## 4 Results and Discussion  
### Multi-Objective Optimization Results of Outdoor Environmental Performance  
#### 4.1.1 Optimization Process  
Figure 7 illustrates the iterative changes in the three objective functions during the optimization process. Figure 7a-c display the standard deviation (SD) variations for each objective function. Each curve represents the data from a generation of samples, where the highest point on the horizontal axis corresponds to the average objective value of that generation. The color transitions from red (initial generation) to blue (final generation). The width of the curve reflects the standard deviation, with narrower curves indicating a more concentrated distribution of objective values.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Dataset** & **Training Set (R2)** & **Testing Set (R2)** \\ \hline UTCI-S & 0.944 & 0.712 \\ UTCI-W & 0.993 & 0.843 \\ SH & 1.000 & 0.966 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Model performance of XGBoost-TPE R2.  
Figure 7: Standard deviations of objectives and average values of Pareto solution sets during the optimization process. (**a**) Standard deviation of objectives in the optimization process for UTCI-S. (**b**) Standard deviation of objectives in the optimization process for UTCI-W. (**c**) Standard deviation of objectives in the optimization process for SH. (**d**) Average values of Pareto solution sets for UTCI-S. (**e**) Average values of Pareto solution sets for UTCI-W. (**f**) Average values of Pareto solution sets for SH.  
As shown in Figure 7a, the average objective value of the samples gradually decreases with iterations, the standard deviation diminishes, and the objective values converge. Overall, Figure 7a-c indicate significant differences between the initial and final values of the three optimization objectives, demonstrating a remarkable optimization effect and an increase in homogeneity among the final generations of samples.  
Figure 7d-f further demonstrate the convergence of the genetic algorithm. Each blue circle in the figures represents the average objective value of 50 experiments in a single iteration, while the blue line shows the trend of the objective values across generations. The red dashed line represents the fitted trendline.  
As shown, the objective value UTCI-W exhibited the most stable optimization process, with the average value increasing from \(-8.08\) to approximately \(-7.90\) during the early iterations, and then gradually stabilizing around \(-7.83\). Figure 7d,f also reveal slight fluctuations in the middle and later iterations, ultimately reaching a stable state.  
The entire optimization process took approximately 195 h, generating 3000 feasible solutions through multiple iterations. Among these, 388 solutions were identified as optimal, and after removing 247 duplicates, a total of 141 Pareto optimal solutions were obtained. Pareto optimal solutions represent a set of trade-offs among the three objectives--UTCI-W, UTCI-S, and sunlight hours--where no single objective can be improved without compromising at least one of the others. These solutions illustrate the balance between conflicting performance criteria, offering a range of options that cater to varying priorities in urban block design. This set of solutions provides urban designers with a foundation for making informed decisions and balancing environmental performance goals tailored to the needs of elderly residents.