Visualizing Tree Structures in Genetic Programming

  • Jason M. Daida
  • Adam M. Hilss
  • David J. Ward
  • Stephen L. Long
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2724)

Abstract

This paper presents methods to visualize the structure of trees that occur in genetic programming. These methods allow for the inspection of structure of entire trees of arbitrary size. The methods also scale to allow for the inspection of structure for an entire population. Examples are given from a typical problem. The examples indicate further studies that might be enabled by visualizing structure at these scales.

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References

  1. [1]
    S.H. Strogatz, “Exploring Complex Networks,” Nature, vol. 410, pp. 268–276, 2001.CrossRefGoogle Scholar
  2. [2]
    J.P. Rosca, “Analysis of Complexity Drift in Genetic Programming,” in GP 1997 Proceedings, J. R. Koza, et al., Eds. San Francisco: Morgan Kaufmann Publishers, 1997, pp. 286–94.Google Scholar
  3. [3]
    J.P. Rosca and D.H. Ballard, “Rooted-Tree Schemata in Genetic Programming,” in Advances in Genetic Programming 3, L. Spector, et al. Eds. Cambridge: The MIT Press, 1999, pp. 243–271.Google Scholar
  4. [4]
    C. Gathercole and P. Ross, “An Adverse Interaction Between Crossover and Restricted Tree Depth in Genetic Programming,” in GP 1996 Proceedings, J. R. Koza, et al., Eds. Cambridge: The MIT Press, 1996, pp. 291–96.Google Scholar
  5. [5]
    N.F. McPhee and N.J. Hopper, “Analysis of Genetic Diversity through Population History,” in GECCO’ 99 Proceedings, vol. 2, W. Banzhaf, et al., Eds. San Francisco: Morgan Kaufmann Publishers, 1999, pp. 1112–1120.Google Scholar
  6. [6]
    M. Mitchell, S. Forrest, and J.H. Holland, “The Royal Road for Genetic Algorithms: Fitness Landscapes and GA Performance,” in Proceedings of the First European Conference on Artificial Life., F.J. Varela and P. Bourgine, Eds. Cambridge: The MIT Press, 1992, pp. 245–254.Google Scholar
  7. [7]
    W. Punch, et al., “The Royal Tree Problem, A Benchmark for Single and Multiple Population GP,” in Advances in GP, vol. 2, P. J. Angeline and J.K.E. Kinnear, Eds. Cambridge: The MIT Press, 1996, pp. 299–316.Google Scholar
  8. [8]
    D.E. Goldberg and U.-M. O’Reilly, “Where Does the Good Stuff Go, and Why?,” in Proceedings of the First European Conference on Genetic Programming, W. Banzhaf, et al., Eds. Berlin: Springer-Verlag, 1998.Google Scholar
  9. [9]
    U.-M. O’Reilly and D.E. Goldberg, “How Fitness Structure Affects Subsolution Acquisition in GP,” in GP 1998 Proceedings, J. R. Koza, et al. Eds. San Francisco: Morgan Kaufmann Publishers, 1998, pp. 269–77.Google Scholar
  10. [10]
    T. Soule, J.A. Foster, and J. Dickinson, “Code Growth in Genetic Programming,” in GP 1996 Proceedings, J.R. Koza, et al., Eds. Cambridge: The MIT Press, 1996, pp. 215–223.Google Scholar
  11. [11]
    T. Soule and J.A. Foster, “Code Size and Depth Flows in Genetic Programming,” in GP 1997 Proceedings, J.R. Koza, et al., Eds. San Francisco: Morgan Kaufmann Publishers, 1997, pp. 313–320.Google Scholar
  12. [12]
    T. Soule and J.A. Foster, “Removal Bias: A New Cause of Code Growth in Tree Based Evolutionary Programming,” in ICEC 1998 Proceedings, vol. 1. Piscataway: IEEE Press, 1998, pp. 781–786.Google Scholar
  13. [13]
    W.B. Langdon, et al., “The Evolution of Size and Shape,” in Advances in Genetic Programming 3, L. Spector, et al., Eds. Cambridge: The MIT Press, 1999, pp. 163–190.Google Scholar
  14. [14]
