Multi-Objective Water Allocation for Wu’an City

Abstract

To solve the prominent problem of water supply and demand contradictions, enhance water resource security capabilities, and improve economic, social, and ecological benefits, this paper comprehensively analyzes the water resource situation in Wu’an City and proposes a method for calculating the rigid water demand and total water demand threshold for the whole city and a method for calculating the water supply capacity of multiple water sources. At the same time, taking economic, social, and ecological benefits as the objective function and water resource allocation rules, water supply balance, water supply capacity, total water consumption, water consumption per Chinese Yuan (CNY) 10,000 of Gross Domestic Product (GDP), water consumption per CNY 10,000 of industrial added value, and non-negative as constraints, the water resource optimization allocation model for Wu’an City was constructed, and the Non-dominated Sorting Genetic Algorithm III (NSGA-III) combined with the Technique for Order Preference by Similarity to an Ideal Solution (TOSPIS) was used to solve it. The results show that the rigid water demand of Wu’an City is met, the Gini coefficient of water supply satisfaction and ecological water shortage in the flat water scenario are both 0, the overall difference in water supply satisfaction of each township is very small, and the ecological water demand is met. Under the current situation, Wu’an City basically achieves a regional supply and demand balance, which can increase water supply by 5.841 million m³ and increase the net economic benefit of water supply by CNY 136.5515 million. The optimized water resource allocation plan has higher economic, social, and ecological benefits. The research can provide technical support for water resource management in Wu’an City.

1. Introduction

Water is a key basic resource required for the development of human societies, and its importance cannot be ignored. For example, agriculture relies on irrigation water to ensure food security [1]; industries require large amounts of water resources for production processes [2]; urban water supply is an indispensable part of the normal operation of cities [3]; and in terms of ecology, large quantities of water resources are needed to maintain the virtuous cycle of river basin ecosystems [4]. With the development of economies and societies, the demand for water resources continues to increase [5]. Therefore, rational development and optimal allocation of water resources are of great significance to the sustainable development of society. In 2023, the State Council issued the Outline of the National Water Network Construction Plan, proposing that they should “rely on the national backbone networks and provincial water networks, optimize the water system layout of rivers and lakes in cities and counties, promote the construction of water conservancy infrastructure, open up the ‘last kilometer’ of flood control and drainage and water resources allocation, and improve the basic public service level of urban and rural water conservancy”. The construction of water networks at all levels is inseparable from the scientific and rational optimization of water resource allocation.

Scholars are actively exploring the optimal allocation of water resources. Zhineng Hu [6] explored the optimal allocation of water resources in the Qujiang River Basin in China based on the principles of fairness and efficiency using a compromise solution method to improve the efficiency and fairness of regional water resource allocation. Xiaona Li [7] proposed a multi-objective, uncertain opportunity-constrained programming method to seek a reasonable allocation plan between multiple water sources and users. Yanbin Li [8] took the maximization of economic benefits, minimization of total water shortage, and improvement of water use efficiency as the goals and took water supply capacity and water demand as constraints to construct a water resource optimization allocation plan for the Yellow River Basin in Henan Province, and then used the NSGA-II algorithm to solve it, improving the water shortage phenomenon in the study area. Tom Roach [9] proposed a multi-objective optimization method based on resilience, which maximized the resilience of the water supply system and minimized the total cost to determine future adaptation strategies to cope with the impact of uncertain factors such as climate change. Mengqi Zhao [10] evaluated the effectiveness of various adaptive water resource management strategies under climate change scenarios based on the system dynamics framework, providing quantitative support for the adaptive management of water resources against the background of climate change.

In addition, commercial water resource allocation software, such as WEAP (Version 2019.2) and MIKE (MIKEBASIN, Version 2007) [11], have enhanced the usability and popularity of water resource allocation. However, since the software are fully encapsulated, it is difficult to fully meet the unique configuration requirements of different research areas, and their scalability is relatively poor. Research on the optimal allocation of water resources in China started late. In the early 1980s, Hua Shiqian conducted research on water resource utilization using systems engineering methods; this was considered the prototype for research on water resource allocation in China [12]. Subsequently, research on water resource allocation developed rapidly in China, going through “allocation only based on water–macroeconomic allocation–ecology-oriented allocation–generalized water resources allocation–trans-basin large-scale system allocation–integrated allocation of quantity and quality”, and has now reached an advanced international level. At the same time, some water resource allocation software with independent property rights have been developed, including WAS (Version 1.0) and GWAS (Version 2.1) [13,14]. These software have functions such as water resource evaluation, water resource scheduling, and water resource allocation.

However, there are still some limitations in the current research. Research on hierarchical water demand mainly focuses on the method of definition of rigid water demand for urban residents, while there is little research on the determination of rigid water demand thresholds for industries, agriculture, and ecology. The existing hierarchical water demand research objects are at provincial and municipal levels, while the county level, as the endpoint of water resource management, is limited by the difficulty in obtaining public information, and there are few research results related to hierarchical water demand by industries. Research on the joint allocation of local water, external water, and unconventional water, especially the special water source category of mine drainage water, is lacking. For resource-based water-scarce areas, mine drainage water is an important source of water for industrial, agricultural, and ecological use. In addition, commercial software for water resource allocation has problems, such as a high degree of encapsulation and difficulty in personalized customization.

As a typical resource-based industrial city, Wu’an City has a prominent water shortage problem. Its socio-economic structure is dominated by industries, especially the steel industry, which has an extremely urgent demand for water resources. In addition, Wu’an City has abundant unconventional water resources (such as mine drainage water). Therefore, the water resource allocation problem in Wu’an City is both universal and special. This study takes Wu’an City, a typical resource-based, water-deficient industrial city, as an example to determine the multi-level water demand thresholds for life, industry, agriculture, and ecology, predicts the water demand for the entire industry under the most stringent water resource management requirements, and solves the problem of determining the water demand thresholds for small-scale regional industries. At the same time, the important role of unconventional water, especially mine drainage water, in water resource allocation is strengthened to achieve multi-source and multi-objective coordinated optimization allocation. In addition, with economic, social, and ecological benefits as the objective function, and water resources allocation rules, water supply balance, water supply capacity, total water use, water use per CNY 10,000 of GDP, water use per CNY 10,000 of industrial added value, and non-negative as constraints, a personalized water resources optimization allocation model for Wu’an City is constructed. The NSGA-III algorithm is then used to solve the model to obtain the Pareto optimal solution set, and TOPSIS is used to select the optimal solution to obtain the optimal water resource optimization allocation plan. Based on the principles of fairness, efficiency, and sustainability, this study comprehensively considers the social, economic, and ecological environmental benefits and proposes a multi-level and multi-objective water resource allocation plan, which has certain theoretical and practical significance for promoting regional human–water harmony and achieving coordinated, high-quality development of social economy and ecological environment.

2. Study Area

Wu’an City is in Handan City, Hebei Province. It is located in the southern part of Hebei Province, at the junction of Shanxi, Hebei, Shandong, and Henan provinces. It is adjacent to Yongnian County to the east, Cixian County and Fengfeng Mining Area to the south, Shexian County and Zuoquan County in Shanxi Province to the west, and Shahe City in Xingtai to the north, and covers a total area of 1806 km². The geographical coordinates are east longitude 113°45′–114°22′ and north latitude 36°28′–37°01′ [15,16]. Wu’an City lies within the continental monsoon climate zone, with hot summers and cold winters. The annual average temperature is 12.4–13.8 °C. The soil types mainly include brown soil, new accumulation soil, rocky soil, and coarse bone soil. Among them, brown soil is the most widely distributed soil type. The average annual precipitation is 560.7 mm, and the per capita water resource is 432 m³, which is only 1/5 of the average level in China. It is a typical resource-based water-scarce area. The geographical location of Wu’an City is shown in Figure 1. Wu’an City is an economically strong county with prominent industries in the Beijing–Tianjin–Hebei region. It is also a resource-based, water-scarce area with limited local water resources, and the contradiction between water supply and demand is relatively prominent. Therefore, it is necessary to refine the scale of regional allocation, optimize the composition of water supply, realize the fine management of water resources in combination with the local development reality and water use efficiency of various industries, and further improve the industrial structure in order to support the green and high-quality development of Wu’an City.

3. Data Sources

Data for the urban and rural population of each township in Wu’an City from 2018 to 2022, the list of industrial enterprises in each township, the industrial added value of various industrial enterprises, cultivated land area, irrigated area, multiple cropping index, per capita green area, etc., were obtained from the “Wu’an Statistical Yearbook” (2018–2022) [17,18,19,20,21]; the total water supply, urban and rural residents’ domestic water consumption, and ecological environment water consumption of Wu’an City from 2018 to 2022 were obtained from the “Wu’an Water Resources Bulletin” (2018–2022) [22,23,24,25,26].

4. Methods

4.1. Calculation of Rigid Water Demand and Total Water Demand Thresholds for Wu’an City

Rigid water demand refers to the basic amount of water needed for human life, biological survival, enterprise production, and basic health of rivers and lakes. If it is insufficient, the water industry will face a threat to survival. Without the constraints of resources and engineering conditions, the water demand at this level should be fully met. Total water demand refers to the amount of water needed to improve the quality of life, meet the demands for food consumption, develop industry, and shape a suitable ecological environment. The amount of water at this level can promote production efficiency and life quality. Under the condition of sufficient water resources, the water demand at this level should be met as far as possible [27]. By considering the different demand processes and mechanisms of water resources in different industries, the threshold calculation methods for rigid water demand and total water demand for daily life, industry, and ecology in Wu’an City were formulated according to the characteristics of water use in different industries.

4.1.1. Domestic Water Demand

Living water demand is divided into rigid water demand and total water demand according to the principles of basic survival and quality of life. Rigid water demand for life mainly refers to the amount of water required to meet the basic water and safety needs for life’s continuation, to solve the physiological needs of human beings for water, and to avoid the threat to survival caused by lack of water. It can be regarded as a basic human right, and this level must be given priority in water resource allocation. Domestic water consumption includes urban domestic water consumption and rural domestic water consumption. The threshold for living stratified water demand is calculated using the quota method. Urban and rural population data for various towns and villages in Wu’an City are collected and sorted in the “Wu’an Statistical Yearbook” [17,18,19,20,21]. According to the “Water Quota for Living and Service Industry in Hebei Province” (DB 13/T 5450.1-2021) [28], the lowest value of the water quota interval for urban residents’ complete residential buildings and the lowest value of the water quota interval for rural residents are used as rigid water quotas, while the highest value of the interval is used as the total water quota. Multiplying this by the number of permanent residents in each town in the planning year gives the corresponding rigid water demand for life or total water demand. The formula for the calculation is as follows:

$$W_{rd}=(q_{urd}\times p_u+q_{rrd}\times p_r)/(1-\upsilon )$$

(1)

$$W_{td}=(q_{utd}\times p_u+q_{rtd}\times p_r)/(1-\upsilon )$$

(2)

where $W_{rd}$ is the rigid water demand for daily life, 10⁴ m³; $p_u$ is the current annual urban population, 10⁴; $q_{urd}$ is the rigid domestic water consumption quota for urban residents, m³/(person·year); $p_{\mathrm{urd}}$ is the current annual rural population, 10⁴; $q_{rrd}$ is the rigid domestic water consumption quota for rural residents, m³/(person·year); $\upsilon$ is the water supply loss coefficient; $W_{td}$ is the total water demand of daily life, 10⁴ m³; $q_{utd}$ is the total domestic water consumption quota for urban residents, m³/(person·year); and $q_{rtd}$ is the total water consumption quota for rural residents, m³/(person·year).

4.1.2. Industrial Water Demand

According to the basic economic support and the needs of rapid industrial development, industrial water demand is divided into rigid water demand and total water demand to calculate the current annual water demand. According to the “Outline of the 14th Five-Year Plan for Wu’an City” [29], “Wu’an Statistical Yearbook” [17,18,19,20,21], “Industrial classification for national economic activities” (GB/T 4754-2017) [30], and other materials, Wu’an City’s leading industrial enterprises (manufacturing; ferrous metal smelting and rolling processing; metal products; non-metallic mining; electricity, heat, gas, and water production and supply) are selected, and the water demand of these enterprises is taken as the industrial rigid water demand, and the water demand of all industrial enterprises is taken as industrial total water demand. Through field research, systems query, and other methods, a list of industrial enterprises in various towns and villages in Wu’an City was collected, sorted, and classified according to the “Industrial classification for national economic activities” (GB/T 4754-2017) [30]. For industrial enterprises belonging to the dominant industry, the target water consumption value of Wu’an City per CNY 10,000 of industrial added value was selected, and the industrial rigid water demand of each town and village was calculated by combining the industrial added value of various industrial enterprises; for the total industrial water demand, the total industrial added value of each town and village was multiplied by the target water consumption value of CNY 10,000 of industrial added value; the formula for the calculation is as follows:

$$W_{ri}=I_{ri}\times \eta \times (1-\upsilon )$$

(3)

$$W_{ti}=I_{ti}\times \eta \times (1-\upsilon )$$

(4)

where $W_{ri}$ is the rigid water demand for industry, m³; $I_{ri}$ is the industrial added value of leading industrial enterprises, CNY 10⁴; $\eta$ is the water consumption for ten thousand yuan industrial added value, m³/CNY 10⁴; $W_{ti}$ is the total industrial water demand, m³; $I_{ti}$ is the industrial added value of industrial enterprises, CNY 10⁴.

