## 3 Results and Discussion
### Distribution Characteristics of Design Variables and Their Formation Causes
#### 3.2.4 Effect of the External Wall's Insulation Layer Thickness
Furthermore, the influence amplitude of the insulation layer thickness on the objective values will also change. Taking the south wall for example, in order to clearly reflect the comparison of two conditions, it is expressed by the difference in the value of objective functions between case-2 and case-1. As shown in Figure 18, for the Xi'an area, when the building orientation changes from south to 30\({}^{\circ}\) south by west, with an increase in insulation layer thickness, the influence amplitude on EC, LCC, and LCCO\({}_{2}\) essentially shows a decreasing trend, while that on TDHP displays a fluctuating state. For the Yulin area, the variation rule of influence amplitude is consistent, but in view of the objective values, the variation amplitude of EC and TDHP is higher than that for Xi'an, while that of LCC and LCCO\({}_{2}\) is lower. Therefore, when rotating the building orientation, the sensitivity and influence degree of the insulation layer thickness to the objectives will be changed. Different orientations corresponding to the optimal insulation thickness may also be different. Figure 16: Relationship between external wall insulation layer thickness and four objectives (case-1): (a) Xi’an and (b) Yulin. Figure 17: Relationship between external wall insulation layer thickness and four objectives (case-2): (a) Xi’an and (b) Yulin. Furthermore, in view of the influence of exterior window type and window-wall ratio, taking the south wall of Xi'an as an example, based on the benchmark building, two cases were set as follows: 1 the thermal performance of exterior windows is improved to type A and 2 the south window-wall ratio is increased to 0.6. Figure 19 shows the variation curves of the objective functions' difference values between case-1 and the benchmark building, and between case-2 and the benchmark building, with the insulation layer thickness. It can be seen that when the thermal performance of the exterior windows is improved, the variation range of EC and LCCO\({}_{2}\) shows an increasing trend, while that of TDHP and LCC decreases with the increase in insulation layer thickness. However, when the south window-wall ratio is increased, the variation range of EC and TDHP increases with the increase in insulation layer thickness, while LCC shows a trend of first decreasing and then increasing linearly, and LCCO\({}_{2}\) increases obviously at first and then decreases slightly. These results indicate that the effect amplitude of changing the insulation layer thickness on each objective is affected by the window type and area. This will also affect the determination of the optimal insulation layer thickness. The above analysis shows that, unlike with single-objective optimization, a unique solution can be obtained. In the process of multi-objective optimization, due to the different action rules of design variables on each objective and the reciprocal effects of other variables, rich value possibilities are formed, which also provide more possibilities for the design scheme. Figure 18: Relationship between south wall insulation layer thickness and difference values of objective functions: (**a**) Xi’an and (**b**) Yulin.