https://orcid.org/0000-0003-1396-6835
Abstract
Nowadays, the conflict between the supply and demand of water resources in many regions is becoming increasingly prominent. Scientific allocation of regional water resources has become the key to solving the contradiction. In this study, a regional multi-objective water resources optimization allocation model considering social, economic, and ecological objectives is established, and four improvement spots are introduced to the sparrow search algorithm (SSA) to form an improved sparrow search algorithm (ISSA). By testing nine benchmark functions including monotonic and multi-peaked, the search efficiency and average convergence results of ISSA are significantly enhanced compared with other intelligent algorithms. Meanwhile, this research uses Luanchuan County, Henan Province, China, as an example to solve the water resource allocation scheme for 2025 and 2030 in the region using ISSA. The results show that the overall water shortage rate decreases to 3.49 and 2.79%, respectively, under the 75% guarantee rate, resulting in an effective reduction in future water shortages. Simultaneously, the scheme proposed has sound comprehensive benefits and can provide important technical support for the refined management of water resources, which is a reference and guidance for solving the contradiction between water supply and demand at the current stage.
HIGHLIGHTS
A multi-objective water resources allocation model that takes into social, economic, and ecological is proposed.
Four improvement spots are introduced to the benchmark sparrow search algorithm.
The improved sparrow optimization algorithm has better convergence efficiency and fitness values.
The proposed optimization scheme has superior comprehensive benefits and reduces the water shortage rate.
INTRODUCTION
Water is a vital substance for human survival and affects all social, economic, and environmental activities. Humans depend primarily on very limited freshwater resources, which account for only 2.5% of the total global water supply (Baggio et al. 2021). Of this limited freshwater resource, glaciers and deep groundwater account for 98%, and only 0.3% of the freshwater resources are directly available (Boretti & Rosa 2019). With economic development, population increase, climate change, and other reasons, water scarcity is becoming more and more serious to different degrees around the world (Zhang et al. 2023). Rational allocation of water resources is important for the sustainable development of society, affecting the harmony and stability of social, economic, ecological and other aspects and complementary promotion (Parsinejad et al. 2022). A correct allocation of water resources can establish a sound water use cycle. Conversely, a faulty water allocation can lead to water use conflicts, causing deterioration of the ecosystem and affecting the normal development of the local economy, which can lead to serious consequences (Feng 2021; Xu et al. 2021). To alleviate the problem of water shortage, rational water allocation to obtain the maximum comprehensive benefits has become an important research and development trend (Shourian & Mousavi 2017).
The water resources allocation model (WRAM) was born in the 1960s. Maass et al. (1962) used water resources system analysis to achieve a rational allocation of water resources, which was the first study that embodied the idea of water resources allocation. Lam (1983) analyzed the connection between the functions and benefits of water resources and applied the concept of system engineering to water resources allocation, and designed a multi-level, multi-objective WRAM. With the development of computing technology and the proposal of linear decision rules for water resources systems, many scholars have solved problems in water resources systems by building mathematical models. Tang (1995) adopted a formal modeling technique in multi-objective decision-making to study a complex water resource problem and used Large-system Hierarchical Dynamic Programming (LHDP) procedure to solve it, which was successfully applied to the Yellow River basin. Wong et al. (1997) suggested the principles and methods of multi-stage, multi-objective optimal management, an approach that supports the joint use of surface water and groundwater in water demand forecasting and identifies effective strategies for meeting water demand and controlling regional water quality problems. Percia et al. (1997) further investigated a multi-parameter water management model with the primary aim of optimizing economic efficiency and developed a model for the management of multiple water resources (groundwater, surface water, wastewater, etc.) in the Eilat region of Israel. The model also considers the issue of substantive demand, i.e., different water-using units have different demands on water quality as a way to allocate water resources. Rosegrant et al. (2000) developed a comprehensive economic–hydrological model to assess the social and economic benefits of water allocation and efficiency improvements by considering the linkages between water allocation, investment options of farmers, agricultural productivity, other water demand, and resource consumption for water resource management in the Maipo River basin in Chile. Kucukmehmetoglu (2009) used linear programming and traditional fuzzy theory to assess the importance of reservoirs in water allocation in the Euphrates and Tigris basins and to measure the plausible economic and political impacts of large reservoir projects across the basin. Abdulbaki et al. (2017) suggested an integer linear programming decision support model to minimize water spending and the analysis found good economic results. Wang et al. (2019) developed a composite model incorporating back propagation (BP) and Hargreaves models to address the problem of agricultural water allocation in arid regions under climate change conditions. Li et al. (2020b) proposed an improved bankruptcy method to construct the model, and the application showed that the allocation method of the model is more flexible and can adapt to complex water environment conditions. Wei et al. (2020) constructed a system dynamics model as an application to a water allocation scheme in Huainan, China, and analyzed the impact of the results on the water system. Li et al. (2022b) developed a water allocation model for arid regions to analyze water scarcity in the Beijing-Tianjin-Hebei region of China.
