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Parameter estimation of nonlinear chaotic system by improved TLBO strategy

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Abstract

Estimation of parameters of chaotic systems is a subject of substantial and well-developed research issue in nonlinear science. From the viewpoint of optimization, parameter estimation can be formulated as a multi-modal constrained optimization problem with multiple decision variables. This investigation makes a systematic examination of the feasibility of applying a newly proposed population-based optimization method labeled here as teaching–learning-based optimization (TLBO) to identify the unknown parameters for a class of chaotic system. The preliminary test demonstrates that despite its global fast coarse search capability, teaching–learning-based optimization often risks getting prematurely stuck in local optima. To enhance its fine (local) searching performance of TLBO, Nelder–Mead simplex algorithm-based local improvement is incorporated into TLBO so as to continually search for the global optima through the reflection, expansion, contraction, and shrink operators. Working with the well-established Lorenz system, we assess the effectiveness and efficiency of the proposed improved TLBO strategy. The empirical results indicate the success of the proposed hybrid approach in which the global exploration and the local exploitation are well balanced, providing the best solutions for all instances used over other state-of-the-art metaheuristics for chaotic identification in literature, including particle swarm optimization, genetic algorithm, and quantum-inspired evolutionary algorithm.

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Acknowledgments

The authors thank Prof. Francesco Marcelloni, Dr. Anand Venugopal and the anonymous referees for their constructive comments. The last author BL is very grateful to Prof. Yew-Soon Ong (Director of the Centre for Computational Intelligence, School of Computer Engineering, Nanyang Technological University, Singapore) who has provided very useful comments and invaluable help to improve this study. The authors thank Prof. Yihui Jin, Prof. Ling Wang (Department of Automation, Tsinghua University), Prof. JiKun Huang (Center for Chinese Agricultural Policy, Chinese Academy of Sciences), Prof. Shouyang Wang (Academy of Mathematics and Systems Science, Chinese Academy of Sciences) and Royal Honored Prof. M.A. Keyzer (Faculty of Economics and Business Administration, SOW-VU, Vrije Universiteit Amsterdam, The Netherlands) for their support and training. This research is partially supported by National Natural Science Foundation of China (Grant Nos. 71101139, 71103013, and 71390330), State Key Laboratory of Intelligent Control and Decision of Complex Systems of Beijing Institute of Technology, as well as Defense Industrial Technology Development Program.

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Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Xiaoyi Feng & Bo Liu

  2. Systems Engineering Research Institute, Beijing, 100094, China

    Hongjun Zhang, Baozhu Li, Jun Zhang & Yuanhui Qin

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  1. Hongjun Zhang
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  2. Baozhu Li
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  3. Jun Zhang
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  4. Yuanhui Qin
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  5. Xiaoyi Feng
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  6. Bo Liu
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Correspondence to Bo Liu.

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Communicated by V. Loia.

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Zhang, H., Li, B., Zhang, J. et al. Parameter estimation of nonlinear chaotic system by improved TLBO strategy. Soft Comput 20, 4965–4980 (2016). https://doi.org/10.1007/s00500-015-1786-2

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