SHADE Algorithm Dynamic Analyzed Through Complex Network

  • Adam ViktorinEmail author
  • Roman Senkerik
  • Michal Pluhacek
  • Tomas Kadavy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10392)


In this preliminary study, the dynamic of continuous optimization algorithm Success-History based Adaptive Differential Evolution (SHADE) is translated into a Complex Network (CN) and the basic network feature, node degree centrality, is analyzed in order to provide helpful insight into the inner workings of this state-of-the-art Differential Evolution (DE) variant. The analysis is aimed at the correlation between objective function value of an individual and its participation in production of better offspring for the future generation. In order to test the robustness of this method, it is evaluated on the CEC2015 benchmark in 10 and 30 dimensions.


Differential evolution SHADE Complex network Centrality 


  1. 1.
    Storn, R., Price, K.: Differential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces, vol. 3. ICSI, Berkeley (1995)Google Scholar
  2. 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)CrossRefGoogle Scholar
  3. 3.
    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)CrossRefGoogle Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    Mininno, E., Neri, F., Cupertino, F., Naso, D.: Compact differential evolution. IEEE Trans. Evol. Comput. 15(1), 32–54 (2011)CrossRefGoogle Scholar
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1(1), 67–82 (1997)CrossRefGoogle Scholar
  9. 9.
    Das, S., Mullick, S.S., Suganthan, P.N.: Recent advances in differential evolution-an updated survey. Swarm Evol. Comput. 27, 1–30 (2016)CrossRefGoogle Scholar
  10. 10.
    Omran, M.G.H., 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). doi: 10.1007/11596448_28 CrossRefGoogle Scholar
  11. 11.
    Zhang, J., Sanderson, A.C.: JADE: adaptive differential evolution with optional external archive. IEEE Trans. Evol. Comput. 13(5), 945–958 (2009)CrossRefGoogle Scholar
  12. 12.
    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 2013Google Scholar
  13. 13.
    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, July 2014Google Scholar
  14. 14.
    Brest, J., Maučec, M.S., Bošković, B.: iL-SHADE: improved L-SHADE algorithm for single objective real-parameter optimization. In: 2016 IEEE Congress on Evolutionary Computation (CEC), pp. 1188–1195. IEEE, July 2016Google Scholar
  15. 15.
    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, July 2016Google Scholar
  16. 16.
    Poláková, R., Tvrdík, J., Bujok, P.: L-SHADE with competing strategies applied to CEC 2015 Learning-based Test Suite. In: 2016 IEEE Congress on Evolutionary Computation (CEC), pp. 4790–4796. IEEE, July 2016Google Scholar
  17. 17.
    Awad, N.H., Ali, M.Z., Suganthan, P.N., Reynolds, R.G.: An ensemble sinusoidal parameter adaptation incorporated with L-SHADE for solving CEC 2014 benchmark problems. In: 2016 IEEE Congress on Evolutionary Computation (CEC), pp. 2958–2965. IEEE, July 2016Google Scholar
  18. 18.
    Tanabe, R., Fukunaga, A.: How far are we from an optimal, adaptive DE? In: Handl, J., Hart, E., Lewis, P.R., López-Ibáñez, M., Ochoa, G., Paechter, B. (eds.) PPSN 2016. LNCS, vol. 9921, pp. 145–155. Springer, Cham (2016). doi: 10.1007/978-3-319-45823-6_14 CrossRefGoogle Scholar
  19. 19.
    Viktorin, A., Pluhacek, M., Senkerik, R.: Network based linear population size reduction in SHADE. In: 2016 International Conference on Intelligent Networking and Collaborative Systems (INCoS), pp. 86–93. IEEE, September 2016Google Scholar
  20. 20.
    Skanderova, L., Fabian, T.: Differential evolution dynamics analysis by complex networks. Soft Comput. 1–15 (2015)Google Scholar
  21. 21.
    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. Computational Intelligence Laboratory, Zhengzhou University, China and Nanyang Technological University, Singapore, Technical Report (2014)Google Scholar
  22. 22.
    Viktorin, A., Senkerik, R., Pluhacek, M., Kadavy, T.: CSoNet 2017 data (2017).

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Adam Viktorin
    • 1
    Email author
  • Roman Senkerik
    • 1
  • Michal Pluhacek
    • 1
  • Tomas Kadavy
    • 1
  1. 1.Faculty of Applied InformaticsTomas Bata University in ZlinZlinCzech Republic

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