Due to the limitations of early models that only consider single-objective planning and optimization methods, it is difficult to obtain feasible results with comprehensive benefits (Ahmad & Zhang 2022). So, more and more researchers are using multi-objective models (Moudi et al. 2021). Practical applications of water allocation problems have complexities, such as the need to consider multiple benefits simultaneously, or the existence of constraints with regionally different characteristics. Conventional mathematical techniques are difficult to solve overly complex models, so more and more researchers are introducing intelligent optimization algorithms to solve this problem (Elsawah et al. 2017; Phan et al. 2021; Lu et al. 2022; Tan et al. 2023). There are many common intelligent optimization algorithms. Among them, the classical ones are the genetic algorithm (GA) (Katoch et al. 2021), simulated annealing algorithm (SA) (Bertsimas & Tsitsiklis 1993), particle swarm optimization algorithm (PSO) (Marini & Walczak 2015), etc. Several new intelligent optimization algorithms have also emerged in recent years, such as the whale optimization algorithm (WOA) (Mirjalili & Lewis 2016), the artificial bee colony algorithm (ABC) (Chen et al. 2023; Xu et al. 2023), the slime mould algorithm (SMA) (Li et al. 2020a; Cui et al. 2023), the grasshopper optimization algorithm (GOA) (Wang et al. 2023), and the seagull optimization algorithm (SOA) (Dhiman & Kumar 2019).
Solving multi-objective water allocation models by using intelligent optimization algorithms has become a major direction of research in recent years (Mirfenderesgi & Mousavi 2016; Ebrahimi & Shourian 2022; Zanfei et al. 2022; Zhou et al. 2023). Hou et al. (2014) used the Pareto ant colony algorithm (PAC) and combined remote sensing and GIS technology to establish water resources allocation model, which has good performance and application value. Song et al. (2016) developed the prospective behaviour theory and NSGA-III algorithm to develop a water allocation model to prevent flood and drought through rational water transfer from reservoirs. Yu & Lu (2018) proposed a transboundary basin WRAM (PPMGWO) using the projection tracing model (PPM) with the grey wolf optimization algorithm (GWO), with minimal average differences compared to using the firefly algorithm (FA) with the PSO algorithm. Qi et al. (2020) developed a multi-user, multi-water model to solve the water allocation scheme in Harbin, China for 2020 and 2030. Naghdi et al. (2021) combined dynamics simulation optimization techniques with Nash bargaining theory to develop a model that was solved using the NSGA-II multi-objective optimization algorithm, and the applicability of the model was demonstrated after experimental analysis. In the context of ecological priority, Li et al. (2022a) developed a water resources allocation model that prioritizes ecological benefits and takes into account other objectives and applied it to the Sha Ying River section in Henan, China, to calculate water resources supply and demand in 2030, effectively helping river management authorities in their daily work. Wang et al. (2022) established a water allocation model with three objectives: economic, social, and environmental, and applied it to solve the water allocation scenario for Yinchuan, Ningxia, China in 2025 using the PSO algorithm. Wu & Wang (2022) used SMA to solve water allocation scenarios for 2025 and 2030 for Wuzhi County, Henan Province, China, and the analysis found the results to be integrally beneficial.
