## 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  
Figure 15 displays the statistical results for the insulation layer thickness for external walls. The common characteristic is that, subject to the mutual restriction of the four objectives, the values are distributed over many points within the threshold, and there exist multiple extreme value points, whose corresponding insulation layer thicknesses are not exactly the same. This is different from the roof results, indicating that when considering multiple objectives comprehensively, a thicker external wall insulation layer is not better, and there is greater selectivity. Comparing the two regions, the average values of south, north, east, and west wall insulation layer thickness in Yulin are 0.13 m, 0.14 m, 0.13 m, and 0.13 m, respectively, which are higher than the values for Xi'an (0.12 m, 0.11 m, 0.12 m, and 0.09 m, respectively), and the differences reflected in the north and west wall insulation layer thickness are obvious. The mapping relationship between insulation layer thickness and the four objectives is analyzed below. First of all, considering the influence of building orientation, two cases were set to analyze the relationship between insulation layer thickness and objective functions: 1 the building orientation is to the south and 3 the building orientation is south by west 30. The simulation results of case-1 are shown in Figure 16. Firstly, with the increase in insulation layer thickness, EC and TDHP show a gradual decrease, LCC increases linearly, and LCCO\({}_{2}\) first presents a significant decrease and then a slow increase. Secondly, the change in the insulation layer thickness with different orientations has a diverse response degree to each objective. In the Xi'an area, the sensitivity order for EC is south wall \(\approx\) east wall \(>\) west wall \(>\) north wall, for TDHP, it is east wall \(>\) north wall \(>\) west wall \(>\) south wall, for LCC, it is north wall \(>\) west wall \(\approx\) east wall \(>\) south wall, and for LCCO\({}_{2}\), it is south wall \(\approx\) east wall \(>\) west wall \(>\) north wall. Due to the different climate and solar radiation conditions, Yulin is essentially the same as Xi'an in terms of the influence rule, but there are differences in the response degree; for example, the sensitivity order for EC becomes east wall \(>\) west wall \(>\) north wall \(>\) south wall; for LCCO\({}_{2}\), it becomes east wall \(>\) west wall \(>\) north wall \(>\) south wall; and for TDHP and LCC, the sensitivity ranking remains unchanged. Figure 14: Relationship between roof insulation layer thickness and four objectives: (**a**) Xi’an and (**b**) Yulin. The simulation results of case-2 are displayed in Figure 17. When the building orientation changes, the solar radiation heat gain of the four orientation walls will also be different. It can be observed from Figure 17 that the change rule of each objective with the increase in insulation layer thickness is consistent with case-1, but the response degree for some objectives is different. In the Xi'an area, the sensitivity ranking of EC is changed as follows: south wall (south by west \(30^{\circ}\)) \(\approx\) east wall (east by north \(30^{\circ}\)) \(\approx\) west wall (west by south \(30^{\circ}\)) \(>\) north wall (north by east \(30^{\circ}\)); for TDHP, it is east wall \(\approx\) north wall \(\approx\) west wall \(>\) south wall; and for LCCO\({}_{2}\), it is south wall \(\approx\) east wall \(\approx\) west wall \(>\) north wall. For the Yulin area, the sensitivity ranking of EC is changed as follows: west wall \(>\) east wall \(>\) north wall \(\approx\) south wall; for TDHP, it is north wall \(>\) west wall \(\approx\) east wall \(>\) south wall; for LCCO\({}_{2}\), it is west wall \(>\) east wall \(>\) south wall \(\approx\) north wall. The ranking remains essentially unchanged for LCC in both regions. Figure 15: Value distribution of insulation layer thickness for external walls in Pareto solutions: (**a**) Xi’an and (**b**) Yulin.