Skip to main content

Hybridization of Multi-chaotic Dynamics and Adaptive Control Parameter Adjusting jDE Strategy

  • Conference paper
  • First Online:
Recent Advances in Soft Computing (ICSC-MENDEL 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 576))

Included in the following conference series:


This research deals with the hybridization of several approaches for evolutionary algorithms, which are the adaptive control parameter adjusting strategy and multi-chaotic dynamics driving the selection of indices in Differential Evolution (DE). The novelty of the paper is given by the experiments with the multi-chaos-driven adaptive DE concept inside adaptive parameter adjusting DE strategies. These experiments are representing the investigations on the mutual influences of several different randomizations types together with adaptive DE strategies. The multi-chaotic concept is representing the adaptive switching between two different chaotic systems based on the progress of individuals within population. This paper is aimed at the embedding of discrete dissipative chaotic systems in the form of multi-chaotic pseudo random number generators for the jDE, which is the state of the art representative of simple adaptive control parameter adjusting strategy for DE. Repeated simulations for two different combinations of driving chaotic systems were performed on the IEEE CEC 13 benchmark set. Finally, the obtained results are compared with the canonical not-chaotic jDE.

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

Access this chapter

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions


  1. Price, K.V.: An introduction to differential evolution. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization, pp. 79–108. McGraw-Hill Ltd., London (1999)

    Google Scholar 

  2. Brest, J., Greiner, S., Boskovic, B., Mernik, M., Zumer, V.: Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans. Evol. Comput. 10(6), 646–657 (2006)

    Article  Google Scholar 

  3. Mallipeddi, R., Suganthan, P.N., Pan, Q.K., Tasgetiren, M.F.: Differential evolution algorithm with ensemble of parameters and mutation strategies. Appl. Soft Comput. 11(2), 1679–1696 (2011)

    Article  Google Scholar 

  4. Neri, F., Tirronen, V.: Recent advances in differential evolution: a survey and experimental analysis. Artif. Intell. Rev. 33(1–2), 61–106 (2010)

    Article  Google Scholar 

  5. Weber, M., Neri, F., Tirronen, V.: A study on scale factor in distributed differential evolution. Inf. Sci. 181(12), 2488–2511 (2011)

    Article  Google Scholar 

  6. Neri, F., Iacca, G., Mininno, E.: Disturbed Exploitation compact Differential Evolution for limited memory optimization problems. Inf. Sci. 181(12), 2469–2487 (2011)

    Article  MathSciNet  Google Scholar 

  7. Iacca, G., Caraffini, F., Neri, F.: Compact differential evolution light: high performance despite limited memory requirement and modest computational overhead. J. Comput. Sci. Technol. 27(5), 1056–1076 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Zamuda, A., Brest, J.: Self-adaptive control parameters׳ randomization frequency and propagations in differential evolution. Swarm Evol. Comput. 25, 72–99 (2015)

    Article  Google Scholar 

  9. Caponetto, R., Fortuna, L., Fazzino, S., Xibilia, M.G.: Chaotic sequences to improve the performance of evolutionary algorithms. IEEE Trans. Evol. Comput. 7(3), 289–304 (2003)

    Article  Google Scholar 

  10. Davendra, D., Zelinka, I., Senkerik, R.: Chaos driven evolutionary algorithms for the task of PID control. Comput. Math Appl. 60(4), 1088–1104 (2010)

    Article  MATH  Google Scholar 

  11. Zelinka, I.: SOMA — self-organizing migrating algorithm. In: Onwubolu, G.C., Babu, B.V. (eds.) New Optimization Techniques in Engineering. STUDFUZZ, vol. 141, pp. 167–217. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. dos Santos Coelhoa, L., Mariani, V.C.: A novel chaotic particle swarm optimization approach using Hénon map and implicit filtering local search for economic load dispatch. Chaos, Solitons Fractals 39(2), 510–518 (2009)

    Article  Google Scholar 

  13. Pluhacek, M., Senkerik, R., Davendra, D., Kominkova Oplatkova, Z., Zelinka, I.: On the behavior and performance of chaos driven PSO algorithm with inertia weight. Comput. Math Appl. 66(2), 122–134 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  14. Pluhacek, M., Senkerik, R., Zelinka, I., Davendra, D.: Chaos PSO algorithm driven alternately by two different chaotic maps - An initial study. In: 2013 IEEE Congress on Evolutionary Computation (CEC), 20–23 June 2013, pp 2444–2449 (2013)

