Study on Multi-Objective Optimal Allocation of Agricultural Water and Soil Resources from the Perspective of Water, Carbon and Economic Coupling in the Tailan River Irrigation District of Xinjiang

Abstract

Aiming at the problems of a fragile ecological environment, water shortage and system uncertainty in inland arid irrigation districts in Xinjiang, this study takes sustainable development as the guide, selects the Tailan River Irrigation District in Xinjiang as an example, and constructs a multi-objective optimal allocation model of agricultural water and soil resources in irrigation districts driven by water–carbon–economy synergy. The model aims to minimise irrigation water shortage, maximise crop carbon absorption and maximise economic benefits. By comparing six multi-objective algorithms such as APSEA, CMEGL, DCNSGA-III, DRLOS-EMCMO, MOEA/D-CMT and θ-DEA-CPBI, the optimal is selected based on the hypervolume (HV) index. The surface water, groundwater and crop-planting structure of five decision-making units in the irrigation district from 2021 to 2024 were optimised. Further, combined with the entropy weight–TOPSIS coupling-coordination comprehensive-evaluation model, the scheme evaluation system is constructed to screen the optimal configuration scheme of each year and unit. The results show that the MOEA/D-CMT algorithm has the highest HV value in each unit model over the years, which is the best solution algorithm for the model in this paper. The comprehensive evaluation value and coupling coordination degree of the optimal scheme of each unit fluctuate between years, and the difference between units is significant. Compared with the original planting and water source allocation scheme of the irrigation district from 2021 to 2024, the overall planting area of the optimised irrigation district is moderately reduced, forming an optimised pattern of ‘cotton pressure, grain expansion, economic increase and strong forest’; after optimization, the overall water shortage in the irrigation district is reduced by 1.4~11 million m³; the total amount of crop carbon absorption increased by 90.3~128.8 million kg; the net economic benefits increased by CNY 21.5~68.2 million. The research can provide decision support for the optimisation of the water and soil resource system in arid irrigation districts and has a scientific reference value for promoting the sustainable development and modernisation of agriculture in the inland irrigation districts of Northwest China.

1. Introduction

Against the backdrop of global climate change and increasing water scarcity [1,2], inland arid irrigation districts such as Xinjiang shoulder multiple missions, including ensuring food security, developing regional economies, and maintaining ecological balance [3]. However, the ecological environment in these areas is fragile, and water resources are limited and unevenly distributed in space and time, posing a serious challenge [4,5]. The optimal allocation of agricultural water and soil resources plays an important role in ensuring regional food security, ecological security and achieving regional sustainable development [6]. The integration of water, soil, and ecological environment resources through scientifically and effectively optimised methods to achieve a fair, efficient, and sustainable use of water and soil resources is a key issue in agricultural resource management in irrigation districts [7].

Traditional research on the optimal allocation of agricultural water and soil resources in irrigation districts focuses on the single goal of maximising economic benefits [8] and minimising irrigation water shortages [9]. In recent years, thanks to the emergence of many intelligent algorithms, research on agricultural water and soil optimisation has developed rapidly. Guo constructed an agricultural–ecological water and soil resource allocation model with multiple objective functions through type 2 fuzzy programming and optimised the planting structure and water allocation of multiple decision-making units in the Hongyashan Irrigation District [10]. In view of the uncertainty of agricultural water and soil resources in the middle reaches of the Heihe River, Li constructed a bi-level fractional programming model that accounts for the randomness of incoming water and used an interactive fuzzy algorithm to solve it [11]. Based on the characteristics of water shortage and environmental problems in the Aksu River Basin, Wang constructed an agricultural water and soil optimal allocation model under the genetic algorithm (NSGA-II) solution [12]. At the same time, Wang established a water, soil, and crop space optimisation model using the grey wolf algorithm [13]. Although the two are based on different data sources, the optimisation results align with the actual needs. With the advancement of the ‘double carbon’ strategic goal, the carbon-sink function of agricultural ecosystems and their role in mitigating climate change have received increasing attention [14]. In summary, the existing allocation of water and soil resources in arid irrigation districts has not realised the three-dimensional deep coupling of water–carbon–economy, and lacks annual dynamic optimisation for zonal heterogeneity [6]; the multi-objective solution mostly adopts a single algorithm [15], and the adaptability of the frontier evolutionary algorithm is not systematically compared, so the scientificity and robustness of the solution results are insufficient. The optimisation of schemes is mostly based on the analytic hierarchy process [13,16] and TOPSIS [17,18]. The integrated screening framework of ‘objective weighting-scheme ranking-system coordination’ is not constructed, and the scheme is weak in practicality. Therefore, this study, firstly, included the dynamic data of five sub-regions of the irrigation district from 2021 to 2024; this study further develops a multi-objective optimal allocation model of agricultural water and soil resources from the perspectives of water, carbon, and economic coupling (MOAWCE); secondly, six frontier multi-objective evolutionary algorithms are applied to water and soil allocation in arid irrigation districts, and the optimal algorithm is selected by the HV index. Finally, the entropy weight, TOPSIS, and improved coupling-coordination degree model are integrated to realise the ‘sorting + coordination’ screening of Pareto solutions. The Tailan River Irrigation District, a typical representative of an arid oasis irrigation district in the Tarim Basin, Xinjiang, which has the characteristics of ‘water shortage, ecological fragility, cotton–grain dominance and regional heterogeneity’, is used for verification.

Through the whole chain analysis of model construction, algorithm comparison and scheme evaluation, this study hopes to provide decision makers with a set of scientific and systematic water and soil resource allocation schemes that meet the actual development needs of irrigation districts, to provide scientific reference for the modernisation construction and sustainable development of agriculture in the inland arid irrigation districts of Northwest China.

2. Materials and Methods

2.1. Study Area

The Tailan River Irrigation District is situated within the eastern part of Wensu County, Aksu Prefecture, Xinjiang (Figure 1). Positioned at the southern foot of the Tianshan Mountains and the northern margin of the Tarim Basin (80°20′–80°45′ E, 40°55′–41°25′ N), it serves as a principal area for developing grain, cotton, oil, livestock, and fruit production bases [19]. Long-term meteorological records indicate that the area experiences an average annual precipitation of 82.6 mm, a mean annual sunshine duration of 2618.7 h, and an average annual temperature of 11.67 °C. Water supply for the district is primarily derived from the surface and groundwater resources of the Tailan River and its tributaries, supporting extensive agricultural zones in the vicinity. The district is essential for ensuring regional food security, fostering sustainable socio-economic development, and maintaining ecological balance.

Based on water utilisation patterns, service areas, and integrated management needs, the irrigation district is delineated into five computational units aligned with township administrative boundaries: Jiamu Town, Communist Youth League Town, Kezile Town, Yixilaimuqi Township, and Guleawati Township [20].

2.2. Data Source

The data sources of this study can be seen in

Table 1. Data types and sources.

Data Type	Name	Unit	Data Source	Time Range	Specific Value	Missing Value Processing
Basic water and crop cultivation	annual surface water and groundwater withdrawal in each sub-region	m3	①	2021~2024	Table S1	-
	annual crop planting area of each district	hm2	②	2021~2024	Tables S2–S5	-
Crop parameters	unit yield	kg/hm2	③	2021~2024 average	Table S6	⑦
	unit price	CNY/kg	③	2021~2024 average	Table S6	⑦
	materialised cost	CNY/hm2	④	2021~2024 average	Table S6	-
	irrigation quota	m3/hm2	⑤	2021~2024 average	Table S6	-
	carbon absorption rate	-	References [21,22,23]	-	Table S7	-
	moisture content	-	References [21,22,23]	-	Table S7	-
	economic coefficient	-	References [21,22,23]	-	Table S7	-
Other parameters	population of each district	people	⑥	2019	Table S8	-
	per capita food possession	kg/person	③	2021~2024	Table S6	-

Note: ① Tailan River Water Pipe Station; ② Wensu County Water Conservancy Bureau; ③ Wensu County Statistical Yearbook; ④ Wensu County Agricultural and Rural Bureau; ⑤ Wensu County Water Conservancy Bureau ‘Xinjiang Aksu area Wensu County’ 14th Five-Year ’water conservancy development special planning’; ⑥ Wensu County Water Conservancy Bureau ‘Tailan River Irrigation District’ 14th Five-Year ‘Continued Construction Supporting and Modernization Reconstruction Project Preliminary Design Report’; ⑦ query the ‘National Agricultural Products Cost–benefit Data Compilation’.

