Multi-Objective Optimization of Water Resource Allocation with Spatial Equilibrium Considerations: A Case Study of Three Cities in Western Gansu Province

Abstract

Against the background of increasingly scarce water resources and intensifying water use conflicts, achieving the scientific and optimized allocation of water resources has become crucial to ensuring regional sustainable development. Based on the traditional water resource optimization models that consider social, economic, and ecological objectives, this study introduces a spatial equilibrium level as a fourth optimization objective, constructing a multi-objective water resource allocation optimization model. The model simultaneously incorporates constraints on water supply, water demand, and decision variable non-negativity, as well as coupling coordination constraints among the water resources, socio-economic, and ecological subsystems within each water use unit. The NSGA-III algorithm is employed to obtain the Pareto front solution set for the four objectives, followed by a comprehensive ranking of the Pareto solutions using an entropy-weighted TOPSIS method. The solution exhibiting the best trade-off among the four objectives is selected as the decision basis for the water allocation scheme. Taking Jiuquan, Jiayuguan, and Zhangye cities in western Gansu Province as the study area, the results indicate that the optimal allocation scheme can guide the cities to shift from “water-deficit usage” toward “water-saving usage,” achieving a reasonable balance between meeting water demand and water conservation requirements. This promotes coordinated development among the water resource, socio-economic, and ecological subsystems within each city as well as among the cities themselves, thereby facilitating sustainable utilization of water resources and sustainable development of socio-economics and the ecological environment. The findings can serve as a reference for water resource allocation strategies in the study region.

1. Introduction

Water resources, as a fundamental element for sustaining life, supporting socio-economic development, and maintaining ecosystem functions, play a critical role in ensuring the sustainable development of both human society and the natural environment [1,2]. In recent years, the challenges of uneven spatial and temporal distribution of water resources, increasing supply-demand conflicts, and water pollution have become more severe due to population growth, rapid industrialization, and intensifying climate change. Consequently, water scarcity has emerged as a key bottleneck hindering high-quality socio-economic development and the healthy functioning of ecosystems [3,4]. Against this backdrop, scientifically optimizing the allocation of limited water resources to meet diverse water demands has become not only a pressing issue in the field of water resources management but also an important research focus in related academic disciplines.

Internationally, academic studies on water resource optimization began as early as 1946, when Massé, P. introduced the concept of reservoir operation optimization [5]. Since then, research on water resource allocation has gradually expanded across countries and has contributed significantly to solving practical water-related issues. For example, S. Naghdi et al. [6] integrated system dynamics simulation-optimization with Nash bargaining theory, using the Najaf-Abad sub-basin in Iran as the study area. By employing the NSGA-II algorithm, they maximized water supply, minimized groundwater extraction, and addressed issues related to water scarcity and over-extraction. M. Kalhori et al. [7] developed the Multi-Objective Invasive Weed Optimization Algorithm (MOIWOA) and applied it to the conjunctive optimization of surface and groundwater resources under climate change conditions, thereby enhancing the reliability and resiliency of the water supply system. S. M. Far et al. [8] developed a multi-objective reservoir water allocation model to address conflicts between agricultural and ecological water use, integrating non-cooperative game theory with four bankruptcy theory methods (PRO, AP, CEA, MPA), capable of addressing complex allocation problems under climate change.

In China, research on scientific water resource allocation began in the 1960s, initially focusing on reservoir operation optimization. Although it started later than in some countries, the field has since developed rapidly [9]. Z. Wang et al. [10] developed a multi-objective optimal allocation model for the sustainable use of regional water resources based on multi-objective programming theory. The model was solved using a simulated annealing particle swarm optimization (SA-PSO) algorithm and applied to Yinchuan City to address water supply and demand conflicts under rapid economic development. X. Wu et al. [11] used Wuzhi County, Henan Province, as a case study to develop a multi-objective water resources allocation model integrating social, economic, and environmental objectives, which was optimized using the slime mold algorithm (SMA) to guide water allocation and regional development. G. Liu et al. [12] constructed a multi-source, multi-user, multi-objective allocation model based on the GWAS system for Handan City, addressing challenges such as upstream flow reduction, ground water overexploitation control, and cross-basin water source substitution. The model’s results aligned well with actual water use characteristics, providing decision-making support for scientific water management in the region.

Although existing studies have made significant progress in multi-objective optimization of water resources, considering water as a critical component of ecosystems, the integration of ecological process modeling with multi-objective optimization techniques provides new research avenues for water resource management. For example, A. S. Akopov et al. [13] developed an agent-based modeling (ABM) framework for ecological-economic systems, combining system dynamics and genetic algorithms to achieve a balance between emission reduction and industrial production growth. A. Nabhani et al. [14] employed mixed-integer programming and the ε-constraint method to perform multi-objective optimization of forest ecosystem services, evaluating trade-offs and synergies under uncertainty and spatial constraints. These studies provide important insights for analyzing trade-offs between economic and ecological objectives in water resource allocation.

Furthermore, regarding the choice of multi-objective optimization algorithms, many studies have proposed efficient and innovative evolutionary algorithms, which also provide methodological references for water resource optimization. For instance, A. S. Akopov [15] proposed a matrix-based hybrid genetic algorithm (MBHGA), which performs excellently in large-scale multi-objective optimization problems, capable of finding non-dominated solutions and achieving optimal trade-offs, offering guidance for complex water resource allocation problems across multiple sub-basins and water-use units. E. A. Zaripov et al. [16] proposed an improved hybrid GA-PSO algorithm, achieving a good balance between convergence speed and solution quality, which can also serve as a reference for solving water resource optimization models, thereby enhancing the efficiency and quality of allocation schemes.

The spatial equilibrium proposed in this study is realized through a coupling coordination model. Previous research indicates that coupling coordination models have been primarily applied in areas such as the relationships between economic development and ecological environment [17,18,19], as well as urbanization and ecological environment [20,21], whereas studies linking them to water resources remain relatively scarce, and most of these merely employ the coupling coordination degree as a qualitative evaluation [22,23]. Research explicitly incorporating coupling coordination as an optimization objective in water resource allocation is even rarer, and existing studies are largely concentrated in economically developed regions or major river basins [24,25]. In this context, the present study integrates spatial equilibrium (coupling coordination degree) alongside the conventional social, economic, and ecological objectives as a fourth optimization goal in water resource allocation, and applies it for the first time to the study area in western Gansu Province, comprising the three cities of Jiuquan, Jiayuguan, and Zhangye. The NSGA-III algorithm is employed to solve the Pareto front of the four-objective model, and the resulting Pareto solutions are further ranked using an entropy-weighted TOPSIS method to identify a water allocation scheme for the planning year that promotes not only social, economic, and ecological development but also coordination among the three cities.

2. Water Resources Optimization Model and Solution Approach

2.1. Construction of the Water Resources Optimization Model

In this study, a static multi-objective water resources optimization allocation model is developed for a specific planning year. On the basis of traditional allocation models, the proposed model introduces a coupling coordination constraint and explicitly incorporates spatial equilibrium as an optimization objective. The model aims to simultaneously enhance the coupling coordination among water resources, socio-economic, and ecological subsystems within each water use unit, while also promoting coordination among different units in the region. Specifically, the internal coupling coordination among subsystems is reflected through constraints, whereas the inter-unit coordination is achieved via the spatial equilibrium objective, together forming an internally–externally nested structural framework.

In terms of optimization objectives, the model considers minimizing functions $f_1\left(x\right)$ and $f_3\left(x\right)$ (corresponding to social and ecological objectives, respectively), and maximizing functions $f_2\left(x\right)$ and $f_4\left(x\right)$ (corresponding to economic and spatial equilibrium objectives, respectively). In terms of constraints, the model integrates available water supply constraints, water demand constraints, non-negativity constraints of decision variables, and coupling coordination constraints.

