Community detection decomposes large-scale, complex networks “optimally” into sets of smaller sub-networks. It finds sub-networks that have the least inter-connections and the most intra-connections. This article presents an efficient community detection algorithm that detects community structures in a weighted network by solving a multi-objective optimization problem. The whale optimization algorithm is extended to enable it to handle multi-objective optimization problems with discrete variables and to solve the problems on parallel processors. To this end, the population's positions are discretized using a transfer function that maps real variables to discrete variables, the initialization steps for the algorithm are modified to prevent generating unrealistic connections between variables, and the updating step of the algorithm is redefined to produce integer numbers. To identify the community configurations that are Pareto optimal, the non-dominated sorting concept is adopted. The proposed algorithm is tested on the Tennessee Eastman process and several benchmark community-detection problems.

中文翻译：

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复杂加权网络中社区检测的有效算法

社区检测将大规模、复杂的网络“最优地”分解为一组较小的子网络。它找到具有最少相互连接和最多内部连接的子网。本文提出了一种有效的社区检测算法，该算法通过解决多目标优化问题来检测加权网络中的社区结构。扩展了鲸鱼优化算法，使其能够处理具有离散变量的多目标优化问题并解决并行处理器上的问题。为此，使用将真实变量映射到离散变量的传递函数对总体位置进行离散化，修改算法的初始化步骤以防止在变量之间产生不切实际的联系，并且重新定义算法的更新步骤以生成整数。为了识别帕累托最优的社区配置，采用了非支配排序概念。所提出的算法在田纳西伊士曼过程和几个基准社区检测问题上进行了测试。