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Symbolic Regression by Means of Grammatical Evolution with Estimation Distribution Algorithms as Search Engine

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Fuzzy Logic Augmentation of Neural and Optimization Algorithms: Theoretical Aspects and Real Applications

Part of the book series: Studies in Computational Intelligence ((SCI,volume 749))

Abstract

Grammatical Evolution (GE) is a Grammar-based form of Genetic Programming (GP) and it has been used to evolve programs or rules. The GE uses a population of linear genotypic strings and it is transformed by mapping process, those string are evolved using a search engine like the Genetic Algorithm (GA), Differential Evolution (DE), Particle Swarm Optimization (PSO), among others. One of the big trouble of these algorithms is the parameter tuning. In this paper is proposed an Estimation Distribution Algorithm (EDA) as search engine using the Symbolic Regression as a benchmark, due to the few parameters used by the EDA. The results were compared against the obtained by DE as search engine using the Friedman nonparametric test.

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References

  1. D.A. Augusto, H.J.C. Barbosa, Symbolic regression via genetic programming, in Proceedings of the VI Brazilian Symposium on Neural Networks (SBRN ’00) (IEEE Computer Society, Washington, DC, USA, 2000), p. 173. http://dl.acm.org/citation.cfm?id=827249.827526

  2. S. Baluja, Population-based incremental learning: a method for integrating genetic search based function optimization and competitive learning. Tech. rep., Pittsburgh, PA, USA (1994)

    Google Scholar 

  3. P. Barmpalexis, K. Kachrimanis, A. Tsakonas, E. Georgarakis, Symbolic regression via genetic programming in the optimization of a controlled release pharmaceutical formulation. Chemom. Intell. Lab. Syst. 107(1), 75–82 (2011). http://www.sciencedirect.com/science/article/pii/S0169743911000153

  4. J.S. De Bonet, C.L. Isbell, P. Viola, Mimic: finding optima by estimating probability densities, in Advances in Neural Information Processing Systems, vol. 9 (1997)

    Google Scholar 

  5. I. Dempsey, M. O’Neill, A. Brabazon, Foundations in grammatical, in Foundations in Grammatical Evolution for Dynamic Environments, vol. 194 (Springer, New York, 2009)

    Google Scholar 

  6. A. Eiben, S. Smit, Parameter tuning for configuring and analyzing evolutionary algorithms. Swarm Evol. Comput. 1(1), 19–31 (2011)

    Article  Google Scholar 

  7. A. Espinal, M. Carpio, M. Ornelas, H. Puga, P. Melín, M. Sotelo-Figueroa, Evolutionary Indirect Design of Feed-Forward Spiking Neural Networks, vol. 101 (Springer International Publishing, 2015), p. 89. http://dx.doi.org/10.1007/978-3-319-17747-2\s\do5(7)

  8. M. Hauschild, M. Pelikan, An introduction and survey of estimation of distribution algorithms. Swarm Evol. Comput. 1(3), 111–128 (2011). http://www.sciencedirect.com/science/article/pii/S2210650211000435

  9. D. Karaboga, C. Ozturk, N. Karaboga, B. Gorkemli, Artificial bee colony programming for symbolic regression. Inf. Sci. 209, 1–15 (2012). http://www.sciencedirect.com/science/article/pii/S0020025512003295

  10. T.M. Khoshgoftaar, N. Seliya, Y. Liu, Genetic programming-based decision trees for software quality classification, in Proceedings of the 15th IEEE International Conference on Tools with Artificial Intelligence, pp. 374–383 (Nov 2003)

    Google Scholar 

  11. J.R. Koza, R. Poli, Genetic programming, in Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques, ed. by E.K. Burke, G. Kendall (Kluwer, Boston, 2005), pp. 127–164

    Chapter  Google Scholar 

  12. P. Larrañaga, J.A. Lozano, Estimation of Distribution Algorithms, vol. 2 (Springer, US, 2002)

    MATH  Google Scholar 

  13. A. Moraglio, S. Silva, Geometric differential evolution on the space of genetic programs, in Genetic Programming, vol. 6021, Lecture notes in computer science, ed. by A. Esparcia-Alcázar, A. Ekárt, S. Silva, S. Dignum, A. Uyar (Springer, Berlin, 2010), pp. 171–183

    Chapter  Google Scholar 

  14. H. Mühlenbein, The equation for response to selection and its use for prediction. Evol. Comput. 5(3), 303–346 (1997). https://doi.org/10.1162/evco.1997.5.3.303

