Structural Balance Computation of Signed Hypergraphs via Memetic Algorithm

The potential imbalances among entities and connections within complex systems can pose significant threats to their overall functionality. In order to enhance the functional security of these complex systems, it becomes imperative to address and alleviate these underlying imbalances. Structural balance computation has gained attention because of its ability to balance relationships among entities within systems. Traditional methods in structural balance computation aim to minimize imbalances within signed networkss. However, signed networkss have limitations in effectively representing complex data relationships in multi-modal or multi-type data. In order to address this constraint, we propose a novel framework called SHMA (Structural Balance of Signed Hypergraphs based on Memetic Algorithm) which aims to identify and minimize imbalances within signed hypergraphs. More specifically, we formulate the degree of imbalance in signed hypergraphs as an extended energy function, thereby transforming the computation of structural balance of the hypergraphs into an optimization problem. Then, we utilize a multi-level memetic algorithm to optimize the energy function and obtain a solution with the least imbalances. To assess the performance of SHMA, we performed experiments on various real-world datasets and conducted a comparative analysis. The experimental results illustrate that SHMA outperforms the alternative algorithms in terms of structural balance computation of signed hypergraphs. In addition, SHMA exhibits fast convergence, enabling it to reach a balanced state more efficiently.