To formally describe this problem, the proposed water resources allocation model can be expressed as a multi-objective optimization problem. Let $X_{ijk}$ denote the decision variables, representing the amount of water allocated from source i to sector k in unit j across the study area. The optimization problem is then formulated as follows:

$$\min {\mathrm{f}}_1\left(\mathrm{x}\right)=\sum _{\mathrm{J}=1}^{\mathrm{J}}\sum _{\mathrm{K}=1}^{\mathrm{K}}{\left(1-{\displaystyle \frac{\sum _{\mathrm{i}=1}^{\mathrm{I}}{\mathrm{X}}_{\mathrm{i}\mathrm{j}\mathrm{k}}}{{\mathrm{D}}_{\mathrm{j}\mathrm{k}}}}\right)}^2\times 100\%$$

(1)

$$\max {\mathrm{f}}_2\left(\mathrm{x}\right)=\left(\sum _{\mathrm{i}=1}^{\mathrm{I}}\sum _{\mathrm{j}=1}^{\mathrm{J}}\sum _{\mathrm{k}=1}^{\mathrm{K}}{\mathrm{a}}_{\mathrm{j}\mathrm{k}}{\mathrm{e}}_{\mathrm{j}\mathrm{k}}{\mathrm{f}}_{\mathrm{i}\mathrm{j}\mathrm{k}}{\mathrm{X}}_{\mathrm{i}\mathrm{j}\mathrm{k}}\right)$$

(2)

$$\min {\mathrm{f}}_3\left(\mathrm{x}\right)=\sum _{\mathrm{j}=1}^{\mathrm{J}}\sum _{\mathrm{k}=1}^{\mathrm{K}}\left(0.001·{\mathrm{d}}_{\mathrm{j}\mathrm{k}}{\mathrm{h}}_{\mathrm{j}\mathrm{k}}\sum _{\mathrm{i}=1}^{\mathrm{I}}{\mathrm{X}}_{\mathrm{i}\mathrm{j}\mathrm{k}}\right)$$

(3)

$$\max {\mathrm{f}}_4\left(\mathrm{x}\right)=\mathrm{F}=\sqrt{\mathrm{C}\times \mathrm{T}}$$

(4)

$$\mathrm{Where} \mathrm{C}={\left[{\prod }_{\mathrm{j}=1}^3{\mathrm{F}}_{\mathrm{j}}÷{\left({\displaystyle \frac{{\sum }_{\mathrm{j}=1}^3{\mathrm{F}}_{\mathrm{j}}}{3}}\right)}^3\right]}^{{\displaystyle \frac{1}{3}}}$$

(5)

$$\mathrm{T}=\sum _{\mathrm{j}=1}^3{\mathrm{\alpha }}_{\mathrm{j}}{\mathrm{F}}_{\mathrm{j}}$$

(6)

The constraints of the optimization model are formulated as follows:

$$\sum _{\mathrm{j}=1}^{\mathrm{J}}\sum _{\mathrm{k}=1}^{\mathrm{K}}{\mathrm{X}}_{\mathrm{i}\mathrm{j}\mathrm{k}}\le {\mathrm{W}}_{\mathrm{i}}$$

(7)

$${\mathrm{D}}_{\mathrm{j}\mathrm{k} \mathrm{m}\mathrm{i}\mathrm{n}}\le \sum _{\mathrm{i}=1}^{\mathrm{I}}{\mathrm{X}}_{\mathrm{i}\mathrm{j}\mathrm{k}}\le {\mathrm{D}}_{\mathrm{j}\mathrm{k} \mathrm{m}\mathrm{a}\mathrm{x}}$$

(8)

$${\mathrm{X}}_{\mathrm{i}\mathrm{j}\mathrm{k}}\ge 0$$

(9)

$${\mathrm{F}}_{\mathrm{j}}=\sqrt{{\mathrm{C}}_{\mathrm{j}}\times {\mathrm{T}}_{\mathrm{j}}}\ge 0.4$$

(10)

$$\mathrm{where} {\mathrm{C}}_{\mathrm{j}}={\left[{\prod }_{\mathrm{n}=1}^{\mathrm{N}}{\mathrm{Y}}_{\mathrm{n}}÷{\left({\displaystyle \frac{\sum _{\mathrm{n}=1}^{\mathrm{N}}{\mathrm{Y}}_{\mathrm{n}}}{\mathrm{N}}}\right)}^{\mathrm{N}}\right]}^{{\displaystyle \frac{1}{\mathrm{N}}}}$$

(11)

$$\mathrm{T}=\sum _{\mathrm{j}=1}^3{\mathrm{\alpha }}_{\mathrm{j}}{\mathrm{F}}_{\mathrm{j}}$$

(12)

To enhance clarity, the variables and parameters used in Equations (1)–(12) are summarized in

Table 1. Summary of variables and parameters.

Symbol	Definition	Unit
f1(x)	Minimization of the squared regional water shortage rate	%
f2(x)	Total regional economic benefit achieved through water resources allocation	CNY 108
f3(x)	Total COD emissions in wastewater discharge	t
f4(x) = F	Spatial equilibrium level (i.e., coupling coordination degree), 0 < F < 1
i	Index of water supply sources
j	Index of water use units
k	Index of water use sectors
$D_{jk}$	Water demand of sector k in unit j	108 m3
$X_{ijk}$	Amount of water allocated from source i to sector k in unit j	108 m3
$a_{jk}$	Total water use benefit coefficient of sector k in unit j	CNY/m3
$e_{jk}$	Water use equity coefficient of sector k in unit j
$f_{ijk}$	Allocation relationship between source i in unit j and sector k
$d_{jk}$	Wastewater discharge coefficient of sector k in unit j
$h_{jk}$	Concentration of COD in the wastewater discharged by water use sector k in unit j	mg/L
C	Attainable coupling degree among the water use units
T	Attainable coordination degree among the water use units
$W_i$	Available water supply of source i
$D_{jk min}$	Lower bound of water demand for sector k in unit j	108 m3
$D_{jk max}$	Upper bound of water demand for sector k in unit j	108 m3
${\alpha }_j$	Weighting coefficient of the unit j, ${\alpha }_1={\alpha }_2={\alpha }_3={\displaystyle \frac{1}{3}}$
$F_j$	coupling coordination degree of the water resources, socio-economic, and ecological subsystems within the unit j
$C_j$	coupling degree of the water resources, socio-economic, and ecological subsystems within the unit j
$T_j$	coordination degree of the water resources, socio-economic, and ecological subsystems within the unit j
$Y_n$	Indicators used to calculate the coupling coordination degree of the water resources, socio-economic, and ecological subsystems for each unit
${\alpha }_n$	Weighting coefficient of indicator n, ${\alpha }_1={\alpha }_2={\alpha }_3\dots ={\alpha }_n={\displaystyle \frac{1}{n}}$
n	Total number of indicators considered

. This table provides a concise overview of all decision variables, parameters, and indices.

Based on existing research on the application of the coupling coordination degree model, the value of F is divided into five levels to evaluate the degree of coordination between C and T. The specific classification criteria are shown in

Table 2. Classification criteria for coupling coordination degree and spatial equilibrium level.

Coupling Coordination Degree (F)		Spatial Equilibrium Level
[0, 0.2]	Barely coupled	Imbalanced
(0.2, 0.4]	Generally coupled	Relatively imbalanced
(0.4, 0.6]	Moderately coupled	Balanced
(0.6, 0.8]	Well coupled	Well balanced
(0.8, 1.0]	Highly coupled	Highly balanced

.

2.2. Model Solution Approach

In this study, the NSGA-III multi-objective evolutionary algorithm is used to solve the proposed model. As an improved version of NSGA-II, NSGA-III is designed for many-objective problems with high-dimensional decision spaces [26,27]. Unlike NSGA-II, which relies on crowding distance to maintain population diversity, NSGA-III employs a reference point-based mechanism that steers solutions toward predefined directions, enhancing solution set diversity. Furthermore, by combining non-dominated sorting with this mechanism, NSGA-III produces a more uniformly distributed Pareto front and improves convergence, thereby overcoming the potential premature convergence of NSGA-II in multi-objective optimization.

