## 5 Conclusions  
In this study, the elastic modulus of the steel, the thickness of the bridge deck panel, the height of the vertical stiffening rods, and the relative distance between double-layer main beams were selected as the structural parameters to be optimized based on the characteristics of bridge structures supported by engineering. Via the static analysis of the initial FE model in ABAQUS, the mid-span vertical deflection, the axial internal force of the stiffening chord, the longitudinal internal force of the bottom plate of the bridge deck panel, the axial internal force of the compressed chord of the pier top truss, and the quantity of upper structure engineering were selected as the objective functions. A lightweight calculation equation based on the RSM was established for the optimization of the design parameters, and the following conclusions were drawn. Figure 16: The comparison of the optimization of the computation accuracy. Figure 15: The comparison of the objective function correction results. 1. A lightweight calculation equation based on the FE model of the engineering structure supported by the RSM was established. Via significance analysis, it was found that the use of a simplified incomplete quadratic polynomial as the response surface equation can accurately fit the numerical relationships between the optimized parameters and the target response function to be corrected. The fitting accuracy was found to be high, which greatly reduces the workload of structural modeling in the optimization design and ensures the accuracy and reliability of the optimization. 2. Based on the lightweight equation established using the RSM, two optimization methods, namely, WPSO and NSGA-II, were used to minimize the quantity of upper structure engineering as the primary control objective and to minimize the mid-span vertical deflection and the axial compression force in the hollow pier top tie rod as the secondary control objectives. After comparing the optimization results, WPSO was chosen as the final optimization scheme. After optimizing the design parameters, the mid-span vertical deflection under constant load, the axial internal force of the stiffening chord, the longitudinal internal force of the bottom plate of the bridge deck panel, and the axial internal force of the compressed chord of the pier top truss were reduced by 3% to 11% as compared with the original design. Furthermore, the quantity of upper structure engineering was reduced by 8.38%, which improved the structural performance while reducing the engineering cost. 3. In the design stage, bridge structures usually require the manual adjustment of a large number of design parameters to achieve the control of the structural performance, material usage, and engineering cost. The process of establishing complex FE models and adjusting parameter combinations is time-consuming and difficult to control and involves many iterations. This article proposed a method that can achieve the accurate optimization reasoning of certain control indicators of bridge structures via mathematical optimization using lightweight response surface equations. Moreover, when bridge structures enter the service period, this method can still be used to simulate the actual parameters of the bridge structure under current conditions by using health monitoring data. Thus, the precise simulation of the entire life cycle of the bridge structure can be achieved. Therefore, this method is suitable not only for the optimization of structural parameters in the bridge design stage but also for the simulation of the structural health status of bridge structures in the operation stage. Conceptualization, L.W. and Y.M. ; methodology, L.W. ; software, L.W. and R.X. ; validation, R.X., X.G. and Y.M. ; formal analysis, L.W. ; investigation, R.X. ; resources, X.G. ; data curation, R.X. and Y.M. ; writing--original draft preparation, R.X., X.G. and L.W. ; writing--review and editing, R.X. and L.W. ; visualization, Y.M. ; supervision, L.W. ; project administration, R.X. and X.G.