Skip to main content
SpringerLink
Log in

Multi-chaotic System Induced Success-History Based Adaptive Differential Evolution

  • Conference paper
  • First Online:
Book cover Artificial Intelligence and Soft Computing (ICAISC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9692))

Included in the following conference series:

Abstract

This research paper combines two soft computing fields – chaos theory and evolutionary computing. The proposed multi-chaotic system implements five different chaotic maps as a Pseudo-Random Number Generators (PRNGs) for parent selection process in Differential Evolution (DE) and Success-History based Adaptive Differential Evolution (SHADE) algorithms. The probabilities for selecting chaotic maps are adapted and the adaptation process is based on the previous successful solutions. Therefore, PRNG varies for different test functions. The performance of multi-chaotic system induced DE and SHADE is compared against their canonical versions on CEC2015 benchmark set. Acquired results show that replacing classic PRNG with multi-chaotic PRNG can lead sto improvement in terms of convergence speed and ability to reach the global optimum.

A. Viktorin—This work was supported by the Programme EEA and Norway Grants for funding via grant on Institutional cooperation project nr. NF-CZ07-ICP-4-345-2016, also 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 Programme Project no. LO1303 (MSMT-7778/2014. Also by the European Regional Development Fund under the Project CEBIA-Tech no. CZ.1.05/2.1.00/03.0089 and by Internal Grant Agency of Tomas Bata University under the Projects no. IGA/CebiaTech/2016/007.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

References

  1. Price, K., Storn, R.M., Lampinen, J.A.: Differential Evolution: A Practical Approach to Global Optimization. Springer Science & Business Media, Heidelberg (2006)

    MATH  Google Scholar 

  2. Kim, H.K., Chong, J.K., Park, K.Y., Lowther, D.: Differential evolution strategy for constrained global optimization and application to practical engineering problems. IEEE Trans. Magn. 43(4), 1565–1568 (2007)

    Article  Google Scholar 

  3. Chauhan, N., Ravi, V., Chandra, D.K.: Differential evolution trained wavelet neural networks: Application to bankruptcy prediction in banks. Expert Syst. Appl. 36(4), 7659–7665 (2009)

    Article  Google Scholar 

  4. Storn, R.: On the usage of differential evolution for function optimization. In: 1996 Biennial Conference of the North American on Fuzzy Information Processing Society, NAFIPS 1996, pp. 519–523. IEEE, June 1996

    Google Scholar 

  5. Babu, B. V., Jehan, M.: Differential evolution for multi-objective optimization. In: The 2003 Congress on Evolutionary Computation, CEC 2003, Vol. 4, pp. 2696–2703. IEEE, December 2003

    Google Scholar 

  6. Storn, R., Price, K.: Differential Evolution-a Simple and Efficient Adaptive Scheme for Global Optimization Over Continuous Spaces, vol. 3. ICSI, Berkeley (1995)

    MATH  Google Scholar 

  7. Brest, J., Greiner, S., Bošković, 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 

  8. Omran, M.G., Salman, A., Engelbrecht, A.P.: Self-adaptive differential evolution. In: Hao, Y., Liu, J., Wang, Y., Cheung, Y., Yin, H., Jiao, L., Ma, J., Jiao, Y.C. (eds.) CIS 2005. LNCS, vol. 3801, pp. 192–199. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  9. Qin, A.K., Huang, V.L., Suganthan, P.N.: Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans. Evol. Comput. 13(2), 398–417 (2009)

    Article  Google Scholar 

  10. Zhang, J., Sanderson, A.C.: JADE: adaptive differential evolution with optional external archive. IEEE Trans. Evol. Comput. 13(5), 945–958 (2009)

    Article  Google Scholar 

  11. Tanabe, R., Fukunaga, A.: Success-history based parameter adaptation for differential evolution. In: 2013 IEEE Congress on Evolutionary Computation (CEC), pp. 71–78. IEEE, June 2013

    Google Scholar 

  12. Skanderova, L., Zelinka, I., Ŝaloun, P.: Chaos Powered Selected Evolutionary Algorithms. In: Zelinka, I., Chen, G., Rössler, O.E., Snasel, V., Abraham, A. (eds.) Nostradamus 2013: Prediction, Modeling and Analysis of Complex Systems. AISC, vol. 210, pp. 111–124. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  13. Senkerik, R., Pluhacek, M., Kominkova Oplatkova, Z., Davendra, D.: On the parameter settings for the chaotic dynamics embedded differential evolution. In: IEEE Congress on Evolutionary Computation, CEC 2015, pp. 1410–1417. IEEE, May 2015

    Google Scholar 

  14. 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 

  15. 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  MathSciNet  MATH  Google Scholar 

  16. Pluhacek, M., Senkerik, R., Zelinka, I.: Particle swarm optimization algorithm driven by multichaotic number generator. Soft Comput. 18(4), 631–639 (2014)

    Article  Google Scholar 

  17. Senkerik, R., Pluhacek, M., Oplatkova, Z.K.: An initial study on the new adaptive approach for multi-chaotic differential evolution. In: Silhavy, R., Senkerik, R., Oplatkova, Z.K., Prokopova, Z., Silhavy, P. (eds.) Artificial Intelligence Perspectives and Applications. AISC, vol. 347, pp. 355–362. Springer, Heidelberg (2015)

    Google Scholar 

  18. Chen, Q., Liu, B., Zhang, Q., Liang, J.J., Suganthan, P.N., Qu, B.Y.: Problem definition and evaluation criteria for CEC 2015 special session and competition on bound constrained single-objective computationally expensive numerical optimization. In: Computational Intelligence Laboratory, Zhengzhou University, China and Nanyang Technological University, Singapore, Technical report (2014)

    Google Scholar 

  19. Sprott, J.C., Sprott, J.C.: Chaos and Time-Series Analysis, vol. 69. Oxford University Press, Oxford (2003)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Applied Informatics, Tomas Bata University in Zlin, Nam T.G. Masaryka 5555, 760 01, Zlin, Czech Republic

    Adam Viktorin, Michal Pluhacek & Roman Senkerik

Authors
  1. Adam Viktorin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michal Pluhacek
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Roman Senkerik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Adam Viktorin .

Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Czestochowa, Poland

    Leszek Rutkowski

  2. Częstochowa University of Technology, Czestochowa, Poland

    Marcin Korytkowski

  3. Częstochowa University of Technology, Czestochowa, Poland

    Rafał Scherer

  4. AGH University of Science and Technology, Krakow, Poland

    Ryszard Tadeusiewicz

  5. University of California, Berkeley, California, USA

    Lotfi A. Zadeh

  6. University of Louisville, Louisville, Kentucky, USA

    Jacek M. Zurada

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Viktorin, A., Pluhacek, M., Senkerik, R. (2016). Multi-chaotic System Induced Success-History Based Adaptive Differential Evolution. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2016. Lecture Notes in Computer Science(), vol 9692. Springer, Cham. https://doi.org/10.1007/978-3-319-39378-0_44

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-39378-0_44

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-39377-3

  • Online ISBN: 978-3-319-39378-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation