Community detection aims to identify topological structures and discover patterns in complex networks, which presents an important problem of great significance. The problem can be modeled as an NP hard combinatorial optimization problem, to which multi-objective optimization has been applied, addressing the common resolution limitation problem in modularity-based optimization. In the literature, ant colony optimization (ACO) algorithm, however, has been only applied to community detection with single objective. This is due to the main difficulties in defining and updating the pheromone matrices, constructing the transition probability model, and tuning the parameters. To address these issues, a multi-objective ACO algorithm based on decomposition (MOACO/D-Net) is proposed in this paper, minimizing negative ratio association and ratio cut simultaneously in community detection. MOACO/D-Net decomposes the community detection multi-objective optimization problem into several subproblems, and each one corresponds to one ant in the ant colony. Furthermore, the ant colony is partitioned into groups, and ants in the same group share a common pheromone matrix with information learned from high-quality solutions. The pheromone matrix of each group is updated based on updated nondominated solutions in this group. New solutions are constructed by the ants in each group using a proposed transition probability model, and each of them is then improved by an improvement operator based on the definition of strong community. After improvement, all the solutions are compared with the solutions in the external archive and the nondominated ones are added to the external archive. Finally each ant updates its current solution based on a better neighbor, which may belong to an adjacent group. The resulting final external archive consists of nondominated solutions, and each one corresponds to a different partition of the network. Systematic experiments on LFR benchmark networks and eight real-world networks demonstrate the effectiveness and robustness of the proposed algorithm. The ranges of proper values for each parameter are also analyzed, addressing the key issue of parameter tuning in ACO algorithms based on a large number of tests conducted.
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Adriano P, Paolo S (1984) Scalarizing vector optimization problems. J Optim Theory Appl 42(4):499–524
Angelini L, Boccaletti S, Marinazzo D, Pellicoro M, Stramaglia S (2007) Identification of network modules by optimization of ratio association. Chaos Interdiscip J Nonlinear Sci 17(2):023114
Bullnheimer B, Hartl R, Strauss C (1999) An improved ant System algorithm for the vehicle Routing Problem. Ann Oper Res 89:319–328
Chang H, Feng Z, Ren Z (2013) Community detection using Ant Colony Optimization. In: IEEE congress on evolutionary computation, pp 3072–3078
Clauset A, Newman ME, Moore C (2004) Finding community structure in very large networks. Phys Rev E 70(2):066111
Colorni A, Dorigo M, Maniezzo V, Trubian M (1994) Ant system for job-shop scheduling. Belg J Oper Res Stat Comput Sci 34(1):39–53
Costa D, Hertz A (1997) Ants can colour graphs. J Oper Res Soc 48(3):295–305
Danon L, Diaz-Guilera A, Duch J, Arenas A (2005) Comparing community structure identification. J Stat Mech: Theory Exp 9:09008
Dorigo M (1992) Optimization, learning and natural algorithms. Ph. D. Thesis, Politecnico di Milano, Italy
Dorigo M, Gambardella L (1997) Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans Evolut Comput 1(1):53–66
Ehrgott M (2005) Multicriteria optimization. Springer, Berlin
Eichfelder G (2008) Adaptive scalarization methods in multi-objective optimization. Springer, New York
Fortunato S (2010) Community detection in graphs. Phys Rep 486(3):75–174
Fortunato S, Barthélemy M (2007) Resolution limit in community detection. Proc Natl Acad Sci USA 104(1):36–41
Fortunato S, Hric D (2016) Community detection in networks: a user guide. Phys Rep 659:1–44
Girvan M, Newman M (2002) Community structure in social and biological networks. Proc Natl Acad Sci 99(12):7821–7826
Gong M, Fu B, Jiao L, Du H (2011) Memetic algorithm for community detection in networks. Phys Rev E 84:056101
Gong M, Ma L, Zhang Q, Jiao L (2012) Community detection in networks by using multi-objective evolutionary algorithm with decomposition. Phys Rev A 391(15):4050–4060
Gong M, Cai Q, Chen X, Ma L (2014) Complex network clustering by multiobjective discrete particle swarm optimization based on decomposition. IEEE Trans Evolut Comput 18(1):82–97
Guédon O, Vershynin R (2016) Community detection in sparse networks via grothendieck’s inequality. Probab Theory Relat Fields 165(3–4):1–25
Handl J, Knowles J (2007) An evolutionary approach to multi-objective clustering. IEEE Trans Evolut Comput 11(1):56–76
He D, Liu J, Liu D, Jin D, Jia Z (2011) Ant colony optimization for community detection in large-scale complex networks. In: 2011 seventh international conference on natural computation (ICNC), IEEE, vol. 2, pp 1151–1155
Ji J, Hu R, Zhang H, Liu C (2011) A hybrid method for learning bayesian networks based on ant colony optimization. Appl Soft Comput J 11(4):3373–3384