Although more pioneering and complex algorithms (e.g., RCGA-PSO, MBHGA, FCGA) have been proposed and have demonstrated excellent performance in empirical studies in other fields [15,28,29], and these algorithms can also serve as a reference for multi-objective water resources optimization, considering the wide application of NSGA-III in water resources optimization studies [30,31,32] and the relatively moderate complexity of the optimization model constructed in this paper, NSGA-III can sufficiently generate diverse and well-converged Pareto fronts. Therefore, NSGA-III is adopted in this study as an appropriate and adequate solution method, achieving a balance between solution quality, computational efficiency, and comparability with existing research.

In addition, although the objective functions in this study are formally expressed in a linear manner, the decision variables are subject to multiple constraints (e.g., water supply upper bounds, water demand lower bounds, and spatial balance constraints), which render the feasible solution space highly non-convex. Moreover, the four objectives are inherently conflicting, making it difficult for traditional linear programming or single-objective optimization methods to obtain a uniformly distributed set of Pareto-optimal solutions. Accordingly, the use of NSGA-III enables the generation of trade-off allocation schemes that balance social, economic, environmental, and spatial equilibrium objectives.

The flowchart of the NSGA-III algorithm is shown in Figure 1.

3. Empirical Application Analysis

3.1. Overview of the Study Area

This study focuses on a region composed of three cities in western Gansu Province: Jiuquan, Jiayuguan, and Zhangye. A water resources optimization allocation model incorporating spatial equilibrium is employed to investigate optimal water allocation in the area. These cities are geographically adjacent and share similar climatic conditions, all characterized by a typical continental arid climate. Due to the combined effects of climate, geography, and topography, significant spatiotemporal disparities exist in the distribution of water resources. Temporally, precipitation is concentrated between June and October, resulting in an abundance of water resources during summer and autumn, and scarcity during winter and spring. Spatially, the southern Qilian Mountains receive higher precipitation, with annual rainfall reaching up to 300 mm, while the northern Gobi and desert regions experience much lower precipitation, with annual rainfall less than 100 mm. Consequently, water resources are more abundant in the south and scarce in the north.

In addition, all three cities face common water-related challenges, including: low efficiency in water use leading to the need for optimization of the water use structure; resource-based water shortages due to insufficient total water availability; indicator-based water shortages caused by mismatches between water use control targets and the actual socio-economic water demands; project-based water shortages resulting from a lack of rainwater and floodwater storage infrastructure or serious sedimentation in existing storage facilities; and quality-based water shortages due to poor protection of drinking water sources. Therefore, it is necessary to carry out optimal water resources allocation for these three cities. The overview map of the study area is shown in Figure 2.

3.2. Data Collection and Forecasting

3.2.1. Data Collection

Data on water resources, national economy, and ecological environment from 2013 to 2023 for Jiuquan, Jiayuguan, and Zhangye in western Gansu Province were obtained from publicly available sources on official websites of Gansu provincial government departments. Specifically, water resource data were sourced from the Gansu Water Resources Bulletin (2013–2023) published by the Gansu Provincial Department of Water Resources; economic data were obtained from the Gansu Development Yearbook (2013–2023) released by the Gansu Provincial Bureau of Statistics; and ecological and environmental data were retrieved from the Gansu Environmental Status Bulletin (2013–2023) issued by the Gansu Provincial Department of Ecology and Environment.

In this study, administrative divisions were used as the basic units. Water use units are denoted as j₁, j₂ and j₃, representing Jiuquan, Jiayuguan, and Zhangye, respectively. Water supply sources are represented by i₁, i₂ and i₃, corresponding to surface water, ground water, and alternative water sources (such as reclaimed wastewater and mine drainage). Water use sectors are categorized as k₁ to k₄, referring to agriculture, industry, domestic, and ecological use, respectively.

3.2.2. Data Forecasting

The year 2023 was taken as the base year, and 2030 as the planning year. Different forecasting methods were employed to project population, economic, and water-related indicators for each water use unit by 2030. Population was forecasted using the growth rate method; economic output and available water supply were estimated via trend extrapolation; and water demand was forecasted using the quota method. The forecasted data for 2030, along with water resource allocation and water shortage condition are presented in

Table 3. Forecasted data for 2030.

Water Use Unit	Population (104 People)	GDP (CNY 108)	Available Water Supply (108 m3)	Water Demand (108 m3)	Water Shortage (108 m3)
Jiuquan	105.37	1189.73	25.39	26.39	−1.00
Jiayuguan	33.34	477.97	2.70	2.71	−0.01
Zhangye	111.45	739.39	20.10	20.52	−0.42
Study Area	250.16	2407.09	48.18	49.61	−1.43

and Figure 3, The water supply proportion by source and the water use proportion by sector are shown in Figure 4 and Figure 5, respectively.

The historical data from 2013 to 2023 used in this study were obtained from bulletins and yearbooks published on the official website of the Gansu provincial government. These data are publicly accessible; however, due to copyright and publication restrictions, they are not provided again in this paper. Based on these historical datasets, the proposed forecasting method was employed to project water resources, population, and economic data for the planning year of 2030. The reliability of the projected results can be validated through the adopted methodological framework, while their rationality and representativeness were further confirmed by comparison with the development plans of the respective cities and related studies.

3.3. Model Parameters Specification

3.3.1. Indicators for Coupling Coordination

The indicators used to evaluate the coupling coordination among the water resources, socio-economic, and ecological subsystems include Y₁, Y₂ and Y₃ representing per capita water supply, water consumption per CNY 10,000 of GDP, and COD emissions per CNY 10,000 of GDP, respectively. The selection of these three indicators is not only based on the reference to similar studies [33] but also grounded in the following considerations:

Theoretical rationale: According to coupling coordination theory, the selected indicators should represent the core states and operational levels of the subsystems. Per capita water supply reflects the capacity of regional water resources to meet population demand; water consumption per CNY 10,000 of GDP measures the dependency of economic growth on water resources and the efficiency of water use; and COD emissions per CNY 10,000 of GDP indicate the pressure of economic activities on the water environment and the intensity of pollution. Together, these three indicators comprehensively characterize the coordination among the water–economy–environment system.

Data availability and continuity: All three indicators are consistently reported in water resources bulletins and statistical yearbooks, providing continuous and comparable historical data across different study units and periods, thereby ensuring the reliability and consistency of the data for model calculations.

Model parsimony: A compact and mutually independent set of indicators reduces computational complexity and avoids redundancy that may interfere with the calculation of the coupling coordination degree.

Due to the differences in units and magnitudes among these three indicators, this study employs the threshold method to normalize them and eliminate dimensional disparities prior to calculating their coupling coordination degree. The threshold method is defined as follows:

$${\mathrm{Y}}_{\mathrm{i}}=\left\{\begin{array}{c}{\mathrm{C}}_{\mathrm{i}}/{\mathrm{S}}_{\mathrm{i}},\mathrm{P}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{r}\\ {\mathrm{S}}_{\mathrm{i}}/{\mathrm{C}}_{\mathrm{i}}, \mathrm{N}\mathrm{e}\mathrm{g}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{r}\end{array}\right.$$

(13)

where is the dimensionless value of indicator i; C_i is the actual value; and S_i is the standard (reference) value of the indicator.

3.3.2. Benefit Coefficients for Water Use Sectors

The water use benefit coefficients for agricultural and industrial sectors are defined as the ratio of economic benefit generated to the amount of water used, which corresponds to the inverse of their respective total water use quotas. According to the study by C. Dai et al. [34] in 2018, the benefit coefficient for domestic water use is determined as the maximum value between the benefit coefficients of the agricultural and industrial sectors. The benefit coefficient for ecological water use is set identical to that for domestic water use, considering their close association [31]. The water use benefit coefficients for each sector in each city are shown in

Table 4. Water use benefit coefficients.

Water Use Unit	Agricultural Sector (CNY/m3)	Industrial Sector (CNY/m3)	Domestic Sector (CNY/m3)	Ecological Sector (CNY/m3)
Jiuquan	10.43	555.07	555.07	555.07
Jiayuguan	17.76	285.71	285.71	285.71
Zhangye	12.06	563.38	563.38	563.38

.

