## 3 Algorithm Improvement and Scheme Evaluation
### Improvement Strategy for the NSGA-III Algorithm
#### 3.1.4 Algorithm Implementation Process:
To alleviate the conflict between water supply and demand, a multi-objective water resource optimization model is established, comprehensively considering social, economic, and ecological benefits. Previous studies on Jinzhong City have \begin{table}
\begin{tabular}{c c c c c} \hline  & **Scheme** & **Water Shortage (10\({}^{4}\) m\({}^{3}\))** & **Economic Benefit (10\({}^{8}\) CNY)** & **COD Emission (10\({}^{4}\) t)** \\ \hline \multirow{2}{*}{2030} & P = 50\% & 1390 & 175.6215 & 6.3144 \\  & P = 75\% & 8447 & 161.9397 & 6.0303 \\ \hline \multirow{2}{*}{2035} & P = 50\% & 1319 & 218.1919 & 6.7996 \\  & P = 75\% & 6155 & 212.7355 & 6.9074 \\ \hline \end{tabular}
\end{table} 
Table 11: The target values of different planning schemes. Figure 6: The proportion of water consumption in different scenarios of each water user in the planning year. only considered two objectives in water resource allocation models [42], which are relatively simple. In contrast, this study uses three objective functions: minimizing water shortages, maximizing economic benefits, and minimizing emissions of major pollutants. The model is constrained by water supply balance, supply capacity, total water usage, and non-negativity of variables, providing a more comprehensive approach to optimizing water resource allocation. Since the data used in this model is specific and can be adjusted for different regions, it can be applied to other similar water-scarce cities. (2) A comparative analysis of the water demand data for the current and planning years in Jinzhong City reveals an increase in water supply for the planning years, with the available water supply in 2035 exceeding that of 2030. This is due to the further increase in reclaimed water supply in 2035, which improves the regional water supply structure and effectively alleviates the tension of insufficient water resources. This aligns with existing policy documents such as the _14 th Five-Year Plan of Shanxi Province_ and the _Jinzhong City Central Urban Area Water Supply Special Plan_ (2024 ZXG-036). In the current year, the production of reclaimed water is relatively low, and its price is similar to that of regular water, leading to low acceptance and utilization by enterprises. Most reclaimed water is directly used to supplement river flows, with the excess beyond ecological needs resulting in waste. Therefore, managers need to provide specific guidance measures, such as reducing the price of reclaimed water and constructing comprehensive reclaimed water supply pipelines to lower the barriers to its use, thereby encouraging enterprises to recognize and use reclaimed water. (3) In multi-objective optimization problems with constraints, the Pareto front is unknown and can vary due to the influence of these constraints. The reference points in the traditional NSGA-III algorithm are predefined, which may not accurately reflect the development trend of the Pareto front. To address this issue, this study improves the NSGA-III algorithm by incorporating a reference point adjustment strategy, a dynamic solution retention mechanism, and a selection strategy, resulting in the I-NSGA-III algorithm. Comparative experiments using test functions show that the IGD metric of I-NSGA-III is reduced by 5.17% to 50.22%, and the HV metric is increased by 2.47% to 7.63%, demonstrating that this algorithm offers better optimization accuracy and overall performance. (4) A comparison of the allocation schemes across different planning years shows that, under the drought scenario, water shortages increase and economic benefits decline compared to the normal scenario. However, COD emissions decrease due to reduced water consumption, highlighting a significant trade-off between economic objectives and ecological and social goals. This result aligns with the \"economic-ecological\" conflict observed by [PERSON] et al. [7] in their study on water resource optimization in Shanxi Province.