Study on the Development of Complex Network for Evolutionary and Swarm Based Algorithms

  • Roman Senkerik
  • Ivan Zelinka
  • Michal Pluhacek
  • Adam Viktorin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10062)


This contribution deals with the hybridization of complex network frameworks and metaheuristic algorithms. The population is visualized as an evolving complex network that exhibits non-trivial features. It briefly investigates the time and structure development of a complex network within a run of selected metaheuristic algorithms – i.e. PSO and Differential Evolution (DE). Two different approaches for the construction of complex networks are presented herein. It also briefly discusses the possible utilization of complex network attributes. These attributes include an adjacency graph that depicts interconnectivity, while centralities provide an overview of convergence and stagnation, and clustering encapsulates the diversity of the population, whereas other attributes show the efficiency of the network. The experiments were performed for one selected DE/PSO strategy and one simple test function.


Complex networks Graphs Analysis Differential Evolution PSO 



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 Programme 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.


  1. 1.
    Zelinka, I., Davendra, D., Lampinen, J., Senkerik, R., Pluhacek, M.: Evolutionary algorithms dynamics and its hidden complex network structures. In: 2014 IEEE Congress on Evolutionary Computation (CEC), pp. 3246–3251 (2014)Google Scholar
  2. 2.
    Davendra, D., Zelinka, I., Metlicka, M., Senkerik, R., Pluhacek, M.: Complex network analysis of differential evolution algorithm applied to flowshop with no-wait problem. In: 2014 IEEE Symposium on Differential Evolution (SDE), pp. 1–8 (2014)Google Scholar
  3. 3.
    Davendra, D., Zelinka, I., Senkerik, R., Pluhacek, M.: Complex network analysis of evolutionary algorithms applied to combinatorial optimisation problem. In: Kömer, P., Abraham, A., Snášel, V. (eds.) Proceedings of the Fifth International Conference on Innovations in Bio-Inspired Computing and Applications IBICA 2014. AISC, vol. 303, pp. 141–150. Springer, Cham (2014). doi: 10.1007/978-3-319-08156-4_15 Google Scholar
  4. 4.
    Skanderova, L., Fabian, T.: Differential evolution dynamics analysis by complex networks. Soft. Comput. 21, 1–15 (2015)Google Scholar
  5. 5.
    Metlicka, M., Davendra, D.: Ensemble centralities based adaptive Artificial Bee algorithm. In: 2015 IEEE Congress on Evolutionary Computation (CEC), pp. 3370–3376 (2015)Google Scholar
  6. 6.
    Gajdos, P., Kromer, P., Zelinka, I.: Network visualization of population dynamics in the differential evolution. In: 2015 IEEE Symposium Series on Computational Intelligence, pp. 1522–1528 (2015)Google Scholar
  7. 7.
    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. (1999)Google Scholar
  8. 8.
    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: IEEE International Conference on Neural Networks, Nov/Dec 1995, pp. 1942–1948 (1995)Google Scholar
  9. 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)CrossRefGoogle Scholar
  10. 10.
    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
  11. 11.
    Jabeen, H., Jalil, Z., Baig, A.R.: Opposition based initialization in particle swarm optimization (O-PSO). Paper Presented at the Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference (2009)Google Scholar
  12. 12.
    Engelbrecht, A.P.: Heterogeneous particle swarm optimization. In: Dorigo, M., et al. (eds.) ANTS 2010. LNCS, vol. 6234, pp. 191–202. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-15461-4_17 CrossRefGoogle Scholar
  13. 13.
    Janostik, J., Pluhacek, M., Senkerik, R., Zelinka, I.: Particle swarm optimizer with diversity measure based on swarm representation in complex network. 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. 561–569. Springer, Cham (2016). doi: 10.1007/978-3-319-29504-6_52 CrossRefGoogle Scholar
  14. 14.
    Das, S., Mullick, S.S., Suganthan, P.: Recent advances in differential evolution – an updated survey. Swarm Evol. Comput. 27, 1–30 (2016)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Roman Senkerik
    • 1
  • Ivan Zelinka
    • 2
  • Michal Pluhacek
    • 1
  • Adam Viktorin
    • 1
  1. 1.Faculty of Applied InformaticsTomas Bata University in ZlinZlinCzech Republic
  2. 2.Faculty of Electrical Engineering and Computer ScienceTechnical University of OstravaOstrava-PorubaCzech Republic

Personalised recommendations