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Designing a Phenotypic Distance Index for Radial Basis Function Neural Networks

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Computational Methods in Neural Modeling (IWANN 2003)

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Abstract

MultiObjective Evolutionary Algorithms (MOEAs) may cause a premature convergence if the selective pressure is too large, so, MOEAs usually incorporate a niche-formation procedure to distribute the population over the optimal solutions and let the population evolve until the Pareto-optimal region is completely explored. This niche-formation scheme is based on a distance index that measures the similarity between two solutions in order to decide if both may share the same niche or not. The similarity criterion is usually based on a Euclidean norm (given that the two solutions are represented with a vector), nevertheless, as this paper will explain, this kind of metric is not adequate for RBFNNs, thus being necessary a more suitable distance index. The experimental results obtained show that a MOEA including the proposed distance index is able to explore sufficiently the Pareto-optimal region and provide the user a wide variety of Pareto-optimal solutions.

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References

  1. H. Bersini, A. Duchateau, and N. Bradshaw. Using Incremental Learning Algorithms in the Search for Minimal and E_ective Fuzzy Models. In Proceedings of the 6th IEEE International Conference on Fuzzy Systems, pages 1417–1422, Barcelona, Spain, July 1997. IEEE Computer Society Press.

    Google Scholar 

  2. V. Chankong and Y. Y. Haimes. Multiobjective Decision Making Theory and Methodology. North-Holland, New York, 1983.

    MATH  Google Scholar 

  3. I. De Falco, A. Della Cioppa, A. Iazzetta, P. Natale, and E. Tarantino. Optimizing Neural Networks for Time Series Prediction. In R. Roy, T. Furuhashi, and P. K. Chawdhry, editors, Proceedings of the 3rd On-line World Conference on Soft Computing (WSC3). Advances in Soft Computing — Engineering Design and Manufacturing, Internet, June 1998. Springer Verlag.

    Google Scholar 

  4. K. Deb. Evolutionary Algorithms for Multi-Criterion Optimization in Engineering Design. In K. Miettinen, P. Neittaanmäki, M. M. Mäkelä, and J. Périaux, editors, Proceedings of Evolutionary Algorithms in Engineering and Computer Design, EU-ROGEN’99. JohnWiley, Apr. 1999.

    Google Scholar 

  5. K. Deb and D. E. Goldberg. An Investigation of Niche and Species Formation in Genetic Function Optimization. In J. D. Schaffer, editor, Proceedings of the Third International Conference on Genetic Algorithms, pages 42–50, San Mateo, CA, 1989. Morgan Kaufmann.

    Google Scholar 

  6. C. M. Fonseca and P. J. Fleming. Genetic Algorithms for Multiobjective Optimization: Formulation, Discussion and Generalization. In S. Forrest, editor, Proceedings of the Fifth International Conference on Genetic Algorithms, pages 416–423. Morgan Kaufmann, 1993.

    Google Scholar 

  7. D. E. Goldberg and K. Deb. A Comparison of Selection Schemes used in Genetic Algorithms. pages 69–93. Morgan Kaufmann, San Mateo, CA, 1991.

    Google Scholar 

  8. J. González, I. Rojas, H. Pomares, and J. Ortega. RBF Neural Networks, Multiobjective Optimization and Time Series Forecasting. In Mira and Prieto [14], pages 498–505.

    Google Scholar 

  9. J. González, I. Rojas, H. Pomares, and M. Salmerón. Expert Mutation Operators for the Evolution of Radial Basis Function Neural Networks. In Mira and Prieto [14], pages 538–545.

    Google Scholar 

  10. A. E. Hans. Multicriteria optimization for highly accurate systems. In W. Stadler, editor, Multicriteria Optimization in Engineering and Sciences, Mathematical Concepts and Methods in Science and Engineering, volume 19, pages 309–352, New York, 1988. Plenum Press.

    Google Scholar 

  11. C. L. Hwang and A. S. M. Masud. Multiple Objective Decision Making — Methods and Applications, volume 164 of Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, Berlin, 1979.

    MATH  Google Scholar 

  12. J. S. R. Jang. ANFIS: Adaptive Network-based Fuzzy Inference System. IEEE Trans. Syst., Man, Cybern., 23:665–685, May 1993.

    Google Scholar 

  13. M. C. Mackey and L. Glass. Oscillation and Chaos in Physiological Control Systems. Science, 197(4300):287–289, 1977.

    Article  Google Scholar 

  14. J. Mira and A. Prieto, editors. Connectionist Models of Neurons, Learning Processes and Artificial Intelligence, volume 2084 of Lecture Notes in Computer Science. Springer-Verlag, 2001.

    MATH  Google Scholar 

  15. J. E. Moody and C. J. Darken. Fast Learning in Networks of Locally-Tuned Processing Units. Neural Computation, 1:281–294, 1989.

    Article  Google Scholar 

  16. V. Pareto. Cours D’Economie Politique, volume I and II. F. Rouge, Lausanne, 1896.

    Google Scholar 

  17. J. Platt. A Resource Allocation Network for Function Interpolation. Neural Computation, 3:213–225, 1991.

    Article  MathSciNet  Google Scholar 

  18. I. Rojas, J. González, A. Cañas, A. F. Díaz, F. J. Rojas, and M. Rodriguez. Short-Term Prediction of Chaotic Time Series by Using RBF Network with Regression Weights. Int. Journal of Neural Systems, 10(5):353–364, 2000.

    Google Scholar 

  19. I. Rojas, H. Pomares, J. González, J. L. Bernier, E. Ros, F. J. Pelayo, and A. Prieto. Analysis of the Functional Block Involved in the Design of Radial Basis Function Networks. Neural Processing Letters, 12(1):1–17, Aug. 2000.

    Google Scholar 

  20. R. Rosipal, M. Koska, and I. Farkš. Prediction of Chaotic Time-Series with a Resource-Allocating RBF Network. Neural Processing Letters, 7:185–197, 1998.

    Article  Google Scholar 

  21. N. Srinivas and K. Dev. Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms. Evolutionary Computation, 2(3):221–248, 1995.

    Article  Google Scholar 

  22. B. A. Whitehead and T. D. Choate. Cooperative-Competitive Genetic Evolution of Radial Basis Function Centers and Widths for Time Series Prediction. IEEE Trans. Neural Networks, 7(4):869–880, July 1996.

    Google Scholar 

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González, J., Rojas, I., Pomares, H., Ortega, J. (2003). Designing a Phenotypic Distance Index for Radial Basis Function Neural Networks. In: Mira, J., Álvarez, J.R. (eds) Computational Methods in Neural Modeling. IWANN 2003. Lecture Notes in Computer Science, vol 2686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44868-3_58

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  • DOI: https://doi.org/10.1007/3-540-44868-3_58

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  • Print ISBN: 978-3-540-40210-7

  • Online ISBN: 978-3-540-44868-6

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