.

2.3. Model Introduction

The MOAWCE model is used to compare the advantages and disadvantages of different algorithms for allocating water and soil resources in irrigation districts and to select the optimal scheme. It is mainly composed of 3 modules: the optimisation model, algorithm comparison and configuration scheme selection (Figure 2).

2.3.1. Optimise the Objective Function of the Model

To ensure the long-term sustainable development of each unit in the irrigation district, it is necessary to consider the utilisation of water resources, the ecological environment, and economic benefits. To this end, this study established the following objective functions.

(1)

The irrigation water shortage is the smallest.

Due to inconsistent water and soil resource conditions across the irrigation district’s units, some units may not be able to irrigate crops fully or excessive irrigation may result in water waste and a low irrigation efficiency. Therefore, the goal of minimising irrigation water shortage is established [24]. The optimisation objective function is as follows:

$${minF}_{1,m}=W_m-\sum _{i=1}^n\left[\left(W_{m,i}^b+W_{m,i}^x\right)A_{m,i}/G\right]$$

(1)

where F_1,m is the irrigation water shortage of the m unit of the irrigation district, m³; W_m is the total amount of surface and underground water available for irrigation in the m unit of the irrigation district, m³; W^b_m,i is the surface irrigation quota of crop i in unit m, m³/hm²; W^x_m,i is the underground irrigation quota of crop i in unit m, m³/hm²; A_m,i is the m unit in the crop i planting area, hm²; G is the comprehensive irrigation water utilisation coefficient of the irrigation area, the value of which is 0.586, which is determined according to the measured value of the ‘Preliminary Design Report of Tailan River Irrigation District’ 14th Five-Year Plan ‘Continuation Supporting and Modernization Reconstruction Project’.

(2)

The carbon absorption of the crops in the ecosystem of the irrigation district is the largest.

As part of the ecosystem, although the crop-planting structure in the irrigation district is diverse, each crop’s carbon absorption capacity differs. Therefore, based on the root–shoot ratio coefficient, carbon absorption rate, and water content of the different crops, the following optimisation function is established to maximise carbon absorption in the irrigation district ecosystem [25,26].

$${maxF}_{2,m}=\sum _{i=1}^n\left[(1+R_{m,i})A_{m,i}{P}_{m,i}{Q}_{m,i}\left(1-Y_i\right)/D_i\right]$$

(2)

where F_2,m is the total amount of crop carbon absorption in the m-th unit of the irrigation district, kg; R_m,i is the crop root–shoot ratio coefficient of crop i in unit m; P_m,i is the current crop yield of crop i in unit m, kg/hm²; Q_m,i is the carbon absorption rate of crop i in unit m, %; Y_i is the moisture content of i crops, and %; D_i is the crop economic coefficient. The above R_m,i, Q_m,i, Y_i and other parameters (Table S7) are static parameters, which are determined based on the measured data of crops in similar irrigation districts in arid areas of Xinjiang and the related literature [21,22,23].

(3)

The economic benefit of crops in the irrigation district is the largest.

The purpose of optimising water and soil resources in the irrigation district is to achieve higher yields as much as possible, while ensuring water demand and crop planting areas, to achieve better economic benefits and to take into account ecological balance and sustainable development in the process. Therefore, the goal of maximising the economic benefits of crops in the irrigation district is established [8,27]. The optimisation objective function is as follows:

$${maxF}_{3,m}=\sum _{i=1}^n{A}_{m,i}\left[P_{m,i}{C}_i-K\left(W_{m,i}^b+W_{m,i}^x\right)/G-S_{m,i}\right]$$

(3)

where F_3,m is the economic benefit of the m-th unit of the irrigation district, CNY; C_i is the price of crop i, CNY/kg; K is the average irrigation water price, 0.12 CNY/m³—according to the agricultural water price policy of Wensu County from 2021 to 2024, the water price in this study does not change with the water source (surface water/groundwater) and the year, which is the benchmark unified water price— and S_m,i is the unit m i crop agricultural cost, CNY/hm².

2.3.2. Constraint Condition

(1)

Crop planting area constraint

The planting area of each crop in each unit of the irrigation district should be within the soil area provided by the unit for each crop, and the total maximum planting area of the crop should not exceed the total area before optimisation. The calculation formula is as follows:

$${ A}_{m,i}^{max}\ge A_{m,i}\ge { A}_{m,i}^{min}$$

(4)

$$0\le \sum _{i=1}^n{ A}_{m,i}^{max}\le \sum _{i=1}^n{A}_{m,i}$$

(5)

where A^max_m,i is the maximum planting area of unit m i crop, hm²; and A^min_m,i is the minimum planting area of unit m i crop, hm². The value is determined according to the annual crop planting area of each district and the results of the ‘14th Five-Year Water Conservancy Development Special Plan’ in Wensu County, Aksu Prefecture, Xinjiang, covering 8 types of crops such as cotton, wheat and corn.

(2)

Water supply constraints of surface water and groundwater

The amount of surface and groundwater irrigation in each unit of the irrigation district should be within the available water supply of the unit, that is,

$$\sum _{i=1}^n{W}_{m,i}^b{A}_{m,i}/G\le W_m^b$$

(6)

$$\sum _{i=1}^n{W}_{m,i}^x{A}_{m,i}/G\le W_m^x$$

(7)

where W^b_m is the surface available water supply of the m-th unit, m³; and W^x_m is the underground water supply of unit m, m³.

(3)

Food production constraints

$$\sum _{i=1}^n{A}_{m,t}{P}_{m,t}\ge \sum _{i=1}^n{V}_m{B}_{m,t}$$

(8)

where A_m,t is the irrigation district of unit m, t grain crop planting area, hm²; P_m,t is the yield of grain crops in unit m of the irrigation district, kg/hm²; V_m is the population of unit m in the irrigation district—the value can be seen in the Supplementary Materials, Table S8— and B_m,t is the per capita possession of t grain crops in unit m of the irrigation district, kg. The food crops are wheat, corn and rice; the values can be seen in the Supplementary Materials, Table S6.

(4)

Non-negativity constraints

$$\left\{\begin{array}{c}{A}_{m,i}\ge 0\\ W_{m,i}^b\ge 0\\ W_{m,i}^x\ge 0\end{array}\right.$$

(9)

2.3.3. Decision Variables

The decision variable of the model is the planting area of each crop in different partition units over the years.

2.4. Model Multi-Algorithm Comparison Solution

The multi-objective optimisation model constructed in this paper contains three objective functions and four constraints. The optimisation time span is from 2021 to 2024, and the model solution comparison is mainly carried out in matalb2023 b through the Platemo (https://github.com/BIMK/PlatEMO, accessed on 16 April 2024) platform, which contains many algorithms suitable for different optimisation problems. Aiming at the characteristics of high variable dimension, complex constraints and large time span of the model in this paper, six real-coded, strong constraint processing, wide coverage and novel (nearly 6 years) algorithms are selected, including the adaptive population type (APSEA) [28], multi-task type (CMEGL) [29], improved NSGA type (DCNSGA-III) [30], reinforcement-learning-assisted type (DRLOS-EMCMO) [31], decomposition type (MOEA/D-CMT) [32], and DEA fusion type (θ-DEA-CPBI) [33].

The necessity of adopting multiple algorithms lies in the following: first, different algorithms have significant differences in dealing with high-dimensional, multi-constrained, and long-term span problems, and a single algorithm may not be able to fully capture the structural characteristics of the solution set [34]; secondly, the comparison of multiple algorithms can comprehensively evaluate the quality of the solution set from multiple dimensions such as convergence, distribution uniformity and coverage, and avoid the result deviation caused by the limitations of the algorithm itself [35].