3.3.3. Wastewater Discharge Coefficient and COD Emission Concentration

Based on the review of pollutant discharge data from the Gansu Development Yearbooks and the Gansu Environmental Status Bulletins over recent years, this study calculates the wastewater discharge coefficients and COD emission concentrations only for the industrial and domestic sectors. The wastewater discharge coefficient is defined as the ratio of wastewater discharge volume to water consumption volume for each sector, while the COD emission concentration is defined as the ratio of COD discharge volume to wastewater discharge volume. The wastewater discharge coefficients and COD emission concentrations for the industrial and domestic sectors in each city are presented in

Table 5. Wastewater discharge coefficients and COD emission concentrations.

Water Use Unit	Wastewater Discharge Coefficient		COD Emission Concentration (mg/L)
	Industrial Sector	Domestic Sector	Industrial Sector	Domestic Sector
Jiuquan	0.02	0.58	25.89	124.88
Jiayuguan	0.31	0.34	3.12	165.95
Zhangye	0.05	0.56	92.81	196.30

.

3.3.4. Upper and Lower Bounds of Water Demand

The upper bounds of water consumption for each water use sector are set equal to their respective forecasted water demand values. The lower bounds are determined based on relevant regulations and policies, actual water use structures of each city, water conservancy planning guidelines, and water-saving requirements. Specifically, the lower bounds for agricultural water demand in Jiuquan, Jiayuguan, and Zhangye are set at 93%, 95%, and 95% for their respective forecasted agricultural water demands; The lower bounds of industrial water demand are set at 95%, 95%, and 96% of their forecasted industrial water demands; The lower bounds for ecological water demand are set at 95%, 96%, and 96% of their respective forecasted ecological water demands.

In accordance with the Water Resources Dispatching Management Measures, which stipulate that “domestic water demand shall be given priority, followed by the basic ecological needs, and then coordinated agricultural, industrial, hydropower, and navigation water demands” [35,36], as well as the social principle of “putting people first” and the fundamental role of domestic water in ensuring basic human needs, the lower bounds for domestic water demand in all three cities are set equal to the forecasted domestic water demand.

The lower bounds of water demand are regarded as a water-saving scenario. The regional water supply and demand situation under this scenario in 2030 is presented in

Table 6. Water supply and demand under the water-saving scenario.

Water Use Unit	Available Water Supply (108 m3)	Water Demand (108 m3)	Water Surplus (108 m3)
Jiuquan	24.68	25.39	0.70
Jiayuguan	2.53	2.70	0.17
Zhangye	19.14	20.10	0.96
Study Area	46.35	48.18	1.83

, with the corresponding water allocation results shown in Figure 6 and the sectoral water use proportions as shown in Figure 7.

3.3.5. Water Use Equity Coefficient

The calculation formula for the water use equity coefficient of each water use sector is as follows:

$${\mathrm{e}}_{\mathrm{j}\mathrm{k}}={\displaystyle \frac{1+{\mathrm{n}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{n}}_{\mathrm{j}\mathrm{k}}}{\sum _{\mathrm{i}=1}^{\mathrm{K}}(1+{\mathrm{n}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{n}}_{\mathrm{j}\mathrm{k}})}}$$

(14)

where $n_{max}$ is the maximum water use priority value among all water use sectors; and $n_{jk}$ is the water use priority of sector k in unit j.

The water use equity coefficient reflects the relative importance of each sector [37]. In accordance with the legal principle of “domestic water use first, followed by ecological water use, and then production water use” stipulated in the Water Resources Dispatching Management Measures [35,36], the equity coefficients for the domestic and ecological water use sectors in each city are set to 0.4 and 0.3, respectively.

For Jiuquan and Zhangye, which are agricultural-oriented cities, the equity coefficient for the agricultural water use sector is set to 0.2, and that for the industrial water use sector is set to 0.1.

For Jiayuguan, an industrial-oriented city, the equity coefficient for the industrial water use sector is set to 0.2, and that for the agricultural water use sector is set to 0.1.

3.3.6. Water Allocation Relationships Between Water Supply Sources and Water Use Sectors

In accordance with the principle of “prioritizing surface water over ground water” [38], surface water resources are allocated with priority and can be supplied to the agricultural, industrial, domestic, and ecological sectors. Considering the safety of domestic water use and food security, other water sources (e.g., treated wastewater, mine drainage, etc.) are restricted to industrial and ecological uses only, and are not permitted to be allocated to agricultural or domestic sectors. Ground water, being a high-quality source, is primarily allocated to domestic water use. Given the strict regulatory controls on ground water exploitation in the study area, the remaining exploitable ground water is designated exclusively for agricultural and industrial supplementation, and is not used for ecological purposes. The detailed allocation relationships are shown in

Table 7. Allocation relationship between water supply sources and water use sectors.

Water Source	Agricultural Sector	Industrial Sector	Domestic Sector	Ecological Sector
Surface water	1	1	1	1
Ground water	1	1	1	0
Other water	0	1	0	1

.

3.4. Model Parameter Settings and Results Analysis

3.4.1. Model Implementation and Parameter Settings

The model parameters and mathematical expressions are encoded in MATLAB 2022b. The solution process is carried out using the PLATEMO 4.12 optimization toolbox [39], where the NSGA-III algorithm is selected. The population size is set to 300, the maximum number of function evaluations is set to 30,000, the crossover probability is set to 0.9, and the mutation probability is defined as 1/36. The number 36 corresponds to the total number of decision variables, derived from 3 water use units, 3 water supply sources, and 4 water use sectors, resulting in 3 × 3 × 4 = 36 decision variables.

3.4.2. Pareto Front Solutions for the Four Objectives

A total of 94 Pareto front solutions were obtained from the model after execution. The distribution of these solutions across the four objectives is shown in Figure 8.

Based on the characteristics presented in Figure 8, the social objective shows a negative correlation with both the economic and ecological objectives, indicating conflicts between the social objective and the other two. An increase in water shortage implies a decrease in the amount of water allocated to water-use sectors, which subsequently leads to reductions in both the economic benefits generated and the amount of COD emissions. The economic and ecological objectives exhibit a positive correlation, suggesting a consistent preference in water resource allocation. This aligns with the practical development pattern that “greater economic benefits are often accompanied by greater impacts on the ecological environment” [40,41,42].

The spatial equilibrium level exhibits a negative correlation with the social objective but shows a positive correlation with both the economic and ecological objectives, indicating a conflict between spatial equilibrium and the social objective, while demonstrating consistency in allocation preference with the economic and ecological objectives. As spatial equilibrium involves a nested bi-level calculation process, its variation with respect to the other three objectives is relatively complex.

When the degree of water shortage increases, indicators such as per capita water supply, water consumption per CNY 10,000 of GDP, and COD emissions per CNY 10,000 of GDP decrease across the cities. Among them, per capita water supply is a positive indicator, and its normalized value decreases accordingly. In contrast, water consumption per CNY 10,000 of GDP and COD emissions per CNY 10,000 of GDP are negative indicators, and their normalized values increase. The trend that the inter-city coupling coordination degree decreases as the social objective increases suggests that the intra-city coordination among water resources, socio-economic, and ecological subsystems also weakens with higher social objective values. This trend is consistent with the decline in the normalized value of per capita water supply, indicating that per capita water supply is the most influential indicator in determining both intra-city and inter-city coupling coordination variations.

Conversely, the upward trends of the economic and ecological objectives indicate a reduction in water scarcity. As scarcity lessens, per capita water supply, water use per CNY 10,000 of GDP, and COD emissions per CNY 10,000 of GDP all increase. The normalized value of per capita water supply (a positive indicator) increases, while those of the latter two (negative indicators) decrease. Consequently, the inter-city coupling coordination degree improves with the rise in the normalized value of per capita water supply, leading to the overall observed trend: the spatial equilibrium level increases with improvements in the economic and ecological objectives, as illustrated in Figure 8.

In addition, the results shown in the figure indicate that the spatial equilibrium levels of all Pareto solutions exceed 0.86, suggesting that the water resource allocation outcomes obtained by the model are conducive to promoting coordinated development among the cities.

3.4.3. Inter-City Comparison of Subsystem Coupling Coordination Degrees

The coupling coordination degrees among the water resources, socio-economic, and ecological subsystems within each city are shown in Figure 9.

