Discovery of the Boolean Functions to the Best Density-Classification Rules Using Gene Expression Programming
Cellular automata are idealized versions of massively parallel, decentralized computing systems capable of emergent behaviors. These complex behaviors result from the simultaneous execution of simple rules at multiple local sites. A widely studied behavior consists of correctly determining the density of an initial configuration, and both human and computer-written rules have been found that perform with high efficiency at this task. However, the two best rules for the density-classification task, Coevolution1 and Coevolution2, were discovered using a coevolutionary algorithm in which a genetic algorithm evolved the rules and, therefore, only the output bits of the rules are known. However, to understand why these and other rules perform so well and how the information is transmitted throughout the cellular automata, the Boolean expressions that orchestrate this behavior must be known. The results presented in this work are a contribution in that direction.
KeywordsGenetic Program Variation Distance Edit Distance Mutation Distance Program Behavior
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- 1.W. Banzhaf, P. Nordin, R. Keller and F. Francone, Genetic Programming-An Introduction. On the Automatic Evolution of Computer Programs and its Application.dpunkt/Morgan Kaufmann, Heidelberg/San Francisco, 1998.Google Scholar
- 2.C.L. Blake and C.J. Merz, UCI Repository of Machine Learning Databases http://www.ics.uci.edu/~mlearn/MLRepository.html. University of California,Department of Information and Computer Science.
- 3.M. Brameier and W. Banzhaf, A Comparison of Linear Genetic Programming and Neural Networks in Medical Data Mining. IEEE Transactions on Evolutionary Computation, vol. 5(1), pp. 17–26, 2001.Google Scholar
- 4.M. Brameier and W. Banzhaf, Effective Linear Program Induction. Collaborative Research Center SFB 531, Computational Intelligence, Technical Report No. CI-108/01, University of Dortmund, 2001.Google Scholar
- 5.P. Dittrich, F. Liljeros, A. Soulier, and W. Banzhaf, Spontaneous Group Formation in the Seceder Model. Physical ReviewLetters, vol. 84, pp. 3205–3208, 2000.Google Scholar
- 6.D. Gusfield, Algorithms on Strings, Trees and Sequences. Cambridge University Press, 1997.Google Scholar
- 7.C. Igel and K. Chellapilla, Investigating the Influence of Depth and Degree of Genotypic Change on Fitness in Genetic Programming. In W. Banzhaf et al. eds., Proceedings of the Genetic and Evolutionary Computation Conference, pp. 1061–1068, MIT Press, Cambridge, 1999.Google Scholar
- 8.E.D. de Jong, R.A. Watson, and J.B. Pollack, Reducing Bloat and Promoting Diversity using Multi-Objective Methods. In L. Spector et al. eds., Proceedings of the Genetic and Evolutionary Computation Conference, pp. 11–18, MIT Press,Cambridge, 2001.Google Scholar
- 9.R. Keller and W. Banzhaf, Explicit Maintenance of Genetic Diversity on Genospaces, Internal Report, University of Dortmund, 1995.Google Scholar
- 11.P. Nordin, A Compiling Genetic Programming System that Directly Manipulates the Machine-Code. In K.E. Kinnear ed. Advances in Genetic Programming, 311–331, MIT Press, Cambridge, MA, 1994.Google Scholar
- 12.I. Rechenberg, Evolutionsstrategie’94. Frommann-Holzboog, 1994.Google Scholar
- 13.U.-M. O’Reilly, Using a Distance Metric on Genetic Programs to Understand Genetic Operators. In J.R. Kozaed., Late Breaking Papers at the Genetic Programming’ 97 Conference, Standford University, 1997.Google Scholar
- 14.J.P. Rosca and D.H. Ballard, Causality in Genetic Programming. In L.J. Eshelmann ed., Proceedings of the Sixth International Conference on Genetic Algorithms, pp. 256–263, Morgan Kaufmann, San Francisco, 1995Google Scholar
- 15.D. Sanko. and J.B. Kruskal eds., Time Warps, String Edits, and Macromolecules:The Theory and Practice of Sequence Comparison, Addison-Wesley,1983.Google Scholar
- 16.R. Tanese, Distributed Genetic Algorithmss. In J.D. Scha.er ed. Proceedings of the Third International Conference on Genetic Algorithms, 434-439, Morgan Kaufmann, San Mateo, CA, 1989.Google Scholar