Skip to main content

Advertisement

Springer Nature Link
Log in

A hybrid adaptive cuckoo search optimization algorithm for the problem of chaotic systems parameter estimation

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

This paper introduces a novel hybrid adaptive cuckoo search (HACS) algorithm to establish the parameters of chaotic systems. In order to balance and enhance the accuracy and convergence rate of the basic cuckoo search (CS) algorithm, the adaptive parameters adjusting operation is presented to tune the parameters properly. Besides, the exploitation capability of the CS algorithm is enhanced a lot by integrating the orthogonal design strategy. The functionality of the HACS algorithm is tested through the Lorenz system under the noise-free and noise-corrupted conditions, respectively. The numerical results demonstrate that the algorithm can estimate parameters efficiently and accurately, and the capability of noise immunity is also powerful. Compared with the basic CS algorithm, genetic algorithm, and particle swarm optimization algorithm, the HACS algorithm is energy efficient and superior.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

References

  1. Parlitz U (1996) Estimating model parameters from time series by autosynchronization. Phys Rev Lett 76(8):1232–1244

    Article  Google Scholar 

  2. Sitz A, Schwarz U, Kurths J, Voss HU (2002) Estimation of parameters and unobserved components for nonlinear systems from noisy time series. Phys Rev E 66(1):016210–016223

    Article  Google Scholar 

  3. Guo LX, Hu MF, Xu ZY (2013) Synchronization and chaos control by quorum sensing mechanism. Nonlinear Dyn 73(3):1253–1269

    Article  MathSciNet  MATH  Google Scholar 

  4. Abarbanel HDI, Rulkov NF, Sushchik MM (1996) Generalized synchronization of chaos: the auxiliary system approach. Phys Rev E 53(5):4528–4535

    Article  Google Scholar 

  5. Quinn JC, Bryant PH, Creveling DR, Klein SR, Abarbanel HDI (2009) Parameter and state estimation of experimental chaotic systems using synchronization. Phys Rev E 80(1):016201–016213

    Article  MathSciNet  Google Scholar 

  6. Agiza HN, Yassen MT (2001) Synchronization of Rossler and Chen chaotic dynamical systems using active control. Phys Lett A 278(4):191–197

    Article  MathSciNet  MATH  Google Scholar 

  7. Garcia-Nieto J, Olivera AC, Alba E (2013) Optimal cycle program of traffic lights with particle swarm optimization. IEEE Trans Evol Comput 17(6):823–839

    Article  Google Scholar 

  8. Salahi M, Jamalian A, Taati A (2013) Global minimization of multi-funnel functions using particle swarm optimization. Neural Comput Appl 23(7–8):2101–2106

    Article  Google Scholar 

  9. Gandomi AH, Yang XS, Alavi AH (2011) Mixed variable structural optimization using firefly algorithm. Comput Struct 89(23–24):2325–2336

    Article  Google Scholar 

  10. Chao T, Yu Z, Jack JJ (2007) Estimating system parameters from chaotic time series with synchronization optimized by a genetic algorithm. Phys Rev E 76(1):016209–016214

    Article  Google Scholar 

  11. Deb K, Pratap A, Agarwal S (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  12. Yao L, Sethares WA (1994) Nonlinear parameter estimation via the genetic algorithm. IEEE Trans Signal Process 42(4):927–935

    Article  Google Scholar 

  13. Yang XS, Deb S (2009) Cuckoo search via Lévy flights. Proceedings of world congress on nature & biologically inspired computing. IEEE Publications, UAS, pp 210–214

    Google Scholar 

  14. Yang XS, Deb S (2010) Engineering optimization by cuckoo search. Int J Math Model Num Opt 1(4):330–343

    MATH  Google Scholar 

  15. Amir HG, Yang XS, Amir HA (2013) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Eng Comput 29(1):17–35

    Article  Google Scholar 

  16. Li XT, Wang JN, Yin MH (2014) Enhancing the performance of cuckoo search algorithm using orthogonal learning method. Neural Comput Appl 24(6):1233–1247

    Article  Google Scholar 

  17. Gandomi AH, Yang XS, Talatahari S, Deb S (2012) Coupled eagle strategy and differential evolution for unconstrained and constrained global optimization. Comput Math Appl 63(1):191–200

    Article  MathSciNet  MATH  Google Scholar 

  18. Long W, Liang X, Huang YF (2014) An effective hybrid cuckoo search algorithm for constrained global optimization. Neural Comput Appl 25(3–4):911–926

    Article  Google Scholar 

  19. Zheng HQ, Zhou Y (2012) A novel cuckoo search optimization algorithm based on Gauss distribution. J Comput Inf Syst 8:4193–4200

    Google Scholar 

  20. Valian E, Mohanna S, Tavakoli S (2011) Improved cuckoo search algorithm for feedforward neural network training. Int J Artif Intell Appl 2(3):36–43

    Google Scholar 

  21. Ouaarab A, Ahiod B, Yang XS (2014) Discrete cuckoo search algorithm for the travelling salesman problem. Neural Comput Appl 24(7–8):1659–1669

    Article  Google Scholar 

  22. Walton S, Hassan O, Morgan K, Brown MR (2011) Modified cuckoo search: a new gradient free optimization algorithm. Chaos Solitons Fractals 44(9):710–718

    Article  Google Scholar 

  23. Yang XS, Deb S (2014) Cuckoo search: recent advances and applications. Neural Comput Appl 24(1):169–174

    Article  Google Scholar 

  24. Payne RB, Sorenson MD, Klitz K (2005) The cuckoos. Oxford University Press, Oxford, pp 12–58

    Google Scholar 

  25. Barthelemy P, Bertolotti J, Wiersma DS (2008) A Lévy flight for flight. Nature 453(7194):495–498

    Google Scholar 

  26. Pavlyukevich I (2007) Lévy flight, non-local search and simulated annealing. J Comput Phys 226(2):1830–1844

    Article  MathSciNet  MATH  Google Scholar 

  27. Li XT, Yin XT (2012) Parameter estimation for chaotic systems using the cuckoo search algorithm with an orthogonal learning method. Chin Phys B 21(5):050507–050513

    Article  Google Scholar 

  28. Leung TW, Wang Y (2001) An orthogonal genetic algorithm with quantization for global numerical optimization. IEEE Trans Evol Comput 5(1):41–53

    Article  Google Scholar 

  29. Hick CR (1993) Fundamental concepts in the design of experiments. Saunders College Publishing, TX, pp 12–36

    Google Scholar 

  30. Montgomery DC (1991) Design and analysis of experiments. Wiley, New York, pp 10–21

    Google Scholar 

Download references

Acknowledgments

This work is supported by National Natural Science Foundation of China under Grant No. 61271106.

Author information

Authors and Affiliations

  1. National Key Laboratory on Electromagnetic Environmental Effects and Electro-optical Engineering, PLA University of Science and Technology, Nanjing, 210007, Jiangsu, People’s Republic of China

    Jun Wang & Bihua Zhou

Authors
  1. Jun Wang
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Bihua Zhou
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Jun Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, J., Zhou, B. A hybrid adaptive cuckoo search optimization algorithm for the problem of chaotic systems parameter estimation. Neural Comput & Applic 27, 1511–1517 (2016). https://doi.org/10.1007/s00521-015-1949-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-015-1949-1

Keywords