Based on Figure 9, the coupling coordination degrees among the water resources, socio-economic, and ecological subsystems in Jiuquan are all greater than 0.78, indicating a well coupled and well balanced state; in Jiayuguan, these degrees exceed 0.83, representing a highly coupled and highly balanced; and in Zhangye, they are all above 0.62, also corresponding to a well coupled and well balanced state. These findings demonstrate that the water resource allocation obtained from the model solution facilitates the coordinated development of the water resources, socio-economic, and ecological subsystems within each city.

4. Decision-Making for Water Resource Allocation Schemes

The entropy-weighted TOPSIS method is employed to identify the optimal solutions from the Pareto front. As an effective multi-criteria decision-making technique, this method comprehensively considers both the weights of each evaluation criterion and the proximity of each alternative to the ideal and anti-ideal solutions, thereby enhancing the scientific rigor and reliability of decision-making [32,43].

4.1. Weight Calculation

To minimize the influence of subjective factors on the weighting results, this study prioritizes the use of the entropy weight method for calculating the weights of each evaluation criterion. The entropy weight method is an objective weighting technique based on information entropy. In this context, information measures the degree of order within a system, whereas entropy reflects the degree of disorder. When determining weights using this method, a higher entropy value indicates lower data dispersion under a specific indicator, suggesting that the indicator has less influence on the overall evaluation outcome. Conversely, a lower entropy value implies greater data dispersion, meaning that the indicator has a greater impact on the comprehensive evaluation result [44].

4.1.1. Constructing the Initial Decision Matrix A

$$\mathrm{A}={\left\{{\mathrm{a}}_{\mathrm{i}\mathrm{j}}\right\}}_{\mathrm{m}\times \mathrm{n}}=\left[\begin{array}{cccc}{\mathrm{a}}_{11}& {\mathrm{a}}_{12}& \dots & {\mathrm{a}}_{1\mathrm{n}}\\ {\mathrm{a}}_{21}& {\mathrm{a}}_{22}& \dots & {\mathrm{a}}_{2\mathrm{n}}\\ ⋮& ⋮& \ddots & ⋮\\ {\mathrm{a}}_{\mathrm{m}1}& {\mathrm{a}}_{\mathrm{m}2}& \dots & {\mathrm{a}}_{\mathrm{m}\mathrm{n}}\end{array}\right]$$

(15)

where i denotes the evaluation indicator; j denotes the evaluation object; m represents the total number of evaluation indicators; n represents the total number of evaluation objects; and $a_{ij}$ is the actual value of indicator i for evaluation object j.

4.1.2. Constructing the Normalized Decision Matrix A*

$$\left\{\begin{array}{c}{\mathrm{a}}_{\mathrm{i}\mathrm{j}}^{\mathrm{*}}={\displaystyle \frac{{\mathrm{a}}_{\mathrm{i}\mathrm{j}}-{\mathrm{a}}_{\mathrm{m}\mathrm{i}\mathrm{n},\mathrm{j}}}{{\mathrm{a}}_{\mathrm{m}\mathrm{a}\mathrm{x},\mathrm{j}}-{\mathrm{a}}_{\mathrm{m}\mathrm{i}\mathrm{n},\mathrm{j}}}},\mathrm{P}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{r}\\ {\mathrm{a}}_{\mathrm{i}\mathrm{j}}^{\mathrm{*}}={\displaystyle \frac{{\mathrm{a}}_{\mathrm{m}\mathrm{a}\mathrm{x},\mathrm{j}}-{\mathrm{a}}_{\mathrm{i}\mathrm{j}}}{{\mathrm{a}}_{\mathrm{m}\mathrm{a}\mathrm{x},\mathrm{j}}-{\mathrm{a}}_{\mathrm{m}\mathrm{i}\mathrm{n},\mathrm{j}}}},\mathrm{N}\mathrm{e}\mathrm{g}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{i}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{r}\end{array}\right.$$

(16)

$${\mathrm{A}}^{\mathrm{*}}={\left\{{\mathrm{a}}_{\mathrm{i}\mathrm{j}}^{\mathrm{*}}\right\}}_{\mathrm{m}\times \mathrm{n}}=\left[\begin{array}{cccc}{\mathrm{a}}_{11}^{\mathrm{*}}& {\mathrm{a}}_{12}^{\mathrm{*}}& \dots & {\mathrm{a}}_{1\mathrm{n}}^{\mathrm{*}}\\ {\mathrm{a}}_{21}^{\mathrm{*}}& {\mathrm{a}}_{22}^{\mathrm{*}}& \dots & {\mathrm{a}}_{2\mathrm{n}}^{\mathrm{*}}\\ ⋮& ⋮& \ddots & ⋮\\ {\mathrm{a}}_{\mathrm{m}1}^{\mathrm{*}}& {\mathrm{a}}_{\mathrm{m}2}^{\mathrm{*}}& \dots & {\mathrm{a}}_{\mathrm{m}\mathrm{n}}^{\mathrm{*}}\end{array}\right]$$

(17)

4.1.3. Computing Indicator Weight ${\mathrm{W}}_{\mathrm{j}}$

$${\mathrm{E}}_{\mathrm{j}}={\displaystyle \frac{1}{-\mathrm{l}\mathrm{n}\left(\mathrm{m}\right)}}\sum _{\mathrm{i}=1}^{\mathrm{m}}{\mathrm{f}}_{\mathrm{i}\mathrm{j}}\mathrm{l}\mathrm{n}{\mathrm{f}}_{\mathrm{i}\mathrm{j}}$$

(18)

$${\mathrm{f}}_{\mathrm{i}\mathrm{j}}={\displaystyle \frac{{\mathrm{a}}_{\mathrm{i}\mathrm{j}}}{\sum _{\mathrm{i}=1}^{\mathrm{m}}{\mathrm{a}}_{\mathrm{i}\mathrm{j}}}}$$

(19)

$${\mathrm{W}}_{\mathrm{j}}={\displaystyle \frac{1-{\mathrm{E}}_{\mathrm{j}}}{\sum _{\mathrm{j}=1}^{\mathrm{n}}(1-{\mathrm{E}}_{\mathrm{j}})}}$$

(20)

where $E_j$ denotes the information entropy; and $f_{ij}$ represents the characteristic weight of indicator i.

4.2. Entropy-Weighted TOPSIS Method

The TOPSIS method is a widely used and effective technique in multi-criteria decision analysis, also known as the distance-to-ideal-solution method [45,46]. It ranks decision alternatives based on the Euclidean distance of each alternative’s evaluation indicators from the positive ideal solution and the negative ideal solution [47]. An alternative that is closer to the PIS and farther from the NIS is considered more favorable than others [48,49]. Unlike the traditional TOPSIS method, which relies on subjective approaches such as expert judgment or fuzzy evaluation to determine indicator weights, the entropy-weighted TOPSIS method assigns weights based on the degree of variability in the data, thereby objectively reflecting the relative importance of each evaluation criterion.