In order to ensure fairness, the number of populations and the maximum number of evaluations of each algorithm are set to 200 and 10,000, respectively. In addition, the parameters of each algorithm are not adjusted and remain the default. (For example, the minimum feasible solution ratio and the minimum change rate of the target value of the APSEA algorithm population are both 0.05, and the downward trend of the dynamic constraint boundary is: 5; the DCNSGA-III algorithm dynamic constraint boundary downward trend is 5; the possibility of the MOEA/D-CMT algorithm to select the local parent is: 0.9, and the maximum number of solutions replaced by each offspring is 2.) The principle details can be seen in its literature [28,29,30,31,32,33]. Finally, the hypervolume indexes of different algorithms are compared systematically to find the most suitable optimisation algorithm for the characteristics of the model in this paper.

Hypervolume (HV) is a comprehensive index used to evaluate the quality of the solution set obtained by the multi-objective evolutionary algorithm. It reflects the convergence and diversity of the solution set by measuring the volume of the hypercube bounded by the non-dominated solutions and a reference point in the target space. When the HV value is larger, the solution set is closer to the real Pareto frontier and the distribution is more uniform. The algorithm outperforms the model solution [36]. Its calculation formula is as follows:

$$HV\left(S,Z^{ref}\right)=volume\left(\bigcup _{i=1}^{\left|S\right|}{C}_i\right)$$

(10)

$$volume\left(C_i\right)=\left\{\begin{array}{c}{\displaystyle \prod _{k=1}^m}\left(Z_k^{ref}-f_k\left(x_i\right)\right), \mathrm{i}\mathrm{f} \forall k,{ Z}_k^{ref}>f_k\left(x_i\right)\\ 0, otherwise\end{array}\right.$$

(11)

Among them, HV is the super volume index; S represents the approximate Pareto optimal solution set obtained by the algorithm; Z^ref denotes the reference point, usually taking the point that is worse than all solutions on their respective objectives; volume represents the volume of the calculated geometry; ∪ is union; |S| is the number of solutions in the set S; C_i is the m-dimensional hypercube defined by the i-th solution and the reference point; Z_k^ref is the coordinate value of the reference point Zref on the kth target; and f_k(x_i) is the function value of the i-th solution on the k-th objective function.

In this study, the selection of HV reference points follows the principle of ‘inferior to all Pareto solutions’, that is, for the three objective functions (F₁, F₂, F₃) of each partition, the Pareto worst solution obtained by each algorithm in each year is taken respectively, and the three coordinates (Z₁, Z₂, Z₃) are raised by 5% as the reference point. For a fair comparison, only one reference point is set for different periods of the same unit [37]. After several verifications, when the HV calculation results for each algorithm and each unit are greater than 0 simultaneously, the following reference points (Z₁, Z₂, Z₃) are determined (

Table 2. The selection of reference points for the HV value of each unit in the Tailan River Irrigation District from 2021 to 2024.

Unit	Reference Point (Z1, Z2, Z3)
Jiamu Town	8.677 × 106	−9.103 × 107	−2.365 × 108
Yixilaimuqi Township	6.169 × 107	−9.694 × 107	−2.582 × 108
Kezile Town	3.957 × 107	−1.191 × 108	−3.237 × 108
Guleawati Township	1.169 × 108	−1.267 × 108	−4.001 × 108
Communist Youth League Town	4.389 × 107	−8.437 × 107	−2.411 × 108

). The sensitivity analysis (+ 5% adjustment) of the reference point has been carried out. The results show that the HV value of the MOEA/D-CMT algorithm is still higher than that of other algorithms, which proves the robustness of the reference point selection (the sensitivity analysis results can be seen in the Supplementary Materials).

2.5. Entropy Weight–TOPSIS Coupling-Coordination Scheme Optimisation

Under the multi-objective optimisation framework, the obtained non-inferior solution set provides a variety of alternatives for decision makers, but it also brings the problem of scheme optimisation. Therefore, this paper constructs an optimisation model and systematically evaluates the Pareto solution set for each unit in the Tailan River Irrigation District from 2021 to 2024 using a comprehensive evaluation system, aiming to select the best allocation scheme for water and soil resources in each unit over the years [38]. The model has the characteristics of objective weighting, accurate sorting and scheme coordination identification. It avoids focusing only on index weight and ranking, like CRITIC–TOPSIS; VIKOR and PROMETHEE are more suitable for single-scheme ranking models without system coupling. Firstly, the entropy weight method is used to determine the index weights based on the dispersion of the evaluation system data, thereby effectively avoiding subjective bias and enhancing the scientific nature of the evaluation basis [39]. Secondly, using the entropy weight, the relative closeness of each scheme to the positive and negative ideal solutions is calculated and sorted using the TOPSIS method, so as to identify the best scheme for each unit [40]. Finally, the coordination level between the evaluation scheme’s systems is analysed in depth through coupling coordination.

2.5.1. Entropy Weight–TOPSIS Coupling-Coordination Calculation Steps

(1)

Data normalisation and standardisation

Suppose there are n schemes and m indices. The original data matrix is X = (x_ij)_n×m, where x_ij is the value of the j-th index of the i-th scheme.

$$y_{ij}=\left\{\begin{array}{c}{\displaystyle \frac{x_{ij}-\underset{1\le k\le n}{\min }\left(x_{kj}\right)}{\underset{1\le k\le n}{\max }\left(x_{kj}\right)- \underset{1\le k\le n}{\min }\left(x_{kj}\right)}}, Positive indicator (the larger the better)\\ {\displaystyle \frac{\underset{1\le k\le n}{\max }\left(x_{kj}\right)- x_{ij} }{\underset{1\le k\le n}{\max }\left(x_{kj}\right)- \underset{1\le k\le n}{\min }\left(x_{kj}\right)}}, Negative indicator (the smaller the better)\end{array}, 0\le y_{ij}\le 1\right.$$

(12)

$$p_{ij}=y_{ij}/\sum _{i=1}^n{y}_{ij}$$

(13)

where y_ij is the normalised value (dimensionless), and the min(x_kj) and max(x_kj) are the minimum and maximum values of the j-th index in all schemes, respectively. p_ij is the proportion of the i-th scheme on the j-th index; ${\sum }_{i=1}^n{y}_{ij}$ is the sum of the standardised values of all schemes for the j-th index.

(2)

Entropy value and weight calculation

$$e_j=-{\left(\mathit{ln}n\right)}^{-1}\sum _{i=1}^n{p}_{ij}\mathit{ln}\left(p_{ij}\right)$$

(14)

$$w_j=1-e_j/m-\sum _{j=1}^m{e}_j$$

(15)

where e_j is the entropy value of the j-th index, and w_j is the weight of the j-th index.

(3)

Construction of a weighted standardised matrix and determination of positive and negative ideal solutions

$$\left\{\begin{array}{c}{z}_{ij}=w_j·y_{ij}\\ Z={\left(z_{ij}\right)}_{n\times m}\end{array}\right.$$

(16)

$$\left\{\begin{array}{c}{Z}^{+}=\left(z_1^{+},z_2^{+},\dots ,z_m^{+}\right)=\left(\underset{1\le i\le n}{\mathit{max}}{z}_{i1},\underset{1\le i\le n}{\mathit{max}}{z}_{i2},\dots ,\underset{1\le i\le n}{\mathit{max}}{z}_{im}\right)\\ Z^{-}=\left(z_1^{-},z_2^{-},\dots ,z_m^{-}\right)=\left(\underset{1\le i\le n}{\mathit{min}}{z}_{i1},\underset{1\le i\le n}{\mathit{min}}{z}_{i2},\dots ,\underset{1\le i\le n}{\mathit{min}}{z}_{im}\right)\end{array}\right.$$

(17)

where z_ij is the weighted standardised value of the i-th scheme on the j-th index; Z is the weighted standardisation matrix; and Z⁺ and Z⁻ are the positive and negative ideal solutions, respectively.

