A decomposition-based multi-objective optimization for simultaneous balance computation and transformation in signed networks

Many social systems have a set of opposite interactions such as friend/enemy, cooperation/competition and support/opposition. In these signed systems, there exist functional imbalances from the system-level view because of the existence of unbalanced interactions. However, it is difficult to compute the unbalance degree and transform unbalanced factors to balanced ones in real signed systems. Earlier studies tackled these two issues separately and gave a unique solution, and thus cannot be well applied to real applications with constraints. In this paper, we devise a decomposition-based and network-specific multi-objective optimization algorithm to solve the balance computation and transformation of signed networks simultaneously. The devised algorithm aims at finding a set of optimal balance transformation solutions, and each of which is the trade-off between the twin objectives (i.e., the minimization of inter-cluster positive links and the minimization of intra-cluster negative links). Of these solutions, the one with the fewest unbalanced links corresponds to the solution to the balance computation. And each trade-off solution corresponds to an optimal balance transformation way under a certain transformation cost. Extensive experiments on four social networks demonstrate the effectiveness of the devised algorithm on both the computation and the transformation of structural balance. They also show that the devised algorithm can provide multiple optimal solutions at the same transformation cost.