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Stability analysis of the reproduction operator in bacterial foraging optimization. (English) Zbl 1190.90285
Summary: In his seminal paper published in 2002, {\it K. M. Passino} [IEEE Control Systems Magazine 22, No. 3, 52--67 (2002)] pointed out how individual and groups of bacteria forage for nutrients and how to model it as a distributed optimization process, which he named the Bacterial Foraging Optimization Algorithm (BFOA). One of the major operators of BFOA is the reproduction phenomenon of virtual bacteria, each of which models one trial solution of the optimization problem. During reproduction, the least healthy bacteria (with a lower accumulated value of the objective function in one chemotactic lifetime) die and the other healthier bacteria each split into two, which then starts exploring the search place from the same location. The phenomenon has a direct analogy with the selection mechanism of classical evolutionary algorithms. This paper attempts to model reproduction as a dynamics and then analyses the stability of the reproductive system very near to an equilibrium point, which in this case is an isolated optimum. It also finds conditions under which a stable reproduction event can take place, to direct a worse bacterium towards a better one. Our analysis reveals that a stable reproduction event contributes to the quick convergence of the bacterial population near optima.

90C59Approximation methods and heuristics
90C31Sensitivity, stability, parametric optimization
Full Text: DOI
[1] Passino, K. M.: Biomimicry of bacterial foraging for distributed optimization and control, IEEE control systems magazine, 52-67 (2002)
[2] 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, No. 3, 603-628 (2002) · Zbl 1031.92038 · doi:10.1023/A:1021207331209
[3] Kim, D. H.; Abraham, A.; Cho, J. H.: A hybrid genetic algorithm and bacterial foraging approach for global optimization, Information sciences 177, No. 148, 3918-3937 (2007)
[4] Mishra, S.: A hybrid least square-fuzzy bacterial foraging strategy for harmonic estimation, IEEE transactions on evolutionary computation 9, No. 1, 61-73 (2005)
[5] M. Tripathy, S. Mishra, L.L. Lai, Q.P. Zhang, Transmission loss reduction based on FACTS and bacteria foraging algorithm, PPSN, 2006, pp. 222--231.
[6] D.H. Kim, C.H. Cho, Bacterial foraging based neural network fuzzy learning, IICAI 2005, pp. 2030--2036.
[7] Mishra, S.; Bhende, C. N.: Bacterial foraging technique-based optimized active power filter for load compensation, IEEE transactions on power delivery 22, No. 1, 457-465 (2007)
[8] Tripathy, M.; Mishra, S.: Bacteria foraging-based to optimize both real power loss and voltage stability limit, IEEE transactions on power systems 22, No. 1, 240-248 (2007)
[9] Bonabeau, E.; Dorigo, M.; Theraulaz, G.: Swarm intelligence: from natural to artificial systems, (1999) · Zbl 1003.68123
[10] Kennedy, J.; Eberhart, R.; Shi, Y.: Swarm intelligence, (2001)
[11] J Kennedy, R. Eberhart, Particle swarm optimization. in: Proc. IEEE Int. Conf. Neural Networks., 1995, pp. 1942--1948.
