A Discrete Moth-Flame Optimization With an $l_2$-Norm Constraint for Network Clustering

Complex network clustering problems have been gained great popularity and widespread researches recently, and plentiful optimization algorithms are aimed at this problem. Among these methods, the optimization methods aiming at multiple objectives can break the limitations (e.g., instability) of those optimizing single objective. However, one shortcoming stands out that these methods cannot balance the exploration and exploitation well. In another sentence, it fails to optimize solutions on the basis of the good solutions obtained so far. Inspired by nature, a new optimized method, named multi-objective discrete moth-flame optimization (DMFO) method is proposed to achieve such a tradeoff. Specifically, we redefine the simple flame generation (SFG) and the spiral flight search (SFS) processes with network topology structure to balance exploration and exploitation. Moreover, we present the DMFO in detail utilizing a Tchebycheff decomposition method with an $l_2$-norm constraint on the direction vector (2-Tch). Besides that, experiments are taken on both synthetic and real-world networks and the results demonstrate the high efficiency and promises of our DMFO when tackling dividing complex networks.