Computational Complexity, Genetic Programming, and Implications
Recent theory work has shown that a Genetic Program (GP) used to produce programs may have output that is bounded above by the GP itself [l]. This paper presents proofs that show that 1) a program that is the output of a GP or any inductive process has complexity that can be bounded by the Kolmogorov complexity of the originating program; 2) this result does not hold if the random number generator used in the evolution is a true random source; a nd 3) an optimization problem being solved with a GP will have a complexity that can be bounded below by the growth rate of the minimum length problem representation used for the implementation. These results are then used to provide guidance for GP implementation.
KeywordsGenetic Program Turing Machine Convergence Time String Length Kolmogorov Complexity
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- 1.Rylander, B.: On GP Complexity, Proceedings of the Genetic and Evolutionary Computation Conference Workshop Program (2000), pp. 309–311Google Scholar
- 2.Soule, T., Foster, J., Dickinson, J.: Using Genetic Programming to Approximate Maximum Cliques, Proceedings Genetic Programming Conference (1998), pp. 400–405Google Scholar
- 3.Li, M., Vitanyi, P.: Kolmogorov Complexity and its Applications, Handbook of Theoretical Computer Science Volume A. Algorithms and Complexity, pp. 189–254. The MIT Press, Cambridge, Massachusetts (1990)Google Scholar
- 4.O’Reilly, U.: An Analysis of Genetic Programming, Doctoral Thesis, School of Computer Science, Carleton University, Ottawa, Ontario, Canada (1995), pp. 14Google Scholar
- 5.Rylander, B., Foster, J.: GA-Hard Problems, Proceedings of the Genetic and Evolutionary Computation Conference (2000), pp. 367Google Scholar
- 6.Rylander, B., Foster, J.: Computational Complexity and Genetic Algorithms, Proceedings of the World Science and Engineering Society’s Conference on Soft Computing (2001)Google Scholar
- 7.Rylander, B., Foster, J.: Genetic Algorithms, and Hardness, Proceedings of the World Science and Engineering Society’s Conference on Soft Computing (2001)Google Scholar
- 8.Langdon, W., Soule, T., Poli, R., Foster, J.: The Evolution of Size and Shape, Advances in Genetic Programming Volume III, pp. 163–190. The MIT Press, Cambridge, Massachusetts (1999)Google Scholar
- 9.Soule, T., Foster, J., Dickinson, J.: Code Growth in Genetic Programming, Proceedings Genetic Programming Conference (1996), pp. 215–223Google Scholar
- 10.Rylander, B., Soule, T., Foster, J.: Quantum Genetic Algorithms, proceedings of the Genetic and Evolutionary Computation Conference (2000), pp. 373Google Scholar
- 11.Ge, Y., Watson, L., Collins, E.: Genetic Algorithms for Optimization on a Quantum Computer, Unconventional Models of Computation, Springer-Verlag, London (1998)Google Scholar
- 12.Narayan, A., Moore, M.: Quantum Inspired Genetic Algorithms, Technical Report 344, Department of Computer Science, University of Exeter, England (1998)Google Scholar