In this study, we first propose an improved sparrow search algorithm (ISSA) that introduces a total of four improvements with the elite chaotic backward learning strategy, the Lévy flight strategy, the idea of the sine cosine algorithm, and the Cauchy–Gaussian change strategy, to overcome the problems of the baseline sparrow search algorithm (SSA), which is prone to falling into local optima and weak stagnation resistance (Liu & Wang 2021, Yuan et al. 2021; Bao et al. 2022; Wu et al. 2022, 2023; Gharehchopogh et al. 2023). Second, simulation experiments are conducted to compare ISSA with other intelligent optimization algorithms to verify its superiority. Third, three objective functions of social, economic, and ecological are used, and ISSA is used to solve these three objectives independently. Fourth, a comprehensive benefit objective containing the three objectives is established using weighting coefficients and solved using ISSA. Finally, based on the available data, the water resources allocation schemes for 2025 and 2030 in Luanchuan County, Henan Province, China, are solved and analyzed and discussed to provide effective data support for local economic development and water resources utilization.
The paper is organized as follows: section 2 introduces the mathematical model (including objective functions, constraints and overall flow), ISSA algorithm and simulation experiments (to verify the performance of ISSA). Next, section 3 presents the research and related data. Then section 4 describes the results of solving the model from different perspectives. Subsequently, section 5 discusses the results and offers analysis and policy recommendations for water allocation in the region. Lastly, section 6 concludes this study and provides a research outlook.
METHODOLOGY
Mathematical model
Objective functions
The rational allocation of water resources is a complex multi-objective planning problem, which usually needs to take into account social, economic, and ecological benefits. In this research, three objective functions of social, economic, and ecological benefits are selected as the optimization objectives, and the optimal value of the combined benefits of the three objectives is considered for solving the multi-objective allocation model of water resources. This subsection mainly introduces the three objective functions.
represents the water demand (
), and 
represents the amount of water allocated (
). The measurement of social benefits is more difficult, and to simplify the problem, this study uses water shortage to express, and Equation (1) indicates minimizing the water shortage. Simply put, the more adequate the water supply for each sector, the fewer social water conflicts, and the higher the social benefits (Guo & Wang 2022).
stands for the unit water supply benefit coefficient (
), 
stands for the unit water supply cost coefficient (
), 
stands for the weight of the sub-region using water, 
stands for the priority of water supply from the source, and 
stands for water equity coefficient. Equation (2) is the economic benefit function, and the economic benefit can be considered as the contribution of the rational water allocation to the economic growth of the region. Equations (3) and (4) represent the water supply priority and water supply equity factor in Equation (2), respectively, with higher values indicating higher priority or higher water demand.
and 
represent the supply order of source i and the use order of user j in sub-region k, respectively, and both take values in the range of [0,1], where 1 indicates the highest priority.
stands for emission pollutant content and 
stands for emission modulus. Equation (5) indicates the eco-efficiency. In this study, the volume of pollutants in wastewater produced by each sector is used to measure the ecological benefits, and the less pollutants produced, the more ecologically friendly and the higher the ecological benefits (Wang et al. 2021; Wu et al. 2021).Constraint conditions
The multi-objective optimal allocation model of water resources is subject to four conditions, namely, availability constraints, demand constraints, delivery capacity constraints and non-negative constraints. The availability constraints represent that the total amount of water provided by a source cannot exceed the total amount of water resources available to it on its own, as shown in Equation (6). The demand constraints indicate that the total volume of water obtained by j-th user must not exceed the total amount of its own demand, as shown in Equation (7), otherwise waste occurs; And the amount of water obtained must not be less than the minimum water consumption, otherwise it will not meet the minimum water standard and will have a greater negative effect; In general, take 
and 
. Delivery capacity constraints represent the water source user water supply cannot exceed the maximum delivery capacity, such as Equation (8). The non-negative constraints mean that the amount of water allocated cannot be negative, as in Equation (9); otherwise, it is invalid meaning.
