## 3 Results and Discussion
### Optimal Design Solutions and Comparative Analysis of Different Regions  
The optimized Pareto non-dominated solution set consists of a series of points, each of which is a solution associated with a set of decision variables representing the design scenario, all of which are acceptable. Associating the objective functions with design variables, the clustering parallel coordinate graphs are shown in Figure 20. It can be seen that it is impossible for all four objective values of any scheme to be better than those of the others; at least one objective will be unfavorable. Thus, these schemes are not directly comparable to one another. The corresponding design variable value is not the larger or smaller the better, but there is a coordination relationship with other variables. In order to verify the interpretability of the design variables to the objective functions and evaluate the robustness of the optimization results, the standard regression coefficient method was used for sensitivity analysis. The results show that the adjusted R\({}^{2}\) values for the four objectives of EC, TDHP, LCC, and LCCO\({}_{2}\) are 0.94, 0.93, 0.99, and 0.90 (Xi'an) and 0.93, 0.93, 0.99, and 0.90 (Yulin), respectively, with \(p<0.01\), indicating a very significant difference. It is evident that the design variables have a high degree of interpretation for the objective function, and the optimization results have high reliability, so they can be used for further analysis. Different decision-makers may have different tendencies toward energy consumption, comfort demands, cost-effectiveness, and environmental impact, and they will ultimately need to adopt a decision method to determine the optimal design scheme. The TOPSIS decision-making method is used to make further comprehensive decisions to choose the optimal solutions from the Pareto solution set. Considering the balance of the four objectives, the scheme in which EC, LCC, TDHP, and LCCO\({}_{2}\) are equally important is the optimal scheme (case-1), so the weight value of each objective was set to 0.25. Meanwhile, the corresponding schemes where each objective is optimal were selected for comparison, i.e., EC optimal (case-2), TDHP optimal (case-3), LCC optimal (case-4), and LCCO\({}_{2}\) optimal (case-5). Table 4 indicates the optimal values of the objective functions and the corresponding design parameters of the four-objective optimization problem in Xi'an and Yulin. Figure 19: Variation curve of objective functions’ difference values between case-1, case-2, and the benchmark building: (**a**) Case-1 and (**b**) Case-2. As can be seen from Table 4 and Figure 5, case-1 is considered from the perspective of comprehensive performance and located in the middle region of the Pareto solution set. In the Xi'an area, the energy-saving rate of this scheme is 61.7% (the EC of the reference building is 43.9 KWh/m\({}^{2}\)), the TDHP improvement rate is 20.3% (the TDHP of the reference building is 49.2%), the LCC is 254.8 CNY/m\({}^{2}\), and the LCCO\({}_{2}\) is 72.3 kgCO\({}_{2}\)/m\({}^{2}\). In the Yulin area, the corresponding values are 69.7% (the EC of the reference building is 53.4 KWh/m\({}^{2}\)), 19.4% (the TDHP of the reference building is 49.9%), 230.2 CNY/m\({}^{2}\), and 0 kgCO\({}_{2}\)/m\({}^{2}\). Comparing the two regions, although the difference in building energy consumption is small, from the perspective of the energy-saving rate, the energy-saving potential of Yulin is higher, mainly because the region is rich in solar energy resources, and its photovoltaic power generation is significantly higher than that of Xi'an. If the photovoltaic power generation is not included, the energy-saving rate of the two regions is 39.2% and 41.2%, respectively; this difference is small, indicating that in the area of solar resource enrichment, the use of photovoltaic power generation can effectively reduce buildings' energy consumption. The TDHP of Yulin is slightly higher than that of Xi'an, while the opposite is true for LCC and LCCO\({}_{2}\).