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Optimization of Zero-Order TSK-Type Fuzzy System Using Enhanced Particle Swarm Optimizer with Dynamic Mutation and Special Initialization

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Abstract

This paper proposes an enhanced particle swarm optimization with dynamic mutation and special initialization, the EPSODM-I, for improving the accuracy of zero-order TSK-type fuzzy systems design. The EPSODM-I can be regarded as a new population-based evolutionary optimization algorithm. Unlike the generic initialization used in most popular population-based algorithms, the EPSODM-I applies a proposed special initialization method to generate the initial PSO particles for fuzzy system design. The generated initial PSO particles are iteratively improved by a new approach incorporating the dynamic mutation into the existing PSO to provide more diverse search directions. Application examples of the zero-order fuzzy system designs for the tracking control of nonlinear dynamic systems have been simulated to validate the proposed algorithm. In terms of tracking errors, performance comparisons with the typical PSO and different advanced PSO variants verify the superiority of the proposed algorithm. The effects on the convergence rate and optimization accuracy yielded by the proposed special initialization and dynamic mutation have also been discussed and verified crossly in the simulation results.

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References

  1. Goldberg, D.E.: Genetic Algorithms in Search Optimization and Machine Learning. Addison-Wesley, Reading, MA (1989)

    MATH  Google Scholar 

  2. Kennedy, J., Eberhart, R., Shi, Y.: Swarm Intelligence. Morgan Kaufmann, San Mateo, CA (2001)

    Google Scholar 

  3. Homaifar, A., McCormick, E.: Simultaneous design of membership functions and rule sets for fuzzy controllers using genetic algorithms. IEEE Trans. Fuzzy Syst. 3(2), 129–139 (1995)

    Article  Google Scholar 

  4. Shi, Y., Eberhart, R., Chen, Y.: Implementation of evolutionary fuzzy systems. IEEE Trans. Fuzzy Syst. 7(2), 109–119 (1999)

    Article  Google Scholar 

  5. Belarbi, K., Titel, F.: Genetic algorithm for the design of a class of fuzzy controllers: an alternative approach. IEEE Trans. Fuzzy Syst. 8(4), 398–405 (2000)

    Article  Google Scholar 

  6. Juang, C.F.: A TSK-type recurrent fuzzy network for dynamic systems processing by neural network and genetic algorithms. IEEE Trans. Fuzzy Syst. 10(2), 155–170 (2002)

    Article  Google Scholar 

  7. Cordón, O., Gomide, F., Herrera, F., Hoffmann, F., Magdalena, L.: Ten years of genetic fuzzy systems: current framework and new trends. Fuzzy Sets Syst. 141(1), 5–31 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Lin, C.J.: A GA-based neural fuzzy system for temperature control. Fuzzy Sets Syst. 143(2), 311–333 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Chou, C.H.: Genetic algorithm-based optimal fuzzy controller design in the linguistic space. IEEE Trans. Fuzzy Syst. 14(3), 372–385 (2006)

    Article  Google Scholar 

  10. Mucients, M., Moreno, D.L., Bugarin, A., Barro, S.: Design of a fuzzy controller in mobile robotics using genetic algorithms. Appl. Soft Comput. 7(2), 540–546 (2007)

    Article  Google Scholar 

  11. Dorigo, M., Maniezzo, V., Colorni, A.: Ant system: optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern. B 26(1), 29–41 (1996)

    Article  Google Scholar 

  12. Dorigo, M., Gambardella, L.M.: Ant colony system: a cooperating learning approach to the traveling salesman problem. IEEE Trans. Evol. Comput. 1(1), 53–66 (1997)

    Article  Google Scholar 

  13. Socha, K., Dorigo, M.: Ant colony optimization for continuous domains. Eur. J. Oper. Res. 185(3), 1155–1173 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Juang, C.F., Chang, P.H.: Designing fuzzy-rule based systems using continuous ant-colony optimization. IEEE Trans. Fuzzy Syst. 18(1), 138–149 (2010)

    Article  Google Scholar 

  15. Chen, C.C., Shen, L.P., Huang, C.F., Chang, B.R.: Assimilation-accommodation mixed continuous ant colony optimization for fuzzy system design. Eng. Comput. 33(7), 1882–1898 (2016)

    Article  Google Scholar 

  16. Eberchart, R., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the International Symposium on Micro Machine and Human Science, Nagoya, Japan, pp. 39–43 (1995)

  17. Shi, Y., Eberchart, R.: A modified particle swarm optimizer. In: Proceedings of the IEEE World Conference on Computational Intelligence, pp. 69–73 (1998)

  18. Ratnaweera, A., Halgamuge, S., Watson, H.: Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Trans. Evol. Comput. 8, 240–255 (2004)

    Article  Google Scholar 

  19. Chen, X., Li, Y.: A modified PSO structure resulting in high exploration ability with convergence guaranteed. IEEE Trans. Syst. Man Cybern. B 37(5), 1271–1289 (2007)

    Article  Google Scholar 

  20. Gao, H., Xu, W.B.: A new particle swarm algorithm and its globally convergent modifications. IEEE Trans. Syst. Man Cybern. B 41(5), 1334–1351 (2011)

    Article  Google Scholar 

  21. Li, N.J., Wang, W.J., Hsu, C.C.J., Chang, W., Chou, H.G.: Enhanced particle swarm optimizer incorporating a weighted particle. Neurcomputing 24, 218–237 (2014)

