To effectively increase the performance of free-form grid structures

the multi-objective optimization method of free-form grid structures was improved. The free-form surface was generated based on the non-uniform rational B-spline (NURBS) technology. The height of control points was taken as the optimization variable and structural strain energy as the optimization objective of the static behavior. The geometric comprehensive quantitative index was proposed to be taken as the geometric optimization objective

which comprehensively considers the similarity of the surface and the fluency and regularity of the free-form grids. Combined the sensitivity of the objective function with the NSGA-II algorithm

the sensitivity-NSGA-II hybrid algorithm (referred to as SH-NSGA-II) was proposed. The multi-objective optimization of free-form cable-braced grid shell and free-form spatial grid structures was carried out. Results show that compared with other three algorithms

the proposed algorithm not only achieved the Pareto optimal solution set with better accuracy and uniformity

but also had higher computational efficiency. The strain energy of the two optimized structures decreased by 21.2% and 60.9% respectively

and the geometric comprehensive quantitative index decreased by 15.4% and 30.9% respectively. The mechanical performance of the structures was improved

and the similarity of the surface as well as the fluency and regularity of the free-form grids was effectively improved by taking the geometric comprehensive quantitative index as the geometric objective function.