Soft Computing

, Volume 22, Issue 24, pp 8317–8339 | Cite as

Parameter identification of chaotic systems using a shuffled backtracking search optimization algorithm

  • Morteza Alinia Ahandani
  • Amir Rikhtehgar Ghiasi
  • Hamed Kharrati
Methodologies and Application


An accurate mathematical model has a vital role in controlling and synchronization of chaotic systems. But generally in real-world problems, parameters are mixed with mismatches and distortions. This paper proposes two simple but effective estimation methods to detect the unknown parameters of chaotic models. These methods focus on improving the performance of a recently proposed evolutionary algorithm called backtracking search optimization algorithm (BSA). In this research firstly, a new operator to generate initial trial population is proposed. Then a group search ability is provided for the BSA by proposing a shuffled BSA (SBSA). Grouping population into several sets can provide a better exploration of search space, and an independent local search of each group increases exploitation ability of the BSA. Also new proposed operator to generate initial trial population, by providing a deep search, increases considerably the quality of solutions. The superiority of the proposed algorithms is investigated on parameter identification of 10 typical chaotic systems. Practical experiences and nonparametric analysis of obtained results show that both of the proposed ideas to improve performance of original BSA are very effective and robust so that the BSA by aforementioned ideas produces similar and promising results over repeated runs. A considerably better performance of proposed algorithms based on average of objective functions demonstrates that the proposed ideas can evolve robustness and consistence of BSA. A comparison of the proposed algorithms in this study with respect to other algorithms reported in the literature confirms a considerably better performance of proposed algorithms.


Chaotic models Backtracking search optimization algorithm Group search Shuffled BSA 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Humans were not involved in this submission.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Morteza Alinia Ahandani
    • 1
  • Amir Rikhtehgar Ghiasi
    • 1
  • Hamed Kharrati
    • 1
  1. 1.Department of Control Engineering, Faculty of Electrical and Computer EngineeringUniversity of TabrizTabrizIran

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