(340m) A Method of Community Detection in Complex Weighted Networks

Real-world networks are complex and large scale, represent very interacting entities, and generate diverse types of data. Biological networks [1], power networks [2], internet networks, and chemical plants [3, 4] are some examples of complex networks. Moreover, modern manufacturing plants are increasingly integrated [4], leading to structural and computational complexities. In recent years the problem of decomposing a complex network into a set of interacting small networks that adequately capture the interactions of the original large network has received great attention, as the decomposition has applications in many engineering and science fields.

Community detection has been used to decompose large networks into a set of small interacting networks [1]. Generally, it exploits this structure via optimization to find sub-networks that have the least inter-connections and the most intra-connections. Recently, several methods and algorithms have been proposed [5]; among them, modularity optimization is the most popular one [6]. Modularity is defined as the difference between the fraction of edges within communities in the network and the expected fraction of such edges, which are randomly distributed [6]. Most of the existing optimization-based algorithms partition a network using a single objective function. Since these algorithms are unable to determine multiple community structures, the use of multi-objective optimization approaches has been proposed [7].

In this paper, we present a novel multi-objective method to community detection, and adopt the whale optimization algorithm (WOA)[8], a recently-introduced nature-inspired meta-heuristic optimization algorithm, to solve the multi-objective optimization problem. This method uses a nondominated sorting approach to calculate all non-dominated solutions. To achieve the optimal typology, sensitivity analyses are conducted to evaluate the strength of the interaction between each pair of nodes (variables), and the causal relationship between each pair of nodes is represented by a directed graph. The slow speed of the convergence of the existing community detection algorithms, especially for large-scale networks, is addressed by applying parallel WOA. The proposed method is applied to the Tennessee Eastman Process, which has been extensively used as a benchmark throughout the chemical industries.

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