4.2.1. Constructing the Weighted Decision Matrix Y

$$\mathrm{Y}={\left\{{\mathrm{Y}}_{\mathrm{i}\mathrm{j}}\right\}}_{\mathrm{m}\times \mathrm{n}}={\mathrm{W}}_{\mathrm{j}}\times {\mathrm{A}}^{\mathrm{*}}={\mathrm{w}}_{\mathrm{j}}\times {\left\{{\mathrm{a}}_{\mathrm{i}\mathrm{j}}^{\mathrm{*}}\right\}}_{\mathrm{m}\times \mathrm{n}}=\left[\begin{array}{cccc}{{\mathrm{w}}_1\mathrm{a}}_{11}^{\mathrm{*}}& {\mathrm{w}}_2{\mathrm{a}}_{12}^{\mathrm{*}}& \dots & {\mathrm{w}}_{\mathrm{n}}{\mathrm{a}}_{1\mathrm{n}}^{\mathrm{*}}\\ {{\mathrm{w}}_1\mathrm{a}}_{21}^{\mathrm{*}}& {\mathrm{w}}_2{\mathrm{a}}_{22}^{\mathrm{*}}& \dots & {\mathrm{w}}_{\mathrm{n}}{\mathrm{a}}_{2\mathrm{n}}^{\mathrm{*}}\\ ⋮& ⋮& \ddots & ⋮\\ {{\mathrm{w}}_1\mathrm{a}}_{\mathrm{m}1}^{\mathrm{*}}& {{\mathrm{w}}_2\mathrm{a}}_{\mathrm{m}2}^{\mathrm{*}}& \dots & {\mathrm{w}}_{\mathrm{n}}{\mathrm{a}}_{\mathrm{m}\mathrm{n}}^{\mathrm{*}}\end{array}\right]$$

(21)

4.2.2. Determining the Ideal Solution Y⁺ and Y⁻

$$\left\{\begin{array}{c}{\mathrm{Y}}_j^{+}=\left\{\max {\mathrm{y}}_{\mathrm{i}\mathrm{j}}|\mathrm{i}=\mathrm{1,2},\dots ,\mathrm{m}\right\}=\left\{{\mathrm{y}}_1^{+},{\mathrm{y}}_2^{+},\dots ,{\mathrm{y}}_{\mathrm{q}}^{+},\dots ,{\mathrm{y}}_{\mathrm{m}}^{+}\right\}\\ {\mathrm{Y}}_j^{-}=\left\{\min {\mathrm{y}}_{\mathrm{i}\mathrm{j}}|\mathrm{i}=\mathrm{1,2},\dots ,\mathrm{m}\right\}=\left\{{\mathrm{y}}_1^{-},{\mathrm{y}}_2^{-},\dots ,{\mathrm{y}}_{\mathrm{q}}^{-},\dots ,{\mathrm{y}}_{\mathrm{m}}^{-}\right\}\end{array}\right.$$

(22)

4.2.3. Calculating the Euclidean Distances ${\mathrm{D}}_{\mathrm{i}}^{+}$ and ${\mathrm{D}}_{\mathrm{i}}^{-}$

$$\left\{\begin{array}{c}{\mathrm{D}}_{\mathrm{i}}^{+}=\sqrt{{\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}}{\left({\mathrm{Y}}_{\mathrm{i}\mathrm{j}}-{\mathrm{Y}}_{\mathrm{j}}^{+}\right)}^2}\\ {\mathrm{D}}_{\mathrm{i}}^{-}=\sqrt{{\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{n}}}{\left({\mathrm{Y}}_{\mathrm{i}\mathrm{j}}-{\mathrm{Y}}_{\mathrm{j}}^{-}\right)}^2}\end{array}\right.$$

(23)

4.2.4. Calculating the Comprehensive Score ${\mathrm{L}}_{\mathrm{i}}$

$${\mathrm{L}}_{\mathrm{i}}={\displaystyle \frac{{\mathrm{D}}_{\mathrm{i}}^{-}}{{\mathrm{D}}_{\mathrm{i}}^{+}+{\mathrm{D}}_{\mathrm{i}}^{-}}}$$

(24)

where $L_i$ represents the closeness of the evaluation object to the ideal solution, $L_i\in \left[\mathrm{0,1}\right]$; the closer $L_i$ is to 1, the higher the closeness between the evaluation object and the ideal solution [50].

4.3. Decision Results and Analysis

4.3.1. Entropy Weight Calculation Results

The entropy values $E_j$ and weights $w_j$ calculated using the aforementioned entropy weight method, are shown in Figure 10a and Figure 10b, respectively. It can be observed that among the four objectives in the Pareto front solution set, the ecological objective has the lowest entropy and the highest weight, indicating the greatest data dispersion and the most significant impact on the final water allocation decision. This is followed by the ecological objective and spatial equilibrium level, while the social objective has a relatively smaller impact on the decision outcome.

4.3.2. Comprehensive Score Calculation Results

After performing a comprehensive evaluation and ranking of the Pareto front solution set using the entropy-weighted TOPSIS method described above, the calculated results of the comprehensive scores are shown in Figure 11.

It can be observed that the majority of solutions have comprehensive scores (closeness coefficients) within the range of 0.35 to 0.60, with only a small number exceeding 0.60, indicating that the overall closeness remains at a moderate level. Given the complex trade-offs among the four objectives, a perfectly ideal solution that optimizes all objectives simultaneously does not exist. Therefore, the five solutions with the highest comprehensive scores are selected as candidate recommendations for the water allocation scheme (highlighted in the figure). These five solutions, ranked from 1st to 5th, are Solution 22, Solution 9, Solution 18, Solution 24, and Solution 65, with respective scores of 0.665, 0.649, 0.639, 0.638, and 0.632. These scores are noticeably higher than the main density interval (0.35–0.60), making them elite solutions within the efficient solution set.

4.3.3. Decision Results

The actual outcomes of the four objectives corresponding to all Pareto front solutions are illustrated in Figure 12. The highlighted sections indicate the actual values of the four objectives for the five Pareto front solutions with the highest overall scores.

The top five Pareto optimal solutions with the highest overall scores exhibit social objective values ranging from 1.10% to 1.36%, economic objective values between CNY 167.86 and 167.96 billion, ecological objective values between 15,661.0 and 15,664.0 tons, and spatial equilibrium levels ranging from 0.8612 to 0.8619. Compared with the overall Pareto front solution set, these five solutions exhibit superior performance in terms of economic objective and spatial equilibrium level, while demonstrating an above-average performance in the social objective, and a moderately low level in the ecological objective. This reflects the inherent compromises among the multiple objectives, where improvements in economic and social benefits are partially attained at the expense of ecological outcomes.

To facilitate a more intuitive comparative analysis of the differences in performance across the four objectives among the top five solutions with the highest comprehensive scores, the objective values of each solution were normalized. The results are presented in Figure 13.

As shown in the figure, Solution 22 and Solution 9 are quite similar, with their corresponding water allocation schemes achieving a relatively good balance among the four objectives and being the most favorable for ecological protection among the five schemes. The water allocation scheme corresponding to Solution 18 focuses more on ensuring social fairness and stability as well as promoting economic development in the study area, but is less favorable for ecological protection. Solutions 24 and 65 are also quite similar, and their corresponding schemes exhibit significant advantages in economic development and coordinated development among cities, yet they are likewise less favorable for ecological protection.

Overall, the five solutions exhibit very similar performance in terms of the economic objective. Therefore, three water allocation schemes were selected from those exhibiting outstanding performance in the other three objectives as the recommended allocation schemes for the study area under different preference orientations, namely: Scheme 22 (comprehensive and ecologically friendly allocation), Scheme 18 (socially fair and stable allocation), and Scheme 65 (allocation promoting coordinated development among cities), as the recommended water allocation schemes. The actual objective values of each water allocation scheme are presented in

Table 8. Actual objective values of each scheme.

Index	Social Objective (%)	Economic Objective (CNY 108)	Ecological Objective (t)	Spatial Equilibrium Level
22	1.273	1678.65	15,661.12	0.8614
18	1.106	1679.02	15,663.08	0.8615
65	1.216	1678.74	15,663.15	0.8618

, and their corresponding water allocation distributions are shown in

Table 9. Water allocation distribution of Scheme 22.

Water Use Unit	Water Source	Water Allocation Amount (104 m3)
		Agricultural Sector	Industrial Sector	Domestic Sector	Ecological Sector
Juiquan	Surface water	123,947.47	0.00	0.00	52,255.62
	Ground water	58,542.23	4166.73	7720.84	0.00
	Other water	0.00	3220.62	0.00	0.00
Jiayuguan	Surface water	57.65	0.00	0.00	7832.64
	Ground water	5602.74	4372.53	3359.24	0.00
	Other water	0.00	5467.01	0.00	0.00
Zhangye	Surface water	125,525.78	0.00	0.00	2843.96
	Ground water	60,935.50	0.00	7247.94	0.00
	Other water	0.00	1597.24	0.00	1475.39

,

Table 10. Water allocation distribution of Scheme 18.

