A HiDeNN-Opt framework for cable force optimization in cable-stayed bridges

Modern cable-stayed bridges present challenges in cable force optimization due to their long spans, composite structures, and multi-cable systems. To address the limitations of traditional methods in efficiency, accuracy, and robustness, this study proposes HiDeNN-Opt (Hierarchical Deep Neural Network Optimization) . This integrated framework extends the HiDeNN-FEM ( Hierarchical Deep Neural Network Finite Element Method ) surrogate model by embedding evolutionary optimization algorithms. HiDeNN-FEM replaces traditional FEM computations with a deep neural network, enabling fast and accurate mapping between cable forces and structural responses. Based on this, HiDeNN-Opt incorporates genetic (GA) and differential evolution (DE) algorithms to solve high-dimensional, nonlinear optimization problems without simplifications. Two hybrid strategies, HiDeNN-Opt-GA and HiDeNN-Opt-DE , are proposed to efficiently achieve the “Smooth Girder and Straight Pylon” design goal. Applications to two cable-stayed bridges with fan-shaped and harp-shaped cable systems demonstrate the accuracy and generalizability of the method. Results show significant reductions in girder displacement, pylon drift, and bending moments, highlighting the proposed method’s advantages in accuracy, efficiency, and adaptability.