is the available water supply of headstream i in subsegment k, 
is the lower bound of water demand of user j in subarea k, 
is the upper bound of water demand of user j in subarea k. 
is the maximum water delivery capacity of water source i to user j in subarea k.Comprehensive objectives
- (1)For the water allocation scheme, the following equations are used to represent the water supply plan based on the mathematical principles of the multi-objective WRAM.(10)
(11)
(12)
- (2)
Use ISSA to solve the optimal values of the three objectives individually to obtain the optimal solution
. - (3)For the construction of the comprehensive efficiency objective function, it is necessary to include the above three objective functions and solve them comprehensively, the specific objective function is Equation (13), where there is
.(13)
- (4)
Again, ISSA is used to solve the integrated benefit function F and output the optimal water resource allocation scheme
.
Framework for optimal allocation of water resources using ISSA.
Improved sparrow search algorithm
Sparrow search algorithm
SSA is a new kind of intelligent optimization algorithm, which mainly simulates the predatory and anti-predatory behavior of sparrow populations, and has the advantages of a strong ability to search for merit and a high speed of convergence (Xue & Shen 2020). Its main components include the update of the location of the three types of sparrows: finders, followers, and observers. The details of SSA are shown in Equations (14)–(18), where the variables or parameters appear and their meanings are shown in Table 1.
Parameters of SSA
| Parameter | Description | |
|---|---|---|
| Population | N | Number of sparrows |
| d | Dimension | |
| Fitness | f | Fitness function |
| Founder | t | Iteration counter |
 | Position of sparrow i in dimension j | |
 | Maximum iterations | |
 | Random number in range of (0,1) | |
 | Warning value in range of [0,1] | |
 | Safety value in range of [0.5,1] | |
| Q | Random number subject to [0,1] normal distribution | |
| L |  matrix with each element is 1 | |
| Follower |  | Global worst position |
 |  , A is a  matrix with each element randomly assigned 1 or −1 | |
| Watcher |  | Global best position |
 | A normal distribution random number with mean value of 0 and variance of 1 | |
| k | Random number in range of [−1,1] | |
 | Fitness of sparrow i | |
 | Best fitness | |
 | Worst fitness | |
 | A very small constant |
| Parameter | Description | |
|---|---|---|
| Population | N | Number of sparrows |
| d | Dimension | |
| Fitness | f | Fitness function |
| Founder | t | Iteration counter |
| | Position of sparrow i in dimension j | |
| | Maximum iterations | |
| | Random number in range of (0,1) | |
| | Warning value in range of [0,1] | |
| | Safety value in range of [0.5,1] | |
| Q | Random number subject to [0,1] normal distribution | |
| L | matrix with each element is 1 | |
| Follower | | Global worst position |
| | , A is a matrix with each element randomly assigned 1 or −1 | |
| Watcher | | Global best position |
| | A normal distribution random number with mean value of 0 and variance of 1 | |
| k | Random number in range of [−1,1] | |
| | Fitness of sparrow i | |
| | Best fitness | |
| | Worst fitness | |
| | A very small constant |
- Watcher's update:(18)
Equation (14) represents the location matrix of the sparrow population. Equation (15) represents the fitness matrix of the sparrow. Equation (16) represents the finder location update, 
means safe to forage and vice versa indicates danger to other areas. Equation (17) indicates follower position update, and 
indicates that the sparrow has a low fitness value to travel to other regions. Equation (18) indicates that the discoverer's position is updated, the discoverer's fitness value is lower, and 
indicates that the sparrow is far from the best position.
Improvement
Although SSA has many advantages, it also has some problems, such as insufficient population diversity, stagnant search, insufficient global search ability, and so on. For some of the problems, this study adopts four methods to improve the main content as follows, and the relevant parameters and their meanings are shown in Table 2.
