Optimization of the cable forces of completed cable-stayed bridges with differential evolution method

Long-span cable-stayed bridges have been massively erected worldwide in recent decades, and reasonable cable forces play an essential role in achieving the desired configurations of completed bridges. In the current research, a differential evolution (DE) algorithm is adopted to optimize the cable forces considering the counterweight. An asymmetrical cable-stayed bridge is taken as a case study, and the numerical model of the bridge is established with the OpenSees platform. The cable sag effect and geometric nonlinearity are considered in the numerical model. The weighted total bending energy of the girder and pylons is taken as the objective function of the optimization problem. In addition, the constraints of the cable forces, the range and magnitude of the coun-terweight, and the bearing reaction forces at the transition and auxiliary piers are considered. The numerical results reveal that the proposed framework is efficient and stable for optimizing the cable forces, and several optimum solutions can be obtained. In addition, the performance of the proposed optimum algorithm is less sensitive to the values of the initial parameters (feasible regions and population size). Moreover, the proposed algorithm automatically determines the control parameters (scaling factor and crossover rate) of the DE method, which makes it easy to use in practical engineering. In addition, the proposed algorithm can be used to optimize the cable forces in the final stage and the construction stages.