Abstract
Nonlinear regression is a statistical technique widely used in research which creates models that conceptualize the relation among many variables that are related in complex forms. These models are widely used in different areas such as economics, biology, finance, engineering, etc. These models are subsequently used for different processes, such as prediction, control or optimization. Many standard regression methods have been proved that produce misleading results in certain data sets; this is especially true in ordinary least squares. In this article three metaheuristic models for parameter estimation of nonlinear regression models are described: Artificial Bee Colony, Particle Swarm Optimization and a novel hybrid algorithm ABC-PSO. These techniques were tested on 27 databases of the NIST collection with different degrees of difficulty. The experimental results provide evidence that the proposed algorithm finds consistently good results.
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References
Cheng, S., Zhao, C., Wu, J., Shi, Y.: Particle swarm optimization in regression analysis: a case study. In: Tan, Y., Shi, Y., Mo, H. (eds.) ICSI 2013. LNCS, vol. 7928, pp. 55–63. Springer, Heidelberg (2013). doi:10.1007/978-3-642-38703-6_6
de-los-Cobos-Silva, S.G., Gutiérrez-Andrade, M.A., Rincón-García, E.A., Lara-Velázquez, P., Aguilar-Cornejo, M.: Estimación de parámetros de regresión no lineal mediante colonia de abejas artificiales. Revista de Matemática: Teoría y Aplicaciones 20(1), 49–60 (2013)
de-los-Cobos-Silva, S.G., Gutiérrez-Andrade, M.A., Rincón-García, E.A., Lara-Velázquez, P., Aguilar-Cornejo, M.: Colonia de Abejas Artificiales y Optimización por Enjambre de Partículas para la Estimación de Parámetros de Regresión No Lineal. Revista de Matemática: Teoría y Aplicaciones 21(1), 107–126 (2014)
de-los-Cobos-Silva, S.G., Terceño-Gómez, A., Gutiérrez-Andrade, M.A., Rincón-García, E.A., Lara-Velázquez, P., Aguilar-Cornejo, M.: Particle swarm optimization an alternative for parameter estimation in regression. Fuzzy Econ. Rev. 21(1), 107–126 (2014)
Kapanoglu, M., Koc, I.O., Erdogmus, S.: Genetic algorithm in parameter estimation for nonlinear regression models: an experimental approach. J. Stat. Comput. Simul. 77(10), 851–867 (2007)
Karaboga, D.: An idea based on honey bee swarm for numerical optimization. Technical report, Erciyes University, Engineering Faculty, Computer Engineering Department (2005)
Karaboga, D., Akay, B.: Artificial bee colony (ABC) algorithm on training artificial neural networks. In: Proceedings of 15th IEEE Signal Processing and Communications Applications (2007)
Karaboga, D., Akay, B.: A comparative study of artificial bee colony algorithm. Appl. Math. Comput. 214, 108–132 (2009)
Karaboga, D., Osturk, C.: Fuzzy clustering with artificial bee colony algorithm. Sci. Res. Essays 5(14), 1899–1902 (2010)
Kennedy, J., Eberhart, R.C., Shi, Y.: Swarm Intelligence. Morgan Kaufmann, San Francisco (2001)
Kennedy, J., Eberhart, R.C.: Intelligent Swarm Systems. Academic Press, New York (2000)
Kriv, I., Tvrdík, J., Krepec, R.: Stochastic algorithms in nonlinear regression. Comput. Stat. Data Anal. 33, 277–290 (2000)
McCullough, B.D., Wilson, B.: On the accuracy of statistical procedures in Microsoft Excel 2003. Comput. Stat. Data Anal. 49, 1244–1252 (2005)
National Institute of Standards and Technology. http://www.itl.nist.gov/div898/strd/index.html
Osturk, C., Karaboga, D.: Classifications by neural networks and clustering with artificial bee colony (ABC) algorithm. In: Proceedings of 6th International Symposium on Intelligent and Manufacturing Systems, Features, Strategies and Innovation (2008)
Schwaab, M., Biscaia, E.C., Monteiro, J.L., Pinto, J.C.: Nonlinear parameter estimation through particle swarm optimization. Chem. Eng. Sci. 63, 1542–1552 (2008)
Tvrdík, J., Kriv, I.: Comparison of algorithms for nonlinear regression estimates. In: Antoch, J. (ed.) COMSTAT, pp. 1917–1924. Physica-Verlag, New York (2004)
Tvrdík, J.: Adaptation in differential evolution: a numerical comparison. Appl. Soft Comput. 9(3), 1149–1155 (2009)
Zilinskas, A., Zilinskas, J.: Interval arithmetic based optimization in nonlinear regression. Informatica 21(1), 149–158 (2010)
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de-los-Cobos-Silva, S.G., Gutiérrez Andrade, M.Á., Lara-Velázquez, P., Rincón García, E.A., Mora-Gutiérrez, R.A., Ponsich, A. (2017). ABC-PSO: An Efficient Bioinspired Metaheuristic for Parameter Estimation in Nonlinear Regression. In: Pichardo-Lagunas, O., Miranda-Jiménez, S. (eds) Advances in Soft Computing. MICAI 2016. Lecture Notes in Computer Science(), vol 10062. Springer, Cham. https://doi.org/10.1007/978-3-319-62428-0_31
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DOI: https://doi.org/10.1007/978-3-319-62428-0_31
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