    Article  Google Scholar 

  22. Olivas, F., Valdez, F., Castillo, O., Melin, P.: Dynamic parameter adaptation in particle swarm optimization using interval type-2 fuzzy logic. Soft. Comput. 20(3), 1057–1070 (2016)

    Article  Google Scholar 

  23. Wang, H., Wang, W., Wu, Z.: Particle swarm optimization with adaptive mutation for multimodal optimization. Appl. Math. Comput. 221, 296–305 (2013)

    MathSciNet  MATH  Google Scholar 

  24. Liang, H.T., Kang, F.H.: Adaptive mutation particle swarm algorithm with dynamic nonlinear changed inertia weight. Optik 127, 8036–8042 (2016)

    Article  Google Scholar 

  25. Tanweer, M.R., Suresh, S., Sundararajan, N.: Self regulating particle swarm optimization algorithm. Inf. Sci. 294, 182–202 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  26. Meng, A., Li, Z., Yin, H., Chen, S., Guo, Z.: Accelerating particle swarm optimization using crisscross search. Inf. Sci. 329, 52–72 (2016)

    Article  Google Scholar 

  27. Clerc, M., Kennedy, J.: The particle swarm explosion, stability, and convergence in a multidimensional complex space. IEEE Trans. Evol. Comput. 6, 58–73 (2002)

    Article  Google Scholar 

  28. Ruben, E.P., Kamran, B.: Particle swarm optimization in structural design. In: Chan, F.T.S., Tiwari, M.K. (eds.) Swarm Intelligence: Focus on Ant and Particle Swarm Optimization, pp. 373–394. I-Tech Education and Publishing, Vienna (2007)

    Google Scholar 

  29. Juang, C.F.: A hybrid of genetic algorithm and particle swarm optimization for recurrent network design. IEEE Trans. Syst. Man Cybern. B 34(2), 997–1006 (2004)

    Article  Google Scholar 

  30. Juang, C.F., Chung, I.F., Hsu, C.H.: Automatic construction of feedforward/recurrent fuzzy systems by clustering-aided simplex particle swarm optimization. Fuzzy Sets Syst. 158(18), 1979–1996 (2007)

    Article  MATH  Google Scholar 

  31. Juang, C.F., Lo, C.: Zero-order TSK-type fuzzy system learning using a two-phase swarm intelligence. Fuzzy Sets Syst. 159(21), 2910–2926 (2008)

    Article  MathSciNet  Google Scholar 

  32. Juang, C.F., Wang, C.Y.: A self-generating fuzzy system with ant and particle swarm cooperative optimization. Exp. Syst. Appl. 36(3), 5362–5370 (2009)

    Article  Google Scholar 

  33. Glerc, M.: Initialisations for particle swarm optimization. http://clerc.maurice.free.fr/pso (2008). Accessed 24 July 2017

  34. Parsopoulos, K.E., Vrahatis, M.N.: Modification of the particle swarm optimizer for locating all the global minima. In: Kurkova, V., Steele, N.C., Neruda, R., Karny, M. (eds.) Artificial Neural Nets and Genetic Algorithms, pp. 324–327. IASTED/ACTA Press, Springer (2001)

    Chapter  Google Scholar 

  35. Parsopoulos, K.E., Vrahatis, M.N.: Initializing the particle swarm optimizer using the nonlinear simplex methods. In: Grmela, A., Mastorakis, N.E. (eds.) Advances in Intelligent Systems, Fuzzy Systems, Evolutionary Computation, pp. 216–221. WSEAS Press, Interlaken, Switzerland (2002)

    Google Scholar 

  36. Richards, M., Ventura, D.: Choosing a starting configuration for particle swarm optimization. In: Proceedings of the International Joint Conference on Neural Networks, pp. 2309–2312 (2004)

  37. Rahnamayan, S., Wang, G.G.: Center-based sampling for population-based algorithms. In: IEEE Proceedings of the Eleventh Conference on Congress on Evolutionary Computation, Trondheim, Norway, May 18–21, 2009, pp. 933–938

  38. Cordón, O., Herrera, F.: A three-stage evolutionary process for learning descriptive and approximate fuzzy-logic-controller knowledge bases from examples. Int. J. Approx. Reason. 17, 369–407 (1997)

    Article  MATH  Google Scholar 

  39. Cordón, O., Herrera, F.: A two-stage evolutionary process for designing TSK fuzzy rule-based systems. IEEE Trans. Syst. Man Cybern. B 29(6), 703–715 (1999)

    Article  Google Scholar 

  40. Yahya, A.A., Osman, A., El-Bashir, M.S.: Rocchio algorithm-based particle initialization mechanism for effective PSO classification of high dimensional data. Swarm Evol. Comput. 34, 18–32 (2017)

    Article  Google Scholar 

  41. Derrac, J., García, S., Molina, D., Herrera, F.: A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol. Comput. 1(1), 3–18 (2011)

    Article  Google Scholar 

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Acknowledgements

This work was supported by Ministry of Science and Technology, Taiwan under Grants MOST 104-2221-E-415-006 and MOST 105-2221-E-415-018.

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  1. Department of Electrical Engineering, National Chiayi University, 300 Syuefu Road, Chiayi City, 60004, Taiwan

    Chi-Chung Chen

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  1. Chi-Chung Chen
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Correspondence to Chi-Chung Chen.

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Chen, CC. Optimization of Zero-Order TSK-Type Fuzzy System Using Enhanced Particle Swarm Optimizer with Dynamic Mutation and Special Initialization. Int. J. Fuzzy Syst. 20, 1685–1698 (2018). https://doi.org/10.1007/s40815-018-0453-z

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