This paper investigates the structural performance of flat double-layer grids with various constitutive units, addressing a notable gap in the literature on diverse geometries. Six common types of flat double-layer grids are selected to provide a comprehensive comparison to understand their structural performance. Parametric models are built using Rhino and Grasshopper plugins. Single- and multi-objective optimization processes are conducted on the considered models to evaluate structural mass and maximum deflection. The number of constitutive units, the structural depth, and the cross-section diameter of the members are selected as design variables. The analysis reveals that the semi-octahedron upon square-grid configuration excels in minimizing structural mass and deflection. Furthermore, models lacking a full pyramid form exhibit higher deflections. Sensitivity analyses disclose the critical influence of the design variables, particularly highlighting the sensitivity of structural mass to the number of constitutive units and cross-section diameter. These findings offer valuable insights and practical design considerations for optimizing double-layer grid space structures.