A New Multi-objective Evolution Model for Community Detection in Multi-layer Networks

  • Xuejiao Chen
  • Xianghua Li
  • Yue Deng
  • Siqi Chen
  • Chao GaoEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11775)


In reality, many complex network systems can be abstracted to community detection in multi-layer networks, such as social relationships networks across multiple platforms. The composite community structure in multi-layer networks should be able to comprehensively reflect and describe the community structure of all layers. At present, most community detection algorithms mainly focus on the single layer networks, while those in multi-layer networks are still at the initial stage. In order to detect community structures in multi-layer networks, a new multi-objective evolution model is proposed in this paper. This model introduces the concept of modularity in different decision domains and the method of local search to iteratively optimize each layer of a network. Taking NSGA-II as the benchmark algorithm, the proposed multi-objective evolution model is applied to optimize the genetic operation and optimal solution selection strategies. The new algorithm is denoted as MulNSGA-II. The MulNSGA-II algorithm adopts the locus-based representation strategy, and integrates the genetic operation and local search. In addition, different optimal solution selection strategies are used to determine the optimal composite community structure. Experiments are carried out in real and synthetic networks, and results demonstrate the performance and effectiveness of the proposed model in multi-layer networks.


Community detection Multi-layer networks Multi-objective optimization Evolutionary algorithm 



This work is supported by National Natural Science Foundation of China (Nos. 61602391, 61402379), Natural Science Foundation of Chongqing (No. cstc2018jcyjAX0274), and in part of Southwest University Training Programs of Innovation and Entrepreneurship for Undergraduates (No. X201910635045).