Water Use Unit	Water Source	Water Allocation Amount (104 m3)
		Agricultural Sector	Industrial Sector	Domestic Sector	Ecological Sector
Juiquan	Surface water	123,947.47	0.00	0.00	52,255.62
	Ground water	58,542.23	4166.73	7720.84	0.00
	Other water	0.00	3220.62	0.00	0.00
Jiayuguan	Surface water	57.65	0.00	0.00	7832.64
	Ground water	5553.37	4318.88	3359.24	0.00
	Other water	0.00	5467.01	0.00	0.00
Zhangye	Surface water	125,452.97	0.00	0.00	2916.77
	Ground water	61,008.30	0.00	7247.94	0.00
	Other water	0.00	1648.03	0.00	1424.60

and

Table 11. Water allocation distribution of Scheme 65.

Water Use Unit	Water Source	Water Allocation Amount (104 m3)
		Agricultural Sector	Industrial Sector	Domestic Sector	Ecological Sector
Juiquan	Surface water	123,947.47	0.00	0.00	52,255.62
	Ground water	58,542.23	4166.73	7720.84	0.00
	Other water	0.00	3220.62	0.00	0.00
Jiayuguan	Surface water	57.65	0.00	0.00	7832.64
	Ground water	5491.08	4404.90	3359.24	0.00
	Other water	0.00	5467.01	0.00	0.00
Zhangye	Surface water	125,498.82	0.00	0.00	2870.93
	Ground water	59,709.24	9.88	7247.94	0.00
	Other water	0.00	1622.43	0.00	1450.20

, respectively.

Among these three recommended schemes, Scheme 22 has the highest comprehensive score and achieves the best balance across all four objectives; thus, it is identified as the optimal water allocation scheme.

5. Discussion

In this section, the discussions in Section 5.1, Section 5.2 and Section 5.3 are centered on the optimal water allocation scheme (Scheme 22) for an in-depth analysis. Although the other shortlisted schemes also provide valuable references for policymakers, their analytical procedures are essentially identical to those of the optimal scheme. Therefore, to avoid redundancy, only the results of the optimal scheme are presented and discussed as a representative case.

5.1. Analysis of Water-Saving Efficiency

5.1.1. Analysis of Water-Saving Efficiency of Water Supply Sources

The optimal water allocation schemes in Table 9 were aggregated by water supply source and compared with the projected available water supply of each city in the study area. The results of this analysis are presented in

Table 12. Comparison between optimal water allocation and projected available water supply.

Projected Available Water Supply (104 m3)
Water Use Unit	Surface Water	Ground Water	Other Water	Total
Jiuquan	176,203.09	70,429.80	3220.62	249,853.51
Jiayuguan	7890.29	13,334.51	5467.01	26,691.82
Zhangye	128,369.74	68,183.44	3072.63	199,625.81
Study Area	312,463.13	151,947.75	11,760.27	476,171.14
Optimal Allocation Water Supply (104 m3)
Jiuquan	176,203.09	70,429.80	3220.62	249,853.51
Jiayuguan	7890.29	13,334.51	5467.01	26,691.82
Zhangye	128,369.74	68,183.44	3072.63	199,625.81
Study Area	312,463.13	151,947.75	11,760.27	476,171.14
Remaining Available Water Resources (104 m3)
Jiuquan	0.000	4000.00	0.000	4000.00
Jiayuguan	0.000	295.76	0.000	295.76
Zhangye	0.000	1337.24	0.000	1337.24
Study Area	0.00	5633.00	0.00	5633.00

.

A detailed analysis of the results presented in the table above reveals that, following the optimal allocation of water resources, the study area as a whole exhibits a residual available water supply of 1.17%. Specifically, the residual water supply in Jiuquan, Jiayuguan, and Zhangye accounts for 1.58%, 1.10%, and 0.67%, respectively. All of this residual volume originates from groundwater sources, aligning with the water supply principle of “prioritizing surface water before groundwater.”

The relatively low residual supply in each city is primarily attributed to the stringent lower-bound constraints imposed on sectoral water demand in the model, reflecting a conservative water-saving strategy. During the optimization process, the allocated water must ensure that the basic water demands (i.e., the lower bounds) of each water-use sector are satisfied. Simultaneously, allocations are pushed as close as possible to the upper bounds of demand without exceeding the available water supply, in order to alleviate pre-existing water shortages. As a result, the model outputs tend to be compact, leaving limited surplus water resources.

5.1.2. Analysis of Water-Saving Efficiency of Water Reserves

The optimal water allocation scheme in Table 9 is summarized by water use sectors and compared with the projected water demand (upper demand limits) of each sector. The comparison results are shown in

Table 13. Comparison between optimal water allocation and projected water demand.

Projected Water Demand (104 m3)
Water Use Unit	Agricultural Sector	Industrial Sector	Domestic Sector	Ecological Sector	Total
Jiuquan	193,369.13	7776.16	7720.84	55,005.92	263,872.04
Jiayuguan	5677.33	9893.42	3359.24	8159.00	27,088.99
Zhangye	191,909.20	1672.99	7247.94	4355.42	205,185.55
Study Area	390,955.66	19,342.57	18,328.02	67,520.34	496,146.59
Optimal Allocation Water Demand (104 m3)
Jiuquan	182,489.69	7387.35	7720.84	52,255.62	249,853.51
Jiayuguan	5660.40	9839.54	3359.24	7832.64	26,691.82
Zhangye	186,461.28	1597.24	7247.94	4319.35	199,625.81
Study Area	374,611.37	18,824.14	18,328.02	64,407.62	476,171.14
Saved Water Reserves (104 m3)
Jiuquan	10,879.43	388.80	0.00	2750.29	14,018.53
Jiayuguan	16.94	53.87	0.00	326.36	397.17
Zhangye	5447.92	75.75	0.00	36.07	5559.74
Study Area	16,344.29	518.43	0.00	3112.72	19,975.44

.

The term available water supply refers to the volume of water resources that can be provided by various water supply projects, rather than the actual water reserves. If the original projected water demand (upper demand limits) were to be fully satisfied, it would necessitate the construction of additional supply infrastructure and the intensified extraction of water reserves, which would be detrimental to the sustainable utilization of water resources. Although the table above indicates that agricultural, industrial, and ecological water uses have all achieved certain water-saving effects, water savings in the agricultural and industrial sectors can directly reduce water resource consumption through specific conservation measures, thereby making a substantive contribution to the preservation of water reserves. In contrast, while ecological replenishment does not directly extract groundwater, excessive reliance on surface water may indirectly compel increased groundwater extraction by agriculture and industry, which could in turn hinder the sustainable protection of groundwater reserves. Therefore, the water-saving effect of ecological use merely reflects the control of water use intensity and does not provide substantive benefits in reducing water reserves.

According to Table 13, the optimal water allocation plan can reduce water reserves consumption relative to the projected water demand by 5.31%, 1.47%, and 2.71% in Jiuquan, Jiayuguan, and Zhangye, respectively. Combined with the data from Table 12, the contribution of agriculture and industry to conserving water reserves is mainly reflected in the reduction in groundwater abstraction. Specifically, in Jiuquan, the agricultural and industrial sectors reduce groundwater reserves consumption by 5.63% and 5.00%, respectively; in Jiayuguan, by 0.30% and 0.54%; and in Zhangye, by 2.84% and 4.53%, respectively.

In summary, the optimal water allocation scheme meets the basic water demands of all sectors while enabling a transition from a water-scarce model to a water-conserving model in the three cities. It achieves a relatively balanced trade-off between demand satisfaction and water-saving goals, aligning well with the actual water resource conditions.

5.2. Changes in Water Use Indicators and Policy Implications

5.2.1. Analysis of Water Use Indicator Changes

According to the Water Resources Bulletin, the indicators for agricultural, industrial, and domestic water use are defined as follows: irrigation water use per mu of farmland, water use per unit of industrial added value for industry, and per capita domestic water use. The indicator for ecological protection is the COD emissions per CNY 10,000 of GDP. The trends of these indicators in the three cities of the study area for the years 2023 and 2030 before optimization, and 2030 after optimization, are shown in Figure 14a–d.

