###### Abstract  
The free-form single-layer reticulated shell structure has the characteristics of complex shape, a high degree of static indeterminacy, and difficult node positioning in the construction process, and the nodal deviations that may occur in the construction stage have a significant impact on the reliability performance of the structure. In order to evaluate the influence of the nodal deviation on the reliability performance of the structure in the process of shape optimization, this paper takes the free-form surface of the rectangular plane as the initial structure. Shape optimization is carried out with the objective function of minimizing the strain energy under the uniform vertical load, and the influence  
structure and used genetic algorithms to improve the free-form surface creation method and proposed the \"NURBS-GM\" method. [PERSON] et al. [3] established a numerical inverse hanging method based on the inverse hanging test method, applied vertical uniformly distributed loads to the structure, and provided an improvement idea for the shortcomings of the inverse hanging test method, such as low precision and similar shape after optimization. [PERSON] et al. [4] proposed a node coordinate sensitivity analysis method, which established an explicit relationship between the control point displacement and the strain energy change through analytical derivation, and simultaneously monitored the volume change in the structure during the optimization process. In response to the optimization needs of complex shell structures, [PERSON] et al. [5] proposed a structural sizing and shape optimization procedure to obtain optimum designs for plates and shells under dynamic loads. [PERSON] et al. [6] proposed an algorithm that can increase the buckling strength substantially, especially under shape variation in the out-of-plane direction. [PERSON] et al. [7] introduced the bionic algorithm into the field of shape optimization. While ensuring the smoothness of the surface, the optimization efficiency was improved by more than 40%. [PERSON] et al. [8] developed a method for dynamic reliability-based topology optimization of continuum structures with the optimization goal of minimizing the material volume. [PERSON] et al. [9] proposed a unit topology encoding method for the topological optimization problem of lattice shell structures with a large scale of bars, which not only reduced the optimization variables but also reduced the probability of the occurrence of the mechanism system, thereby improving optimization efficiency.  
In the optimization of free-form surfaces, strain energy is usually used as the optimization target, and the structural stiffness is improved by minimizing the structural strain energy [10,11]. As a defect-sensitive structure, the bearing capacity of a single-layer reticulated shell is greatly affected by the initial geometric defects. A small geometric deviation will cause a large change in the structural bearing capacity [12]. Therefore, in addition to strain energy, the influence of node deviations on structural reliability performance during structural optimization should also be examined. This study compared the influence of node deviation on the structure before and after performance-based optimization.  
Figure 1: Shanghai Sun Valley.  
Figure 2: Centre Pompidou-Metz.