An improved multi-objective evolutionary algorithm for simultaneously detecting separated and overlapping communities

In our previous work, a multi-objective evolutionary algorithm (MEA_CDPs) was proposed for detecting separated and overlapping communities simultaneously. However, MEA_CDPs has a couple of defects, like individuals cannot be transformed to community structure by the decoder when the quality of community structure is lower certain thresholds, many vertices with weak overlapping nature are identified as overlapping nodes, and the objective functions can not control the ratio of separated nodes to overlapping nodes. Therefore, in this paper, to overcome these defects, we improve MEA_CDPs by designing more efficient objective functions. We also extend MEA_CDPs' capability in detecting hierarchical community structures. The improved algorithm is named as iMEA_CDPs. In the experiments, a set of computer-generated networks are first used to test the effect of parameters in iMEA_CDPs, and then four real-world networks are used to validate the performance of iMEA_CDPs. The experimental results show that iMEA_CDPs outperforms MEA_CDPs. Moreover, compared with MEA_CDPs, iMEA_CDPs can detect various kinds of overlapping and hierarchical community structures.