• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology


Indian Journal of Science and Technology

Year: 2021, Volume: 14, Issue: 26, Pages: 2164-2174

Original Article

Modified Approach of NaFA based on its Step Size and its Performance in Bioreactor Processes

Received Date:17 January 2021, Accepted Date:14 July 2021, Published Date:30 July 2021


Objectives: The objective of this work is to fine tune the variant of FA (Firefly Algorithm), NaFA (Firefly Algorithm with neighbourhood Attraction) by parameter tuning such as a, b , g . Furthermore, a new variant called Step Size Modified FA with neighbourhood attraction (SSMFA-N) has been proposed in which the step size is updated during the algorithm run so that a balance between local and global search is achieved. The considered objective functions are PO and ITAE. Methods: It is well known that parameters that are considered initially for any metaheuristic algorithms are purely trial and error basis and this leads to erroneous optimized results. While analysing the algorithms, NaFA (a variant of FA) has been considered for efficient convergence and good performance. On analysing it is noticed that FA and its variants’ performances and convergence depend on Step Size(a), brightness (b ) and adsorption coefficient(g ). In both the FA and NaFA the parameters to be tuned for effective convergence are a, b and g . It is also understood that the parameter b had been done separately and the parameters a and g cannot be fine-tuned simultaneously. Therefore, in NaFA the parameter tuning for a has been done for the processes FOPDT, stable and unstable SOPDT and the new variant SSMFA-N is thus proposed. Findings: The algorithm is made to run in MATLAB and Simulink environment for three different processes such as FOPDT, Stable and Unstable Second order Process (bioreactor processes) with the objective functions of less PO and ITAE. The obtained results from all the three processes are compared with the conventional and optimization methods (PSO) and shown that SSMFA-N outperforms the conventional and optimization approaches in both the time domain and performance indices. Novelty: The novelty is the modification of step size of NaFA, which ultimately leads to a new variant called SSMFA-N.

Keywords: FA; FA with neighbourhood attraction; Step size tuning; Bioreactor Process


  1. Garpinger O. Analysis and Design of Software Based Optimal PID Controllers. Lund University thesis
  2. Dwyer AO. Handbook of PI and PID controller tuning rules. (pp. 392-608) 2006.
  3. Yang XS, Deb S. Engineering optimization by cuckoo search. Int. J. Math. Modelling & Num. Optimization. 2010;1:330–343. Available from: arXiv:1005.2908
  4. Yang XS. Firefly algorithm. Nature-Inspired Metaheuristic Algorithms. 2008;20:79–90.
  5. Fister I, Fister I, Yang XS, Brest J. A comprehensive review of firefly algorithms. Swarm and Evolutionary Computation. 2013;13:34–46. Available from: https://dx.doi.org/10.1016/j.swevo.2013.06.001
  6. Windarto W, Eridani E. Comparison of particle swarm optimization and firefly algorithm in parameter estimation of Lotka-Volterra. The 4th Indoms International Conference on Mathematics and Its Application. 2020. Available from: 10.1063/5.0017245
  7. Gebremedhen HS, Woldemichael DE, Hashim FM. A firefly algorithm based hybrid method for structural topology optimization. Advanced Modeling and Simulation in Engineering Sciences. 2020;7:44. Available from: https://dx.doi.org/10.1186/s40323-020-00183-0
  8. Zhao C, Jiang L, Teo LK. A hybrid chaos firefly algorithm for three-dimensional irregular packing problem. Journal of Industrial & Management optimization. 2020(1):409–429. Available from: 10.3934/jimo.2018160
  9. Talib MHA, Darus IZM, Samin PM, Yatim HM, Ardani MI, Shaharuddin NMR, et al. Vibration control of semi-active suspension system using PID controller with advanced firefly algorithm and particle swarm optimization. Journal of Ambient Intelligence and Humanized Computing. 2021;12(1):1119–1137. Available from: https://dx.doi.org/10.1007/s12652-020-02158-w
  10. Eiben A, Smith J. Introduction to Evolutionary Computing. Berlin. Springer-Verlag. 2003.
  11. Eiben AE, Smit SK. Parameter tuning for configuring and analyzing evolutionary algorithms. Swarm and Evolutionary Computation. 2011;1(1):19–31. Available from: https://dx.doi.org/10.1016/j.swevo.2011.02.001
  12. Fister JI, Yang XS, Fister I, Brest J. Memetic firefly algorithm for combinatorial optimization. Bioinspired Optim. Methods Appl. (BIOMA). 2012;p. 1–14. Available from: arxiv:1204.5165
  13. Carbas S. Design optimization of steel frames using an enhanced firefly algorithm. EngineeringOptimization. 2007;48(12):2007–2025. Available from: 10.1080/0305215X.2016.1145217
  14. Yu SH, Su SB, Lu QP, Huang L. A novel wise step strategy for firefly algorithm. Int. J. Comput. Math. 2014;91(12):2507–2513. Available from: https://doi.org/10.1080/00207160.2014.907405
  15. Yu SH, Zhu SL, Ma Y, Mao DM. A variable step size firefly algorithm for numerical optimization. Appl.Math. Comput. 2015;263:214–220. Available from: 10.1016/j.amc.2015.04.065
  16. Wang H, Zhou XY, Sun H, Yu X, Zhao J, Zhang H, et al. Firefly algorithm with adaptive control parameters. Soft Computing. 2016. Available from: 10.1007/s00500-016-2104-3
  17. Gandomi AH, Yang XS, Alavi AH. Mixed variable structural optimization using Firefly Algorithm. Computers & Structures. 2011;89(23-24):2325–2336. Available from: https://dx.doi.org/10.1016/j.compstruc.2011.08.002
  18. Kwiecień J, Filipowicz B. Firefly algorithm in optimization of queueing systems. Bulletin of the Polish Academy of Sciences: Technical Sciences. 2012;60(2):363–368. Available from: https://dx.doi.org/10.2478/v10175-012-0049-y
  19. Chai-Ead N, Aungkulanon P, Luangpaiboon P. Bees and firefly algorithms for noisy non-linear optimization problems. Proceedings of the International Multi Conference of Engineering and Computer Scientists. 2011;2:1449–1454. Available from:
  20. Meena S, Chitra K. An approach of firefly algorithm with modified brightness for PID and I-PD controllers of SISO systems. Journal of Ambient Intelligence and Humanized Computing. 2018. Available from: https://dx.doi.org/10.1007/s12652-018-0747-x
  21. Wang H, Wang W, Zhou X, Sun H, Zhao J, Yu X, et al. Firefly algorithm with neighborhood attraction. Information Sciences. 2017;382-383:374–387. Available from: https://dx.doi.org/10.1016/j.ins.2016.12.024
  22. Huang HP, Chen CC. Control-system synthesis for open-loop unstable process with time delay. IEE Proceedings - Control Theory and Applications. 1997;144(4):334–346. Available from: https://dx.doi.org/10.1049/ip-cta:19971222
  23. Ang KH, Chong G, Li Y. PID control system analysis, design, and technology. IEEE Transactions on Control Systems Technology. 2005;13(4):559–576. Available from: https://dx.doi.org/10.1109/tcst.2005.847331


© 2021 Meena et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)


Subscribe now for latest articles and news.