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Multiobjective RBFNNs Designer for Function Approximation: An Application for Mineral Reduction

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Advances in Natural Computation (ICNC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4221))

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Abstract

Radial Basis Function Neural Networks (RBFNNs) are well known because, among other applications, they present a good performance when approximating functions. The function approximation problem arises in the construction of a control system to optimize the process of the mineral reduction. In order to regulate the temperature of the ovens and other parameters, it is necessary a module to predict the final concentration of mineral that will be obtained from the source materials. This module can be formed by an RBFNN that predicts the output and by the algorithm that designs the RBFNN dynamically as more data is obtained. The design of RBFNNs is a very complex task where many parameters have to be determined, therefore, a genetic algorithm that determines all of them has been developed. This algorithm provides satisfactory results since the networks it generates are able to predict quite precisely the final concentration of mineral.

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References

  1. Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New York (1981)

    MATH  Google Scholar 

  2. Bors, A.G.: Introduction of the Radial Basis Function (RBF) networks. In: OnLine Symposium for Electronics Engineers, February 2001, vol. 1, pp. 1–7 (2001)

    Google Scholar 

  3. Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evolutionary Computation 6(2), 182–197 (2002)

    Article  Google Scholar 

  4. González, J., Rojas, I., Ortega, J., Pomares, H., Fernández, F.J., Díaz, A.: Multiobjective evolutionary optimization of the size, shape, and position parameters of radial basis function networks for function approximation. IEEE Transactions on Neural Networks 14(6), 1478–1495 (2003)

    Article  Google Scholar 

  5. Guillén, A., Rojas, I., González, J., Pomares, H., Herrera, L.J., Valenzuela, O., Prieto, A.: Improving Clustering Technique for Functional Approximation Problem Using Fuzzy Logic: ICFA algorithm. In: Cabestany, J., Prieto, A.G., Sandoval, F. (eds.) IWANN 2005. LNCS, vol. 3512, pp. 272–280. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  6. Guillén, A., Rojas, I., González, J., Pomares, H., Herrera, L.J., Valenzuela, O., Prieto, A.: A possibilistic approach to rbfn centers initialization. In: Ślęzak, D., Yao, J., Peters, J.F., Ziarko, W., Hu, X. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3642, pp. 174–183. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  7. Herrera, F., Lozano, M., Verdegay, J.L.: Tackling real-coded genetic algorithms: operators and tools for the behavioural analysis. Artificial Intelligence Reviews 12(4), 265–319 (1998)

    Article  MATH  Google Scholar 

  8. Marquardt, D.W.: An Algorithm for Least-Squares Estimation of Nonlinear Inequalities. SIAM J. Appl. Math. 11, 431–441 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  9. Pal, N.R., Pal, K., Bezdek, J.C.: A Mixed C–Means Clustering Model. In: Proceedings of the 6th IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 1997), Barcelona, July 1997, vol. 1, pp. 11–21 (1997)

    Google Scholar 

  10. Park, J., Sandberg, J.W.: Universal approximation using radial basis functions network. Neural Computation 3, 246–257 (1991)

    Article  Google Scholar 

  11. Poggio, T., Girosi, F.: Networks for approximation and learning. Proceedings of the IEEE 78, 1481–1497 (1990)

    Article  Google Scholar 

  12. Rivera Rivas, A.J., Ortega Lopera, J., Rojas Ruiz, I., del Jesus Daz, M.J.: Co-evolutionary Algorithm for RBF by Self-Organizing Population of Neurons. In: Mira, J., Álvarez, J.R. (eds.) IWANN 2003. LNCS, vol. 2686, pp. 470–477. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  13. Rojas, I., Anguita, M., Prieto, A., Valenzuela, O.: Analysis of the operators involved in the definition of the implication functions and in the fuzzy inference proccess. International Journal of Approximate Reasoning 19, 367–389 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  14. Zhang, J., Leung, Y.: Improved possibilistic C–means clustering algorithms. IEEE Transactions on Fuzzy Systems 12, 209–217 (2004)

    Article  MathSciNet  Google Scholar 

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Guillén, A., Rojas, I., González, J., Pomares, H., Herrera, L.J., Fernández, F. (2006). Multiobjective RBFNNs Designer for Function Approximation: An Application for Mineral Reduction. In: Jiao, L., Wang, L., Gao, Xb., Liu, J., Wu, F. (eds) Advances in Natural Computation. ICNC 2006. Lecture Notes in Computer Science, vol 4221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11881070_71

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  • DOI: https://doi.org/10.1007/11881070_71

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45901-9

  • Online ISBN: 978-3-540-45902-6

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