Jin D, Liu D, Yang B, Liu J, He D (2011) Ant colony optimization with a new random walk model for community detection in complex networks. Adv Complex Syst 14(05):795–815
Ke L, Zhang Q, Battiti R (2013) MOEA/D-ACO: a multiobjective evolutionary algorithm using decomposition and ant colony. IEEE Trans Cybern 43(6):1845–1859
Lancichinetti A, Fortunato S, Radicchi F (2008) Benchmark graphs for testing community detection algorithms. Phys Rev E: Stat, Nonlinear, Soft Matter Phys 78:046110
Lancichinetti A, Fortunato S, Kertesz K (2009) Detecting the overlapping and hierarchical community structure of complex networks. N J Phys 11(3):033015
Li Z, Zhang S, Wang R, Zhang X, Chen L (2008) Quantitative function for community detection. Phys Rev E 77(3):036109
Liao T, Stützle T, Oca MAMD, Dorigo M (2014) A unified ant colony optimization algorithm for continuous optimization. Eur J Oper Res 234(3):597–609
Lusseau D, Schneider K, Boisseau O, Haase P, Slooten E, Dawson S (2003) The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations. Behav Ecol Sociobiol 54(4):396–405
Lyzinski V, Tang M, Athreya A, Park Y, Priebe CE (2017) Community detection and classification in hierarchical stochastic block models. IEEE Trans Netw Sci Eng 4(1):13–26
Miettinen K (1999) Nonlinear multi-objective optimization, vol 12. Springer
Mu C, Liu Y, Liu Y, Jianshe Wu, Licheng Jiao (2014a) Two-stage algorithm using influence coefficient for detecting the hierarchical, non-overlapping and overlapping community structure. Physica A 408(408):47–61
Mu C, Zhang J, Jiao L (2014b) An intelligent Ant Colony optimization for community detection in complex networks. IEEE Congr Evolut Comput, Beijing, pp 700–706
Mu C, Xie J, Liu Y, Chen F, Liu Y, Jiao J (2015) Memetic algorithm with simulated annealing strategy and tightness greedy optimization for community detection in networks. Appl Soft Comput 34:485–501
Newman M (2004) Fast algorithm for detecting community structure in networks. Phys Rev E 69(2):066133
Newman M (2006) Modularity and community structure in networks. Proc Natl Acad Sci USA 103(23):8577–8582
Newman M (2011) Communities, modules and large-scale structure in networks. Nat Phys 8(1):25–31
Newman M, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E 69(2):026113
Pizzuti C (2008) Ga-net: a genetic algorithm for community detection in social networks. In: Parallel problem solving from nature–PPSN X, Springer, Berlin, p 1081
Pizzuti C (2009) A multi-objective genetic algorithm for community detection in networks. In: Proceedings of the 21st IEEE international conference on tools with artificial intelligence, Newark, New Jersey, pp 379–386
Radicchi F, Castellano C, Cecconi F, Loreto V, Parisi D (2004) Defining and identifying communities in networks. Proc Natl Acad Sci USA 101(9):2658–2663
Schaub MT, Delvenne JC, Rosvall M, Lambiotte R (2017) The many facets of community detection in complex networks. Appl Netw Sci 2(1):4
Shi C, Wang Y, Wu B, Zhong C (2009) A new genetic algorithm for community detection. Complex part II. LNICST 5:1298–1309
Stützle T, Hoos H (2000) Max-min ant system. Future Gener Comput Syst 16(8):889–914
Wei Y, Cheng C (1991) Ratio cut partitioning for hierarchical designs. IEEE Trans Comput-Aided Des Integr Circ Syst 10(7):911–921
Zachary W (1977) An information flow model for conflict and fission in small groups. J Anthropol Res 33(4):452–473
Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evolut Comput 11(6):712–731
Zhang AY, Zhou HH (2016) Minimax rates of community detection in stochastic block models. Comput Sci 44(5):2252–2280
Zhou HF, Li J, Li JH, Zhang FC, Cui YA (2017) A graph clustering method for community detection in complex networks. Physica A 469:551–562
The authors would like to thank the School of Computer Science, University of Nottingham, for providing the essential research facilities to this joint research. The authors would like to thank Tianhuan Huang, who made a great effort to conduct additional experiments when we revised the paper. The authors would also like to thank the anonymous reviewers and editors for their valuable and constructive suggestions, which are helpful for improving our paper. This work was supported by the National Natural Science Foundation of China (No. 61672405), Project supported the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (61621005), the Fundamental Research Funds for the Central Universities (Nos. JB170204 and JBG160229), China Scholarship Council (CSC), the National Natural Science Foundation of China (U1701267, 61473215, 61772399, 61773304, 61773300, and 61772393), the Fund for Foreign Scholars in University Research and Teaching Programs (the 111 Project) (No. B07048), the Major Research Plan of the National Natural Science Foundation of China (Nos. 91438201 and 91438103), and the Program for Cheung Kong Scholars and Innovative Research Team in University (No. IRT_15R53).
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Mu, C., Zhang, J., Liu, Y. et al. Multi-objective ant colony optimization algorithm based on decomposition for community detection in complex networks. Soft Comput 23, 12683–12709 (2019). https://doi.org/10.1007/s00500-019-03820-y
- Complex networks
- Community detection
- Multi-objective optimization
- Ant colony optimization