Multi-objective ant colony optimization algorithm based on decomposition for community detection in complex networks

  • Caihong Mu
  • Jian Zhang
  • Yi LiuEmail author
  • Rong Qu
  • Tianhuan Huang
Methodologies and Application


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.


Complex networks Community detection Multi-objective optimization Ant colony optimization 



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).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, International Research Center for Intelligent Perception and Computation, Joint International Research Laboratory of Intelligent Perception and Computation, School of Artificial IntelligenceXidian UniversityXi’anChina
  2. 2.School of Electronic EngineeringXidian UniversityXi’anChina
  3. 3.School of Computer ScienceUniversity of NottinghamNottinghamUK

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