Optimization on Reasonable Construction State for Cable-Stayed Bridge with Steel Box Girder Based on Multi-Objective Programming Algorithm

The reasonable construction state of a cable-stayed bridge refers to the state achieved after construction is carried out according to a specific sequence of procedures, leading to the reasonable completion status the bridge. The corresponding construction states at each stage are considered as part of the reasonable construction state. For the optimization of the construction state of cable-stayed bridges with steel box girders, a method combining a multi-objective programming algorithm with a forward iteration method is proposed to determine a reasonable construction state based on the structural characteristics and optimization principles of such bridges. First, a multi-objective programming model was established, taking the bending moments of the main girder and pylon, as well as cable forces, as objective functions. The weighted square sum method, a type of evaluation function method, was then employed to convert the multi-objective programming model into an unconstrained single-objective quadratic programming model. Subsequently, the damped Newton method was utilized to solve the quadratic programming problem. By integrating this algorithm with the forward iteration method, the reasonable construction state of a large-span and double-tower steel box girder cable-stayed bridge was optimized. The influence of different objective functions on the optimization results was analyzed. The findings demonstrate that the proposed method produces a smooth structural configuration under the optimized construction state, with internal forces and normal stresses within a reasonable range. In the completed state derived from this construction state, internal forces, normal stresses, and cable forces are uniformly distributed, while the reactions at transition piers and auxiliary piers exhibit sufficient pressure reserves. The structural state under dead load achieved through this method closely aligns with the desired reasonable completed state.