4.1.3. Agricultural Water Demand

Agricultural water demand includes water demand for agricultural irrigation and water demand for forestry, animal husbandry, fishery, and livestock. Based on the need to meet food security and achieve self-sufficiency in consumption, agricultural water demand is divided into rigid water demand and total water demand. The total food demand depends on the population, per capita food consumption level, and the degree of food self-sufficiency, while the total food production depends on factors such as cultivated land area, irrigated area, multiple cropping index, grain-to-economic ratio, and yield per unit area. From the perspective of food supply and demand balance, on the premise of meeting regional food security, the irrigation area that meets regional food security is determined based on the regional irrigation area and its yield per unit area, thereby determining the rigid water demand for agriculture; similarly, on the premise of achieving self-sufficiency in consumption, the total agricultural water demand is determined. The formula for the calculation is as follows:

$$W_{ra}=A_{\mathrm{m}}{Q}_{\mathrm{i}}$$

(5)

$$W_{ta}=A_n{Q}_{\mathrm{i}}$$

(6)

where $A_{\mathrm{m}}$ is the irrigation area that meets regional food security, hm²; $A_n$ is the irrigation area of the region to achieve self-sufficiency in consumption, hm²; and $Q_{\mathrm{i}}$ is the water quota for crop irrigation, m³/hm².

4.1.4. Ecological Water Demand

According to the ecological guarantee water quantity of Beiminghe River and Nanminghe River proposed in the Minghe River Quantity Allocation Plan [31], the lengths of two rivers in each township of Wu’an City were calculated using the ArcGIS 10.2 software, and the rigid threshold value of ecological water demand within the river channel of each township was calculated according to the length. In view of the current water resource management assessment requirements, the most basic ecological water use should be guaranteed; thus, the total ecological water demand is not calculated in this project.

4.2. Calculation of Available Water Supply from Multi-Water Sources

4.2.1. Available Surface Water Supply

The typical year method was adopted to calculate the reservoir operation for beneficial use based on a monthly period [32], and the maximum available water supply of years with the guaranteed rate of P = 50% and P = 75% was obtained.

The calculation of reservoir operation for beneficial use was mainly based on the principle of reservoir water balance. The reservoir water balance equation for a complete hydrological year calculation period is as follows:

Wend = Wbegin + Wenter − Wdischarge

(7)

where W_end is the storage capacity of the reservoir at the end of the period; W_begin is the storage capacity of the reservoir at the beginning of the period; W_enter is the amount of water entering the reservoir during the period; and W_discharge is the amount of water discharged from the reservoir during the period, including the amount of water supply, evaporation, and leakage losses.

4.2.2. Available Groundwater Supply

According to the Groundwater Utilization and Protection Plan of Wu’an City, the exploitable modulus and area of groundwater in each hydrological unit of different zones were obtained through ArcGIS. The formula for the calculation is as follows:

$$W_G{ =\mathrm{m}}_{\mathrm{g}}\times A$$

(8)

where W_G is the groundwater supply, m_g is the groundwater exploitable modulus, and A is the area.

4.2.3. Available Mine Drainage Water Supply

The available mine drainage water supply refers to the amount of water supplied to other water users by mining enterprises during the development of mineral resources, which is generated by reducing the groundwater level of the mine so as to meet production or safety requirements [33]. Open-pit mine water, mine water, or drainage water, which are not directly utilized or recycled after purification within the enterprise, mainly supply industries, agriculture, and ecology. The quantity of mine drainage water available in Wu’an City can be calculated according to the water resource tax paid by mining enterprises when the mine drainage water is discharged. The formula for the calculation is as follows:

$$W_k={\displaystyle \frac{T_Q}{S}}$$

(9)

where W_k is the available water supply of mine drainage water, T_Q is the water resource tax that mining enterprises need to pay when mine drainage water is discharged, and S is the unit water resource tax.

4.2.4. Calculation of Available Reclaimed Water Supply

The available reclaimed water supply refers to the amount of sewage recycling and utilization of urban domestic water consumption and industrial water consumption [34]. The calculation equation is as follows:

$$W_R=W_D\times \alpha \times \beta \times \delta$$

(10)

where $W_R$ is the available reclaimed water supply, 10⁴ m³; $W_D$ is the water consumption, 10⁴ m³; $\alpha$ is the convert coefficient of pollution; $\beta$ is the sewage collection coefficient; and $\delta$ is the reuse rate of treated sewage, %.

4.3. Construction of a Multi-Water Source and Multi-Objective Collaborative Configuration Model

4.3.1. Water Resource Allocation Network

According to the characteristics and current situation of the water resource allocation system of Wu’an City, the situation of planned water conservancy projects, and the requirements of water resources allocation, various physical elements (important water conservancy projects, towns, river channel intersections, etc.) in the water supply and consumption process of Wu’an City were taken as nodes. The nodes were connected through various line segments of the above-mentioned water resource transmission systems to form a network diagram (or node diagram, system diagram) for the water resource allocation system in Wu’an City. Requirements for drawing the system network diagram are as follows: Firstly, it is necessary to fully reflect the main characteristics of the water resource allocation system (such as the supply, consumption, and discharge characteristics) and their various relationships (such as the relationships between water systems at all levels, the geographical relationships between various calculation units, the hydraulic connections between water conservancy projects and calculation units, and the topological relationships between water flow). The second is to appropriately meet the needs of the water resource allocation model and correctly reflect the various factors involved in the operation of the model system (such as various water sources, projects, water users, and water resources transmission systems) by drawing the system diagram. The water resource allocation network diagram for Wu’an City is shown in Figure 2.

4.3.2. Quantification of Water Supply and Consumption Priority

The principle of “water supply in different quality” proposes the order of priority of different water sources for each water user and the priority of supplying water for different water users. In the multi-water source and multi-objective collaborative configuration model, it is necessary to quantitatively characterize the above qualitative relationships. To this end, the priority coefficient of water supply and the priority coefficient of water received by users were proposed to realize water resource allocation according to the corresponding priority coefficients in the process of solving the objective function of the model. The order of priority of water supply and the priority of users receiving water were calculated using the following equations:

$${\alpha }_{ij}={\displaystyle \frac{1+n_{ij\max }-n_{ij}}{{\displaystyle \sum _{i=1}^I}\left(1+n_{ij\max }-n_{ij}\right)}}$$

(11)

$${\beta }_j={\displaystyle \frac{1+m_{j\max }-m_j}{{\displaystyle \sum _{j=1}^J}\left(1+m_{j\max }-m_j\right)}}$$

(12)

where α_ij is the priority coefficient of water supply from the i-th water source to the j-th water user; n_ij is the serial number of water supply from the i-th water source to the j-th water user; n_ijmax is the maximum of water supply numbers from the i-th water source to the j-th water user; β_j is the priority coefficient of water received by the j-th water user; m_j is the serial number of water received by the j-th water user; and m_jmax is the maximum serial number of the water received by the j-th water user.

