Soft Computing

, Volume 21, Issue 5, pp 1253–1270 | Cite as

Noisy extremal optimization

Methodologies and Application


Noisy extremal optimization is a new optimization-based heuristic designed to identify the community structure of complex networks by maximizing the modularity function. The extremal optimization algorithm evolves configurations that represent network covers, composed of nodes evaluated separately. Each iteration, a number of nodes having the worst fitness values are randomly assigned different communities. A network shifting procedure is used to induce a noise in the population as a diversity preserving mechanism. Numerical experiments, performed on synthetic and real-world networks, illustrate the potential of this approach.


  1. Amiri B, Hossain L, Crawford JW, Wigand RT (2013) Community detection in complex networks. Knowl Based Syst 46:1–11CrossRefGoogle Scholar
  2. Boettcher S, Percus A (2000) Nature’s way of optimizing. Artif Intell 119(1):275–286CrossRefMATHGoogle Scholar
  3. Boettcher S, Percus AG (2001) Optimization with extremal dynamics. Phys Rev Lett 86:5211–5214CrossRefMATHGoogle Scholar
  4. Boettcher S, Percus AG (2003) Extremal optimization: an evolutionary local-search algorithm. In: Computational modeling and problem solving in the networked world. Springer US, pp 61–77Google Scholar
  5. Duch J, Arenas A (2005) Community detection in complex networks using extremal optimization. Phys Rev E 72:027104CrossRefGoogle Scholar
  6. Folino F, Pizzuti C (2014) An evolutionary multiobjective approach for community discovery in dynamic networks. IEEE Trans Knowl Data Eng 26(8):1–1CrossRefGoogle Scholar
  7. Fortunato S (2010) Community detection in graphs. Phys Rep 486(3):75–174MathSciNetCrossRefGoogle Scholar
  8. Fortunato S, Barthelemy M (2007) Resolution limit in community detection. Proc Natl Acad Sci 104(1):36–41CrossRefGoogle Scholar
  9. Girvan M, Newman MEJ (2002) Community structure in social and biological networks. Proc Natl Acad Sci 99(12):7821–7826MathSciNetCrossRefMATHGoogle Scholar
  10. Gong M, Fu B, Jiao L, Du H (2011) Memetic algorithm for community detection in networks. Phys Rev E 84:056101CrossRefGoogle Scholar
  11. Gong M, Ma L, Zhang Q, Jiao L (2012) Community detection in networks by using multiobjective evolutionary algorithm with decomposition. Phys A 391(15):4050–4060CrossRefGoogle Scholar
  12. Gong M, Cai Q, Chen X, Ma L (2014a) Complex network clustering by multiobjective discrete particle swarm optimization based on decomposition. IEEE Trans Evol Comput 18(1):82–97CrossRefGoogle Scholar
  13. Gong M, Liu J, Ma L, Cai Q, Jiao L (2014b) Novel heuristic density-based method for community detection in networks. Phys A 403:71–84CrossRefGoogle Scholar
  14. Grappiolo C, Togelius J, Yannakakis GN (2013) Shifting niches for community structure detection. In: 2013 IEEE congress on evolutionary computation (CEC), pp 111–118. IEEEGoogle Scholar
  15. Honghao C, Zuren F, Zhigang R (2013) Community detection using ant colony optimization. In: 2013 IEEE congress on evolutionary computation (CEC), pp 3072–3078Google Scholar
  16. Jiang JQ, McQuay LJ (2012) Modularity functions maximization with nonnegative relaxation facilitates community detection in networks. Phys A 391(3):854–865CrossRefGoogle Scholar
  17. Lancichinetti A, Fortunato S (2009) Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities. Phys Rev E 80:016118CrossRefGoogle Scholar
  18. Lancichinetti A, Fortunato S, Kertész J (2009) Detecting the overlapping and hierarchical community structure in complex networks. New J Phys 11(3):033015CrossRefGoogle Scholar
  19. Lancichinetti A, Radicchi F, Ramasco JJ, Fortunato S (2011) Finding statistically significant communities in networks. PloS One 6(4):e18961CrossRefGoogle Scholar
  20. Li Z, Zhang S, Wang R-S, Zhang X-S, Chen Luonan (2008) Quantitative function for community detection. Phys Rev E 77:036109CrossRefGoogle Scholar
  21. Lung RI, Chira C, Andreica A (2014) Game theory and extremal optimization for community detection in complex dynamic networks. PLoS One 9(2):e86891, 02CrossRefGoogle Scholar
  22. Lung RI, Gog A, Chira C (2011) A game theoretic approach to community detection in social networks. In: Nature inspired cooperative strategies for optimization, NICSO 2011, Cluj-Napoca, Romania October 20–22 (2011), pp 121–131Google Scholar
  23. Lusseau D, Schneider K, Boisseau OJ, Haase P, Slooten Elisabeth, Dawson SteveM (2003) The bottlenose dolphin community of doubtful sound features a large proportion of long-lasting associations. Behav Ecol Sociobiol 54(4):396–405CrossRefGoogle Scholar
  24. Nascimento MCV, Pitsoulis L (2013) Community detection by modularity maximization using GRASP with path relinking. Comput Oper Res 40(12):3121–3131MathSciNetCrossRefMATHGoogle Scholar
  25. Newman MEJ (2006) Modularity and community structure in networks. Proc Natl Acad Sci 103(23):8577–8582CrossRefGoogle Scholar
  26. Newman MEJ (2013) Spectral methods for community detection and graph partitioning. Phys Rev E 88(4):042822CrossRefGoogle Scholar
  27. Newman MEJ, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E 69(2):026113CrossRefGoogle Scholar
  28. Pizzuti C (2008) Ga-net: a genetic algorithm for community detection in social networks. Parallel problem solving from nature–PPSN X. Springer, Berlin, pp 1081–1090CrossRefGoogle Scholar
  29. Pizzuti C (2012) A multiobjective genetic algorithm to find communities in complex networks. IEEE Trans Evol Comput 16(3):418–430CrossRefGoogle Scholar
  30. Rosvall M, Bergstrom CT (2008) Maps of random walks on complex networks reveal community structure. Proc Natl Acad Sci 105(4):1118–1123Google Scholar
  31. Sales-Pardo M, Guimerà R, Moreira AA, Amaral LAN (2007) Extracting the hierarchical organization of complex systems. Proc Natl Acad Sci 104(39):15224–15229CrossRefGoogle Scholar
  32. Shang R, Bai J, Jiao L, Jin C (2013) Community detection based on modularity and an improved genetic algorithm. Phys A 392(5):1215–1231CrossRefGoogle Scholar
  33. Shen HW, Cheng XQ (2010) Spectral methods for the detection of network community structure: a comparative analysis. J Stat Mech 2010(10):P10020CrossRefGoogle Scholar
  34. Shi C, Yan Z, Cai Y, Bin W (2012) Multi-objective community detection in complex networks. Appl Soft Comput 12(2):850–859CrossRefGoogle Scholar
  35. Zachary WW (1977) An information flow model for conflict and fission in small groups. J Anthropol Res 33(4):452–473CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Rodica Ioana Lung
    • 1
  • Mihai Suciu
    • 1
  • Noémi Gaskó
    • 1
  1. 1.Babes-Bolyai UniversityCluj-NapocaRomania

Personalised recommendations