In terms of agricultural water use, after the optimized allocation in 2030, the average irrigation water use per mu in the study area is 398.52 m³/mu, representing a 9.64% reduction compared to 2023, among which the values in Jiuquan, Jiayuguan, and Zhangye are 430.95, 340.57, and 372.84 m³/mu, respectively, corresponding to reductions of 14.26%, 3.54%, and 8.76%.

In terms of industrial water use, the optimized allocation for 2030 results in an industrial water use per unit of industrial added value of 23.28 m³/CNY 10⁴ across the study area, representing a 15.13% reduction compared to 2023, among which the values in Jiuquan, Jiayuguan, and Zhangye are 17.11, 34.81, and 16.95 m³/CNY 10⁴, respectively, corresponding to reductions of 14.43%, 12.98%, and 15.27%.

For domestic water use, by 2030, per capita domestic water consumption in the study area is projected to reach 200.73 L/person·day, among which the values in Jiuquan, Jiayuguan, and Zhangye are 200.75, 276.02, and 178.18 L/person·day, respectively, representing increases of 17.42%, 7.32%, and 17.42% compared to 2023.

Regarding ecological and environmental protection, after the optimized allocation in 2030, COD emissions per CNY 10,000 of GDP in the study area are projected to be 0.65 kg/CNY 10⁴, representing a reduction of 23.27% compared to 2023, among which the values in Jiuquan, Jiayuguan, and Zhangye are 0.47, 0.42, and 1.09 kg/CNY 10⁴, respectively, corresponding to reductions of 24.93%, 28.76%, and 18.78%.

5.2.2. Policy Implications and Practical Applications

In terms of agricultural water use, as typical agricultural cities, Jiuquan and Zhangye have a high proportion of agricultural water use in total consumption and thus hold substantial potential for water savings. Therefore, these two cities should promote efficient water-saving irrigation technologies, strictly implement irrigation water regulations, and enhance precision management of agricultural water use to improve irrigation efficiency, increase funding for water-saving facilities, advance high-quality agricultural development, and ensure the sustainable utilization of water resources [51].

In terms of industrial water use, all three cities demonstrate substantial potential for industrial water savings. To achieve this, local governments should optimize industrial structure, advance industrial water-saving technologies, strictly regulate water use in high-consumption industries, and promote the utilization of reclaimed water [51,52]. Considering that industrial water demand is primarily met by groundwater and alternative sources, improving industrial water use efficiency would also help reduce pressure on groundwater extraction, contributing to sustainable groundwater management.

In terms of domestic water use, under the premise of prioritizing basic residential water needs, the optimized water allocation scheme alleviates domestic water supply pressure across the cities to some extent. However, this outcome should not justify any relaxation of water-saving management, and local authorities should continue to enforce water conservation policies. Given that domestic water use relies entirely on groundwater, it is imperative to adhere to the principle of “saving wherever possible,” enhance public awareness of water conservation, strengthen outreach and education efforts, promote the use of water-saving appliances, and institutionalize regular performance assessments for water-saving initiatives. Furthermore, it is essential to actively implement groundwater extraction control and protection measures to ensure the rational and sustainable utilization of groundwater resources [53,54].

In terms of ecological and environmental protection, the COD discharge trends in the three cities show a downward pattern similar to that of industrial water use, indicating that COD emissions are more significantly influenced by industrial water consumption. Therefore, improving industrial water use efficiency, promoting clean production processes, and integrating water allocation planning with pollution control measures are key strategies for safeguarding water quality and supporting the sustainable functioning of regional ecosystems.

In summary, the core policy recommendations for each water use sector are presented in

Table 14. Core policy recommendations for each water use sector.

Water Use Sector	Core Policy Recommendations
Agricultural sector	Promote efficient irrigation, fund water-saving facilities, enforce irrigation regulations, and enhance precision management.
Industrial sector	Optimize industrial structure, adopt water-saving technologies, regulate high-consumption industries, and promote reclaimed water use.
Domestic sector	Implement conservation policies, strengthen public education, promote water-saving appliances, establish performance assessments, and protect groundwater.
Ecological sector	Improve industrial water efficiency, promote clean production, and integrate water allocation with pollution control.

.

5.3. Sensitivity Analysis

In constructing the water resources optimization allocation model, the lower bounds for sectoral water demand were not derived from specific literature or precise formulas, but were set based on local water use policies, introducing a certain degree of subjectivity. As domestic water demand is rigid and ecological water use is essential for ecosystem health, the sensitivity analysis focused exclusively on the lower bounds of agricultural and industrial water demand. Specifically, the lower bounds for agricultural and industrial water demand in the three cities were reduced by 10%, adjusting only one city’s agricultural or industrial demand at a time in 1% increments. For each scenario, the model was run, and the optimal allocation scheme was selected using the method described in Section 4. Under scenarios of varying agricultural and industrial water demand lower bounds for each city, the variation rates of the four objectives are shown in Figure 15 and Figure 16, while the variation rates of the total allocation in the optimal schemes are presented in Figure 17a,b.

Based on all the above Figures, when the lower bounds of agricultural and industrial water demand are reduced by 1–10%, the variation rates of the social, economic, environmental, and spatial balance objectives, as well as the total optimal allocation, remain below 0.5%, 0.15%, 0.025%, 0.6%, and 0.8%, respectively. These minimal variations demonstrate the strong robustness of the model, indicating that the optimal allocation scheme remains essentially stable under moderate fluctuations in the lower bounds of sectoral water demand.

To identify the potential sensitivity of the objectives and total optimal allocation to variations in the lower bounds of water demand, the coefficient of variation (CV) of the four objectives and total allocation was calculated under different scenarios, as shown in Figure 18. The analysis indicates that the social and economic objectives, as well as the total allocation, are most sensitive to the agricultural water demand lower bound in Jiayuguan; the environmental objective is most sensitive to the agricultural water demand lower bound in Zhangye; and the spatial balance level is most sensitive to the industrial water demand lower bound in Jiuquan.

5.4. Research Limitations and Future Directions

Although this study introduces spatial equilibrium into multi-objective water allocation and achieves promising results, several limitations remain.

First, in the calculation of the coupling coordination degree, only a single representative indicator was selected for each subsystem, which simplifies the complex interactions among water resources, socio-economic systems, and ecological systems. Future research could expand the number of indicators for each subsystem to improve the indicator framework and obtain more precise and scientifically robust coupling coordination results.

Second, this study is based on deterministic forecast data for 2030. In reality, future uncertainties such as climate change, policy adjustments, and other socio-economic factors may affect the prediction of water supply and demand. Future work could incorporate additional social, economic, climate, and environmental variables as predictors and compare multiple forecasting methods to enhance the model’s adaptability and robustness.

Finally, this study assumes 2030 represents a normal-year scenario and does not consider the impacts of extreme hydrological conditions. Future research could construct water allocation models under different hydrological scenarios (e.g., wet and dry years) to provide optimal allocation schemes for water resource management under potential extreme climate conditions.

6. Conclusions

Through optimization and objective decision-making, three water allocation schemes were selected, providing a reference for water resource managers to accommodate different preferences, including socially friendly, economically friendly, ecologically friendly, and coordinated development-oriented allocations. Among them, Scheme 22 exhibits a relatively balanced performance across the four objectives and is identified as the optimal water allocation scheme.

The results of the optimal water allocation scheme show that the spatial equilibrium level among the three cities reaches 0.8614, and the coupling coordination degrees of the water–society–ecology systems within the cities are 0.7843, 0.8338, and 0.6248, respectively, indicating that the scheme promotes coordinated development both within each city’s water, socio-economic, and ecological subsystems, as well as across the three cities.

The surplus water under the optimal allocation scheme comes entirely from groundwater, adhering to the “use surface water first, then groundwater” principle, while achieving a reasonable balance between meeting water demand and water-saving goals.

The analysis of water use indicator changes under the optimal allocation scheme shows that Jiuquan and Zhangye have considerable agricultural water-saving potential, while all three cities demonstrate significant industrial water-saving potential. In particular, COD discharge trends in all three cities follow a similar downward pattern to industrial water use, indicating that COD emissions are largely influenced by industrial water consumption. Therefore, all three cities need to focus on pollution control for industrial water use to support the sustainable operation of regional ecosystems.