(4)

Calculation of ideal solution distance and relative closeness

$$\left\{\begin{array}{c}{D}_i^{+}=\sqrt{{\displaystyle \sum _{j=1}^m}{\left(z_{ij}-z_j^{+}\right)}^2}\\ D_i^{-}=\sqrt{{\displaystyle \sum _{j=1}^m}{\left(z_{ij}-z_j^{-}\right)}^2}\end{array}\right.$$

(18)

$$H_i= D_i^{-}/\left(D_i^{+}+D_i^{-}\right) , 0\le H_i\le 1$$

(19)

where D_i⁺ and D_i⁻ are divided into the Euclidean distance between the i-th scheme and the positive and negative ideal solutions; H_i is the relative closeness degree (comprehensive evaluation score) of the i-th scheme. The closer its value to 1, the closer to the optimal evaluation scheme it is.

(5)

The calculation of the comprehensive evaluation value of each system

$$\left\{\begin{array}{c}{U}_{1i}={\displaystyle \sum _{j\in I_S}}{Z}_{ij}\\ U_{2i}={\displaystyle \sum _{j\in I_E}}{Z}_{ij}\\ U_{3i}={\displaystyle \sum _{j\in I_M}}{Z}_{ij}\end{array}\right.$$

(20)

where U_1i, U_2i, and U_3i are the comprehensive evaluation values of the social benefit, environmental resource benefit, and economic benefit subsystems of the i-th scheme, respectively; I_S, I_E, and I_M are the index sets of the social benefit, environmental resource benefit, and economic benefit subsystems, respectively.

(6)

Improved coupling coordination calculation

$$T_i=U_{1i}+U_{2i}+U_{3i}$$

(21)

$$C_i=\sqrt[3]{U_{1i}·U_{2i}·U_{3i} /{ \left[\left(U_{1i}+U_{2i}+U_{3i}\right)/3\right]}^3 }, 0\le C_i\le 1$$

(22)

$$D_i=\sqrt{C_i·T_i} , 0\le D_i\le 1$$

(23)

where T_i is the comprehensive coordination index of the i-th scheme, C_i is the coupling degree of the i-th scheme, where the larger the value, the stronger the interaction between the three subsystems; and D_i is the coupling coordination degree of the i-th scheme, where the larger the value, the higher the degree of coordinated development among the three subsystems.

2.5.2. Establishment of Comprehensive Evaluation Index System

The construction of an evaluation index system for water and soil resource allocation should be based on the theory of sustainable development, follow the principles of science and system, and reflect regional characteristics to ensure clear orientation and feasible operation [41]. As shown in

Table 3. The comprehensive evaluation index system of the water and soil resources allocation scheme in each unit of the Tailan River Irrigation District from 2021 to 2024.

Target Layer	System Criterion Layer	Evaluation Index Layer	Index Definition	Attribute
Comprehensive Evaluation of Water and Soil Resource Allocation Schemes of Each Unit in the Irrigation District (A)	Social Benefit (IS)	Agricultural water productivity (Z1)	Crop yield/Crop irrigation amount	Positive
		Total crop proportion (Z2)	Total crop area/Total soil area of each unit	Positive
		Grain crop proportion (Z3)	Grain crop area/Total crop area	Positive
		Irrigation water shortage rate (Z4)	Formula (1)/Irrigation water shortage before optimisation	Negative *
	Resource Environmental Benefit (IE)	Amount of fertiliser used per unit area (Z5)	Total fertiliser use/Total crop area	Negative
		Rate of irrigation guarantee (Z6)	Average irrigation quota after optimisation/Average irrigation quota before optimisation	Positive
		Proportion of crop carbon absorption (Z7)	Formula (2)/Carbon absorption before optimisation	Positive
		Amount of pesticide used per unit area (Z8)	Pesticide usage/Total crop area	Negative
	Economic Benefit (IM)	Net economic benefit per unit area (Z9)	Formula (3)/Total crop area	Positive
		Ratio of output to input (Z10)	(Crop yield × Crop unit price)/Input funds	Positive
		Proportion of cash crops (Z11)	Economic crop area/Total crop area	Positive
		Proportion of total area (Z12)	Total crop area after optimisation/Total crop area before optimisation	Positive

Note: * Due to the surplus of irrigation water before and after optimisation in Jiamu Town in 2021, 2022 and 2023, the irrigation water deficit rate Z₄ is a positive indicator during this period and a negative indicator for all other units in all years.

, the evaluation index system is divided into three layers: the target layer comprises the water and soil resource allocation scheme for each unit in each year; the system criterion layer comprises three layers: social benefit, environmental resource benefit, and economic benefit. A total of 12 indicators are selected in the evaluation index layer, which are interrelated and have different emphases [42]. In view of the shortage of water resources and regional development, agricultural water productivity, total crop proportion, grain crop proportion, and irrigation water shortage rate are selected for social benefits, aiming to optimise agricultural water-use efficiency and crop-planting structure [43]. The resource and environmental benefits include the amount of fertiliser used per unit area, the amount of pesticide used per unit area, the irrigation guarantee rate, and the proportion of crop carbon absorption, taking into account environmental protection and resource sustainability [44]. The economic benefits include net economic benefits per unit area, the ratio of output to input, the proportion of cash crops, and the proportion of total area, to promote the structure of the planting industry and increase farmers’ income [45]. Using the index system, balanced high-yield and high-efficiency allocation schemes that meet their respective development goals are selected from the water and soil allocation schemes for each unit in the irrigation district.

3. Results and Analysis

3.1. Algorithm Selection for Optimal Allocation of Water and Soil Resources in an Irrigation District

Based on the reference points of each unit, the HV values of the six algorithms fluctuate in time and space. However, the MOEA/D-CMT algorithm performs well in most units and years, especially in 2024, and its HV value reaches a peak in multiple units. Taking Jiamu Town as an example, the HV value of the MOEA/D-CMT algorithm increased from 1.883 in 2021 to 9.281 in 2024, with a four-year average of 3.751, which was much higher than that of other algorithms. In contrast, the APSEA and DCNSGA-III algorithms have significantly reduced HV values in 2024 (to 0.399 and 0.203, respectively), indicating that they perform poorly at coordinating multiple conflicting objectives. The HV values of CMEGL and DRLOS-EMCMO are relatively stable, but their average values (1.274 and 1.398, respectively) are still lower than MOEA/D-CMT. θ-DEA-CPBI performs moderately in 2021–2023 but falls to 0.418 in 2024, reflecting its lack of robustness (

Table 4. The interannual HV values of each algorithm in each unit of the Tailan River Irrigation District from 2021 to 2024.

Unit	Year	APSEA	CMEGL	DCNSGA-III	DRLOS-EMCMO	MOEA/D-CMT	θ-DEA-CPBI
Jiamu Town	2021	1.41	1.408	1.476	1.368	1.883	1.43
	2022	1.039	1.19	1.189	1.391	1.933	1.286
	2023	1.334	1.541	1.331	1.558	1.905	1.302
	2024	0.399	0.957	0.203	1.274	9.281	0.418
	Average	1.046	1.274	1.05	1.398	3.751	1.109
Yixilaimuqi Township	2021	0.672	0.755	0.586	0.781	1.167	0.628
	2022	0.197	0.84	0.166	0.826	3.095	0.216
	2023	1.157	1.092	0.894	1.139	1.546	0.933
	2024	0.407	1.294	0.361	0.558	3.107	0.656
	Average	0.608	0.995	0.502	0.826	2.229	0.608
Kezile Town	2021	0.795	0.758	0.654	1.248	1.82	0.748
	2022	0.336	0.405	0.188	0.409	0.564	0.375
	2023	0.786	1.202	1.142	2.257	7.029	1.076
	2024	0.994	0.982	0.863	1.438	2.388	0.849
	Average	0.728	0.837	0.712	1.338	2.95	0.762
Guleawati Township	2021	0.346	0.706	0.427	0.693	1.61	0.755
	2022	0.209	0.423	0.216	0.341	0.698	0.222
	2023	0.597	0.534	0.179	0.704	2.99	0.417
	2024	0.206	0.406	0.325	0.919	1.328	0.214
	Average	0.34	0.517	0.287	0.664	1.657	0.402
Communist Youth League Town	2021	1.969	1.901	0.852	2.06	3.916	0.983
	2022	0.893	1.558	0.575	1.177	1.683	1.16
	2023	2.135	1.908	0.753	2.101	3.104	1.014
	2024	1.506	2.189	3.161	3.06	12.643	1.005
	Average	1.626	1.889	1.335	2.1	5.337	1.041

).