    Article  Google Scholar 

  15. M., O’Neill., A, Brabazon, Grammatical differential evolution, in International Conference on Artificial Intelligence (ICAI ’06) (CSEA Press, Las Vegas, Nevada, 2006)

    Google Scholar 

  16. M. Pelikan, H. Muehlenbein, The Bivariate Marginal Distribution Algorithm (Springer, London, 1999), pp. 521–535. http://dx.doi.org/10.1007/978-1-4471-0819-1\s\do5(3)9

  17. R. Riolo, T. Soule, B. Worzel (eds.), Genetic Programming Theory and Practice IV, No. 1 (Springer, US, 2007)

    Google Scholar 

  18. C. Ryan, J.J. Collins, M. O’Neill: Grammatical evolution: evolving programs for an arbitrary language, in Proceedings of the First European Workshop on Genetic Programming. Lecture notes in computer science, vol. 1391 (Springer, Berlin, 1998), pp. 83–95

    Google Scholar 

  19. M. Sotelo-Figueroa, H. Puga Soberanes, J. Martin Carpio, H. Fraire Huacuja, L. Cruz Reyes, J. Soria-Alcaraz, Evolving and reusing bin packing heuristic through grammatical differential evolution, in 2013 World Congress on Nature and Biologically Inspired Computing (NaBIC), pp. 92–98 (2013)

    Google Scholar 

  20. Sotelo-Figueroa, M.A., Puga Soberanes, H.J., Carpio, J.M., Fraire Huacuja, H.J., Cruz Reyes, L., Soria-Alcaraz, J.A.: Improving the bin packing heuristic through grammatical evolution based on swarm intelligence. Mathematical Problems in Engineering 2014 (2014)

    Google Scholar 

  21. J. Togelius, R.D. Nardi, A. Moraglio, Geometric pso + gp = particle swarm programming, in IEEE Congress on Evolutionary Computation, pp. 3594–3600 (2008)

    Google Scholar 

  22. P. Widera, J.M. Garibaldi, N. Krasnogor, Gp challenge: evolving energy function for protein structure prediction. Genet. Program Evolvable Mach. 11(1), 61–88 (2010). https://doi.org/10.1007/s10710-009-9087-0

    Article  Google Scholar 

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Acknowledgements

The authors want to thank to Universidad de Guanajuato (UG) for the support to this research.

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Authors and Affiliations

  1. División de Ciencias Económico Administrativas, Departamento de Estudios Organizacionales, Universidad de Guanajuato, Fraccionamiento I El Establo, 36250, Guanajuato, GTO, Mexico

    M. A. Sotelo-Figueroa, Andrés Espinal & J. A. Soria-Alcaraz

  2. Departamento de Ciencias de La Computación, Centro de Investigación En Matemáticas, Jalisco S/N, 36240, Guanajuato, GTO, Mexico

    Arturo Hernández-Aguirre

  3. Escuela Internacional de Doctorado, Universidad de Vigo, Róa do Conde de Torrecedeira 105, 36208, Vigo, Pontevedra, Spain

    Janet Ortiz-López

Authors
  1. M. A. Sotelo-Figueroa
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  2. Arturo Hernández-Aguirre
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  3. Andrés Espinal
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  4. J. A. Soria-Alcaraz
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  5. Janet Ortiz-López
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Corresponding author

Correspondence to M. A. Sotelo-Figueroa .

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Editors and Affiliations

  1. Division of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Oscar Castillo

  2. Division of Graduate Studies and Research , Tijuana Institute of Technology , Tijuana, Baja California, Mexico

    Patricia Melin

  3. Systems Research Institute, Polish Academy of Sciences , Warszawa, Poland

    Janusz Kacprzyk

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Sotelo-Figueroa, M.A., Hernández-Aguirre, A., Espinal, A., Soria-Alcaraz, J.A., Ortiz-López, J. (2018). Symbolic Regression by Means of Grammatical Evolution with Estimation Distribution Algorithms as Search Engine. In: Castillo, O., Melin, P., Kacprzyk, J. (eds) Fuzzy Logic Augmentation of Neural and Optimization Algorithms: Theoretical Aspects and Real Applications. Studies in Computational Intelligence, vol 749. Springer, Cham. https://doi.org/10.1007/978-3-319-71008-2_14

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  • DOI: https://doi.org/10.1007/978-3-319-71008-2_14

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-71008-2

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