    W.B. Langdon, “Size Fair and Homologous Tree Crossovers for Tree Genetic Programming,” Genetic Programming and Evolvable Machines, vol. 1, pp. 95–119, 2000.MATHCrossRefGoogle Scholar
  15. [15]
    W.B. Langdon and R. Poli, Foundations of Genetic Programming. Berlin: Springer-Verlag, 2002.MATHCrossRefGoogle Scholar
  16. [16]
    R. Poli and W.B. Langdon, “A New Schema Theory for GP with One-Point Crossover and Point Mutation,” in GP 1997 Proceedings, J.R. Koza, et al., Eds. San Francisco: Morgan Kaufmann Publishers, 1997, pp. 279–285.Google Scholar
  17. [17]
    R. Poli and W. B. Langdon, “Schema Theory for Genetic Programming with One-Point Crossover and Point Mutation,” Evolutionary Computation, vol. 6, pp. 231–252, 1998.CrossRefGoogle Scholar
  18. [18]
    R. Poli, “Exact Schema Theorem and Effective Fitness for GP with One-Point Crossover,” in GECCO 2000 Proceedings, L. D. Whitley, et al., Eds. San Francisco: Morgan Kaufmann Publishers, 2000, pp. 469–476.Google Scholar
  19. [19]
    W.B. Langdon and R. Poli, “Fitness Causes Bloat,” in Soft Computing in Engineering Design and Manufacturing, P.K. Chawdhry, R. Roy, and R.K. Pant, Eds. London: Springer-Verlag, 1997, pp. 23–27.Google Scholar
  20. [20]
    W.B. Langdon, “Quadratic Bloat in Genetic Programming,” in GECCO 2000 Proceedings, L.D. Whitley, et al., Eds. San Francisco: Morgan Kaufmann Publishers, 2000, pp. 451–458.Google Scholar
  21. [21]
    J.R. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection. Cambridge: The MIT Press, 1992.MATHGoogle Scholar
  22. [22]
    D.E. Knuth, The Art of Computer Programming: Volume 1: Fundamental Algorithms, vol. 1, Third ed. Reading: Addison-Wesley, 1997.MATHGoogle Scholar
  23. [23]
    R.P. Stanley, Enumerative Combinatorics I, vol. 1. Cambridge: Cambridge University Press, 1997.Google Scholar
  24. [24]
    R.P. Stanley, Enumerative Combinatorics II, vol. 2. Cambridge: Cambridge University Press, 1999.Google Scholar
  25. [25]
    C. Jacob, Illustrating Evolutionary Computation with Mathematica. San Francisco: Morgan Kaufmann, 2001.Google Scholar
  26. [26]
    J.M. Daida, et al., “Analysis of Single-Node (Building) Blocks in GP,” in Advances in Genetic Programming 3, L. Spector, W.B. Langdon, U.-M. O’Reilly, and P. J. Angeline, Eds. Cambridge: The MIT Press, 1999, pp. 217–241.Google Scholar
  27. [27]
    J.M. Daida, et al., “What Makes a Problem GP-Hard? Analysis of a Tunably Difficult Problem in Genetic Programming,” in GECCO’ 99 Proceedings, vol. 2, W. Banzhaf, et al., Eds. San Francisco: Morgan Kaufmann Publishers, 1999, pp. 982–989.Google Scholar
  28. [28]
    O.A. Chaudhri, et al. “Characterizing a Tunably Difficult Problem in Genetic Programming,” in GECCO 2000 Proceedings, L.D. Whitley, et al., Eds. San Francisco: Morgan Kaufmann Publishers, 2000, pp. 395–402.Google Scholar
  29. [29]
    J.M. Daida, et al., “What Makes a Problem GP-Hard? Analysis of a Tunably Difficult Problem in Genetic Programming,” Journal of Genetic Programming and Evolvable Hardware, vol. 2, pp. 165–191, 2001.MATHCrossRefGoogle Scholar
  30. [30]
    T. Bickle and L. Thiele, “A Mathematical Analysis of Tournament Selection,” in ICGA95 Proceedings, L.J. Eshelman, Ed. San Francisco: Morgan Kaufmann Publishers, 1995, pp. 9–16.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jason M. Daida
    • 1
  • Adam M. Hilss
    • 1
  • David J. Ward
    • 1
  • Stephen L. Long
    • 1
  1. 1.Center for the Study of Complex Systems and the Space Physics Research LaboratoryThe University of MichiganAnn Arbor

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