The differences in HV values across algorithms reflect their ability to handle different unit optimisation problems. MOEA/D-CMT performs best in most cases, while other algorithms may differ in internal mechanisms such as population diversity maintenance, constraint handling, and solution set update strategies. It is easy to fall into a local optimal state when solving complex problems in this paper, leading to performance declines in some years. Therefore, the MOEA/D-CMT algorithm is most suitable for solving high-dimensional, multi-constraint and nonlinear multi-objective optimisation problems in this paper. Due to the limited space, only the optimisation results in 2024 are listed. The distribution of the Pareto solution sets of each unit under the MOEA/D-CMT algorithm is shown in Figure 3, and the distribution of solution sets of other algorithms can be seen in the Supplementary Materials, Figures S1–S5.

3.2. Selection of Water and Soil Resources Allocation Scheme in the Irrigation District

Due to the large population sizes of each unit algorithm from 2021 to 2024, there are more non-inferior solutions per unit over the years. Therefore, the entropy weight–TOPSIS coupling-coordination scheme optimisation model is used to evaluate the non-inferior solutions of each unit over the years. Using the entropy weight method, the weights of each index for each unit over the years (

Table 5. The weight of evaluation indexes of each unit in the Tailan River Irrigation District from 2021 to 2024.

Unit	Year	Social Benefit				Resource Environmental Benefit				Economic Benefit
		Z1	Z2	Z3	Z4	Z5	Z6	Z7	Z8	Z9	Z10	Z11	Z12
Jiamu Town	2021	0.013	0.056	0.095	0.19	0.07	0.077	0.193	0.07	0.069	0.036	0.076	0.056
	2022	0.047	0.028	0.079	0.13	0.15	0.064	0.144	0.15	0.071	0.042	0.069	0.028
	2023	0.071	0.021	0.147	0.105	0.138	0.12	0.162	0.138	0.034	0.012	0.03	0.021
	2024	0.011	0.104	0.26	0.095	0.106	0.143	0.022	0.106	0.018	0.008	0.024	0.104
Yixilaimuqi Township	2021	0.009	0.075	0.165	0.049	0.272	0.056	0.006	0.272	0.008	0.007	0.006	0.075
	2022	0.029	0.051	0.283	0.068	0.166	0.044	0.073	0.166	0.031	0.006	0.032	0.051
	2023	0.016	0.049	0.243	0.075	0.193	0.125	0.014	0.193	0.015	0.003	0.024	0.049
	2024	0.014	0.063	0.274	0.049	0.154	0.169	0.015	0.154	0.016	0.005	0.024	0.063
Kezile Town	2021	0.012	0.084	0.249	0.074	0.22	0.016	0.015	0.22	0.008	0.011	0.007	0.084
	2022	0.014	0.155	0.158	0.123	0.135	0.022	0.019	0.135	0.025	0.034	0.025	0.155
	2023	0.034	0.095	0.168	0.077	0.184	0.055	0.039	0.184	0.04	0.012	0.018	0.095
	2024	0.015	0.168	0.083	0.09	0.16	0.067	0.019	0.16	0.027	0.023	0.021	0.168
Guleawati Township	2021	0.024	0.111	0.258	0.081	0.121	0.052	0.027	0.121	0.032	0.025	0.037	0.111
	2022	0.021	0.088	0.317	0.121	0.095	0.054	0.025	0.095	0.044	0.02	0.032	0.088
	2023	0.018	0.074	0.332	0.084	0.147	0.063	0.021	0.147	0.017	0.011	0.013	0.074
	2024	0.01	0.09	0.301	0.083	0.18	0.037	0.011	0.18	0.005	0.007	0.006	0.09
Communist Youth League Town	2021	0.009	0.088	0.269	0.094	0.152	0.046	0.017	0.152	0.024	0.022	0.04	0.088
	2022	0.012	0.106	0.181	0.107	0.199	0.035	0.013	0.199	0.017	0.008	0.017	0.106
	2023	0.01	0.074	0.343	0.015	0.146	0.125	0.013	0.146	0.018	0.018	0.016	0.074
	2024	0.01	0.069	0.388	0.04	0.133	0.069	0.011	0.133	0.034	0.018	0.025	0.069

) and the optimal scheme score and coupling coordination relationship for each unit over the years (

Table 6. The best allocation scheme of water and soil resources in each unit of the Tailan River Irrigation District from 2021 to 2024.

Unit	Year	Optimal Scheme	Comprehensive Evaluation Value of Subsystem			Comprehensive Evaluation Score (Hi)	Coupling Coordination Degree (Di)
			Social Benefit (U1i)	Environmental Resource Benefit (U2i)	Economic Benefit (U3i)
Jiamu Town	2021	Scheme104	0.157	0.335	0.068	0.537	0.677
	2022	Scheme45	0.142	0.436	0.040	0.624	0.638
	2023	Scheme17	0.226	0.408	0.021	0.666	0.612
	2024	Scheme141	0.293	0.273	0.012	0.641	0.544
Yixilaimuqi Township	2021	Scheme13	0.094	0.555	0.045	0.715	0.631
	2022	Scheme166	0.292	0.440	0.017	0.786	0.624
	2023	Scheme31	0.204	0.433	0.043	0.691	0.683
	2024	Scheme17	0.301	0.424	0.021	0.783	0.647
Kezile Town	2021	Scheme2	0.304	0.275	0.036	0.669	0.659
	2022	Scheme115	0.283	0.175	0.126	0.591	0.743
	2023	Scheme129	0.124	0.415	0.092	0.613	0.709
	2024	Scheme4	0.199	0.245	0.202	0.663	0.802
Guleawati Township	2021	Scheme105	0.320	0.165	0.058	0.610	0.661
	2022	Scheme147	0.368	0.208	0.041	0.680	0.663
	2023	Scheme11	0.282	0.362	0.007	0.697	0.520
	2024	Scheme2	0.313	0.302	0.005	0.690	0.486
Communist Youth League Town	2021	Scheme44	0.271	0.351	0.035	0.684	0.669
	2022	Scheme90	0.150	0.419	0.049	0.605	0.660
	2023	Scheme9	0.346	0.309	0.020	0.752	0.622
	2024	Scheme142	0.394	0.215	0.037	0.761	0.662

) are obtained.

The index weight of this paper changes dynamically with the year (2021~2024) and the unit (five townships). For example, the proportion of grain crops (Z₃) has a high weight (0.095–0.388) in each unit and each year, reflecting the core position of food security. The spatial and temporal changes in weights are the objective embodiment of regional and annual heterogeneity, which does not reduce the comparability of schemes. In this paper, the entropy weight method is used to objectively assign weights (based on data dispersion), rather than subjectively assigning weights, to ensure that the weights of each unit and each year are based on a unified weighting method and the programme evaluation results are comparable horizontally (between units) and vertically (between years).

From the perspective of time, the comprehensive score H_i of the optimal scheme for each unit shows a trend of increase and decrease, with differences in the timing of the increases and decreases. For H_i, in Jiamu Town and the Guleawati Township, the increase from 2021 to 2023 was offset by the decrease from 2023 to 2024. The H_i of Kezile Town and the Communist Youth League town decreased from 2021 to 2022 and increased from 2022 to 2024. The coupling coordination degree D_i decreases from 0.645 and 0.625 in 2021 to 0.46 and 0.382 in 2024, respectively, in some units, such as Jiamu Town and the Guleawati Township. In the remaining units, there is a trend of decrease, a trend of increase and no obvious trend.

There were significant differences in H_i and D_i across units, but no significant positive or negative correlation was found between the two. In 2022, the highest H_i value per unit in the optimal scheme for the Yixilaimuqi Township was 0.786, and the corresponding D_i value was 0.529. In 2021, the lowest H_i value of the optimal scheme in Jiamu Town was 0.537 and the D_i value was 0.645. On the contrary, the highest D_i value of the optimal scheme in Kizil Town in 2022 was 0.732, and the H_i value was 0.591. In 2024, the minimum D_i value of the optimal scheme in the Guleawati Township was 0.382 and the H_i value was 0.69.