[12] Dorigo, M.; Stiizle, T.: Ant colony optimization, (2004) · Zbl 1092.90066
[13] Back, T.; Fogel, D. B.; Michalewicz, Z.: Handbook of evolutionary computation, (1997) · Zbl 0883.68001
[14] Abraham, A.; Biswas, A.; Dasgupta, S.; Das, S.: Analysis of reproduction operator in bacterial foraging optimization, IEEE world congress on computational intelligence, WCCI 2008 (2008) · Zbl 1190.90285
[15] Tang, W. J.; Wu, Q. H.; Saunders, J. R.: A novel model for bacteria foraging in varying environments, ICCSA 2006, Lecture notes in computer science 3980, 556-565 (2006) · Zbl 1162.92335 · doi:10.1007/11751540_59
[16] Li, M. S.; Tang, W. J.; Tang, W. H.; Wu, Q. H.; Saunders, J. R.: Bacteria foraging algorithm with varying population for optimal power flow, Lecture notes in computer science 4448, 32-41 (2007)
[17] Biswas, A.; Dasgupta, S.; Das, S.; Abraham, A.: Synergy of PSO and bacterial foraging optimization: a comparative study on numerical benchmarks, Advances in soft computing series 44, 255-263 (2007)
[18] Dasgupta, S.; Das, S.; Abraham, A.; Biswas, A.: Adaptive computational chemotaxis in bacterial foraging optimization: an analysis, IEEE transactions on evolutionary computing 13, No. 4, 919-941 (2009)
[19] Ulagammai, L.; Vankatesh, P.; Kannan, P. S.; Padhy, Narayana Prasad: Application of bacteria foraging technique trained and artificial and wavelet neural networks in load forecasting, Neurocomputing, 2659-2667 (2007)
[20] Mario A. Munoz, Jesus A. Lopez, E. Caicedo, Bacteria foraging optimization for dynamical resource allocation in a multizone temperature experimentation platform, in: Anal. and Des. of Intel. Sys. using SC Tech, ASC 41, 2007, pp. 427--435.
[21] Acharya, D. P.; Panda, G.; Mishra, S.; Lakhshmi, Y. V. S.: Bacteria foaging based independent component analysis, International conference on computational intelligence and multimedia applications (2007)
[22] A. Chatterjee, F. Matsuno, Bacteria Foraging Techniques for Solving EKF-Based SLAM Problems.
[23] Anwal, R. P.: Generalized functions: theory and technique, (1998)
[24] Widder, D. V.: Advanced calculus, (1990) · Zbl 0036.31302
[25] Murray, J. D.: Mathematical biology, (1989) · Zbl 0682.92001
[26] Biswas, Arijit; Das, Swagatam; Abraham, Ajith; Dasgupta, Sambarta: Analysis of the reproduction operator in an artificial bacterial foraging system, Applied maths and computation 215, No. 9, 3343-3355 (2010) · Zbl 1180.92011 · doi:10.1016/j.amc.2009.10.023
[27] Okubo, A.: Dynamical aspects of animal grouping: swarms, schools, flocks, and herds, Advanced biophysics 22, 1-94 (1986)
[28] M. Gopal, Digital Control and State Variable Methods, 2nd ed., Tata-McGraw-Hill.
[29] Das, Swagatam; Dasgupta, Sambarta; Biswas, Arijit; Abraham, Ajith; Konar, Amit: On stability of the chemotactic dynamics in bacterial foraging optimization algorithm, IEEE transactions on systems man and cybernetics -- part A 39, No. 3, 670-679 (2009) · Zbl 1200.68185
[30] Biswas, Arijit; Dasgupta, Sambarta; Das, Swagatam; Abraham, Ajith: A synergy of differential evolution and bacterial foraging algorithm for global optimization, Neural network world 17, No. 6, 607-626 (2007)
[31] Das, Swagatam; Biswas, Arijit; Dasgupta, Sambarta; Abraham, Ajith: Bacterial foraging optimization algorithm: theoretical foundations, analysis, and applications, Studies in computational intelligence, 23-55 (2009)
[32] Kim, Dong-Hwa; Abraham, Ajith; Hirota, Kaoru: Hybrid genetic algorithm and bacterial foraging approach for function optimization and robust tuning of PID controller with disturbance rejection, Studies in computational intelligence 75, 171-199 (2007)
[33] Dasgupta, Sambarta; Biswas, Arijit; Das, Swagatam; Panigrahi, Bijaya Ketan; Abraham, Ajith: A micro-bacterial foraging algorithm for high-dimensional optimization, , 785-792 (2009)
[34] Das, Swagatam; Chowdhury, Archana; Abraham, Ajith: A bacterial evolutionary algorithm for automatic data clustering, , 2403-2410 (2009)
[35] Das, Swagatam; Dasgupta, Sambarta; Biswas, Arijit; Abraham, Ajith; Konar, Amit: On stability of the chemotactic dynamics in bacterial foraging optimization algorithm, , 245-251 (2008)