4.3.3. Objective Function

(1)

Economic benefit objective

Governments often focus on the effective use of resources and sustainable economic development. The setting of economic benefit targets aims to ensure that water resource allocation can minimize water resource waste and unnecessary economic expenditure. Reasonable allocation of water resources can enhance the ability of water resources to support economic development. Different industries have different demands and utilization efficiencies for water resources. The setting of economic benefit targets will help various industries reasonably obtain and utilize water resources according to their own development needs, reduce costs, and improve competitiveness. As direct users of water resources, the setting of economic benefit targets means that while ensuring the basic living water needs of residents, the economic burden of residents can be reduced, and the quality of life of residents can be improved by improving the utilization efficiency of water resources. The net economic income of water supply was used to represent the economic benefit objective:

$$\begin{array}{r}\hfill \max F(x)=\left\{{\displaystyle {\displaystyle \sum }_{k=1}^K}{\displaystyle {\displaystyle \sum }_{j=1}^J}\left[{\displaystyle {\displaystyle \sum }_{i=1}^I}\left(b_{ij}^k-c_{ij}^k\right)x_{ij}^k{\alpha }_i^k\right]{\beta }_j^k\right\}\end{array}$$

(13)

where $F(x)$ is the net economic income of water supply, CNY 10⁴; K is the number of calculation units in Wu’an City; J is the number of users of calculation units (life, industry, agriculture, and ecology); I is the number of water sources (surface water, groundwater, mine drainage water, reclaimed water, and South-to-North Water Diversion water); $b_{ij}^k$ is the efficiency coefficient of water supply; $c_{ij}^k$ is the cost coefficient of water supply; and $x_{ij}^k$ is the amount of water supplied from the i-th water source of the k-th calculation unit to the j-th user, 10⁴ m³.

(2)

Social benefit objective

When formulating social policies, the government pays attention to fairness and justice. The setting of social benefit goals aims to ensure the fairness and sustainability of water resource allocation and narrow the water use gap between different regions and different groups. Different industries need fair access to water resources in the process of development. The setting of social benefit goals helps various industries maintain a fair position in competition and avoid conflicts between industries caused by improper allocation of water resources. As the basic unit of society, residents pay attention to the fair distribution of water resources and the quality of water supply services. The setting of social benefit goals means that residents can enjoy more fair and reliable water supply services. For social benefits, the main consideration is to minimize the difference in water supply satisfaction among different calculation units so that the results of water resource allocation are more easily accepted by various water users in different regions. The Gini coefficient is one of the common indicators for evaluating regional income gaps and is widely used in the field of economics. Its value ranges from 0 to 1, and a larger value indicates a more unfair allocation of resources. This paper used the trapezoidal method to calculate the Gini coefficient of satisfaction with water supply. The satisfaction with the water supply was first defined as follows:

$$S_k={\displaystyle \sum _{j=1}^J\frac{{\displaystyle \sum _{i=1}^I{x}_{ij}^k}}{W_j^k}}$$

(14)

$$M_k={\displaystyle \frac{S_k}{{\displaystyle \sum _{k=1}^K{S}_k}}}$$

(15)

where $S_k$ is the satisfaction with the water supply of the k-th calculation unit; $W_j^k$ is the water demand for the j-th user of the k-th calculation unit, 10⁴ m³; and $M_k$ is the proportion of the satisfaction with the water supply of the k-th calculation unit to the total satisfaction with the water supply of all calculation units in Wu’an City.

$M_k$ was arranged in ascending order to generate a set of sequences $M_k^{\prime }$, and the cumulative frequency $P_{s,n}$ of the sequence was calculated as follows:

$$P_{s,n}={\displaystyle \frac{{\displaystyle \sum _{k=1}^n{M}_k^{\prime }}}{{\displaystyle \sum _{k=1}^K{M}_k^{\prime }}}}n\in \left[1,K\right]$$

(16)

According to the definition of the Gini coefficient, the method for calculating the Gini coefficient was derived as follows:

$$G_S={\displaystyle \frac{A}{A+B}}=1-2B=1-{\displaystyle \frac{1}{K}}{\displaystyle \sum _{n=1}^K(P_{s,n-1}+P_{s,n})}=1-{\displaystyle \frac{1}{K}}\left(2{\displaystyle \sum _{n=1}^{K-1}{P}_{s,n}}+1\right)$$

(17)

where $G_S$ is the Gini coefficient of satisfaction with water supply in Wu’an City.

The objective function of social benefits is expressed as follows:

$$\min G(x)=G_S$$

(18)

(3)

Ecological benefits

The government bears important responsibilities in ecological environmental protection. The setting of ecological benefit targets aims to ensure that water resource allocation can protect the ecological environment and maintain ecological balance. Reasonable allocation of water resources requires guaranteeing the basic ecological flow of rivers and lakes and improving the quality of the ecological environment. Different industries need to pay attention to their impact on the ecological environment during their development. The setting of ecological benefit targets will help various industries take environmental protection measures, reduce water resource pollution and damage, and achieve green and sustainable development. As direct beneficiaries of the ecological environment, residents pay attention to the ecological value of water resources. The setting of ecological benefit targets means that residents can enjoy a higher quality of life. Ecological benefits are mainly reflected by guaranteeing the basic ecological flow of rivers and lakes. Therefore, ecological water deficit was used to characterize sustainable development goals, as shown in the following equation:

$$\min E(x)={{\displaystyle \sum }}_{k=1}^K{{\displaystyle \sum }}_{j=1}^2\left[D_j^k-{{\displaystyle \sum }}_{i=1}^I{x}_{ij}^k\right]$$

(19)

where $E(x)$ is the ecological water deficit, 10⁴ m³; and $D_j^k$ is the ecological water demand inside and outside the river, 10⁴ m³.

4.3.4. Constraints

During the process of optimal allocation of water resources, in order to ensure that the results of the calculation conform to the actual situation of water resource management in Wu’an City, constraints should be set to ensure that the results of water resource allocation are rational and scientific.

(1)

Constraints include water resource allocation rules, water supply balance, water supply capacity, total water consumption, water consumption for ten thousand yuan GDP, water consumption for ten thousand yuan industrial added value, and non-negative solution.

According to the topological relationship between water supply and consumption between water sources and water users, $x_{ij}^k$ exists only when there is a clear water supply and consumption relationship between a water source and a water user; otherwise, water resource allocation will not be carried out;

(2)

Constraints of water supply balance

In the process of water resource allocation, it is necessary to ensure that the supply and demand of water resources are balanced. The constraints are as follows:

$${{\displaystyle \sum }}_{j=1}^J{{\displaystyle \sum }}_{i=1}^I{x}_{ij}^k=W_i^k$$

(20)

(3)

Constraints of water supply capacity

The setting of water supply capacity constraints helps to ensure that the water supply system can meet the water demands of various industries and avoid difficulties caused by insufficient water supply capacity. The constraints are as follows:

$${{\displaystyle \sum }}_{j=1}^J{{\displaystyle \sum }}_{i=1}^I{x}_{ij}^k\le Q_i^k$$

(21)

(4)

Constraints of total water consumption

The setting of total water consumption constraints is helpful in limiting the water consumption of various industries and promoting the conservation and efficient use of water resources. The constraints are as follows:

$${{\displaystyle \sum }}_{j=1}^J{{\displaystyle \sum }}_{i=1}^I{x}_{ij}^k\le T$$

(22)

In order to encourage various industries to improve water resource utilization efficiency, reduce water consumption per unit of output value, and achieve the maximum economic utilization of water resources, water consumption constraints per CNY 10,000 of GDP and water consumption constraints per CNY 10,000 of industrial added value are set, as shown in Formulas (23) and (24).

