Abstract
Frequently, when an evolutionary algorithm is applied to a population of symbolic expressions, the shapes of these symbolic expressions are very different at the first generations whereas they become more similar during the evolving process. In fact, when the evolutionary algorithm finishes most of the best symbolic expressions only differ in some of its coefficients. In this paper we present several coevolutionary strategies of a genetic program that evolves symbolic expressions represented by straight line programs and an evolution strategy that searches for good coefficients. The presented methods have been applied to solve instances of symbolic regression problem, corrupted by additive noise. A main contribution of the work is the introduction of a fitness function with a penalty term, besides the well known fitness function based on the empirical error over the sample set. The results show that in the presence of noise, the coevolutionary architecture with penalized fitness function outperforms the strategies where only the empirical error is considered in order to evaluate the symbolic expressions of the population.
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References
Maynard, J.: Evolution and the theory of games. Cambridge University Press, Cambridge (1982)
Axelrod, R.: The evolution of cooperation. Basic Books, New York (1984)
Hillis, D.: Co-evolving parasites improve simulated evolution as an optimization procedure. Artificial Life II, SFI Studies in the Sciences Complexity 10, 313–324 (1991)
Rosin, C., Belew, R.: New methods for competetive coevolution. Evolutionary Computation 5(1), 1–29 (1996)
Wiegand, R.P., Liles, W.C., De Jong, K.A.: An Empirical Analysis of Collaboration Methods in Cooperative Coevolutionary Algorithms. In: Proceedings of the 2001 Conference on Genetic and Evolutionary Computation (GECCO), pp. 1235–1242 (2001)
Casillas, J., Cordón, O., Herrera, F., Merelo, J.: Cooperative coevolution for learning fuzzy rule-based systems. In: Genetic and Evolutionary Computation Conference (GECCO 2006), pp. 361–368 (2006)
Vanneschi, L., Mauri, G., Valsecchi, A., Cagnoni, S.: Heterogeneous Cooperative Coevolution: Strategies of Integration between GP and GA. In: Proc. of the Fifth Conference on Artificial Evolution (AE 2001), pp. 311–322 (2001)
Topchy, A., Punch, W.F.: Faster genetic programming based on local gradient search of numeric leaf values. In: Proceedings of the 2001 Conference on Genetic and Evolutionary Computation (GECCO), pp. 155–162 (2001)
Keijzer, M.: Improving Symbolic Regression with Interval Arithmetic and Linear Scaling. In: Ryan, C., Soule, T., Keijzer, M., Tsang, E.P.K., Poli, R., Costa, E. (eds.) EuroGP 2003. LNCS, vol. 2610, pp. 71–83. Springer, Heidelberg (2003)
Ryan, C., Keijzer, M.: An Analysis of Diversity of Constants of Genetic Programming. In: Ryan, C., Soule, T., Keijzer, M., Tsang, E.P.K., Poli, R., Costa, E. (eds.) EuroGP 2003. LNCS, vol. 2610, pp. 409–418. Springer, Heidelberg (2003)
Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. The MIT Press, Cambridge (1992)
Burguisser, P., Clausen, M., Shokrollahi, M.A.: Algebraic Complexity Theory. Springer, Heidelberg (1997)
Berkowitz, S.J.: On computing the determinant in small parallel time using a small number of processors. Information Processing Letters 18, 147–150 (1984)
Heintz, J., Roy, M.F., Solerno, P.: Sur la complexite du principe de Tarski-Seidenberg. Bulletin de la Societe Mathematique de France 118, 101–126 (1990)
Giusti, M., Heintz, J., Morais, J., Morgenstern, J.E., Pardo, L.M.: Straight Line Programs in Geometric Elimination Theory. Journal of Pure and Applied Algebra 124, 121–146 (1997)
Alonso, C.L., Montana, J.L., Puente, J.: Straight line programs: a new Linear Genetic Programming Approach. In: Proc. 20th IEEE International Conference on Tools with Artificial Intelligence (ICTAI), pp. 517–524 (2008)
Vapnik, V.: Statistical Learning Theory. John Willey and Sons (1998)
Montaña, J.L., Alonso, C.L., Borges, C.E., Crespo, C.L.: Adaptation, Performance and Vapnik-Chervonenkis Dimension of Straight Line Programs. In: Proc. 12th European Conference on Genetic Programming, pp. 315–326 (2009)
Alonso, C.L., Montaña, J.L., Borges, C.E.: Model Complexity Control in Straight Line Program Genetic Programming. Technical Report (2011)
Cherkassky, V., Yunkian, M.: Comparison of Model Selection for Regression. Neural Computation 15(7), 1691–1714 (2003)
Schwefel, H.P.: Numerical Optimization of Computer Models. John Wiley and Sons, New-York (1981)
Michalewicz, Z., Logan, T., Swaminathan, S.: Evolutionary operators for continuous convex parameter spaces. In: Proceedings of the 3rd Annual Conference on Evolutionary Programming, pp. 84–97 (1994)
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Alonso, C.L., Montaña, J.L., Borges, C.E., de la Cruz Echeandía, M., de la Puente, A.O. (2012). Model Regularization in Coevolutionary Architectures Evolving Straight Line Code. In: Madani, K., Dourado Correia, A., Rosa, A., Filipe, J. (eds) Computational Intelligence. IJCCI 2010. Studies in Computational Intelligence, vol 399. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27534-0_4
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DOI: https://doi.org/10.1007/978-3-642-27534-0_4
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