## 3 Algorithm Improvement and Scheme Evaluation
### Improvement Strategy for the NSGA-III Algorithm
#### 3.1.4 Algorithm Implementation Process:
secondary indicators were calculated using the AHP method and the entropy weight method, with the weights of each indicator presented in Table 1. The coupling coordination degree of water resource allocation was obtained using Formulas (12)-(17), and the results are shown in Table 8.

According to the calculation results, after applying the I-NSGA-III algorithm, the coordination degree for Jinzhong City in 2030 under the normal scenario (P = 50%) is 0.8358, which indicates a good level of coordination. Under the drought scenario (P = 75%), the coordination degree is 0.7847, falling into the medium coordination level. In comparison, by 2035, the coordination degree under the normal scenario improves from 0.8358 to 0.8556 (an increase of 0.0199) and, under the drought scenario, it rises from 0.7847 to 0.8701 (an increase of 0.0855), both reaching a good coordination level. Combined with the water supply forecast results, it is evident that the extensive use of reclaimed water can improve regional coordination. However, the four optimized water resource allocation schemes still do not reach the optimal coordination threshold, indicating that solely relying on water resource allocation is insufficient to achieve system optimization; other regulatory measures are needed. Further analysis of system scores reveals that the economic system scores lower than the social and ecological systems, and the coordination degree is constrained by the balanced development of all systems. It is recommended to take measures to promote local economic development and improve the economic system's score to further enhance coordination. ### Water Resource Allocation Results

The specific values for each allocation scheme selected through the TOPSIS method are presented in Tables 9 and 10. The allocation results comply with the Comprehensive Wastewater Discharge Standard of Shanxi Province (DB14/1928-2019) [41]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Scheme**} & **Economic** & **Social** & **Environmental** & **Comprehensive** & **Coupling** & **Coordination** \\  & **Score** & **Score** & **Score** & **Score** & **Degree** & **Degree** \\ \hline \multirow{2}{*}{2030} & P = 50\% & 0.8512 & 0.4017 & 0.9967 & 0.7499 & 0.9315 & 0.8358 \\  & P = 75\% & 0.6855 & 0.4416 & 0.7710 & 0.6327 & 0.9731 & 0.7847 \\ \multirow{2}{*}{2035} & P = 50\% & 0.7097 & 0.6295 & 0.8783 & 0.7392 & 0.9904 & 0.8556 \\  & P = 75\% & 0.7317 & 0.6207 & 0.9556 & 0.7693 & 0.9841 & 0.8701 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Coupling coordination degree of different configuration schemes. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Scheme**} & **Administrative Region** & **Domesticity** & **Agriculture** & **Secondary Industry** & **Tertiary Industry** & **Ecology** & **Total** \\ \hline \multirow{8}{*}{Normal Scenario} & Taigu & 1454 & 10,139 & 731 & 237 & 633 & 13,194 \\  & Yusbe & 490 & 3108 & 407 & 79 & 823 & 4907 \\  & Zuoquan & 644 & 2920 & 834 & 107 & 950 & 5455 \\  & Qixian & 1115 & 9857 & 610 & 207 & 435 & 12,224 \\  & Pingyao & 1965 & 11,939 & 934 & 289 & 624 & 15,751 \\  & Lingshi & 1115 & 1023 & 4939 & 325 & 614 & 8016 \\  & Jiexiu & 1998 & 4134 & 4329 & 329 & 576 & 10,966 \\ \cline{2-7}  & Total & 8781 & 43,120 & 12,784 & 1573 & 4655 & 70,913 \\ \hline \multirow{8}{*}{Drought Scenario} & Taigu & 1375 & 9894 & 660 & 208 & 596 & 12,733 \\  & Yusbe & 490 & 366 & 407 & 79 & 823 & 5465 \\ \cline{1-1}  & Zuoquan & 644 & 3384 & 834 & 107 & 950 & 5919 \\ \cline{1-1}  & Qixian & 1015 & 9878 & 560 & 175 & 405 & 12,033 \\ \cline{1-1}  & Pingyao & 1837 & 10,883 & 874 & 236 & 573 & 14,403 \\ \cline{1-1}  & Lingshi & 1115 & 1172 & 4939 & 325 & 614 & 8165 \\ \cline{1-1}  & Jiexiu & 1758 & 3903 & 4115 & 294 & 563 & 10,632 \\ \cline{1-1} \cline{2-7}  & Total & 8232 & 42,780 & 12,388 & 1424 & 4525 & 69,349 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Water resources allocation results of two schemes in 2030. (1) Analysis of Water Allocation by Sector.