(5)

Constraint of water consumption for ten thousand yuan of GDP

$${\displaystyle \frac{{{\displaystyle \sum }}_{j=1}^J{{\displaystyle \sum }}_{i=1}^I{x}_{ij}^k}{GDP}}\le \gamma$$

(23)

(6)

Constraints of water consumption for ten thousand yuan of industrial added value

$${\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^I{x}_{i2}^k}{EVA}}\le \rho$$

(24)

(7)

Non-negative solution constraints

Attention should be paid to the rationality and operability of water resource allocation. The setting of non-negative constraints helps to ensure that all variables in the water resource allocation plan are non-negative values, which conforms to the actual situation and logical requirements. The constraints are as follows:

$$x_{ij}^k\ge 0$$

(25)

where $W_i^k$ is the actual water supply of the i-th water source to the k-th calculation unit, 10⁴ m³; $Q_i^k$ is the maximum water supply capacity of the i-th water source to the k-th calculation unit, 10⁴ m³; $T$ is the red line of total water consumption control of Wu’an City, 10⁴ m³; $\gamma$ is the assessment value of water consumption for ten thousand yuan of GDP, m³/CNY 10⁴; $\rho$ is the assessment value of water consumption for ten thousand yuan of industrial added value, m³/CNY 10⁴; $EVA$ is industrial added value, CNY 10⁴.

4.3.5. Method for Determining Water Resource Optimal Allocation Scheme Based on NSGA-III Algorithm and TOPSIS

Unlike single-objective problems, multi-objective optimization problems do not have optimal solutions but only satisfactory solutions or optimal trade-off solutions. Therefore, solving multi-objective optimization problems is actually about finding a feasible solution set. Since various objectives often conflict with each other, a solution may be better for a certain objective but worse for other objectives. In this way, there is a set of compromise solutions called the Pareto optimal solution set or the Pareto non-dominated solution set. Among the modern intelligent optimization algorithms, although the NSGA-III algorithm has a limitation of high computational complexity, it can better handle high-dimensional and multi-objective optimization problems and has a good ability to search for the Pareto optimal solution set [35,36].

This study uses the NSGA-III algorithm to solve the model. The points on the Pareto frontier are the feasible solutions to the multi-objective optimization problem. Selecting a trade-off solution as a compromise solution from the many Pareto solutions according to the different preferences of decision-makers is the first problem to be solved. Based on this idea, the TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) decision method is introduced to analyze the decision selection and the final compromise solution. The TOPSIS decision method is a commonly used intra-group comprehensive evaluation method, which is suitable for a variety of decision-making situations in the real world. It can make full use of the original data information without increasing the computational burden. Its results can accurately reflect the advantages and disadvantages of each evaluation scheme [37].

This study uses the NSGA-III algorithm to solve the problem of optimal allocation of water resources in Wu’an City and uses TOPSIS to optimize the Pareto solution to determine the optimal solution. The process is as follows:

(1)

Construction of a water resource optimization allocation model in Wu’an City:

• Define the objective function of the model, that is, the optimization of economic, social, and ecological benefits.
• To ensure the rationality and feasibility of the configuration plan, set constraints, including water resource allocation rules, water supply balance analysis, water supply capacity assessment, total water use control, water use limit per CNY 10,000 of GDP, water use index per CNY 10,000 of industrial added value, and non-negative constraints.
• Construct the Wu’an City water resource optimization configuration model based on the objective function and constraints.

(2)

Solution strategy based on the NSGA-III algorithm:

Step 1: Different available water sources (surface water, groundwater, mine drainage water, recycled water, and water from the South-to-North Water Diversion Project) for different users (living, industrial, agricultural, and ecological) in different regions are used as decision variables;

Step 2: Under the constraints of the water resource optimization allocation model for Wu’an City, randomly generate P_t with a population size of N, and calculate the objective function value based on the objective function of the water resource optimization allocation model;

Step 3: Determine the number and position of reference points on the (M-1)-dimensional hyperplane. M is the dimension of the target space, that is, the number of optimization targets;

Step 4: Generate the offspring Q_t through selection, crossover, and mutation operations, and merge P_t and Q_t to form R_t;

Step 5: Perform non-dominated sorting on R_t and add outstanding individuals in the critical dominance layer to H_t+1 based on the reference point method, that is, the new offspring population, until the number of individuals in H_t+1 reaches N;

Step 6: Repeat Steps 4 and 5 until the termination condition is met to obtain the Pareto optimal solution set for the optimal allocation of water resources in Wuan City.

(3)

TOPSIS-based solution optimization:

Step 1: The various objectives of the Pareto optimal solution set are formed into a matrix, where the rows represent different solutions, and the columns represent different objective function values. The resulting decision matrix X is given as:

$$X=\left[\begin{array}{l}\begin{array}{ccc}{x}_{11}& x_{12}& x_{13}\end{array}\\ \begin{array}{ccc}{x}_{21}& x_{22}& x_{23}\end{array}\\ \begin{array}{ccc}{x}_{31}& x_{32}& x_{33}\end{array}\\ \begin{array}{ccc}⋮& ⋮& ⋮\\ x_{n1}& x_{n2}& x_{n3}\end{array}\end{array}\right]$$

(26)

Step 2: Use the maximum–minimum normalization method to make the decision matrix dimensionless and construct a standardized matrix. The results are as follows:

• ① The smaller the better the target:

$$v_{ij}={\displaystyle \frac{x_{ij}-\min (x_j)}{\max (x_j)-\min (x_j)}}$$

(27)

• ② The bigger the better type of goal:

$$v_{ij}={\displaystyle \frac{\max (x_j)-x_{ij}}{\max (x_j)-\min (x_j)}}$$

(28)

where $v_{\mathit{ij}}$ is the normalized value; and max(x_j) and min(x_j) are the maximum and minimum values j of the j-th indicator, respectively.

Step 3: Multiply each target weight w by the dimensionless matrix v to obtain the weighted decision matrix:

$$r_{ij}=w_j\cdot v_{ij}\hspace{1em}(i=1,2,\cdots \hspace{0.17em},m;j=1,2,\cdots \hspace{0.17em},n)$$

(29)

In the formula, $w_j$ is the weight value of each target. This study assumes that the three targets are of equal importance, so the weight of each target is 1/3.