    Google Scholar 

  15. Pluhacek, M., Senkerik, R., Davendra, D.: Chaos particle swarm optimization with Eensemble of chaotic systems. Swarm Evol. Comput. 25, 29–35 (2015)

    Article  Google Scholar 

  16. Metlicka, M., Davendra, D.: Chaos driven discrete artificial bee algorithm for location and assignment optimisation problems. Swarm Evol. Comput. 25, 15–28 (2015)

    Article  Google Scholar 

  17. Coelho, L.D.S., Ayala, H.V.H., Mariani, V.C.: A self-adaptive chaotic differential evolution algorithm using gamma distribution for unconstrained global optimization. Appl. Math. Comput. 234, 452–459 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  18. Senkerik, R., Pluhacek, M., Davendra, D., Zelinka, I., Oplatkova, Z.K.: Performance testing of multi-chaotic differential evolution concept on shifted benchmark functions. In: Polycarpou, M., Carvalho, A.C.P.L.F., Pan, J.-S., Woźniak, M., Quintian, H., Corchado, E. (eds.) HAIS 2014. LNCS (LNAI), vol. 8480, pp. 306–317. Springer, Cham (2014). doi:10.1007/978-3-319-07617-1_28

    Chapter  Google Scholar 

  19. Senkerik, R., Pluhacek, M., Davendra, D., Zelinka, I., Oplatkova, Z.K., Janostik, J.: Hybridization of adaptivity and chaotic dynamics for differential evolution. In: Matoušek, R. (ed.) Mendel 2015. AISC, vol. 378, pp. 149–158. Springer, Cham (2015). doi:10.1007/978-3-319-19824-8_12

    Chapter  Google Scholar 

  20. Zelinka, I.: A survey on evolutionary algorithms dynamics and its complexity – mutual relations, past, present and future. Swarm Evol. Comput. 25, 2–14 (2015)

    Article  Google Scholar 

  21. Das, S., Abraham, A., Chakraborty, U.K., Konar, A.: Differential evolution using a neighborhood-based mutation operator. IEEE Trans. Evol. Comput. 13(3), 526–553 (2009)

    Article  Google Scholar 

  22. Price, K.V., Storn, R.M., Lampinen, J.A.: Differential Evolution - A Practical Approach to Global Optimization. Natural Computing Series. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  23. Tvrdík, J., Poláková, R., Veselský, J., Bujok, P.: Adaptive variants of differential evolution: towards control-parameter-free optimizers. In: Zelinka, I., Snášel, V., Abraham, A. (eds.) Handbook of Optimization. ISRL, vol. 38, pp. 423–449. Springer, Berlin Heidelberg (2013)

    Chapter  Google Scholar 

  24. ELabbasy, E., Agiza, H., EL-Metwally, H., Elsadany, A.: Bifurcation analysis, chaos and control in the burgers mapping. Int. J. Nonlinear Sci. 4(3), 171–185 (2007)

    MathSciNet  Google Scholar 

  25. Sprott, J.C.: Chaos and Time-Series Analysis. Oxford University Press, New York (2003)

    MATH  Google Scholar 

  26. Liang, J.J., Qu, B.-Y., Suganthan, P.N., Hernández-Díaz, A.G.: Problem Definitions and Evaluation Criteria for the CEC 2013 Special Session and Competition on Real-Parameter Optimization, Technical Report 201212, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical report, Nanyang Technological University, Singapore (2013)

    Google Scholar 

Download references


This work was supported by Grant Agency of the Czech Republic - GACR P103/15/06700S, further by the Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Pro- gramme project No. LO1303 (MSMT-7778/2014) and also by the European Regional Development Fund under the project CEBIA-Tech No. CZ.1.05/2.1.00/03.0089., partially supported by Grant of SGS No. SP2016/175 of VSB - Technical University of Ostrava, Czech Republic and by Internal Grant Agency of Tomas Bata University under the project No. IGA/CebiaTech/2016/007.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Roman Senkerik .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Senkerik, R., Pluhacek, M., Zelinka, I., Viktorin, A., Kominkova Oplatkova, Z. (2017). Hybridization of Multi-chaotic Dynamics and Adaptive Control Parameter Adjusting jDE Strategy. In: Matoušek, R. (eds) Recent Advances in Soft Computing. ICSC-MENDEL 2016. Advances in Intelligent Systems and Computing, vol 576. Springer, Cham.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58087-6

  • Online ISBN: 978-3-319-58088-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics