Abstract
This work presents a metaheuristic based on the use of the beta distribution as a search distribution for solving numerical optimization problems in search spaces defined on two sided intervals. The innovation of this work lies on the efficiency of the proposed method to estimate the parameters of the beta distribution with a minimal cost for each decision variable by using the method of moments. The numerical experiments provided evidence that applying the method of moments for parameter estimation and the beta distribution as a search distribution generates competitive results.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Bosman, P.: Design and application of iterated density-estimation evolutionary algorithms. Ph.D. thesis, University of Utrecht, Utrecht, The Netherlands (2003)
De Bonet, J., Isbell, C., Viola, P.: MIMIC: finding optima by estimating probability densities. In: Advances in Neural Information Processing Systems, vol. 9, pp. 424–430. The MIT Press, Cambridge (1997)
Gonzalez-Fernandez, Y., Soto, M.: Copulaedas: an R package for estimation of distribution algorithms based on copulas. J. Stat. Softw. 58(9), 1–34 (2014)
Larrañaga, P., Etxeberria, R., Lozano, J., Peña, J.: Combinatorial optimization by learning and simulation of Bayesian networks. In: Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence, pp. 343–352 (2000)
Larrañaga, P., Etxeberria, R., Lozano, J., Peña, J.: Optimization in continuous domains by learning and simulation of Gaussian networks. In: Proceedings of the Optimization by Building and Using Probabilistic Models OBUPM Workshop at the Genetic and Evolutionary Computation Conference GECCO-2000, pp. 201–204 (2000)
Larrañaga, P., Lozano, J., Bengoetxea, E.: Estimation of distribution algorithm based on multivariate normal and gaussian networks. Technical report EHU-KZAA-IK-1/01, Department of Computer Science and Artificial Intelligence, University of the Basque Country (2001)
Larrañaga, P., Lozano, J. (eds.): Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Genetic Algorithms and Evolutionary Computation. Kluwer Academic Publishers, Norwell (2002)
Mühlenbein, H.: The equation for response to selection and its use for prediction. Evol. Comput. 5(3), 303–346 (1998)
Mühlenbein, H., Paaß, G.: From recombination of genes to the estimation of distributions I. Binary parameters. In: Voigt, H.-M., Ebeling, W., Rechenberg, I., Schwefel, H.-P. (eds.) PPSN 1996. LNCS, vol. 1141, pp. 178–187. Springer, Heidelberg (1996). doi:10.1007/3-540-61723-X_982
Olive, D.: Statistical Theory and Inference. Springer, Heidelberg (2014)
Pelikan, M., Goldberg, D., Cantú-Paz, E.: BOA: the Bayesian optimization algorithm. In: Banzhaf, W., Daida, J., Eiben, A., Garzon, M., Honavar, V., Jakiela, M., Smith, R. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference GECCO-99, vol. 1, pp. 525–532. Morgan Kaufmann Publishers, Orlando (1999)
Pelikan, M., Mühlenbein, H.: The Bivariate Marginal Distribution Algorithm. In: Roy, R., Furuhashi, T., Chawdhry, P. (eds.) Advances in Soft Computing - Engineering Design and Manufacturing, pp. 521–535. Springer, London (1999). doi:10.1007/978-1-4471-0819-1_39
Salinas-Gutiérrez, R., Hernández-Aguirre, A., Villa-Diharce, E.R.: Using copulas in estimation of distribution algorithms. In: Aguirre, A.H., Borja, R.M., Garciá, C.A.R. (eds.) MICAI 2009. LNCS, vol. 5845, pp. 658–668. Springer, Heidelberg (2009). doi:10.1007/978-3-642-05258-3_58
Salinas-Gutiérrez, R., Hernández-Aguirre, A., Villa-Diharce, E.: D-vine EDA: a new estimation of distribution algorithm based on regular vines. In: GECCO 2010: Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation, pp. 359–366. ACM, New York (2010)
Simon, D.: Evolutionary Optimization Algorithms: Biologically Inspired and Population-Based Approaches to Computer Intelligence. Wiley, Hoboken (2013)
Soto, M., Ochoa, A., Acid, S., de Campos, L.: Introducing the polytree approximation of distribution algorithm. In: Ochoa, A., Soto, M., Santana, R. (eds.) Second International Symposium on Artificial Intelligence, Adaptive Systems, CIMAF 1999, pp. 360–367. Academia, La Habana (1999)
Wasserman, L.: All of Statistics. Springer Texts in Statistics. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Salinas-Gutiérrez, R., Muñoz-Zavala, Á.E., Guerrero-Díaz de León, J.A., Hernández-Aguirre, A. (2017). Estimation of Distribution Algorithms Based on the Beta Distribution for Bounded Search Spaces. 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_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-62428-0_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-62427-3
Online ISBN: 978-3-319-62428-0
eBook Packages: Computer ScienceComputer Science (R0)