Global and Cluster Structural Balance via a Priority Strategy Based Memetic Algorithm

Structural balance in signed networks aims to search for the structure with the least imbalance of relationships. However, most existing studies focus on global structural balance, and little work has considered local structural balance. In this study, an optimization model is proposed based on the weak definition of structural balance theory. The model incorporates both the global imbalance and maximum cluster imbalance as the criterion of structural balance in a signed network. Furthermore, a priority strategy based memetic algorithm, called PSMA, is presented to calculate the structural balance based on this model. In PSMA, a network-specific genetic operation is applied to explore the solution space. A multi-level greedy method is deployed to exploit the optimal solution as the local search. The priority strategy, which aims to recognize the severe unbalanced vertices or clusters as prior objectives and execute search operations on them, is inserted into each level of the local search to make it more efficient. Extensive experiments are conducted on 11 real-world network datasets. The results demonstrate that the proposed model can avoid clusters with over-concentration of unbalanced relationships at the expense of a slight increase in global imbalance and confirm that the proposed PSMA can achieve better global and cluster structural balance compared with the state-of-the-art algorithms.