In the comprehensive evaluation of the optimal scheme subsystem, the social U_1i and environmental resource U_2i values of the optimal schemes for each unit are generally high, highlighting the priority of social and ecological sustainability.

3.3. Results of Water and Soil Resources Allocation Under the Optimal Scheme

3.3.1. Optimisation Results of Irrigation Amount and Water Shortage

From the perspective of the whole irrigation district, the total amount of irrigation did not increase or decrease significantly from 2021 to 2024 after optimisation, and it decreased only slightly compared with before optimisation (Figure 4a,b). In 2021, the total irrigation volume before and after optimisation was 674.0 million m³ and 672.6 million m³, respectively, with little change. In 2022, it was slightly reduced from 717.9 million m³ to 716.1 million m³; in 2023, it was decreased from 696.2 million m³ to 685.2 million m³. In 2024, it fell slightly from 747.2 million m³ to 743.7 million m³. This phenomenon shows that total irrigation water consumption has not decreased in step with the reduction in planting area, reflecting the complexity of crop structure and the difficulty of adjusting irrigation systems.

In-depth analysis found that the spatial distribution of total irrigation and crop allocation within each unit was significantly altered. Taking Jiamu Town as an example, the total amount of irrigation after optimisation in 2021 and 2022 increased slightly from 102.9 million m³ and 103.0 million m³ to 105.0 million m³, respectively. The reason was that the planting area of rice increased from 0 to 324.41 hm² and 337.37 hm², respectively, after optimisation. The new irrigation demand of high water consumption crops exceeded the water saving of cotton compression (compression interval: 300~500 hm²), resulting in a slight increase in total irrigation amount. At the same time, there was no water shortage in Jiamu Town, and the remaining water resources could support the cultivation of high water-consuming crops, so as to realise the efficient utilisation of water resources (rather than waste). On the contrary, the total amount of irrigation after the optimisation of each unit in other years was slightly lower than that before optimisation. For example, from 2021 to 2024, the total amount of irrigation in Kezile Town decreased from 176.3 million m³, 185.4 million m³, 187 million m³ and 180.3 million m³ before optimisation to 175.9 million m³, 185.1 million m³, 184 million m³ and 180.1 million m³ after optimisation, respectively, showing that crop-structure adjustment and irrigation measures were more coordinated.

After optimisation, the water shortage in most units and across the whole irrigation district had significantly improved, as the negative gap had narrowed or the positive surplus had increased, indicating that the water shortage had been alleviated (Figure 4c). The overall improvement is significant. The total water shortage in the irrigation district was optimised from −139.4 million m³ to −138.0 million m³ in 2021, from −207.2 million m³ to −205.3 million m³ in 2022, from −167.7 million m³ to −156.7 million m³ in 2023, and from −213.7 million m³ to −210.1 million m³ in 2024, reflecting the improvement in overall water resource allocation efficiency.

As the unit with the most serious water shortage, the water shortage of the Guleawati Township was optimised from −0.897 million m³ to −0.883 million m³ in 2021, and from −1.066 million m³ to −1.064 million m³ in 2024. Although it is still in a state of severe water shortage, the gap continues to narrow after optimisation, indicating that it has achieved water-saving effects by compressing high-water-consuming cotton and expanding crops such as corn, legumes, and vegetables and fruits. Jiamu Town did not lack water before or after optimisation in 2021, 2022, and 2023. The surplus water in 2021 decreased slightly from 0.136 million m³ to 0.114 million m³. However, combined with the slight increase in total irrigation, it reflected the use of surplus water for more efficient crops, thereby improving the economic efficiency of water resources. After the optimisation of the Communist Youth League Town in 2023, the water shortage improved from −0.373 million m³ to −0.345 million m³, indicating that the balance between water-saving and stable yields of legumes, vegetables, and corn had improved.

3.3.2. Soil Resource Optimisation Results

From 2021 to 2024, the crop-planting area of each unit in the irrigation district was moderately reduced after optimisation, with overall reduction rates of 2.93%, 3.3%, 4.1%, and 3.31%, respectively. From the perspective of the overall crop types of the optimised irrigation district in 2021 and 2024, the cotton planting area was significantly reduced in 2021, and the conventional cotton was reduced from 3358.13 hm² to 1273.71 hm², a decrease of 62.07%. Drip irrigation cotton decreased from 26,404.93 hm² to 21,157.67 hm², a decrease of 19.87%. It shows that the irrigation district can achieve the goal of water conservation by reducing water consumption for high-water-consuming crops. On the contrary, the area of rice, corn, legumes and vegetables increased significantly, and the area of rice increased from 537.20 hm² to 1991.09 hm², an increase of 270.64%. Corn increased from 4432.13 hm² to 5776.50 hm², an increase of 30.33%; legumes and vegetables increased from 6290.33 hm² to 15,412.02 hm², an increase of 145.01%. In addition, the area of alfalfa and forest belt also increased from 109.47 hm² to 190.83 hm² (an increase of 74.33%) and 1509.87 hm² to 1681.46 hm² (an increase of 11.36%), respectively, while the area of orchard decreased from 19,345.60 hm² to 13,459.41 hm² (a decrease of 30.43%) (Figure 5).

In 2024, the optimised cotton planting area was further compressed: conventional cotton decreased from 732.07 hm² to 287.62 hm², a decrease of 60.71%; drip irrigation cotton decreased from 33,009.60 hm² to 25,213.82 hm², a decrease of 23.62%. At the same time, the area of grain crops and economic crops continued to expand, corn increased from 5050.13 hm² to 6678.91 hm², an increase of 32.25%; rice increased from 950.00 hm² to 2377.35 hm², an increase of 150.25%; legumes, vegetables, melons and fruits increased significantly from 7421.73 hm² to 17,437.21 hm², an increase of 134.95%. The forest belt area increased from 1988.73 hm² to 2122.16 hm², an increase of 6.71%, and the ecological function continued to increase. The orchard area decreased from 25,212.87 hm² to 14,863.37 hm², a decrease of 41.05% (Figure 6). In 2022 and 2023, the planting area of each unit before and after crop optimisation in the irrigation district can be seen in the Supplementary Materials, Figures S7 and S8.

After optimisation, the proportions of legumes, vegetables, and fruits in each unit of the irrigation district have increased over the years. Among them, Kezile Town has significantly increased legumes, vegetables, and fruits while reducing cotton; the synchronous growth of corn, legumes, and vegetables in the Guleawati Township and the proportion of legumes and vegetables in Communist Youth League Town increased significantly. After the optimisation of each unit over the years, the characteristics of ‘cotton pressure, grain expansion, economic increase and strong forest’ were presented. The cotton and orchards with high water consumptions continued to decrease. At the same time, the proportion of economic crops and ecological forest belts, such as food crops, legumes, vegetables, and fruits, increased steadily.

3.3.3. Optimisation Results of Crop Carbon Uptake

The optimisation measures for each unit from 2021 to 2024 significantly improved the carbon sequestration capacity of the irrigation ecosystem while reducing water consumption by high-water-consuming crops. From the perspective of the entire irrigation district, the total amount of carbon absorbed after optimisation from 2021 to 2024 was higher than before optimisation. It shows an increasing trend year by year (Figure 7). In 2021, the amount of carbon absorption increased from 324.1 million kg to 414.4 million kg, an increase of 27.87%; in 2022, it increased from 298.2 million kg to 412.3 million kg, an increase of 38.29%; in 2023, it increased from 298.7 million kg to 395 million kg, an increase of 32.23%; and in 2024, it increased from 324.8 million kg to 453.6 million kg, an increase of 39.67%. This indicates that optimising planting structure has significantly enhanced the carbon-sink function of regional agroecosystems.

The increase in carbon uptake after optimisation is mainly due to adjustments in crop area structure. Cotton compression did not reduce carbon uptake. Although the area of conventional and drip-irrigated cotton was significantly reduced, and its carbon uptake decreased accordingly (e.g., conventional-irrigated cotton decreased from 7.9 million kg to 3.0 million kg in 2021), the expansion of the remaining crops effectively compensated for and exceeded this part of the carbon loss.