Step 4: Calculate the positive and negative ideal solutions $S_j^{-}$ and $S_j^{+}$

$$S_j^{+}=\{\begin{array}{c}{\max }_{1\le i\le m}\left\{r_{ij}\right\},j=1,2,\cdots \hspace{0.17em},n;S_{j}is the bigger the better indicator\\ {\min }_{1\le i\le m}\left\{r_{ij}\right\},j=1,2,\cdots \hspace{0.17em},n;S_{j}is the smaller the better indicator\end{array}$$

(30)

$$S_j^{-}=\{\begin{array}{c}{\min }_{1\le i\le m}\left\{r_{ij}\right\},j=1,2,\cdots \hspace{0.17em},n;S_{j}is the bigger the better indicator\\ {\max }_{1\le i\le m}\left\{r_{ij}\right\},j=1,2,\cdots \hspace{0.17em},n;S_{j}is the smaller the better indicator\end{array}$$

(31)

Step 5: Use Euclidean distance to calculate the distance between each solution and the positive ideal solution and the negative ideal solution ${\mathit{Sd}}_{\mathit{i}}^{+}$ and ${\mathit{Sd}}_{\mathit{i}}^{-}$

$$S{d}_i^{+}=\sqrt{{{\displaystyle \sum }}_{j=1}^n{(S_j^{+}-r_{ij})}^2},i=1,2,\cdots \hspace{0.17em},m$$

(32)

$$S{d}_i^{-}=\sqrt{{{\displaystyle \sum }}_{j=1}^n{(S_j^{-}-r_{ij})}^2},i=1,2,\cdots \hspace{0.17em},m$$

(33)

Step 6: Calculate the relative closeness f_i of each solution:

$$f_i={\displaystyle \frac{S{d}_i^{-}}{S{d}_i^{+}+S{d}_i^{-}}},i=1,2,\cdots \hspace{0.17em},m$$

(34)

The larger the f_i, the better the decision-making plan.

The process of determining the best solution for water resource optimization allocation in Wu’an City based on the combination of the NSGA-III algorithm and TOPSIS is shown in Figure 3:

5. Results and Analysis

5.1. Water Demand Thresholds by Industry in Base and Planning Years

By using the rigid water demand threshold and total water demand calculation methods for daily life, industry, agriculture, and ecology mentioned above, the rigid water demand thresholds and total water demand of the whole industry under different water inflow scenarios were summarized. The results are shown in Figure 4.

According to Figure 4, the rigid water demand of Wu’an City in 2022 in the normal water scenario is 12,536.01 × 10⁴ m³, and the total water demand is 16,904.06 × 10⁴ m³. In the low water scenario, the rigid water demand of Wu’an City is 13,766.59 × 10⁴ m³, and the total water demand is 18,084.78 × 10⁴ m³. In addition, according to the total water consumption and efficiency red line control indicator demand for the 14th Five-Year Plan period in Wu’an City, reasonable water demand for various industries in the planning year (2025) was simulated and predicted to meet the strictest water resource management requirements. The results show that the rigid water demand of the whole city in the normal water scenario in 2025 is 12,929.58 × 10⁴ m³, and the total water demand is 18,148.25 × 10⁴ m³. In the low water scenario, the rigid water demand of the whole city is 14,173.34 × 10⁴ m³, and the total water demand is 20,419.52 × 10⁴ m³.

5.2. Available Water Supply from Different Water Sources in Base and Planning Years

The available water supplies of different townships in Wu’an City under different inflow frequencies were determined according to the results of the sub-calculation of the available supply of surface water, groundwater, reclaimed water, and mine drainage water in Wu’an City in the base year. The results are shown in Figure 5a,b. Calculation of water supply in the planning year mainly considered the theoretical water supply from the water conservancy project that is planned to be put into operation in the planning level year. In order to solve the shortage of water resources, Wu’an City is preparing to build a South-to-North Water Diversion Project. The project will start from the middle line of the South-to-North Water Diversion Project Sanling entrance to the Nangushan water source area, Qinghua pumping station, and Chengdong water supply pumping station in Wu’an City. Along the way, it will pass through the Qinhe River Basin, the Shuyuan River Basin, and the Minghe River Basin and enter the Damingyuan Reservoir and the newly built water supply regulation tank in Nangushan. The water supply scale in the planning level year is 2000 × 10⁴ m³/a. In terms of unconventional water utilization, for mine drainage water, by considering the full development and utilization of mine drainage water resources in the planning level year, the available supply of mine drainage water in the planning level year used water intake for mine drainage specified in the water intake license applied for by 26 mining enterprises, including Beiminghe Iron Mine in Wu’an City, with the amount of water used for mine drainage within the enterprise deducted. The available water supply for mine drainage in Wu’an City in 2025 is 3513.69 × 10⁴ m³. For reclaimed water, the available water supply was calculated according to the urban residents’ living and industrial water demand in the planning level year, and the available reclaimed water supply of Wu’an City in 2025 is 624 × 10⁴ m³. The results of the available water supplies from different water sources in Wu’an City in the planning year are shown in Figure 5c,d.

As shown in Figure 5, the water supply of Wu’an City is highly dependent on groundwater, and in the dry water scenario, the surface water supply is significantly reduced, resulting in increased water supply pressure in some towns. In 2022, the total water supply of Wu’an Town decreased from 35.7496 million m³ to 33.1848 million m³ in the normal water scenario, and the total water supply of Wuji Town decreased from 15.7742 million m³ to 13.6092 million m³. The introduction and utilization of the South-to-North Water Diversion Project and mine drainage water in the dry water scenario effectively alleviated the problem of insufficient surface water supply.

5.3. Results of Multi-Water Source and Multi-Objective Collaborative Configuration

5.3.1. Results of Multi-Water Source and Multi-Objective Collaborative Configuration in the Base Year

With the rigid water demand, total water demand, and currently available water supply from multi-water sources under different guarantee rates for Wu’an City in the base year as input conditions, a group of Pareto solution sets was obtained through multi-round iterative optimization of NSGA-III. The TOPSIS decision-making method was used to screen the Pareto solution sets and obtain the final configuration results under different guarantee rates for multi-water sources and multiple objectives in the base year. The results are shown in Figure 6.

Figure 6a,b show the water resource allocation results for rigid demand in the normal water scenario (P = 50%) and the low water scenario (P = 75%) in Wu’an City in 2022. From the perspective of benefit objectives, in the normal water scenario, Wu’an City is in the optimal state, as the rigid water demand has been fully met, and the social and ecological benefits are both 0. The net economic benefits generated by the development and utilization of water resources are CNY 3775.595 million. The social benefit of Wu’an City in the low water scenario is 0.02. According to the regulations of the United Nations Development Programme and other organizations, if the Gini coefficient is below 0.2, it indicates that the region is in a highly fair state. It can be seen that although there is a certain degree of water shortage under the low water scenario, the overall difference in water supply satisfaction among different townships in Wu’an City is small and in a fair state. The ecological benefit value is 0, mainly reflecting that the ecological water demand is met. The economic benefit is CNY 3771.994 million, which is a decrease of four million Chinese yuan compared to the economic benefit of meeting the rigid demand in the normal water scenario. The main reason is that the industrial water allocation is slightly decreased, but the benefits generated by industrial water use far exceed those of daily life and agriculture.

