Fireworks Algorithm (FWA) with Adaptation of Parameters Using Interval Type-2 Fuzzy Logic System

  • Juan Barraza
  • Fevrier ValdezEmail author
  • Patricia Melin
  • Claudia I. González
Part of the Studies in Computational Intelligence book series (SCI, volume 862)


The main goal of this paper is to improve the performance of the Fuzzy Fireworks Algorithm (FFWA), which is a variation of conventional Fireworks Algorithm (FWA). In previous work the FFWA was proposed on Type-1 Fuzzy Logic to adjust parameters dynamically and the difference now in this work is that we use the Interval Type-2 Fuzzy Logic for and adjust the parameter of the explosion amplitude of each firework, and this variation, we called as Interval Type-2 Fuzzy Fireworks Algorithm and we denoted as IT2FFWA. To evaluate the performance of FFWA and IT2FFWA we tested both algorithms with 12 mathematical Benchmark functions.


Fireworks algorithm Fuzzy parameter adaptation Type-2 fuzzy logic 


  1. 1.
    Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks, vol. 4, pp. 1942–1948 (1995)Google Scholar
  2. 2.
    Zheng, Y., Song, Q., Chen, Y.S.: Multiobjective fireworks optimization for variable-rate fertilization in oil crop production. Appl. Soft Comput. 13, 4253–4263 (2013)CrossRefGoogle Scholar
  3. 3.
    Das, S., Abraham, A., Konar, A.: Swarm intelligence algorithms in bioinformatics. Stud. Comput. Intell. 94, 113–147 (2008)Google Scholar
  4. 4.
    Dorigo, M., Maniezzo, V., Colorni, A.: Ant system: optimization by a colony of cooperating agents. In: IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 26(1), 29–41 (1996)CrossRefGoogle Scholar
  5. 5.
    Li, J., Zhang, S.: Adaptive fireworks algorithm. IEEE Congr. Evol. Comput. (CEC), pp. 3214–3221 (2014)Google Scholar
  6. 6.
    Tan, Y.: Fireworks Algorithm, pp. 355–364. Springer, Berlin, Heidelberg (2015)CrossRefGoogle Scholar
  7. 7.
    Tan, Y., Zheng, S.: Enhanced fireworks algorithm. In: IEEE Congress on Evolutionary Computation, pp. 2069–2077 (2013)Google Scholar
  8. 8.
    Zadeh, L.A.: Knowledge representation in fuzzy logic. IEEE Trans. Knowl. Data Eng. I(I), 89–100, Mar 1989Google Scholar
  9. 9.
    Simoes, M., Bose, K., Spiegel, J.: Fuzzy logic based intelligent control of a variable speed cage machine wind generation system. IEEE Trans. Power Electron. 12(1), 87–95 (1997)CrossRefGoogle Scholar
  10. 10.
    Rubio, E., Castillo, O.: Interval type-2 fuzzy possibilistic C-means optimization using particle swarm optimization. In: Nature-Inspired Design of Hybrid Intelligent Systems, pp. 63–78 (2017)Google Scholar
  11. 11.
    Soto, J., Melin, P.: Optimization of the interval type-2 fuzzy integrators in ensembles of ANFIS models for time series prediction: case of the mexican stock exchange. In: Design of Intelligent Systems Based on Fuzzy Logic, Neural Networks and Nature-Inspired Optimization, pp. 27–45 (2015)CrossRefGoogle Scholar
  12. 12.
    Zheng, Y., Xu, X., Ling, H., Sheng-Yong, C.: A hybrid fireworks optimization method with differential evolution operators. Neurocomputing 148, 75–82 (2015)CrossRefGoogle Scholar
  13. 13.
    Barraza, J., Melin, P., Valdez, F., Gonzalez, C.: Fuzzy FWA with dynamic adaptation of parameters. IEEE CEC, pp. 4053–4060 (2016)Google Scholar
  14. 14.
    Tan, Y., Zheng, S.: Dynamic search in fireworks algorithm. In: Evolutionary Computation (CEC 2014), pp. 3222–3229Google Scholar
  15. 15.
    Tan, Y., Zhu, Y.: Fireworks Algorithm for Optimization, pp. 355–364. Springer, Berlin, Heidelberg (2010)Google Scholar
