Feasible and robust optimisation of cable forces in suspended bridges: A two-stage metaheuristic approach

The adjustment of cable pretension in suspended-deck bridges is a critical inverse design problem, where feasibility and robustness are as important as accuracy. Conventional methods such as finite-element (FE) re-analysis or the Influence Matrix Method (IMM) provide algebraic solutions but often produce oscillatory or infeasible patterns once field constraints are applied. This study introduces a two-stage framework that integrates stiffness-based sensitivity analysis with constrained metaheuristic optimisation. In stage-1 a reduced-order banded influence operator is introduced, which reflects how changes at the cable scale propagate over a limited range before combining into the global deck deformation. The effective bandwidth is tied to hanger spacing and deck stiffness, giving a natural connection between actuator-level inputs and system-level response. In Stage-2, cable adjustments are determined through multi-objective optimisation that balances target matching, smoothness, symmetry, and bounded jack capacities. Two population-based strategies, Particle Swarm Optimisation (PSO) and Grey Wolf Optimisation (GWO), are benchmarked against convex regularization baselines on the Gravina Bridge (Italy). Both metaheuristics deliver symmetric, bounded, and contiguous force patterns that reproduce the target profile while remaining compatible with staged field operations. Robustness analysis under structured perturbations confirms near 14% reductions in mean and tail-risk errors relative to convex solutions, while reproducibility is ensured through constrained search and convex polishing. The results demonstrate that the framework provides accurate and constructible re-tensioning strategies, clarifying how scale interactions in cable–deck systems can be exploited for reliable design and maintenance.