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Visualization of Tree Structures: Examples from Genetic Programming and a Model of Tree Growth
Authors

Jason Daida
Organization: The University of Michigan
Department: AOSS
Adam M. Hilss
David J. Ward
Stephen L. Long
Revision date

2004-03-05
Description

TreeForm This Mathematica notebook supports two papers that were presented at GECCO 2003:

Daida, J.M., A.M. Hilss, D.J. Ward, and S.L. Long, “Visualizing Tree Structures in Genetic Programming,”in Proceedings of GECCO 2003. (A long version of the paper appears in the Journal of Genetic Programming and Evolvable Machines.) 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 even though several thousand of nodes may be involved. The methods also scale to allow for the inspection of structure for entire populations and for complete trials even though millions of nodes may be involved. Examples are given that demonstrate how this new way of “seeing” can afford a potentially rich way of understanding dynamics that underpin genetic programming. The examples indicate further studies that might be enabled by visualizing structure at these scales. (Winner, Best Paper Award in GP, GECCO 2003)

Daida, J.M. and A.M. Hilss, “Identifying Structural Mechanisms in Genetic Programming,”in Proceedings of GECCO 2003. This paper presents a hypothesis about an undiscovered class of mechanisms that exist in standard GP. Rather than being intentionally designed, these mechanisms would be an unintended consequence of using trees as information structures. A model is described that predicts outcomes in GP that would arise solely from such mechanisms. Comparisons with empirical results from GP lend support to the existence of these mechanisms.

This notebook includes much of the Mathematica code that was used in the preparation of these papers.

Bibliography: J. M. Daida, A. Hilss, D. J. Ward, and S. Long, “Visualizing Tree Structures in Genetic Programming,” in Genetic and Evolutionary Computation—GECCO 2003: Genetic and Evolutionary Computation Conference, Chicago, IL, USA, July 2003, vol. LNCS 2724, Lecture Notes in Computer Science, E. Cantú-Paz, J. A. Foster, K. Deb, L. D. Davis, R. Roy, U.-M. O’Reilly, H.-G. Beyer, R. Standish, G. Kendall, S. Wilson, M. Harman, J. Wegener, D. Dasgupta, M. A. Potter, A. C. Schultz, K. A. Dowsland, and N. J. J. Miller, Eds. Berlin: Springer-Verlag, 2003, pp. 1652–1664.

J. M. Daida, A. Hilss, D. J. Ward, and S. Long, “Visualizing Tree Structures in Genetic Programming,” Journal of Genetic Programming and Evolutionary Machines, forthcoming.

J. M. Daida and A. Hilss, “Identifying Structural Mechanisms in Standard Genetic Programming,” in Genetic and Evolutionary Computation—GECCO 2003: Genetic and Evolutionary Computation Conference, Chicago, IL, USA, July 2003, vol. LNCS 2724, Lecture Notes in Computer Science, E. Cantú-Paz, J. A. Foster, K. Deb, L. D. Davis, R. Roy, U.-M. O’Reilly, H.-G. Beyer, R. Standish, G. Kendall, S. Wilson, M. Harman, J. Wegener, D. Dasgupta, M. A. Potter, A. C. Schultz, K. A. Dowsland, and N. J. J. Miller, Eds. Berlin: Springer-Verlag, 2003, pp. 1639–1651.
Subjects

*Applied Mathematics > Computer Science
*Applied Mathematics > Visualization
*Mathematics > Discrete Mathematics > Graph Theory
Keywords

Genetic Programming, GP, Structure, Trees, Visualization
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TreeStructures.zip (7.2 MB) - Supporting data for notebook [for Mathematica 5.0]
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daidaGPEM.nb (67.4 KB) - Main notebook [for Mathematica 5.0]