Figure 6c,d show the water resource allocation results of the total water demand under the normal water scenario (P = 50%) and the low water scenario (P = 75%) in Wu’an City in 2022. From the perspective of benefit objectives, the social and ecological benefits of the normal water scenario are still 0, while the economic benefits are increased by CNY 5108.6913 million. Compared with the actual water supply and consumption in the Water Resources Bulletin of Wu’an City in 2022 [26], the allocation result is optimized by the multi-water source and multi-objective collaborative configuration model and under the premise of meeting the strictest water resources management system, a total of 584.1 × 10⁴ m³ of water can be added, and the net economic benefits of water supply can be increased by CNY 136.5515 million. The social benefits in the low water scenario increase from 0.03 to 0.04, indicating an increase in satisfaction with the water supply in different townships; however, the overall satisfaction with the water supply in Wu’an City is still in a fair state. The ecological water supply is fully satisfied; therefore, the ecological benefits remain at 0. The economic benefit is CNY 4915.8941 million, which is a decrease of CNY 192.7966 million compared to the normal water scenario, mainly due to insufficient natural water supply, resulting in a decrease in the amount of water allocated to domestic and industrial users.

5.3.2. Multi-Water Source and Multi-Objective Collaborative Configuration Results in the Planning Year

With the rigid water demand, total water demand, and currently available supply of multi-water sources under different guarantee rates for Wu’an City in the planning level year as input conditions, a group of Pareto solution sets was obtained through multi-round iterative optimization of the NSGA-III algorithm. The TOPSIS decision-making method was used to screen the Pareto solution sets and obtain the final configuration results under different guarantee rates for multi-water sources and multiple objectives in the planning year. The results are shown in Figure 7.

Figure 7a,b show the water resource allocation results of rigid demand in the normal water scenario (P = 50%) and low water scenario (P = 75%) in Wu’an City in 2025. From the perspective of benefit objectives, the normal water scenario is in the optimal state because the rigid water demand has been fully met, and the social and ecological benefits are both 0. The net economic benefits generated by the development and utilization of water resources are CNY 3830.81 million, an increase of 54.486 million yuan compared to 2022. The social benefit in the low water scenario is 0.02, which is basically in the fair state for water supply, and the ecological benefit is 0. The economic benefit is CNY 3830.87 million, which increased by CNY 58.893 million compared with the results of water resource allocation in the low water scenario in 2022.

Figure 7c,d show the water resource allocation results of the total water demand in the normal water scenario (P = 50%) and low water scenario (P = 75%) in Wu’an City in 2025. From the perspective of benefit objectives, the social benefits of the normal water scenario in 2025 are 0, and the regional water supply is basically completely fair. The ecological benefits are still 0, and the economic benefits are CNY 6041.7352 million, an increase of CNY 933.044 million compared with the configuration results of the normal water scenario in 2022. The social benefits in the low water scenario in 2025 increase from 0.05 in 2022 to 0.06, indicating that the overall water supply for Wu’an City is relatively fair in the low water scenario in 2025, and the ecological water demand is fully met; therefore, the ecological benefits are 0, and the economic benefits are CNY 5917.191 million, an increase of CNY 1001.3 million compared to the low water scenario in 2022.

6. Discussion

6.1. Model Performance Analysis

In order to verify the performance of the NSGA-III algorithm, Non-dominated Sorting Genetic Algorithm II (NSGA-II), Generational Distance-based Evolutionary Algorithm with Differential Evolution III (GDE3), and Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) were introduced. DTLZ1, DTLZ2, DTLZ3, and DTLZ4 were used as test functions, and the inverted generational distance (IGD) was used as an evaluation index for evaluating the comprehensive performance of the multi-objective optimization algorithm (the smaller the better). The mean value (MV) and standard deviation (SD) of IGD of different algorithms under different test functions were calculated and ranked from best to worst. The results are shown in

Table 1. IGD means and standard deviations of different test functions for each algorithm.

Test Function	-	NSGA-Ⅲ	NSGA-II	MOEA/D	GDE3
DTLZ1	MV	2.301×10−2	2.494×10−2	3.149×10−2	2.361×10−2
	Rank	1	3	4	2
	SD	3.199×10−4	1.195×10−3	3.594×10−2	8.399×10−4
	Rank	1	3	4	2
DTLZ2	MV	5.531×10−2	6.831×10−2	6.358×10−2	6.264×10−2
	Rank	1	4	3	2
	SD	1.195×10−3	3.199×10−3	6.496×10−4	1.596×10−3
	Rank	2	4	1	3
DTLZ3	MV	9.505×10−2	2.343×10−1	2.715×100	1.562×100
	Rank	1	2	4	3
	SD	1.694×10−1	3.498×10−1	6.495×100	1.498×100
	Rank	1	2	4	3
DTLZ4	MV	5.312×10−2	6.473×10−2	4.571×10−2	6.556×10−2
	Rank	2	3	1	4
	SD	4.963×10−3	6.296×10−3	4.899×10−3	5.096×10−3
	Rank	2	4	1	3
-	MV Rank	5	12	12	11
	SD Rank	6	13	10	11

.

As can be seen in Table 1, the comprehensive ranking of IGD results of the NSGA-III algorithm is better than that of NSGA-II, MOEA/D, and GDE3 for both SD and MV. The results show that the performance of the NSGA-III algorithm is relatively good.

6.2. Analysis of Research Results

Water resource optimization allocation improves water resource utilization efficiency and ensures the coordinated development of economic, social, and ecological benefits by scientifically allocating different types of water resources [38]. Social benefits are directly related to the social acceptance of water resource allocation results. The realization of this goal can greatly promote harmonious development among regions, ensure that the basic water rights and interests of various water users are met, and enhance the effectiveness of water resource management. Ecological benefits, as a key indicator to describe the degree of sustainable development, can reflect the impact of the allocation plan on the ecological environment. In the base year (2022), the results of the rigid demand water resource optimization allocation showed that the social and ecological benefits under the normal water scenario were optimal. Although the social benefit under the low water scenario was 0.02, it was less than 0.2, and the ecological benefit value was 0, indicating that although there was a shortage of water resources under the low water scenario, the ecological and social needs could still be met. The results obtained in the planning year (2025) were similar to those in the base year (2022). This shows that the proposed optimization plan demonstrates its practicality and scientificity and meets the dual needs of society and ecology. Compared with the actual water supply in 2022, the results of water resource optimization allocation for total water demand in normal water years can increase water supply by 5.841 million m³ and increase the net economic benefit of water supply by CNY 136.5515 million, indicating that the results of water resource optimization allocation for total water demand in normal water scenarios have achieved remarkable results, the level of water resource management has been improved, the economic benefits have been significantly enhanced, and the sustainable use of water resources and the sustainable development of the economy and society have been promoted. In the dry year scenario of the planning year, although the social benefit value increases, it is still less than 0.2, indicating that water supply has basically achieved complete fairness.

