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Hybrid Taguchi-chaos of multilevel immune and the artificial bee colony algorithm for parameter identification of chaotic systems. (English) Zbl 1356.90166
Summary: In this paper, a novel evolutionary learning algorithm is proposed by hybridizing the Taguchi method, chaos disturbance operation, multilevel immune algorithm (MIA), and artificial bee colony algorithm (ABC). The algorithm is thus called HTCMIABC to estimate the parameter of chaotic systems. The HTCMIABC comprises two main different phases. First, we use the MIA as the recognition phase to balance local and global searches and accelerate the search speed to enhance the evolutionary phase. Second, the evolutionary phase is built on the ABC and chaos disturbance operation to have the capabilities of exploration and exploitation. Moreover, the Taguchi method and crossover operation are inserted between the recognition phase and evolutionary phase for the recombination and diversification of several antibodies to improve the searching ability. Finally, the HTCMIABC algorithm is examined by parameter identification of the nonlinear chaotic system. Simulation results show that the proposed algorithm is more efficient than some typical existing algorithms. The effects of noise and population size are investigated as well.

90C59 Approximation methods and heuristics in mathematical programming
Full Text: DOI
[1] Liu, B.; Wang, L.; Jin, Y.H.; Tang, F.; Hung, D.X., Directing orbits of chaotic systems by particle swarm optimization, Chaos, solitons and fractals, 29, 454-461, (2006) · Zbl 1147.93314
[2] Chen, G.; Dong, X., From chaos to order: methodologies, perspectives and application, (1998), World Scientific Singapore
[3] Yang, X.H.; Mei, Y.; She, D.X.; Li, J.Q., Chaotic Bayesian optimal prediction method and its application in hydrological time series, Computers and mathematics with applications, 61, 8, 1975-1978, (2011) · Zbl 1219.62147
[4] Usama, M.; Khan, M.K.; Alghathbar, K.; Lee, C., Chaos-based secure satellite imagery cryptosystem, Computers and mathematics with applications, 60, 2, 326-337, (2010) · Zbl 1198.94037
[5] Chen, D.Y.; Zhao, W.L.; Mar, X.Y.; Zhang, R.-F., No-chattering sliding mode control chaos in hindmarsh – rose neurons with uncertain parameters, Computers and mathematics with applications, 61, 10, 3161-3171, (2011) · Zbl 1222.37106
[6] Kuntanapreeda, S., Robust synchronization of fractional-order unified chaotic systems via linear control, Computers and mathematics with applications, 63, 1, 183-190, (2012) · Zbl 1238.93045
[7] Dai, D.; Ma, X.K.; Li, F.C.; You, Y., An approach of parameter estimation for a chaotic system based on genetic algorithm, Acta physica sinica, 51, 11, 2459-2462, (2002)
[8] He, Q.; Wang, L.; Liu, B., Parameter identification for chaotic systems by particle swarm optimization, Chaos, solitons and fractals, 34, 2, 654-661, (2007) · Zbl 1152.93504
[9] Peng, B.; Liu, B.; Zhang, F.Y.; Wang, L., Differential evolution algorithm based parameter identification for chaotic systems, Chaos, solitons and fractals, 39, 5, 2110-2118, (2009)
[10] Chang, J.F.; Yang, Y.S.; Liao, T.L.; Yan, J.J., Parameter identification of chaotic systems using evolutionary programming approach, Expert systems with application, 35, 4, 2074-2079, (2008)
[11] de Castro, L.N.; Timmis, J.I., Artificial immune systems as a novel soft computing paradigm, Soft computing, 7, 8, 526-544, (2003)
[12] Fu, X.; Li, A.; Wang, L.; Ji, C., Short-term scheduling of cascade reservoirs using an immune algorithm-based particle swarm optimization, Computers and mathematics with applications, 62, 6, 2463-2471, (2011) · Zbl 1231.90191
[13] de Castro, L.N.; Von Zuben, F.J., Learning and optimization using the clonal selection principle, IEEE transactions on evolutionary computation, 6, 239-251, (2002)
[14] Karaboga, D.; Basturk, B., A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm, Journal of global optimization, 39, 3, 459-471, (2007) · Zbl 1149.90186
[15] Karaboga, D.; Basturk, B., On the performance of artificial bee colony (ABC) algorithm, Applied soft computing, 8, 1, 687-697, (2008)
[16] Karaboga, D.; Akay, B., A comparative study of artificial bee colony algorithm, Applied mathematics and computation, 214, 108-312, (2009) · Zbl 1169.65053
[17] Tsai, J.T.; Liu, T.K.; Chou, J.H., Hybrid Taguchi-genetic algorithm for global numerical optimization, IEEE transactions on evolutionary computation, 8, 4, 365-377, (2004)
[18] Ho, W.H.; Chou, J.H.; Guo, C.Y., Parameter identification of chaotic systems using improved differential evolution algorithm, Nonlinear dynamics, 61, 1-2, 29-41, (2010) · Zbl 1204.93034
[19] Guo, Z.L.; Wang, S.; Zhuang, J., A novel immune evolutionary algorithm incorporating chaos optimization, Pattern recognition letters, 27, 2-8, (2006)
[20] He, H.; Qian, F.; Du, W., A chaotic immune algorithm with fuzzy adaptive parameters, Asia-Pacific journal of chemical engineering, 3, 695-705, (2008)
[21] Roitt, I.; Brostoff, J., Immunology, (1998), Mosby Int. Ltd New York
[22] Dasgupta, D.; Yu, S.; Majumdar, N.S., MILA—multilevel immune learning algorithm and its application to anomaly detection, Soft computing, 9, 3, 172-184, (2005) · Zbl 1078.68694
[23] Batista, L.D.; Guimaraes, F.G.; Ramirez, J.A., A distributed clonal selection algorithm for optimization in electromagnetics, IEEE transactions on magnetics, 45, 3, 1598-1601, (2009)
[24] Michalewice, Z., Genetic algorithm + data structures = evolution programs, (1996), Spinger-Verlag Berlin, Germany
[25] Ross, P.J., Taguchi techniques for quality engineering, (1989), McGraw-Hill Singapore
[26] Taguchi, G.; Chowdhury, S.; Taguchi, S., Robust engineering, (2000), McGraw-Hill New York
[27] Zhu, G.P.; Kwong, S., Gbest-guided artificial bee colony algorithm for numerical function optimization, Applied mathematics and computation, 217, 6, 3166-3173, (2010) · Zbl 1204.65074
[28] Wang, L.; Xu, Y.; Li, L.P., Parameter identification of chaotic systems by hybrid nelder – mead simplex search and differential evolution algorithm, Expert systems with application, 38, 4, 3238-3245, (2011)
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