Abstract
Community structures are sets of nodes that are densely linked with each other, reflecting the functional modules of real-world systems. Most classical works for community detection (CD) are based on the optimization of an objective function, namely modularity. However, it has been recently demonstrated that there exists a resolution limit in the modularity optimization based CD methods, i.e., the communities cannot be detected if their scales are smaller than a certain threshold. To overcome this resolution limit, in this paper, we propose a decomposition based multiobjective memetic algorithm (called MDMCD) for multiresolution CD (MCD) in complex networks, aiming to detect communities at multiple resolution levels. MDMCD first models the MCD problem as a multiobjective optimization problem (MOP) with two contradictory objectives, namely the intra-link ratio and inter-link ratio. Then, it devises a multiobjective memetic optimization framework that combines a decomposition based multiobjective evolutionary algorithm with a two-level local search to solve the modeled MOP. In this framework, the modeled MOP is first decomposed into a set of single-objective optimization subproblems, each of which corresponds to a CD problem in a certain resolution level. Subsequently, these subproblems are simultaneously optimized by the evolutionary operators and the local search, taking the network-specific knowledge into consideration. Finally, MDMCD returns a population of solutions in a single simulation run, reflecting the community divisions at multiple resolution levels. Experiments on both the simulated and real-world networks show the effectiveness of MDMCD in detecting multiresolution community structures.
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The datasets analysed during the current study are available from the corresponding author on reasonable request.
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Acknowledgements
This work was supported in part by the National Key R &D Program of China under Grant 2020YFA0908700, in part by the National Natural Science Foundation of China under Grants 62173236, 61803269, 61876110, 61806130, 61976142, U1713212, 62072315, 62176164, 61976142 and 61836005, in part by the Natural Science Foundation of Guangdong Province under Grant 2020A1515010790; and in part by the Technology Research Project of Shenzhen City under Grant JCYJ20190808174801673.
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Shao, Z., Ma, L., Bai, Y. et al. Multiresolution community detection in complex networks by using a decomposition based multiobjective memetic algorithm. Memetic Comp. 15, 89–102 (2023). https://doi.org/10.1007/s12293-022-00370-z
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DOI: https://doi.org/10.1007/s12293-022-00370-z