Legumes and vegetables have become the largest contributors to carbon sinks, and the area and carbon absorption of these crops have increased significantly after optimisation. In 2024, its carbon absorption increased from 75.8 million kg to 178.1 million kg, an increase of 134.95%, making it the largest carbon-sink crop in the entire irrigation district. The carbon-sink effect of rice and maise was enhanced. The carbon absorption of rice increased from 6.8 million kg to 25.1 million kg in 2021 and from 12 million kg to 30 million kg in 2024, underscoring its importance as a high-yield carbon-sink crop. Maize also maintained growth in most years, for example, from 34.7 million kg to 45.2 million kg in 2021. The orchard’s carbon absorption decreased, but the unit efficiency did not decrease significantly. The orchard’s area was greatly compressed after optimisation, resulting in a decrease in carbon absorption from 16.6 million kg to 11.5 million kg in 2021. However, its carbon absorption capacity per unit area did not decrease significantly.

All townships improved their carbon absorption after optimisation. Among them, the increase in the Guleawati Township is the most prominent, rising from 82.0 million kg to 113.4 million kg in 2021 and from 94.0 million kg to 101.6 million kg in 2024, demonstrating the remarkable ecological benefits of its structural optimisation. Driven by the expansion of legumes, vegetables, fruits, and rice, the carbon absorption in Jiamu Town and the Yixilaimuqi Township continued to grow, reaching 84.4 million kg and 86.1 million kg, respectively, in 2024. Kizil Town and the Communist Youth League Town also achieved steady growth. Especially from 2023 to 2024, Kizile Town’s carbon absorption exceeded 100 million kg, indicating that structural optimisation could deliver sustainable ecological benefits. Through optimising the planting area for each unit crop over the years, the system’s carbon-sink capacity has been significantly improved while ensuring agricultural production, providing a useful path for achieving low-carbon agricultural transformation and ecological sustainable development.

3.3.4. Optimisation Results of Crop Economic Benefits

From the perspective of the whole irrigation district, the total economic benefits after optimisation from 2021 to 2024 were higher than those before optimisation and showed a continuous growth trend (Figure 8). In 2021, it increased from CNY 990 million to CNY 1.058 billion, an increase of 6.89%; in 2022, it increased from CNY 1.081 billion to CNY 1.116 billion, an increase of 3.22%; and in 2023, it increased from CNY 998.6 million to CNY 1.049 billion, an increase of 5.07%. In 2024, it increased from CNY 1.172 billion to CNY 1.194 billion, up 1.83%. After experiencing a large increase in the initial stage, the optimisation of the planting structure gradually entered the stage of stable improvement, indicating that each optimisation scheme was sustainable and operable.

The growth in economic benefits after optimisation mainly stems from optimising crop and resource allocation. Cotton income decreased, but the structure became more reasonable. The economic benefit of normal irrigation cotton decreased from CNY 61.6 million in 2021 to CNY 5.3 million in 2024, and that of drip irrigation cotton decreased from CNY 448.2 million to CNY 428.0 million. Although the total amount decreased, drip irrigation cotton still maintained a high yield, indicating the important role of water-saving irrigation technology in ensuring economic benefits. Legumes, vegetables, and fruits have become the main source of revenue growth, and economic benefits have improved significantly. In 2021, it increased from CNY 171.5 million to CNY 420.1 million. In 2024, it increased from CNY 202.3 million to CNY 475.3 million, with increases of 145.01% and 134.95%, respectively, becoming the largest source of revenue in the irrigation district. This shows that the contribution of high-value-added crops to farmers’ incomes has become increasingly prominent. The economic benefits of rice have improved significantly. Rice income increased from CNY 9.9 million to CNY 36.7 million in 2021 and from CNY 17.5 million to CNY 43.9 million in 2024, demonstrating its dual value in ensuring food security and improving economic benefits. The orchard’s income decreased, but the unit benefit remained stable. The economic benefit of the orchard decreased from CNY 269.9 million in 2021 to CNY 187.8 million, and from CNY 351.7 million in 2024 to CNY 207.3 million. The decrease in income was mainly due to area compression.

The economic benefits of all the township units have increased after optimisation, but there are differences in the sources and magnitude of growth. The most significant growth was in the Guleawati Township, which increased from CNY 315.8 million to CNY 335.5 million in 2021, and from CNY 323.9 million to CNY 329.3 million in 2024. Compressing cotton greatly expanded the cultivation of legumes, vegetables, and fruits, thereby enabling a smooth transformation of the income structure. Through the coordinated development of legumes, vegetables, fruits, and rice, the economic benefits of the Yixilaimuqi Township increased from CNY 174.8 million in 2021 to CNY 205.9 million and from CNY 210.6 million to CNY 215.8 million in 2024, demonstrating the effect of increased income from diversified operations. While maintaining the comparative advantage of drip-irrigated cotton, Kezile Town actively develops legumes, vegetables, melons, fruits, and rice. The economic benefits increased from CNY 232.8 million to CNY 233.6 million in 2021 and from CNY 282 million to CNY 287 million in 2024, reflecting steady, progressive development. Jiamu Town and the Communist Youth League Town also achieved steady growth, increasing from CNY 126.5 million and 140.1 million to CNY 128.2 million and 155.1 million, respectively, in 2021, demonstrating the adaptability of each optimisation scheme under different basic conditions.

4. Discussion

The MOAWCE model developed in this study and its empirical application provide a new methodological framework and case study insights for multi-objective water and soil resource allocation in arid irrigation districts, but some issues still need further discussion.

4.1. Algorithm Selection and Optimisation Model Versatility

This paper finds that the MOEA/D-CMT algorithm performs best for high-dimensional multi-constraint nonlinear problems. This is mainly due to its decomposition strategy and competitive multi-task mechanism, which effectively improve the quality of the model’s Pareto solution set [46]. However, the performance of the algorithm is often closely related to problem characteristics, such as the target dimension, the degree of constraint nonlinearity, and the scale of the decision variables. Whether the superiority of the MOEA/D-CMT algorithm remains significant when dealing with water–carbon–economy coupling optimisation problems across different irrigation districts or basins needs to be verified through additional cases. Future research can explore adaptive adjustments to algorithm parameters or develop hybrid intelligent algorithms for agricultural resource optimisation problems to enhance the model’s universality and robustness [47].

4.2. Coordination and Conflict in Scheme Selection

The evaluation results of the entropy weight–TOPSIS coupling-coordination model show that the comprehensive score (H_i) of the optimal scheme for each unit over the years is not simply positively correlated with the coupling coordination degree (D_i), and that spatial and temporal fluctuations are significant. This shows that under certain space–time conditions, the development of the three subsystems of society, the resource environment, and the economy cannot always achieve a high degree of coordination [48]. For example, in pursuit of economic benefits (such as the expansion of high-value-added economic crops), some units may temporarily sacrifice absolute water resource conservation (a slight increase in total irrigation). However, their comprehensive water shortage is still being addressed, and significant carbon absorption and economic benefits are being realised. This reveals the inevitable trade-offs in multi-objective optimisation [49]. In practical applications, decision makers need to dynamically adjust the priority of each goal according to the core contradictions of different development stages in the irrigation district (such as water saving first [13,50], increasing income [8] or carbon absorption increase [18,27]) and choose the ‘satisfactory solution’ that best meets the current management needs rather than the theoretical ‘absolute optimal solution.’

4.3. The Ecological and Economic Connotation of the Optimisation Results

After optimisation of the model, the pattern of ‘cotton pressure, grain expansion, economic increase and strong forest’, as well as the vigorous development of high value-added and high-carbon absorption crops such as legumes, vegetables, melons and fruits, not only responds to the national policy orientation of ensuring food security and promoting farmers’ income but also meets the inherent requirements of agricultural green development [51,52]. The total carbon uptake increased significantly (an increase of 27.87~39.67%). Compared with the previous similar studies, the increase in crop carbon uptake (4.5%) under the planting of three kinds of crops, such as cotton, corn and wheat, was greatly improved [18], which confirmed that optimisation of the planting structure could significantly enhance the carbon absorption function of crops in the farmland ecosystem, providing a feasible path for agriculture in arid areas to participate in carbon neutralisation [27]. However, the estimation of crop carbon absorption in this study is mainly based on the static parameters of crop biomass and carbon source items, such as soil respiration and tillage carbon emission, are not included [21,22,23]. Therefore, the calculation result is biomass carbon absorption, rather than the net carbon sink of the agricultural ecosystem, which may be overestimated. Future research can be coupled with the DNDC model to construct a dynamic carbon budget model, incorporating the dynamic process of carbon sources and carbon sinks, and improving the accuracy of carbon absorption estimation [53,54].