  16. 16.
    Barraza, J., Valdez, F., Melin, P., Gonzalez, C.: Fireworks Algorithm (FWA) with adaptation of parameters using fuzzy logic. In: Nature-Inspired Design of Hybrid Intelligent Systems, pp. 313–327 (2017)Google Scholar
  17. 17.
    Abdulmajeed, N.H., Ayob, M.: A firework algorithm for solving capacitated vehicle routing problem. Int. J. Adv. Comput. Technol. (IJACT) 6(1), 79–86 (2014)Google Scholar
  18. 18.
    Ding, K., Zheng, S., Tan, Y.: A GPU-based Parallel Fireworks Algorithm for Optimization, GECCO’13. Amsterdam, The Netherlands, 6–10 July 2013Google Scholar
  19. 19.
    Liu, M., Mernik, S.H.: Exploration and exploitation in evolutionary algorithms, a survey. ACM Comput. Surv. 45(3), 35, 32 (2013)Google Scholar
  20. 20.
    Perez, J., Valdez, F., Castillo, O.: Modification of the bat algorithm using type-2 fuzzy logic for dynamical parameter adaptation. In: Nature-Inspired Design of Hybrid Intelligent Systems, pp. 343–355 (2017)Google Scholar
  21. 21.
    Rodriguez, L., Castillo, O., Soria, J.: Grey Wolf Optimizer (GWO) with dynamic adaptation of parameters using fuzzy logic. IEEE CEC, pp. 3116–3123 (2016)Google Scholar
  22. 22.
    Rodríguez, L., Castillo, O., Soria, J.: A study of parameters of the grey wolf optimizer algorithm for dynamic adaptation with fuzzy logic. In: Nature-Inspired Design of Hybrid Intelligent Systems, pp. 371–390 (2017)Google Scholar
  23. 23.
    Castillo, O., Melin, P.: A review on the design and optimization of interval type-2 fuzzy controllers. Appl. Soft Comput. 12(4), 1267–1278 (2012)CrossRefGoogle Scholar
  24. 24.
    Castillo, O., Martinez-Marroquin, R., Melin, P., et al.: Comparative study of bio-inspired algorithms applied to the optimization of type-1 and type-2 fuzzy controllers for an autonomous mobile robot. Inf. Sci. 192, 19–38 (2012)CrossRefGoogle Scholar
  25. 25.
    Castillo, O., Melin, P.: Optimization of type-2 fuzzy systems based on bio-inspired methods: A concise review. Inf. Sci. 205, 1–19 (2012)CrossRefGoogle Scholar
  26. 26.
    Melin, P., Castillo, O.: A review on type-2 fuzzy logic applications in clustering, classification and pattern recognition. Appl. Soft Comput. 21, 568–577 (2014)CrossRefGoogle Scholar
  27. 27.
    Castillo, O., Melin, P.: A review on interval type-2 fuzzy logic applications in intelligent control. Inf. Sci. 279, 615–631 (2014)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Melin, P., Mendoza, O., Castillo, O.: An improved method for edge detection based on interval type-2 fuzzy logic. Expert Syst. Appl. 37(12), 8527–8535 (2010)CrossRefGoogle Scholar
  29. 29.
    Hidalgo, D., Melin, P., Castillo, O.: An optimization method for designing type-2 fuzzy inference systems based on the footprint of uncertainty using genetic algorithms. Expert Syst. Appl. 39(4), 4590–4598 (2012)CrossRefGoogle Scholar
  30. 30.
    Melin, P., Gonzalez, C.I., Castro, J.R., et al.: Edge-detection method for image processing based on generalized type-2 fuzzy logic. IEEE Trans. Fuzzy Syst. 22(6), 1515–1525 (2014)CrossRefGoogle Scholar
  31. 31.
    Melin, P., Castillo, O.: A review on the applications of type-2 fuzzy logic in classification and pattern recognition. Expert Syst. Appl. 40(13), 5413–5423 (2013)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Juan Barraza
    • 1
  • Fevrier Valdez
    • 1
    Email author
  • Patricia Melin
    • 1
  • Claudia I. González
    • 1
  1. 1.Tijuana Institute of TechnologyTijuanaMexico

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