Research on network structural balance has been of great concern to scholars from diverse fields. In this paper, a two-step approach is proposed for the first time to address the network structural balance problem. The proposed approach involves evolutionary multiobjective optimization, followed by model selection. In the first step, an improved version of the multiobjective discrete particle swarm optimization framework developed in our previous work is suggested. The suggested framework is then employed to implement network multiresolution clustering. In the second step, a problem-specific model selection strategy is devised to select the best Pareto solution (PS) from the Pareto front produced by the first step. The best PS is then decoded into the corresponding network community structure. Based on the discovered community structure, imbalanced edges are determined. Afterward, imbalanced edges are flipped so as to make the network structurally balanced. Extensive experiments on synthetic and real-world signed networks demonstrate the effectiveness of the proposed approach.