4.4. Data Dependence and Uncertainty of the Model

The reliability of the optimisation results of this study depends heavily on the accuracy and integrity of the basic data, such as crop irrigation quotas, carbon absorption parameters, market prices, etc. These parameters themselves exhibit spatial and temporal variability and uncertainty (e.g., climate fluctuations affect crop water demand [55], policy adjustments affect agricultural prices [56]). Although the research is supplemented by the literature review and field research, in the future, interval mathematics [57], fuzzy programming [10] or stochastic programming [58] can be introduced to directly incorporate the uncertainty of key parameters into the optimisation model framework to generate interval solutions or probability distribution solutions with risk response capabilities, to improve the flexibility and adaptability of configuration schemes in the face of future climate change and market fluctuations. In addition, this study did not include soil process parameters such as water stress, soil salinisation, and fertility, and only considered the constraints of the land planting area. In the future, the soil process–crop yield response function will be constructed through field sampling and monitoring to enrich the connotation of water and soil resource allocation [59,60].

4.5. Model Reality Generalisation and Restriction

The model optimisation results have brought feasibility in theory, but whether it can be implemented in the irrigation district still needs further analysis. First is the conditionality of infrastructure. The existing irrigation facilities in the irrigation district are mainly an open-air canal system and a cotton drip irrigation system. The water-saving irrigation facilities and drainage facilities for rice, beans, vegetables, fruits and other crops are insufficient [19]. Some units lack fruit and vegetable preservation and storage facilities, which limits the large-scale cultivation of high-value crops. Second, the irrigation district is located in a remote area of Xinjiang [20]. The market circulation channels of economic crops such as beans, vegetables, melons and fruits are not smooth, and the price fluctuates greatly. Farmers face the market risk of ‘planting, selling and earning’; finally, farmers in the irrigation district, who have mainly planted cotton for a long time and formed mature planting techniques and production habits [61], may not have enough knowledge of the planting techniques of grain and economic crops, fruit and vegetable crops, and there is a problem of ‘low willingness to change’. In view of the above problems, it may be possible to promote structural adjustment through sub-core areas, moderate areas, and protected areas [62]: core areas (Jiamu Town, the Communist Youth League Town, no water shortage or mild water shortage) focus on expanding rice, beans, vegetables and fruits, and compress conventional cotton to less than 5%; moderate areas (Yixilaimuqi Township, Kezile Town) engage in stable cotton and grain expansion, with drip-irrigation cotton retaining 80% of the original area and grain crops such as corn and wheat being undergoing expansion; and the protection zone (the Guleawati Township, relative water shortage) focuses on large pressure cotton (conventional cotton clearing) while expanding drought-tolerant corn and alfalfa and having a moderate development of fruits and vegetables, to ensure the balance of supply and demand of water resources. Carrying out the construction of ‘agricultural technology training + demonstration base,‘ protection zones can cooperate with Xinjiang Agricultural University and the local agricultural and rural bureau to establish a grain, fruit and vegetable crop planting demonstration base, providing free technical training and field guidance for farmers [63,64]. At the same time, we will increase investment in water conservancy infrastructure, establish a water resource management and control system for the Tailan River Irrigation District [65], and formulate differentiated water-use indicators and irrigation quotas based on the water shortage degree and planting structure of the five townships [66], as well as promote the transformation of drip irrigation facilities, adapt the original cotton drip irrigation system to fruits, vegetables and food crops, and add water-saving irrigation and drainage facilities in rice areas [67,68]. We will also strive for major science and technology project funds in the Xinjiang Autonomous Region (this paper relies on this type of funds) and introduce social capital to participate in the transformation and operation of irrigation facilities in irrigation districts. Additionally, we will build an integrated system of ‘production, supply and marketing’, reduce the market risk of farmers [69], build an e-commerce platform for agricultural products in irrigation districts + offline wholesale market, and establish a long-term cooperative relationship with commercial supermarkets and farmers markets in cities such as Aksu and Urumqi, to realise the direct supply of fruits, vegetables, beans and other crops [70]. A price insurance system for agricultural products, which is jointly funded by the government and insurance companies, should also be established to provide price insurance for fruits and vegetables, grain and economic crops to offset the risk of market price fluctuations [71].

5. Conclusions

To address uncertainty in the solution algorithm and the problem of selecting an optimal scheme for the multi-objective optimal allocation model of water and soil resources in the irrigation district, the MOAWCE model is constructed in this study. Six multi-objective algorithms, APSEA, CMEGL, DCNSGA-III, DRLOS-EMCMO, MOEA/D-CMT and θ-DEA-CPBI, are applied to solve the multi-objective allocation model of water and soil resources in an irrigation district for the first time. The entropy weight–TOPSIS coupling-coordination model is the first to realise the optimisation of the ranking and coordination analysis of the allocation schemes for each unit over the years. The main conclusions are as follows:

(1)

The MOEA/D-CMT algorithm shows significantly better comprehensive performance than other algorithms, such as DCNSGA-III and θ-DEA-CPBI, for the high-dimensional multi-constrained regional water and soil resource optimisation problem in this paper. The algorithm achieves the highest HV value in each unit over the years, demonstrating that it balances convergence and diversity better and is the best algorithm for solving the model in this paper.

(2)

Based on the entropy weight–TOPSIS coupling-coordination scheme optimisation model, the optimisation results of each unit configuration scheme over the years show that there is no unique optimal solution suitable for all spatio-temporal units. The comprehensive score and coupling coordination degree of the optimal scheme for each unit fluctuate from year to year, and the differences between units are significant.

(3)

In terms of soil resources, after the optimisation of each unit from 2021 to 2024, its planting structure will transform in the direction of ‘intensive and diversified.’ The total planting area of the irrigation district was moderately reduced, with reduction rates of 2.93%, 3.3%, 4.1%, and 3.31%, respectively. The area of high-water-consuming crops (conventional cotton and drip-irrigated cotton) and orchards was significantly reduced. In contrast, the area of food crops such as rice and corn, as well as high-value-added crops such as legumes, vegetables, melons, and fruits, was greatly increased. The area of the ecological forest belt was also steadily increased, forming an optimised pattern of ‘cotton pressure, grain expansion, economic increase and strong forest.’

(4)

In terms of water resource utilisation, the optimisation scheme achieves the goal of ‘water saving and efficiency increasing.’ Under the premise that the total amount of irrigation water across the region remains stable or only slightly decreases, the irrigation water shortage situation in most units has been significantly improved through adjustments to crop structure and the pressure of water shortage has been effectively alleviated. Although the water consumption of local units has increased slightly due to the expansion of high-efficiency crops, the overall water resource allocation efficiency and economic output per unit of water have improved.

(5)

In terms of ecological and environmental benefits, the optimisation scheme significantly enhanced the crop carbon absorption function of the agricultural ecosystem. From 2021 to 2024, the total carbon uptake of crops in the irrigation district increased by 27.87~39.67% after optimisation, compared with before optimisation. This effect is mainly due to the expansion of crops with strong carbon sequestration capacities, such as legumes, vegetables, fruits, and rice, which fully demonstrates the positive effect of optimising planting structure on improving ecosystem services.

(6)

In terms of economic benefits, the optimisation scheme has achieved sustained economic growth under the constraints of resources and environment. Even with a slight reduction in total area, the irrigation district’s total economic benefits have continued to grow for four consecutive years. Among them, legumes and vegetables have become the primary drivers of economic growth, and their economic benefits have multiplied, effectively offsetting the loss of income from the compression of cotton area, highlighting the importance of developing high-value-added crops to ensure farmers’ incomes and promote the sustainable development of the regional economy.