Complex Network Community Detection by Improved Nondominated Sorting Genetic Algorithm

Abstract

Aimed at the problems of low solution precision and easy to be trapped into local optima by single objective evolutionary algorithm, a self-adaptive multi-objective optimization algorithm based on nondominated sorting genetic algorithm II (NSGA2) and Label Propagation Algorithm (LPA) is proposed. The algorithm takes Kernel K-means (KKM) and Ratio Cut (RC) as the objective functions. Two new crossover operator and the improved mutation operator is used to achieve the evolution of the population. We conducted simulation experiments in the computer-generated networks and the real-world networks environment. The results show that compared with other community detection algorithms, our algorithm has the advantages of high resolution and strong search ability, and it can effectively identify the community structure in complex networks. Introduction Real-world systems are complex, but they can be described by abstract network models, such as ecosystem, social network and so on. By analyzing the community structure in complex network, features in complex networks can be found more intuitively [1,2,3]. Community detection can be modeled as an optimization problem. For example, Pizzuti has proposed a single objective genetic algorithm(GA-net) for community detection[4].Because of the limit of single-objective evolutionary method based on modularity several multi-objective evolutionary methods has been proposed, such as MOGA-net [5]. In this paper, we propose a novel community algorithm based on NSGA2 and LPA, termed as NSGA2-LPA. We use the multi-objective evolutionary algorithm based on NSGA2 which was proposed by Deb in 2002. NSGA2 has high computational efficiency when dealing with low-dimensional problems, and the solution set has good diversity and convergence [6,7]. Related Background Complex Network A complex network is usually represented by G = (V, E), where V represents the set of all nodes in the complex network, and E represents the set of all edges in the complex network. The topology of complex networks is usually represented by adjacent matrix A = (aij)n×n, where n is the number of nodes in the network,aij = 1, if there is a link between node i and j ,otherwise,aij = 0. Optimization Problem The community detection algorithm based on improved NSGA2 selects KKM as the evaluation function of the community‘s internal density and RC as the evaluation function of the community‘s external density [8]. Given an unsigned network denoted as G = (V, E) with |V| = n nodes and |E| = m edges. The adjacency matrix is A . The k partitions are in the network denoted