## 3 Algorithm Improvement and Scheme Evaluation
### Improvement Strategy for the NSGA-III Algorithm
#### 3.1.4 Algorithm Implementation Process:
The available water supply for different scenarios in the planning years for Jinzhong City is shown in Figure 3.

According to the _Shanxi Water Conservation Action Plan Jinzhong Implementation Rules_ and the _Jinzhong City Master Plan_ (2016-2030), by 2030 and 2035, the water supply sources in southern Jinzhong will include reclaimed water in addition to surface water, groundwater, and transferred water. Considering the uncertainty in the total available water supply and the varying water frequencies in different typical years, data from the 2006-2020 _Jinzhong Statistical Yearbook_ and the _Shanxi Province Water Resources Bulletin_ were used. Taking into account the current water supply capacity of existing hydraulic projects in the southern Jinzhong water supply area and the construction layout and progress of water diversion projects during the planning period, the projected available water supply for the planning years is shown in Figure 4. The amount of reclaimed water is calculated based on the water demand for residential living, tertiary industry, and industrial use in the planning years. The available water supply for the normal and drought scenarios in 2030 is 85,411 \(\times\) 10\({}^{4}\) m\({}^{3}\) and 74,307 \(\times\) 10\({}^{4}\) m\({}^{3}\), respectively, while in 2035, it is 87,202 \(\times\) 10\({}^{4}\) m\({}^{3}\) and 77,915 \(\times\) 10\({}^{4}\) m\({}^{3}\), respectively. Notably, with technological advancements, the available

Figure 2: Network diagram of water supply system. reclaimed water in 2035 is projected to be 9901 \(\times\) 10\({}^{4}\) m\({}^{3}\), a significant increase from 4866 \(\times\) 10\({}^{4}\) m\({}^{3}\) in 2030, effectively supplementing the local water resource gap. Figure 4: Water supply of each administrative region in the planning year. Figure 3: Water demand for each administrative region in planning year. ### Model Parameters

(1) Water Supply Benefit Coefficient \(b_{j}^{k}\): By analyzing the relationship between the total output value of different industries in Jinzhong City and their water use quotas, and based on the DB14/T 1049.1-2020 _Shanxi Province Water Use Quotas_, the water supply benefit coefficients for the five categories of water users--domestic, agricultural, secondary industry, tertiary industry, and ecological--are calculated as follows: 600, 34.83, 638.30, 3413.60 \(\text{CNY}/\text{m}^{3}\), and 500 \(\text{CNY}/\text{m}^{3}\). (2) Water Supply Cost Coefficient \(c_{j}^{k}\): A detailed study of the 2020 water fee standards and supporting water price regulations in Jinzhong City determined the water supply cost coefficients for the five categories of water users--domestic, agricultural, secondary industry, tertiary industry, and ecological--as follows: 3.90, 0.25, 4.63, 5.80 \(\text{CNY}/\text{m}^{3}\), and 2.60 \(\text{CNY}/\text{m}^{3}\). (3) Water Supply Priority Coefficient \(a_{i}\): The water supply priority coefficient is determined by Formula (18):

\[a_{i}=(1+m_{max}-m_{i})/\sum_{i=1}^{I}(1+m_{max}-m_{i}) \tag{18}\]

According to the water supply priority principle, the calculated water supply priority coefficients are as follows: surface water 0.4, groundwater 0.1, transferred water 0.3, and reclaimed water 0.2. (4) Water Use Equity Coefficient \(\lambda_{j}\): Based on the importance of various water users in Jinzhong City, the required water supply priority is in the following order: domestic water use, ecological water use, tertiary industry water use, secondary industry water use, and agricultural water use. Using Formula (18), the calculated water use equity coefficients are as follows: domestic water use 0.33, agricultural water use 0.07, secondary industry water use 0.13, tertiary industry water use 0.20, and ecological water use 0.27. (5) Sewage Discharge Coefficient \(a_{j}^{k}\) and pollutant discharge concentration \(\beta_{j}^{k}\): With reference to prior research [25], chemical oxygen demand (COD) was selected as the indicator for \(\beta\) in this study.