EMORBFN: An Evolutionary Multiobjetive Optimization Algorithm for RBFN Design

  • Pedro L. López
  • Antonio J. Rivera
  • M. Dolores Pérez-Godoy
  • María J. del Jesus
  • Cristóbal Carmona
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5517)

Abstract

In this paper a multiobjective optimization algorithm for the design of Radial Basis Function Networks is proposed. The goal of the design algorithm is to obtain networks with a high tradeoff between accuracy and complexity, overcoming the drawbacks of the traditional single objective evolutionary algorithms. The main features of EMORBFN are a selection mechanism based on NSGA-II and specialized operators. To test the behavior of EMORBFN a similar mono-objective optimization algorithm for Radial Basis Function Network design has been developed. Also C4.5, a Multilayer Perceptron network or an incremental method to design of Radial Basis Function Networks have been included in the comparison. Experimental results on six UCI datasets show that EMORBFN obtains networks with high accuracy and low complexity, outperforming other more mature methods.

Keywords

Evolutionary Multi-objective Optimization Radial Basis Function Networks Classification 

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References

  1. 1.
    Alcalá-Fdez, J., Sánchez, L., García, S., Del Jesus, M.J., Ventura, S., Garrell, J.M., Otero, J., Romero, C., Bacardit, J., Rivas, V.M., Fernández, J.C., Herrera, F.: KEEL: A Software Tool to Assess Evolutionary Algorithms to Data Mining Problems. Soft Comput. (2008), doi:10.1007/s00500-008-0323-yGoogle Scholar
  2. 2.
    Asuncion, A., Newman, D.J.: UCI Machine Learning Repository. University of California, Irvine (2007), http://www.ics.uci.edu/~mlearn/MLRepository.html Google Scholar
  3. 3.
    Bäck, T., Hammel, U., Schwefel, H.: Evolutionary computation: comments on the history and current state. IEEE T. Evolut. Comput. 1, 3–17 (1997)CrossRefGoogle Scholar
  4. 4.
    Broomhead, D., Lowe, D.: Multivariable functional interpolation and adaptive networks. Complex System 2, 321–355 (1988)MathSciNetMATHGoogle Scholar
  5. 5.
    Buchtala, O., Klimek, M., Sick, B.: Evolutionary optimization of radial basis function classifiers for data mining applications. IEEE T. Syst. Man Cy. B 35(5), 928–947 (2005)CrossRefGoogle Scholar
  6. 6.
    Deb, K.: Multi-objective optimization using evolutionary algorithms, 1st edn. Wiley, Chichester (2001)MATHGoogle Scholar
  7. 7.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. on Evolutionary Computation 6(2), 182–197 (2002)CrossRefGoogle Scholar
  8. 8.
    González, J., Rojas, I., Ortega, J., Pomares, H., Fernández, F.J., Díaz, A.F.: Multiobjective evolutionary optimization of the size, shape, and position parameters of radial basis function networks for function approximation. IEEE T. Neural Networ. 14(6), 1478–1495 (2003)CrossRefGoogle Scholar
  9. 9.
    Guillén, A., Pomares, H., Rojas, I., González, J., Herrera, L.J., Rojas, F., Valenzuela, O.: Output value-based initialization for radial basis function neural networks. Neural Process Lett. (2007), doi:10.1007/s11063-007-9039-8Google Scholar
  10. 10.
    Harpham, C., Dawson, C., Brown, M.: A review of genetic algorithms applied to training radial basis function networks. Neural Comput. Appl. 13, 193–201 (2004)CrossRefGoogle Scholar
  11. 11.
    Isaacs, A., Ray, T., Smith, W.: An evolutionary algorithm with spatially distributed surrogates for multiobjective optimization. In: Randall, M., Abbass, H.A., Wiles, J. (eds.) ACAL 2007. LNCS (LNAI), vol. 4828, pp. 257–268. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  12. 12.
    Kondo, N., Hatanaka, T., Uosaki, K.: Pattern classification via multi-objective evolutionary RBF networks ensemble 2006. SICE-ICASE  art. no. 4108811, 137–142 (2006)Google Scholar
  13. 13.
    Park, J., Sandberg, I.: Universal approximation using radial-basis function networks. Neural Comput. 3, 246–257 (1991)CrossRefGoogle Scholar
  14. 14.
    Pedrycz, W.: Conditional fuzzy clustering in the design of radial basis function neural networks. IEEE T. Neural Networ. 9(4), 601–612 (1998)CrossRefGoogle Scholar
  15. 15.
    Quinlan, J.R.: C4.5: Programs for Machine Learning. Morgan Kauffman, San Francisco (1993)Google Scholar
  16. 16.
    Rivera, A.J., Rojas, I., Ortega, J., del Jesus, M.J.: A new hybrid methodology for cooperative-coevolutionary optimization of radial basis function networks. Soft Comput. (2007), doi:10.1007/s00500-006-0128-9Google Scholar
  17. 17.
    Santana-Quintero, L.V., Coello, C.A., Hernández-Díaz, A.G.: Hybridizing surrogate techniques, rough sets and evolutionary algorithms to efficiently solve multi-objective optimization problems. In: GECCO 2008, pp. 763–764 (2007)Google Scholar
  18. 18.
    Rojas, R., Feldman, J.: Neural Networks: A Systematic Introduction. Springer, Heidelberg (1996)CrossRefMATHGoogle Scholar
  19. 19.
    Teixeira, C.A., Ruano, M.G., Ruano, A.E., Pereira, W.C.A.: A soft-computing methodology for non invasive time-spatial temperature estimation. IEEE T. Bio-Med. Eng. 55(2), 572–580 (2008)CrossRefGoogle Scholar
  20. 20.
    Whitehead, B., Choate, T.: Cooperative-competitive genetic evolution of radial basis function centers and widths for time series prediction. IEEE T. Neural Networ. 7(4), 869–880 (1996)CrossRefGoogle Scholar
  21. 21.
    Widrow, B., Lehr, M.: 30 Years of adaptive neural networks: perceptron, madaline and backpropagation. Proc. IEEE 78(9), 1415–1442 (1990)CrossRefGoogle Scholar
  22. 22.
    Wilson, D.R., Martinez, T.R.: Improved heterogeneous distance functions. J. Artif. Intell. Res. 6(1), 1–34 (1997)MathSciNetMATHGoogle Scholar
  23. 23.
    Yen, G.G.: Multi-Objective evolutionary algorithm for radial basis function neural network design. Studies in Computational Intelligence 16, 221–239 (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Pedro L. López
    • 1
  • Antonio J. Rivera
    • 1
  • M. Dolores Pérez-Godoy
    • 1
  • María J. del Jesus
    • 1
  • Cristóbal Carmona
    • 1
  1. 1.Department of Computer ScienceUniversity of Jaén. JaénSpain

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