## 4 Optimization of Diagrid Performance Based on the Geometrical Features
The optimization procedure aims at minimizing the unit structural weight of the building, while complying with the stiffness and strength requirements. This is achieved by formulating an objective function (OF) to be minimized, and specifying the constraints of the optimization problem, as thoroughly described in [15; 33]. The results of the analysis are analyzed in terms of unit structural weight, diagonal cross-section distribution along the elevation, deformed configuration, lateral displacements, inter-story drifts and diagonal DCR, highlighting the most efficient solutions from the structural viewpoint. The authors also propose a complexity index, which accounts for the \"constructability\" of the diagrid structure. This is defined by taking into account five main metrics, i.e., the total number of nodes, the number of different cross-sections, the number of diagonal splices necessary for transportation purposes, the total number of diagonals and the number of different diagonal lengths. The results of the complexity index, together with the obtained structural weight, are shown in Figure 11b for each geometrical pattern. Graphs like the one reported in Figure 11b can be extremely useful for evaluating both the structural efficiency and constructability of the investigated diagrid solutions [33]. The analyses shown in the previous paragraph of this Section, for the assessment of diagrid performance, take into account only square and rectangular buildings. To consider also different plan shapes, [PERSON] et al. [34] recently investigate the simultaneous effect of diagonal inclination and planar shape on the top lateral displacement and diagrid weight. A total of 64 parametric models of a 180-m tall building, with various cross-sectional shapes, are generated by randomly increasing the number of sides of both the base and top plans. Five diagonal angles are also considered, in the 33-81\({}^{\circ}\) range. By means of Genetic Algorithms coupled with FE structural analyses, the authors find out that the diagonal angle of 63\({}^{\circ}\) provides the least amount of top lateral deflection, while reducing the required structural material. Furthermore, it is found that increasing the sides of the base and top plans leads to the most efficient solutions in terms of lateral displacement, although the increase of structural performance is not as evident as when changing the diagonal inclination. More recently, a similar analysis has been carried out by [PERSON] et al. [35], to investigate the influence of both the diagonal inclination and plan shape on the structural behavior of diagrid tubes. In this study, the structural response for square, hexagonal, octagonal and circular diagrids is  
Figure 11: (**a**) Geometrical patterns for the 90-story tall diagrid building considered by [PERSON] et al. [33]: uniform-angle patterns (60\({}^{\circ}\), 70\({}^{\circ}\), 80\({}^{\circ}\)), varying-angle pattern according to Zhang approach (VA) [31], double-density pattern (DD), variable-density pattern (VD), stress lines pattern (ISO). (**b**) Unit structural weight (blue bars) and complexity index (red curve) for the investigated diagrid patterns. VA_IDR, VD_1, VD_15, ISO_15, ISO_9, ISO_5, ISO_5* refer to additional subsets of the corresponding patterns, as reported in [33]. Used with permission from [PERSON] et al. [33]. evaluated not only in terms of lateral deflection, but also in terms of torsional rotations. The analysis is carried out by means of the previously developed matrix-based method (MBM) [18], and shows that the diagonal angle is the main parameter governing the structural response, rather than the specific plan shape. As already found out previously by [PERSON] et al. [10], the optimal angle to minimize the lateral displacement increases with the aspect ratio of the building, as it results from the need to limit both shear and bending deformability.