## 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
With the increase in the south window-wall ratio, the EC, LCC, and LCCO\({}_{2}\) showed an increasing trend, while TDHP decreased, affecting each objective in a different direction. There was a single linear relationship between the window-wall ratio and each objective, and the change rate of EC, LCC, and LCCO\({}_{2}\) was higher than that of TDHP,  
Figure 10: Relationship between the south window–wall ratio and the four objectives in Xi’an: (**a**) case-1; (**b**) case-2; and (**c**) case-3. Figure 9: Value distribution of window types in Pareto solutions: (**a**) Xi’an and (**b**) Yulin. so the value range extended to 0.4 after optimization and tradeoff, forming a solution set distribution different from that of Xi'an. Similarly, compared to case-1, the variation amplitude of the four objectives increased in case-2; for case-3, the variation range of EC, TDHP, and LCCO\({}_{2}\) increased, while that of LCC decreased. Comparing the two regions, the influence amplitude of the window-wall ratio on EC was essentially the same under the same conditions, and the effect was in the same direction, while the TDHP was also similar, but the effect was in the opposite direction. The effects on LCC and LCCO\({}_{2}\) were quite different, and the window-wall ratio of residential buildings in Yulin had a greater impact on these two objectives. For the sunvisor, the optimization results show that it is not appropriate or that only a small sunvisor should be used in Yulin, so the influence of sunvisor overhang length on the four objectives was analyzed only for Xi'an. Moreover, considering the interaction of the design variables, three cases were set, as follows: 1 based on the benchmark building, a type A window is adopted; 2 on the basis of case-1, the roof and external wall are provided with a 0.1 m thick insulation layer; 3 on the basis of case-2, the window-wall ratio is set to 0.6. As shown in Figure 12, with the increase in sunvisor overhang length, the EC, LCC, and LCCO\({}_{2}\) increased linearly, while the TDHP first decreased and then increased. Comparing case-2 to case-1, the variation amplitude of the four objectives was slightly reduced, indicating that the influence of the change in sunvisor length on each objective was weakened after the thermal performance of the building envelope was improved. Comparing case-3 and case-2, the variation amplitude of the four targets increased significantly, revealing that the change in sunvisor length enhances the influence on each objective when the south window-wall ratio is increased. Therefore, given the different direction and amplitude of the effect of overhang length on each objective, the value distribution formed by the balance of the multiple objectives is displayed in Figure 8a, where the median value (0.3-0.4 m) and upper limit value (1.0 m) of the variable range are not filtered as the parameter values of the Pareto solution set. Figure 11: Relationship between the south window–wall ratio and the four objectives in Yulin: (a) case-1; (b) case-2; and (c) case-3.