  1. 1.
    Gao, C., Liu, J.M.: Network-based modeling for characterizing human collective behaviors during extreme events. IEEE Trans. Sys. Man Cybern. Syst. 46(1), 171–183 (2017)Google Scholar
  2. 2.
    Chiti, F., Dobson, C.M.: Protein misfolding, amyloid formation, and human disease: A summary of progress over the last decade. Annu. Rev. Biochem. 86, 27–68 (2017)CrossRefGoogle Scholar
  3. 3.
    Strano, E., Viana, M.P., Sorichetta, A.: Mapping road network communities for guiding disease surveillance and control strategies. Sci. Rep-UK 8(1), 4744 (2018)Google Scholar
  4. 4.
    Li, Z.T., Liu, J., Wu, K.: A multiobjective evolutionary algorithm based on structural and attribute similarities for community detection in attributed networks. IEEE Trans. Cybern. 48(7), 1963–1976 (2017)CrossRefGoogle Scholar
  5. 5.
    Liu, C.L., Liu, J., Jiang, Z.Z.: A multiobjective evolutionary algorithm based on similarity for community detection from signed social networks. IEEE Trans. Cybern. 44(12), 2274–2287 (2014)CrossRefGoogle Scholar
  6. 6.
    Gao, C., Liang, M.X., Li, X.H.: Network community detection based on the Physarum-inspired computational framework. IEEE/ACM Trans. Comput. Bi. 15(6), 1916–1928 (2018)CrossRefGoogle Scholar
  7. 7.
    Bravobenitez, B., Alexandrovakabadjova, B., Martinezjaramillo, S.: Centrality measurement of the mexican large Value payments system from the perspective of multiplex networks. Comput. Econ. 47(1), 19–47 (2016)CrossRefGoogle Scholar
  8. 8.
    Yao, Y., Zhang, R., Fan, Y.: Link prediction via layer relevance of multiplex networks. Int. J. Mod. Phys. C 28(08), 1750101 (2017)CrossRefGoogle Scholar
  9. 9.
    Ma, L.J., Gong, M.G., Yan, J.N., Liu, W.F., Wang, S.F.: Detecting composite communities in multiplex networks: a multilevel memetic algorithm. Swarm Evol. Comput. 39, 177–191 (2018)CrossRefGoogle Scholar
  10. 10.
    Taylor, D., Shai, S., Stanley, N., Mucha, P.J.: Enhanced detectability of community structure in multilayer networks through layer aggregation. Phys. Rev. Lett. 116(22), 228301 (2016)CrossRefGoogle Scholar
  11. 11.
    Xuan, Q., Ma, X.D., Fu, C.B., Dong, H., Zhang, G.J.: Heterogeneous multidimensional scaling for complex networks. Int. J. Mod. Phy. C. 26(02), 1550023 (2015)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Dai, C.Y., Chen, L., Li, B., Li, Y.: Link prediction in multi-relational networks based on relational similarity. Inform. Sci. 394, 198–216 (2017)CrossRefGoogle Scholar
  13. 13.
    Pitsik, E., et al.: Inter-layer competition in adaptive multiplex network. New J. Phy. 20(7), 075004 (2018)CrossRefGoogle Scholar
  14. 14.
    Boutemine, O., Bouguessa, M.: Mining community structures in multidimensional networks. ACM Trans. Knowl. Discov. Data 11(4), 51 (2017)CrossRefGoogle Scholar
  15. 15.
    Li, Z.T., Liu, J., Wu, K.: A multiobjective evolutionary algorithm based on structural and attribute similarities for community detection in attributed networks. IEEE Trans. Cybern. 48(7), 1963–1976 (2017)CrossRefGoogle Scholar
  16. 16.
    Wang, Z., Wang, L., Szolnoki, A., Perc, M.: Evolutionary games on multilayer networks: A colloquium. Eur. Phys. J. B 88(5), 124 (2015)CrossRefGoogle Scholar
  17. 17.
    Pizzuti, C.: Evolutionary computation for community detection in networks: A review. IEEE Trans. Evol. Comput. 22(3), 464–483 (2018)CrossRefGoogle Scholar
  18. 18.
    Chen, X.J., Liu, Y.X., Li, X.H., Wang, Z., Wang, S.X., Gao, C.: A new evolutionary multiobjective model for traveling salesman problem. IEEE Access. 7, 66964–66979 (2019). Scholar
  19. 19.
    Purshouse, R.C., Deb, K., Mansor, M.M., Mostaghim, S., Wang, R.: A review of hybrid evolutionary multiple criteria decision making methods. In: 2014 IEEE Congress on Evolutionary Computation (CEC), pp. 1147–1154 (2014)Google Scholar
  20. 20.
    Bródka, P.: A method for group extraction and analysis in multi-layered social networks. Ph.D. disertation, Wroclaw, Poland, (2012).
  21. 21.
    Lancichinetti, A., Fortunato, S., Radicchi, F.: Benchmark graphs for testing community detection algorithms. Phys. Rev. E 78(4), 046110 (2008)CrossRefGoogle Scholar
  22. 22.
    Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. 69(2), 026113 (2004)Google Scholar
  23. 23.
    Amelio, A., Pizzuti, C.: Community detection in multidimensional networks. In: 2014 IEEE Proceedings of the 26th International Conference on Tools with Artificial Intelligence, pp. 352–359 (2014)Google Scholar
  24. 24.
    Pizzuti, C., Socievole, A.: Many-objective optimization for community detection in multi-layer networks. In: 2017 IEEE Congress on Evolutionary Computation (CEC), pp. 411–418 (2017)Google Scholar
  25. 25.
    Liu, W.F., Wang, S.F., Gong, M.: An improved multiobjective evolutionary approach for community detection in multilayer networks. In: 2017 IEEE Congress on Evolutionary Computation (CEC), pp. 443–449 (2017)Google Scholar
  26. 26.
    Lancichinetti, A., Fortunato, S.: Consensus clustering in complex networks. Sci. Rep. 2, 336 (2012). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Xuejiao Chen
    • 1
  • Xianghua Li
    • 1
  • Yue Deng
    • 1
  • Siqi Chen
    • 2
  • Chao Gao
    • 1
    Email author
  1. 1.School of Computer and Information ScienceSouthwest UniversityChongqingChina
  2. 2.College of Intelligence and ComputingTianjin UniversityTianjinChina

Personalised recommendations