Skip to main content

Population Diversity Analysis for the Chaotic Based Selection of Individuals in Differential Evolution

  • Conference paper
  • First Online:
Bioinspired Optimization Methods and Their Applications (BIOMA 2018)

Abstract

This research deals with the modern and popular hybridization of chaotic dynamics and evolutionary computation. It is aimed at the influence of chaotic sequences on the population diversity as well as the algorithm performance of the simple parameter adaptive Differential Evolution (DE) strategy: jDE. Experiments are focused on the extensive investigation of the different randomization schemes for the selection of individuals in DE algorithm driven by the nine different two-dimensional discrete chaotic systems, as the chaotic pseudo-random number generators. The population diversity and jDE convergence are recorded on the 15 test functions from the CEC 2015 benchmark.

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

Access this chapter

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. 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 

  2. dos Santos Coelho, 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 

  3. 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  Google Scholar 

  4. Pluhacek, M., Senkerik, R., Davendra, D., Oplatkova, Z.K., 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  Google Scholar 

  5. 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 

  6. 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 

  7. Gandomi, A.H., Yang, X.S., Talatahari, S., Alavi, A.H.: Firefly algorithm with chaos. Commun. Nonlinear Sci. Numer. Simul. 18(1), 89–98 (2013)

    Article  MathSciNet  Google Scholar 

  8. Wang, G.G., Guo, L., Gandomi, A.H., Hao, G.S., Wang, H.: Chaotic Krill Herd algorithm. Inf. Sci. 274, 17–34 (2014)

    Article  MathSciNet  Google Scholar 

  9. Zhang, C., Cui, G., Peng, F.: A novel hybrid chaotic ant swarm algorithm for heat exchanger networks synthesis. Appl. Therm. Eng. 104, 707–719 (2016)

    Article  Google Scholar 

  10. Jordehi, A.R.: Chaotic bat swarm optimisation (CBSO). Appl. Soft Comput. 26, 523–530 (2015)

    Article  Google Scholar 

  11. Wang, G.G., Deb, S., Gandomi, A.H., Zhang, Z., Alavi, A.H.: Chaotic cuckoo search. Soft. Comput. 20(9), 3349–3362 (2016)

    Article  Google Scholar 

  12. dos Santos Coelho, L., 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)

    MathSciNet  MATH  Google Scholar 

  13. 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 

  14. 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 

  15. 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 

  16. 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  Google Scholar 

  17. 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 

  18. 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 

  19. Price, K., Storn, R.M., Lampinen, J.A.: Differential Evolution: A Practical Approach to Global Optimization. Springer Science & Business Media, Heidelberg (2006). https://doi.org/10.1007/3-540-31306-0

    Book  MATH  Google Scholar 

  20. Das, S., Mullick, S.S., Suganthan, P.N.: Recent advances in differential evolution-an updated survey. Swarm Evol. Comput. 27, 1–30 (2016)

    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. Mininno, E., Neri, F., Cupertino, F., Naso, D.: Compact differential evolution. IEEE Trans. Evol. Comput. 15(1), 32–54 (2011)

    Article  Google Scholar 

  23. 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 

  24. Brest, J., Korošec, P., Šilc, J., Zamuda, A., Bošković, B., Maučec, M.S.: Differential evolution and differential ant-stigmergy on dynamic optimisation problems. Int. J. Syst. Sci. 44(4), 663–679 (2013)

    Article  MathSciNet  Google Scholar 

  25. Tanabe, R., Fukunaga, A.S.: Improving the search performance of shade using linear population size reduction. In: 2014 IEEE Congress on Evolutionary Computation (CEC), pp. 1658–1665. IEEE (2014)

    Google Scholar 

  26. Senkerik, R., Pluhacek, M., Zelinka, I., Viktorin, A., Kominkova Oplatkova, Z.: Hybridization of multi-chaotic dynamics and adaptive control parameter adjusting jDE strategy. In: Matoušek, R. (ed.) ICSC-MENDEL 2016. AISC, vol. 576, pp. 77–87. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-58088-3_8

    Chapter  Google Scholar 

  27. Senkerik, R., Pluhacek, M., Zelinka, I., Davendra, D., Janostik, J.: Preliminary study on the randomization and sequencing for the chaos embedded heuristic. In: Abraham, A., Wegrzyn-Wolska, K., Hassanien, A.E., Snasel, V., Alimi, A.M. (eds.) Proceedings of the Second International Afro-European Conference for Industrial Advancement AECIA 2015. AISC, vol. 427, pp. 591–601. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-29504-6_55

    Chapter  Google Scholar 

  28. Sprott, J.C., Sprott, J.C.: Chaos and Time-Series Analysis, vol. 69. Citeseer (2003)

    Google Scholar 

  29. Poláková, R., Tvrdík, J., Bujok, P., Matoušek, R.: Population-size adaptation through diversity-control mechanism for differential evolution. In: MENDEL, 22th International Conference on Soft Computing, pp. 49–56 (2016)

    Google Scholar 

  30. Viktorin, A., Pluhacek, M., Senkerik, R.: Success-history based adaptive differential evolution algorithm with multi-chaotic framework for parent selection performance on CEC2014 benchmark set. In: 2016 IEEE Congress on Evolutionary Computation (CEC), pp. 4797–4803. IEEE (2016)

    Google Scholar 

Download references

Acknowledgements

This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme Project no. LO1303 (MSMT-7778/2014), further 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/2018/003. This work is also based upon support by COST (European Cooperation in Science & Technology) under Action CA15140, Improving Applicability of Nature-Inspired Optimisation by Joining Theory and Practice (ImAppNIO), and Action IC406, High-Performance Modelling and Simulation for Big Data Applications (cHiPSet).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Roman Senkerik .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Senkerik, R., Viktorin, A., Pluhacek, M., Kadavy, T. (2018). Population Diversity Analysis for the Chaotic Based Selection of Individuals in Differential Evolution. In: Korošec, P., Melab, N., Talbi, EG. (eds) Bioinspired Optimization Methods and Their Applications. BIOMA 2018. Lecture Notes in Computer Science(), vol 10835. Springer, Cham. https://doi.org/10.1007/978-3-319-91641-5_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-91641-5_24

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91640-8

  • Online ISBN: 978-3-319-91641-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics