Bacterial Foraging Algorithm Based on PSO with Adaptive Inertia Weigh for Solving Nonlinear Equations Systems

Abstract:

Bacterial Foraging Algorithm (BFA) has recently emerged as a very powerful technique for optimization,but it also confronts the problems of slow convergence and premature convergence. To overcome the drawbacks of BFA, This article merge the idea of particle swarm optimization algorithm with adaptive inertia weigh into the bacterial foraging to improve the speed and convergence capabilities of BFA, and according to this a bacterial foraging algorithm based on PSO(APSO-BFA) is presented. Simulation results on five systems of nonlinear equations show that the proposed algorithm is superior to the other two kinds of bacterial foraging algorithm

• Periodical: Advanced Materials Research (Volumes 655-657)
• Pages: 940-947
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.655-657.940
• Online since: January 2013
• Authors: Xiong Fa Mai, Ling Li
• Keywords: Adaptive Inertia Weigh, Bacterial Foraging Algorithm, Particle Swarm Optimization (PSO)

References

[1] J. Kennedy and R.C. Eberhart, Particle Swarm Optimization, in Proc. of the IEEE Int. Conf. on Neural Networks. Piscataway, NJ: IEEE Service Center, 1995: 1942–(1948).

[2] K. M. Passino, Biomimicry of bacterial foraging for distributed optimization and contro, IEEE Control Systems Magazine, 2002, 22(3): 52-67.

DOI: 10.1109/mcs.2002.1004010

[3] A. Biswas,S. Dasgupta,S. Das, and A. Abraham, Synergy of PSO and bacterial foraging optimization: A comparative study on numerical benchmarks, in Proc. 2nd Int Symp. Hybrid Artificial Intell. Syst. (HAIS) Advances Soft Computing Ser., Germany, Springer-Verlag, Innovations in Hybrid Intelligent Systems, ASC, 2007, 44: 255–263.

DOI: 10.1007/978-3-540-74972-1_34

[4] Wael Mansour Korani, Bacterial foraging oriented by particle swarm optimization strategy for PID tuning, Proceedings of the 2008 GECCO conference companion on Genetic and evolutionary computation, Atlanta, GA, USA , 2008: 12-16.

DOI: 10.1145/1388969.1388980

[5] HU Hai-bo, HUANG You-rui, Research of fractional order PID controller using hybrid particle swarm optimization, Journal of Computer Application, 2009, 29(9): 2483-2486(in chinese).

DOI: 10.3724/sp.j.1087.2009.02483

[6] MAI Xiong-fa, LI Ling，PENG Yu-zhong, Bacterial Foraging Algorithm Based on PSO and Opposition-based Learning, Computer Engineering, 2011, 37(23): 171-173(in chinese).

[7] Denis J. E. (1967), On Newton's method and nonlinear simultaneous replacements, SIAM J. Numer. Anal., vol. 4, p.103–108.

[8] Conn A. R., Gould N. I. M. and Toint P. L., Trust-Region Methods. Philadelphia, PA: SIAM, (2000).

[9] Broyden C. G., A class of methods for solving nonlinear simultaneous equations, Math. Comput. 1965, 19(92): 577–593.

DOI: 10.1090/s0025-5718-1965-0198670-6

[10] Denis J. E. and Wolkowicz H., Least change secant methods, sizing, and shifting, SIAM J. Numer. Anal., 1993, 30: 1291–1314.

DOI: 10.1137/0730067

[11] Ortega J. M. and Rheinboldt W. C., Iterative Solution of Nonlinear Equations in Several Variables, New York: Academic, (1970).

DOI: 10.1016/b978-0-12-528550-6.50017-x

[12] Yongquan ZHOU, Jiakun LIU, Guangwei ZHAO . Leader Glowworm Swarm Optimization Algorithm for Solving Nonlinear Equations Systems, przeglad elektrotechniczny (Electrical Review), ISSN 0033-2097, R. 88 NR 1b/(2012).

[13] Shi Y, Eberhart RC. Empirical study of particle swarm optimization,. In: Proc IEEE Int Congr Evolutionary Computation, 1999, Washington, DC. p.1945–50.