Cable-stayed bridges have been widely constructed to cross large obstacles in transportation networks and metropolitan cities. As a highly redundant structure, the structural performance of a cable-stayed bridge can be significantly influenced by the cable prestressing forces. Therefore, the determination of optimal cable forces is necessary at the design stage. As computational mechanics matures, numerical computational methods such as high-fidelity finite element analyses facilitate accurate assessment of the bridge state, and evolutionary algorithms have been applied to enhance the global search ability. However, the combination of evolutionary algorithms and finite element model-based evaluations can substantially increase the computational burden, rendering the efficiency of optimization significantly time-consuming for practical engineering projects. To overcome this limitation, this work proposes a new surrogate model-assisted differential evolution method to facilitate the determination of optimal cable forces. Different from the existing methods, the proposed method develops a new individual selection strategy together with an additional archive to manage the diversity of population and further enhance the exploration ability. A new criterion is also proposed for the refinement of the surrogate model in the local search stage to avoid redundant information. Furthermore, B-Spline interpolation curve is integrated within the framework as a high-dimensional model representation technique for the design variables of cable forces. Five classic numerical examples and a practical engineering application validate the performance and advantages of the proposed method.