6.3. Research Value Analysis

This study focuses on Wu’an City, a typical resource-based, water-deficient industrial city, and deeply explores the scientific definition of water demand thresholds in multiple dimensions such as life, industry, agriculture, and ecology. By constructing a water demand forecasting model for the entire city under the background of the most stringent water resources management policy, the determination of water demand thresholds for different sectors in counties is effectively overcome. The important position of unconventional water resources, especially mine drainage water, in water resource allocation is emphasized, and a multi-source, multi-objective collaborative and efficient optimization allocation strategy is formulated. This not only broadens the source of water resources supply but also alleviates the pressure of traditional water resource shortage to a certain extent. It is worth mentioning that the model framework adopted in this study is based on the scientific definition of water demand threshold, the water demand forecasting model for the entire city, and the multi-objective optimization strategy, which can adapt to the actual conditions of different regions. It only needs the input variables to be adjusted according to the characteristics of local data, such as the setting of water demand threshold, the total water use control target, and the optimization target weight setting, so that it can be extended to other similar resource-based industrial cities and even other types of water-deficient areas. On the other hand, this study provides a useful reference for other regions to explore the development and efficient use of alternative water sources, such as the rational use of mine drainage water. In addition, this study uses the NSGA-III algorithm and TOPSIS method as the core to construct a water resource optimization configuration framework with strong applicability and transplantability. Compared with traditional single-objective or dual-objective optimization methods, multi-objective optimization is achieved through the NSGA-III algorithm, which improves the comprehensiveness and scientificity of the model. At the same time, combined with the optimization mechanism of the TOPSIS method, the feasibility and practicality of the scheme are further improved, which can provide a technical solution for water resources management in similar areas.

In recent years, many studies have focused on the problem of optimal allocation of water resources in water-scarce areas. Yun Luo [39] studied the problem of optimal allocation of water resources in Handan City, China, with surface water and groundwater as the main water supply sources. In comparison, this study incorporates the background of unconventional water resource utilization and strict water resource management policies, especially the importance of mine drainage water in water resource allocation, broadening the source of water resource supply and alleviating the pressure of traditional water resource shortages. The model construction is more in line with the refined management needs at the county level. Jie Hou [40] took the Weihe River Basin as the research object, mainly focusing on the maximization of economic and social benefits. This study achieved multi-objective balanced optimization of economic, social, and ecological benefits. Yongyu Qu [41] used the NSGA-II algorithm to solve the problem of optimal allocation of water resources in Luanchuan County, Henan Province. In comparison, this paper uses the NSGA-III algorithm, which has a stronger capability for solving high-dimensional multi-objective optimization problems. At the same time, combined with the TOPSIS method, the best solution is selected from the Pareto solution set, which improves the scientificity and practicality of the model decision.

6.4. Countermeasures and Recommendations

As a resource-based, water-scarce region, Wu’an City should adopt a policy of “increasing revenue” and “saving expenditure” in parallel. While actively introducing external water to ease the contradiction between water supply and demand, the main channels should be repaired to improve the transmission efficiency of water resources, ensure water supply capacity, and reduce water waste. In addition, as an area with relatively abundant reserve water from unconventional water sources, Wu’an City should strengthen the development and utilization of unconventional water resources, especially mine drainage water. At the same time, the collection and utilization rate of recycled water should be improved, the supervision of wastewater collection, reprocessing and reuse should be strengthened, and high-level recycled water reuse technology should be introduced. The city should consider building rainwater cellars and artificial rainwater collection sites in key drought areas to solve the problem of water shortages in agriculture and industry. At the same time, the city should also consider using waste reservoirs and ponds to store and utilize rainwater resources, enhance regional storage capacity, improve regional ecological regulation capacity, and achieve coordinated development of economy and ecology.

6.5. Limitations and Prospects

Due to the particularity of the development and utilization of mine drainage water in Wu’an City, there are cases where mine drainage water is included in groundwater in the statistical process. In addition, some enterprises supply mine drainage water to reservoirs or water supply companies, and the water supply volume is counted twice. In the future, with the improvement in monitoring and statistical systems, the source of water resources will be clearer. In addition, in the current most stringent water resource management system, both the total water use and water use efficiency use a single value to constrain the regional water supply and use process. This value only corresponds to the upper limit of regional water resources development and utilization under the scenario of normal water years and does not clearly define the upper limit of regional available water under the scenario of dry or even extreme drought. As a result, in the process of water resource allocation, the remaining available water can close the water gap, but this water cannot be used under the constraints of the total water use and efficiency red line. In the future, with the establishment of a multi-scenario water resource management system, the total water use and efficiency control indicators under different water inflow scenarios will be determined, and the water demands of various sectors in special years will be met.

In addition, with the advent of the big data era and the rapid development of detection technologies, data acquisition and monitoring equipment will be used on a large scale in future research to achieve more accurate and real-time simulation of the water supply at the nodes of the water supply network, providing higher frequency and higher precision water volume data and capturing small changes in the network, thereby obtaining more comprehensive and accurate information [42,43], building a water-saving society and achieving sustainable use of water resources.

7. Conclusions

(1)

By analyzing the water demand and supply of Wu’an City between 2022 and 2025, it is found that the rigid water demand and total water demand of Wu’an City show an increasing trend in both normal and low water scenarios, but the demand in 2025 is still within the most stringent water resource management red line. At the same time, the assessment of water supply capacity from multiple water sources shows that the water supply capacity of Wu’an City is increasing year by year, reaching 229.9835 million m³ in normal water scenario and 213.9587 million m³ in low water scenario in 2025, which provides strong support for the efficient use and sustainable management of water resources.

(2)

With economic, social, and ecological benefits as the objective function, and water resource allocation rules, water supply balance, water supply capacity, total water use, water use per CNY 10,000 of GDP, water use per CNY 10,000 of industrial added value, and non-negative as constraints, a water resource optimization allocation model was constructed, and the model was solved using the NSGA-III algorithm to obtain the Pareto optimal solution set. Based on this, the TOPSIS decision method was used to select the optimal solution in the Pareto optimal solution set, thereby determining the optimal water resource optimization allocation plan while achieving a balance between water supply and demand and improving economic, social, and ecological benefits.

(3)

The results of water resource allocation show that under the normal water scenario, Wu’an City can fully meet the rigid and total water demand in 2022 and 2025, and both social and ecological benefits are optimal. The net economic benefit under the normal water scenario increased by CNY 933.044 million, and the net economic benefit was significant. Under the low water scenario, despite the challenge of water shortage, Wu’an City can still maintain high water supply equity (the Gini coefficient is less than 0.2) through reasonable allocation, and the ecological water demand is fully guaranteed. The social and ecological benefits are maintained at a low level. Although the economic benefits have declined, they still achieve an increase of CNY 100.130 million in 2025 compared with 2022, indicating that the water resource management strategy has a certain resilience in coping with drought.

(4)

In response to the water shortage problem in Wu’an City, a water resource management strategy of “increasing revenue and reducing expenditure” should be adopted: introducing external water to alleviate the contradiction between supply and demand, upgrading water supply facilities to reduce water resource loss, developing unconventional water sources such as mine drainage water to increase the utilization rate of recycled water, building rainwater collection facilities in arid areas, using abandoned reservoirs to store flood water, and enhancing regional regulation and storage capacity.