## 3 Results and Discussion
### Distribution Characteristics of Design Variables and Their Formation Causes
#### 3.2.2 Effect of Window-Wall Ratio, South Sunvisor Overhang Length, and External Window Type  
The statistical results for the window-wall ratio, south sunvisor overhang length, and external window type in the Pareto non-dominated solution set are shown in Figures 8 and 9. For the north window-wall ratio, the values in Xi'an and Yulin are the same, at 0.15 (i.e., the lower limit of the given window-wall ratio range). Although there is a large difference in solar radiation between the two regions, the impact on the building's north side is small, and the smaller the window-wall ratio, the more conducive to reducing the building energy consumption, cost, and carbon emissions of the external windows. This indicates that the lower limit of the given interval can be directly chosen for the north window-wall ratio design. As for the south window-wall ratio, there exists some difference between the two regions. The values of Xi'an are all at the lower limit of the given interval, i.e., 0.3, while the value of 0.3 occupies the largest proportion in Yulin, but 0.35 and 0.4 are also distributed. The south sunvisor's overhang length in the Yulin area is mainly 0-0.1 m. Mainly due to the colder climate, the heating energy consumption accounts for a relatively high proportion of EC, while the cooling energy consumption is very small, so a smaller sunvisor is more conducive to reducing EC while also decreasing the LCC and LCCO\({}_{2}\). The overhang length in Xi'an ranges from 0 to 0.2 m and from 0.5 to 0.9 m, distributed at both ends, which is mainly formed by multi-objective control. The reasons behind the values of these two variables will be further analyzed in the following text, along with the influence of single factors on objective functions. For the window type, although external windows with better thermal performance are beneficial for reducing energy consumption and improving the indoor thermal environment, the investment cost and production carbon emissions are higher. In the Xi'an area, the south window types are mainly distributed in type A. The winter climate in Yulin is colder, and the proportion of type-C windows increases, but the solar radiation in this area is stronger, and the solar heat gain coefficient of type A is higher, which is more beneficial for the introduction of solar radiation, so the proportion of this type is still high. With respect to the north window, all three types were selected in both regions, and the proportion of type C in Yulin was higher than that in Xi'an. Figure 8: Value distribution of window-wall ratio and sunvisor overhang length in Pareto solutions: (**a**) Xi’an and (**b**) Yulin. Considering the interaction between the window-wall ratio and thermal performance of the building envelope, three cases were set to analyze the effects of the south window-wall ratio on the objective functions based on the benchmark building, as follows: 1 the external window is type A; 2 the external window is type C; 3 the insulation layer thickness of the roof and external wall is set as 0.1 m, and the external window is type A. Figure 10 presents the relationship between the south window-wall ratio and the four objectives in Xi'an. With an increase in the south window-wall ratio, the values of the four objectives all show an increasing trend, but the degree of influence on each objective is different. Compared with case-1, the change in the window-wall ratio increases the variation amplitude of the four objectives in case-2, while for case-3, the changes in EC, TDHP, and LCCO\({}_{2}\) increased, and the change in LCC decreased. In general, the influence of the south window-wall ratio on the four optimization objectives in the Xi'an area is in the same direction, and the larger the window-wall ratio, the more unfavorable, so its value is the lower limit of the given range. Figure 11 shows the relationship between the south window-wall ratio and the four objectives in Yulin. Compared with Xi'an, the influence rule demonstrated in Yulin is different.