Multi-objective ant colony optimization algorithm based on decomposition for community detection in complex networks

Community detection aims to identify topological structures and discover patterns in complex networks, which presents an important problem of great significance. The problem can be modeled as an NP hard combinatorial optimization problem, to which multi-objective optimization has been applied, addressing the common resolution limitation problem in modularity-based optimization. In the literature, ant colony optimization (ACO) algorithm, however, has been only applied to community detection with single objective. This is due to the main difficulties in defining and updating the pheromone matrices, constructing the transition probability model, and tuning the parameters. To address these issues, a multi-objective ACO algorithm based on decomposition (MOACO/D-Net) is proposed in this paper, minimizing negative ratio association and ratio cut simultaneously in community detection. MOACO/D-Net decomposes the community detection multi-objective optimization problem into several subproblems, and each one corresponds to one ant in the ant colony. Furthermore, the ant colony is partitioned into groups, and ants in the same group share a common pheromone matrix with information learned from high-quality solutions. The pheromone matrix of each group is updated based on updated nondominated solutions in this group. New solutions are constructed by the ants in each group using a proposed transition probability model, and each of them is then improved by an improvement operator based on the definition of strong community. After improvement, all the solutions are compared with the solutions in the external archive and the nondominated ones are added to the external archive. Finally each ant updates its current solution based on a better neighbor, which may belong to an adjacent group. The resulting final external archive consists of nondominated solutions, and each one corresponds to a different partition of the network. Systematic experiments on LFR benchmark networks and eight real-world networks demonstrate the effectiveness and robustness of the proposed algorithm. The ranges of proper values for each parameter are also analyzed, addressing the key issue of parameter tuning in ACO algorithms based on a large number of tests conducted.