Brownian Distribution Guided Bacterial Foraging Algorithm for Controller Design Problem

  • N. Sri Madhava Raja
  • V. Rajinikanth
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 248)


Bacterial Foraging Optimization (BFO) algorithm is widely adopted to solve a variety of engineering optimization tasks. In this paper, the Brownian Distribution (BD) strategy guided BFO algorithm is proposed. During the optimization exploration, BD monitors and controls the chemotaxis operation of the BFO algorithm inorder to enhance the search speed and optimization accuracy. In the proposed algorithm, after undergoing a chemotaxis step, each bacterium gets mutated by a BD operator. In the proposed work, this algorithm is employed to design the PID controller for an AVR system and unstable reactor models. The success of the proposed method has been confirmed through a comparative analysis with PSO, BFO, adaptive BFO and PSO + BFO based hybrid methods existing in the literature. The result shows that, for unstable reactor models, the BD guided BFO algorithm provides better optimization accuracy compared to other algorithms considered in this study.


Bacterial Foraging Algorithm Brownian Distribution PID controller design AVR system unstable reactor 


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  1. 1.
    Liu, G.P., Yang, J.-B., Whidborne, J.F.: Multiobjective Optimization and Control. Prentice Hall, New Delhi (2008)Google Scholar
  2. 2.
    Yang, X.-S.: Nature-Inspired Metaheuristic Algorithms. Luniver Press, UK (2008)Google Scholar
  3. 3.
    Passino, K.M.: Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Systems Magazine 22(3), 52–67 (2002)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Chen, H., Zhu, Y., Hu, K.: Cooperative Bacterial Foraging Optimization. Discrete Dynamics in Nature and Society 2009, Article ID 815247, 17 pages (2009), doi:10.1155/2009/815247Google Scholar
  5. 5.
    Rajinikanth, V., Latha, K.: Controller Parameter Optimization for Nonlinear Systems Using Enhanced Bacteria Foraging Algorithm. Applied Computational Intelligence and Soft Computing 2012, Article ID 214264, 12 pages (2012), doi:10.1155/2012/214264Google Scholar
  6. 6.
    Pandi, V.R., Biswas, A., Dasgupta, S., Panigrahi, B.K.: A hybrid bacterial foraging and differential evolution algorithm for congestion management. Euro. Trans. Electr. Power 20(7), 862–871 (2010), doi:10.1002/etep.368Google Scholar
  7. 7.
    Ganesan, T., Vasant, P., Elamvazuthy, I.: A hybrid PSO approach for solving non-convex optimization problems. Archives of Control Sciences 22(1), 87–105 (2012)CrossRefMATHGoogle Scholar
  8. 8.
    Kim, D.H.: Hybrid GA–BF based intelligent PID controller tuning for AVR system. Applied Soft Computing 11(1), 11–22 (2011)CrossRefGoogle Scholar
  9. 9.
    Korani, W.M., Dorrah, H.T., Emara, H.M.: Bacterial foraging oriented by particle swarm optimization strategy for PID tuning. In: Proceedings of the 8th IEEE International Conference on Computational Intelligence in Robotics and Automation, pp. 445–450 (2008)Google Scholar
  10. 10.
    Anguluri, R., Abraham, A., Snasel, V.: A Hybrid Bacterial Foraging - PSO Algorithm Based Tuning of Optimal FOPI Speed Controller. Acta Montanistica Slovaca 16(1), 55–65 (2011)Google Scholar
  11. 11.
    Das, S., Biswas, A., Dasgupta, S., Abraham, A.: Bacterial Foraging Optimization Algorithm: Theoretical Foundations, Analysis, and Applications. In: Abraham, A., Hassanien, A.-E., Siarry, P., Engelbrecht, A. (eds.) Foundations of Computational Intelligence Volume 3. SCI, vol. 203, pp. 23–55. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Rajinikanth, V., Latha, K.: Bacterial Foraging Optimization Algorithm based PID controller tuning for Time Delayed Unstable System. The Mediterranean Journal of Measurement and Control 7(1), 197–203 (2011)Google Scholar
  13. 13.
    Rajinikanth, V., Latha, K.: Setpoint weighted PID controller tuning for unstable system using heuristic algorithm. Archives of Control Sciences 22(4), 481–505 (2013), doi:10.2478/v10170-011-0037-8MathSciNetGoogle Scholar
  14. 14.
    Nurzaman, S.G., Matsumoto, Y., Nakamura, Y., Shirai, K., Koizumi, S.: From Lévy to Brownian: A Computational Model Based on Biological Fluctuation. PLoS ONE 6(2), e16168 (2011), doi:10.1371/journal.pone.0016168Google Scholar
  15. 15.
    Metzler, R., Klafter, J.: The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Physics Reports 339(1), 1–77 (2000)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Gandomi, A.H., Yang, X.-S., Talatahari, S., Alavi, A.H.: Firefly algorithm with chaos, Commun. Nonlinear Sci. Numer. Simulat. 18(1), 89–98 (2013)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Mukherjee, V., Ghoshal, S.P.: Intelligent particle swarm optimized fuzzy PID controller for AVR system. Electric Power Systems Research 77(12), 1689–1698 (2007)CrossRefGoogle Scholar
  18. 18.
    Pan, I., Das, S.: Frequency domain design of fractional order PID controller for AVR system using chaotic multi-objective optimization. Electrical Power and Energy Systems 51, 106–118 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • N. Sri Madhava Raja
    • 1
  • V. Rajinikanth
    • 1
  1. 1.Department of Electronics and InstrumentationSt. Joseph’s College of EngineeringChennaiIndia

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