Bacterial Foraging Optimization Algorithm: Theoretical Foundations, Analysis, and Applications

  • Swagatam Das
  • Arijit Biswas
  • Sambarta Dasgupta
  • Ajith Abraham
Part of the Studies in Computational Intelligence book series (SCI, volume 203)


Bacterial foraging optimization algorithm (BFOA) has been widely accepted as a global optimization algorithm of current interest for distributed optimization and control. BFOA is inspired by the social foraging behavior of Escherichia coli. BFOA has already drawn the attention of researchers because of its efficiency in solving real-world optimization problems arising in several application domains. The underlying biology behind the foraging strategy of E.coli is emulated in an extraordinary manner and used as a simple optimization algorithm. This chapter starts with a lucid outline of the classical BFOA. It then analyses the dynamics of the simulated chemotaxis step in BFOA with the help of a simple mathematical model. Taking a cue from the analysis, it presents a new adaptive variant of BFOA, where the chemotactic step size is adjusted on the run according to the current fitness of a virtual bacterium. Nest, an analysis of the dynamics of reproduction operator in BFOA is also discussed. The chapter discusses the hybridization of BFOA with other optimization techniques and also provides an account of most of the significant applications of BFOA until date.


Particle Swarm Optimization Differential Evolution Independent Component Analysis Fitness Landscape Unit Step Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Passino, K.M.: Biomimicry of Bacterial Foraging for Distributed Optimization and Control. IEEE Control Systems Magazine, 52–67 (2002)Google Scholar
  2. 2.
    Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Harbor (1975)Google Scholar
  3. 3.
    Fogel, L.J., Owens, A.J., Walsh, M.J.: Artificial Intelligence through Simulated Evolution. John Wiley, Chichester (1966)zbMATHGoogle Scholar
  4. 4.
    Rechenberg, I.: Evolutionsstrategie 1994. Frommann-Holzboog, Stuttgart (1994)Google Scholar
  5. 5.
    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks, pp. 1942–1948 (1995)Google Scholar
  6. 6.
    Dorigo, M., Gambardella, L.M.: Ant Colony System: A Cooperative Learning Approach to the Traveling Salesman Problem. IEEE Transactions on Evolutionary Computation 1(1), 53–66 (1997)CrossRefGoogle Scholar
  7. 7.
    Berg, H., Brown, D.: Chemotaxis in escherichia coli analysed by three-dimensional tracking. Nature 239, 500–504 (1972)CrossRefGoogle Scholar
  8. 8.
    Berg, H.: Random Walks in Biology. Princeton Univ. Press, Princeton (1993)Google Scholar
  9. 9.
    Liu, Y., Passino, K.M.: Biomimicry of Social Foraging Bacteria for Distributed Optimization: Models, Principles, and Emergent Behaviors. Journal of Optimization Theory And Applications 115(3), 603–628 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York (1972)zbMATHGoogle Scholar
  11. 11.
    Bracewell, R.: Heaviside’s Unit Step Function, H(x), The Fourier Transform and Its Applications, 3rd edn., pp. 57–61. McGraw-Hill, New York (1999)Google Scholar
  12. 12.
    Snyman, J.A.: Practical Mathematical Optimization: An Introduction to Basic Optimization Theory and Classical and New Gradient-Based Algorithms. Springer Publishing, Heidelberg (2005)zbMATHGoogle Scholar
  13. 13.
    Dasgupta, S., Das, S., Abraham, A., Biswas, A.: Adaptive Computational Chemotaxis in Bacterial Foraging Optimization: An Analysis. IEEE Transactions on Evolutionary Computation (in press, 2009)Google Scholar
  14. 14.
    Abraham, A., Biswas, A., Dasgupta, S., Das, S.: Anaysis of Reproduction Operator in Bacterial Foraging Optimization. In: IEEE Congress on Evolutionary Computation CEC 2008, IEEE World Congress on Computational Intelligence, WCCI 2008, pp. 1476–1483. IEEE Press, USA (2008)CrossRefGoogle Scholar
  15. 15.
    Murray, J.D.: Mathematical Biology. Springer, New York (1989)zbMATHGoogle Scholar
  16. 16.
    Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm Intelligence: From Natural to Artificial Systems. Oxford Univ. Press, New York (1999)zbMATHGoogle Scholar
  17. 17.
    Okubo, A.: Dynamical aspects of animal grouping: swarms, schools, flocks, and herds. Advanced Biophysics 22, 1–94 (1986)CrossRefGoogle Scholar
  18. 18.
    Wolpert, D.H., Macready, W.G.: No Free Lunch Theorems for Optimization. IEEE Transactions on Evolutionary Computation 1(1), 67–82 (1997)CrossRefGoogle Scholar
  19. 19.
    Kim, D.H., Abraham, A., Cho, J.H.: A hybrid genetic algorithm and bacterial foraging approach for global optimization. Information Sciences 177(18), 3918–3937 (2007)CrossRefGoogle Scholar
  20. 20.
