## 3 Algorithm Improvement and Scheme Evaluation
### Improvement Strategy for the NSGA-III Algorithm
#### 3.1.4 Algorithm Implementation Process:

Table 3: Comparison of IGD and HV Metrics between Improved and Original Algorithms. \[\lambda_{u,m}=\frac{\theta_{u,m}W_{u,m}}{\sum_{u}\theta_{u,m}W_{u,m}} \tag{13}\]

In the formula: \(W\) represents the subjective weight; \(\theta\) is the objective weight obtained using the entropy method; \(\lambda_{u}\) is the first-level composite weight, and \(\lambda_{u,m}\) is the second-level composite weight. Here, \(u\) is the number of first-level indicators, and \(m\) is the number of second-level indicators under the same parent indicator \(u\). The first-level composite weights refer to the weights of the economic, social, and ecological systems, denoted as \(\lambda_{1}\), \(\lambda_{2}\) and \(\lambda_{3}\) respectively. The second-level composite weights refer to the weights of the second-level evaluation indicators within each system: for the economic system, they are \(\lambda_{u,m}\) (\(m\) = 1,2,3); for the social system, they are \(\lambda_{2,m}\) (\(m\) = 1,2); and for the ecological system, they are \(\lambda_{3,m}\) (\(m\) = 1,2). The comprehensive evaluation score for each system is calculated according to Formula (14):

\[X_{u}=\sum_{1}^{m}X_{u,m}\lambda_{u,m} \tag{14}\]

In the formula: \(X_{u}\) represents the comprehensive evaluation score for system \(u\), while \(X_{1}\), \(X_{2}\) and \(X_{3}\) denote the comprehensive scores for the economic, social, and ecological systems, respectively. \(X_{u,m}\) is the score for each second-level indicator within system \(u\). The scores for each indicator are calculated as follows:

When \(X_{u,m}\) is a positive indicator

\[X_{u,m}=\frac{y_{u,m}-min(y_{u,m})}{max(y_{u,m})-min(y_{u,m})} \tag{15}\]

When \(X_{u,m}\) is a negative indicator

\[X_{u,m}=\frac{max(y_{u,m})-y_{u,m}}{max(y_{u,m})-min(y_{u,m})} \tag{16}\]

In the formula, \(y_{u,m}\) represents the condition of the \(m\)-th second-level indicator within system \(u\). Since the evaluation model established is a system coupling coordination degree model, the formula for calculating the coupling degree is as follows:

\[C_{3}=\sqrt[3]{X_{1}X_{2}X_{3}/\left[(X_{1}+X_{2}+X_{3})/3\right]^{3}} \tag{17}\]

In the formula, \(C_{3}\) represents the coupling degree between systems (ranging from 0 to 1, where a smaller coupling degree indicates lower correlation between systems). Then, the comprehensive score of the multi-system is calculated using the formula \(T_{3}=\lambda_{1}X_{1}+\lambda_{2}X_{2}+\lambda_{3}X_{3}\). Finally, the coordination degree of the multi-system is calculated using the formula \(Z_{3}=\sqrt{C_{3}T_{3}}\). Drawing on relevant research results [38], the evaluation standards for multi-system coordination degree are shown in Table 5. The calculated weights for each level of indicators are presented in Table 6. In this study, it is assumed that the comprehensive contribution values of the three systems in the model are equal, so the first-level weights are all set to \(1/3\). ## 4 Overview of the Study Area and Model Setup

### Overview of the Study Area

Jinzhong City is located in the central-eastern part of Shanxi Province and serves as an important economic, cultural, and transportation hub in the region. The city covers a total area of 16,347 km\({}^{2}\), with geographical coordinates of 111\({}^{\circ}\)25\({}^{\prime}\)-114\({}^{\circ}\)05\({}^{\prime}\) E longitude and 36\({}^{\circ}\)40\({}^{\prime}\)-38\({}^{\circ}\)06\({}^{\prime}\) N latitude. Situated in a temperate monsoon climate zone, Jinzhong exhibits typical continental climate characteristics, with an average annual temperature ranging from 3.0 to 11.0 \({}^{\circ}\)C. The average annual precipitation is 512 mm, mostly concentrated between June and September, with significant geographical spatial differences. The per capita water resource availability is 367 m\({}^{3}\), which is below the provincial average and only one-sixth of the national average in China, classifying it as a water-scarce region. The insufficiency of surface water resources has led Jinzhong City to rely heavily on groundwater supplies.