Research on Multi-Objective Optimization of Cable Forces in Cable-Stayed Bridges with Reliability as the Objective

The rational determination of cable forces is critical for ensuring the desired mechanical behavior of long-span cable-stayed bridges during construction and service. However, conventional deterministic optimization methods often overlook uncertainties in construction processes, which may lead to deviations in the as-built state. This paper proposes a reliability-oriented multi-objective cable force optimization method. Taking a single-tower hybrid girder cable-stayed bridge as the case study, a finite element model is established in MIDAS Civil, and the influence matrix method is employed to construct the mapping between cable forces and structural responses. Sensitivity analysis is conducted on four parameters to identify the most influential factors. Cable tensioning error is treated as a random variable following a normal distribution, and Monte Carlo simulation is adopted to evaluate the reliability index β. A multi-objective particle swarm optimization (MOPSO) algorithm is then implemented to jointly minimize cable force deviations and maximize β. A Sobol global sensitivity analysis shows that the back cables S1~S3 dominate the variance in the cable-force deviation, and that cable-to-cable interactions contribute about 32% of the output variance. The deterministic scheme achieves an average deviation of 0.85% and reduces construction steps from 11 to 6. When the coefficient of variation is 0.5%, the failure-probability-based reliability index of the optimized scheme exceeds 3.72 (Pf < 10−4), meeting the target of 3.5. At 1.0%, the failure-probability-based index decreases to 2.27, while the second-moment index of the optimized scheme increases from 1.96 to 3.29. A benchmark against NSGA-II under the same evaluation budget shows that MOPSO covers a wider range of reliability–accuracy trade-offs, while NSGA-II produces a more uniform and better-converged Pareto front. The method embeds reliability in the optimization process, overcoming the limitation of post hoc verification. It is recommended that the tensioning variation be controlled within 0.5%.