    Biswas, A., Dasgupta, S., Das, S., Abraham, A.: Synergy of PSO and Bacterial Foraging Optimization: A Comparative Study on Numerical Benchmarks. In: Corchado, E., et al. (eds.) Second International Symposium on Hybrid Artificial Intelligent Systems (HAIS 2007), Innovations in Hybrid Intelligent Systems, ASC. Advances in Soft computing Series, vol. 44, pp. 255–263. Springer, Germany (2007)Google Scholar
  21. 21.
    Storn, R., Price, K.: Differential evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces. Journal of Global Optimization 11(4), 341–359 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Biswas, A., Dasgupta, S., Das, S., Abraham, A.: A Synergy of Differential Evolution and Bacterial Foraging Algorithm for Global Optimization. Neural Network World 17(6), 607–626 (2007)Google Scholar
  23. 23.
    Ulagammai, L., Vankatesh, P., Kannan, P.S., Padhy, N.P.: Application of Bacteria Foraging Technique Trained and Artificial and Wavelet Neural Networks in Load Forecasting. Neurocomputing, 2659–2667 (2007)Google Scholar
  24. 24.
    Munoz, M.A., Lopez, J.A., Caicedo, E.: Bacteria Foraging Optimization for Dynamical resource Allocation in a Multizone temperature Experimentation Platform. In: Anal. and Des. of Intel. Sys. using SC Tech., ASC, vol. 41, pp. 427–435 (2007)Google Scholar
  25. 25.
    Acharya, D.P., Panda, G., Mishra, S., Lakhshmi, Y.V.S.: Bacteria Foaging Based Independent Component Analysis. In: International Conference on Computational Intelligence and Multimedia Applications. IEEE Press, Los Alamitos (2007)Google Scholar
  26. 26.
    Chatterjee, A., Matsuno, F.: Bacteria Foraging Techniques for Solving EKF-Based SLAM Problems. In: Proc. International Control Conference (Control 2006), Glasgow, UK, August 30- September 01 (2006)Google Scholar
  27. 27.
    Tripathy, M., Mishra, S.: Bacteria Foraging-Based to Optimize Both Real Power Loss and Voltage Stability Limit. IEEE Transactions on Power Systems 22(1), 240–248 (2007)CrossRefGoogle Scholar
  28. 28.
    Mishra, S., Bhende, C.N.: Bacterial Foraging Technique-Based Optimized Active Power Filter for Load Compensation. IEEE Transactions on Power Delivery 22(1), 457–465 (2007)CrossRefGoogle Scholar
  29. 29.
    Mishra, S.: A hybrid least square-fuzzy bacterial foraging strategy for harmonic estimation. IEEE Trans. on Evolutionary Computation 9(1), 61–73 (2005)CrossRefGoogle Scholar
  30. 30.
    Tang, W.J., Wu, Q.H., Saunders, J.R.: A Novel Model for Bacteria Foraging in Varying Environments. In: Gavrilova, M.L., Gervasi, O., Kumar, V., Tan, C.J.K., Taniar, D., Laganá, A., Mun, Y., Choo, H. (eds.) ICCSA 2006. LNCS, vol. 3980, pp. 556–565. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  31. 31.
    Biswas, A., Das, S., Dasgupta, S., Abraham, A.: Dynamics of Reproduction in Artificial Bacterial Foraging System: Modeling and Stability Analysis. In: IEEE International Conference on Soft Computing as Trans-disciplinary Science and Technology (CSTST 2008), Paris, France, October 27-31 (to appear, 2008)Google Scholar
  32. 32.
    Fernandes, C., Ramos, V., Agostinho, C.: Varying the Population Size of Artificial Foraging Swarms on Time Varying Landscapes. In: Duch, W., Kacprzyk, J., Oja, E., Zadrożny, S. (eds.) ICANN 2005. LNCS, vol. 3696, pp. 311–316. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  33. 33.
    Tripathy, M., Mishra, S., Lai, L.L., Zhang, Q.P.: Transmission Loss Reduction Based on FACTS and Bacteria Foraging Algorithm. In: PPSN, pp. 222–231 (2006)Google Scholar
  34. 34.
    Mishra, S., Bhende, C.N.: Bacterial Foraging Technique-Based Optimized Active Power Filter for Load Compensation. IEEE Transactions on Power Delivery 22(1), 457–465 (2007)CrossRefGoogle Scholar
  35. 35.
    Kim, D.H., Cho, C.H.: Bacterial Foraging Based Neural Network Fuzzy Learning. In: IICAI 2005, pp. 2030–2036 (2005)Google Scholar
  36. 36.
    Dasgupta, S., Biswas, A., Das, S., Abraham, A.: Automatic Circle Detection on Images with an Adaptive Bacterial Foraging Algorithm. In: 2008 Genetic and Evolutionary Computation Conference. GECCO 2008. ACM Press, New York (2008)Google Scholar
  37. 37.
    Chen, H., Zhu, Y., Hu, K., He, X., Niu, B.: Cooperative Approaches to Bacterial Foraging Optimization. In: ICIC (2), pp. 541–548 (2008)Google Scholar
  38. 38.
    Wu, C., Zhang, N., Jiang, J., Yang, J., Liang, Y.: Improved Bacterial Foraging Algorithms and Their Applications to Job Shop Scheduling Problems. In: Beliczynski, B., Dzielinski, A., Iwanowski, M., Ribeiro, B. (eds.) ICANNGA 2007. LNCS, vol. 4431, pp. 562–569. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Swagatam Das
    • 1
  • Arijit Biswas
    • 1
  • Sambarta Dasgupta
    • 1
  • Ajith Abraham
    • 2
  1. 1.Department of Electronics and Telecommunication EngineeringJadavpur UniversityKolkataIndia
  2. 2.Norwegian University of Science and TechnologyNorway

Personalised recommendations