp. 47–74. The MIT Press, Cambridge (1994)Google Scholar
  2. 2.
    Clergue, M., Collard, P., Tomassini, M., Vanneschi, L.: Fitness distance correlation and problem difficulty for genetic programming. In: Langdon, W.B., et al. (eds.) Proceedings of the genetic and evolutionary computation conference GECCO 2002, pp. 724–732. Morgan Kaufmann, San Francisco (2002)Google Scholar
  3. 3.
    Daida, J.M., Bertram, R., Stanhope, S., Khoo, J., Chaudhary, S., Chaudhary, O.: What makes a problem GP-hard? analysis of a tunably difficult problem in genetic programming. Genetic Programming and Evolvable Machines 2, 165–191 (2001)zbMATHCrossRefGoogle Scholar
  4. 4.
    Deb, K., Goldberg, D.E.: Analyzing deception in trap functions. In: Whitley, D. (ed.) Foundations of Genetic Algorithms, 2, pp. 93–108. Morgan Kaufmann, San Francisco (1993)Google Scholar
  5. 5.
    Forrest, S., Mitchell, M.: What makes a problem hard for a genetic algorithm? some anomalous results and their explanation. Machine Learning 13, 285–319 (1993)CrossRefGoogle Scholar
  6. 6.
    Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Boston (1989)zbMATHGoogle Scholar
  7. 7.
    Grefenstette, J.: Predictive models using fitness distributions of genetic operators. In: Whitley, D., Vose, M. (eds.) Foundations of Genetic Algorithms, 3, pp. 139–161. Morgan Kaufmann, San Francisco (1995)Google Scholar
  8. 8.
    Horn, J., Goldberg, D.E.: Genetic algorithm difficulty and the modality of the fitness landscapes. In: Whitley, D., Vose, M. (eds.) Foundations of Genetic Algorithms, 3, pp. 243–269. Morgan Kaufmann, San Francisco (1995)Google Scholar
  9. 9.
    Igel, C., Chellapilla, K.: Fitness distributions: Tools for designing efficient evolutionary computations. In: Spector, L., Langdon, W.B., O’Reilly, U.-M., Angeline, P. (eds.) Advances in Genetic Programming 3, pp. 191–216. The MIT Press, Cambridge (1999)Google Scholar
  10. 10.
    Jones, T.: Evolutionary Algorithms, Fitness Landscapes and Search. PhD thesis, University of New Mexico, Albuquerque (1995) Google Scholar
  11. 11.
    Kimura, M.: The Neutral Theory of Molecular Evolution. Cambridge University Press, Cambridge (1983)CrossRefGoogle Scholar
  12. 12.
    Kinnear, K.E.: Fitness landscapes and difficulty in genetic programming. In: Proceedings of the First IEEEConference on Evolutionary Computing, pp. 142–147. IEEE Press, Piscataway (1994)Google Scholar
  13. 13.
    Koza, J.R.: Genetic Programming. The MIT Press, Cambridge (1992)zbMATHGoogle Scholar
  14. 14.
    Koza, J.R., Streeter, M.J., Keane, M.A.: Genetic Programming IV: Routine Human- Competitive Machine Intelligence. Kluwer Academic Publishers, Boston (2003)zbMATHGoogle Scholar
  15. 15.
    Langdon, W.B., Poli, R.: Foundations of Genetic Programming. Springer, Berlin (2002)zbMATHGoogle Scholar
  16. 16.
    Madras, N.: Lectures on Monte Carlo Methods. American Mathematical Society, Providence, Rhode Island (2002)zbMATHGoogle Scholar
  17. 17.
    Manderick, B., de Weger, M., Spiessens, P.: The genetic algorithm and the structure of the fitness landscape. In: Belew, R.K., Booker, L.B. (eds.) Proceedings of the Fourth International Conference on Genetic Algorithms, pp. 143–150. Morgan Kaufmann, San Francisco (1991)Google Scholar
  18. 18.
    Mitchell, M., Forrest, S., Holland, J.: The royal road for genetic algorithms: fitness landscapes and ga performance. In: Varela, F.J., Bourgine, P. (eds.) Toward a Practice of Autonomous Systems, Proceedings of the First European Conference on Artificial Life, pp. 245–254. The MIT Press, Cambridge (1992)Google Scholar
  19. 19.
    Nikolaev, N.I., Slavov, V.: Concepts of inductive genetic programming. In: Banzhaf, W., Poli, R., Schoenauer, M., Fogarty, T.C. (eds.) EuroGP 1998. LNCS, vol. 1391, pp. 49–59. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  20. 20.
    Rosé, H., Ebeling, W., Asselmeyer, T.: The density of states - a measure of the difficulty of optimisation problems. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) PPSN 1996. LNCS, vol. 1141, pp. 208–217. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  21. 21.
    Smith, Husbands, Layzell, O’Shea: Fitness landscapes and evolvability. Evolutionary Computation 1(10), 1–34 (2001)Google Scholar
  22. 22.
    Stadler, P.F.: Fitness landscapes. In: Lässig, M., Valleriani (eds.) Biological Evolution and Statistical Physics. Lecture Notes Physics, vol. 585, pp. 187–207. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  23. 23.
    Vanneschi, L., Tomassini, M., Clergue, M., Collard, P.: Difficulty of unimodal and multimodal landscapes in genetic programming. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2724, pp. 1788–1799. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  24. 24.
    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
  25. 25.
    Vérel, S., Collard, P., Clergue, M.: Where are bottleneck in nk-fitness landscapes? In: CEC 2003: IEEE International Congress on Evolutionary Computation, Canberra, Australia, pp. 273–280. IEEE Press, Piscataway (2003)CrossRefGoogle Scholar
  26. 26.
    Weinberger, E.D.: Correlated and uncorrelated fitness landscapes and howto tell the difference. Biol. Cybern. 63, 325–336 (1990)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Leonardo Vanneschi
    • 2
  • Manuel Clergue
    • 1
  • Philippe Collard
    • 1
  • Marco Tomassini
    • 2
  • Sébastien Vérel
    • 1
  1. 1.I3S LaboratoryUniversity of NiceSophia AntipolisFrance
  2. 2.Information Systems DepartmentUniversity of LausanneLausanneSwitzerland

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