Parameters of ISSA
| Parameter | Description | |
|---|---|---|
| (1) |  | Upper bound of solution |
 | Lower bound of solution | |
 | Minimum value of dimension j | |
 | Maximum value of dimension j | |
 | Zoom factor | |
| (2) |  | Current optimal position |
 | Random number in range of [0,1] | |
 | Random number in range of [0,1] | |
 | A constant(generally, 1.5) | |
| (3) |  | Random number in range of [0, ] |
 | Random number in range of [0,2] | |
 | Minimum value of  | |
 | Maximum value of  | |
| (4) |  | Random variables satisfying Cauchy distribution |
 | Random variables satisfying Gauss distribution |
| Parameter | Description | |
|---|---|---|
| (1) | | Upper bound of solution |
| | Lower bound of solution | |
| | Minimum value of dimension j | |
| | Maximum value of dimension j | |
| | Zoom factor | |
| (2) | | Current optimal position |
| | Random number in range of [0,1] | |
| | Random number in range of [0,1] | |
| | A constant(generally, 1.5) | |
| (3) | | Random number in range of [0,] |
| | Random number in range of [0,2] | |
| | Minimum value of | |
| | Maximum value of | |
| (4) | | Random variables satisfying Cauchy distribution |
| | Random variables satisfying Gauss distribution |
The elite chaos reverse learning strategy
Lévy flight
Sine cosine algorithm
Cauchy–Gauss mutation strategy
Flowchart of ISSA.
Algorithm 1: the framework of Improved SSA
| Input: MaxIter: the maximum iterations n: the number of sparrows PD: the number of producers SD: the number of sparrows who perceive the danger and etc. Output:  ,
|
| Input: MaxIter: the maximum iterations n: the number of sparrows PD: the number of producers SD: the number of sparrows who perceive the danger and etc. Output: ,
|
Simulation experiment
To demonstrate the superiority of the proposed ISSA, a set of benchmark test functions is selected, as shown in Table 3, with a total of nine functions, which can be divided into two categories: unimodal functions and multimodal functions. Four optimization algorithms, including SSA, were selected to compare the results with those of ISSA. The names of the algorithms and their parameters are given in Table 4.
Test functions
| Type | Function | Dim | Range | Global optimum |
|---|---|---|---|---|
| Unimodal test function |  | 30 |  | 0 |
 | 30 |  | 0 | |
 | 30 |  | 0 | |
 | 30 |  | 0 | |
 | 30 |  | 0 | |
| Multimodal test function |  | 30 | [−500,500] | −418.9829 *Dim |
 | 30 |  | 0 | |
 | 30 |  | 0 | |
 | 4 | [−5,5] | 0.0003075 |
| Type | Function | Dim | Range | Global optimum |
|---|---|---|---|---|
| Unimodal test function | | 30 | | 0 |
| | 30 | | 0 | |
| | 30 | | 0 | |
| | 30 | | 0 | |
| | 30 | | 0 | |
| Multimodal test function | | 30 | [−500,500] | −418.9829 *Dim |
| | 30 | | 0 | |
| | 30 | | 0 | |
| | 4 | [−5,5] | 0.0003075 |
Parameters setting for algorithms
| Algorithm | Pop size | Iterations | Parameters setting |
|---|---|---|---|
| ISSA | 30 | 1,000 |  |
| SSA | 30 | 1,000 |  |
| WOA | 30 | 1,000 |  |
| SMA | 30 | 1,000 |  |
| SOA | 30 | 1,000 |  |
| Algorithm | Pop size | Iterations | Parameters setting |
|---|---|---|---|
| ISSA | 30 | 1,000 | |
| SSA | 30 | 1,000 | |
| WOA | 30 | 1,000 | |
| SMA | 30 | 1,000 | |
| SOA | 30 | 1,000 | |
Simulation results
| Statistic | Algorithm | f1 | f2 | f3 | f4 | f5 | f6 | f7 | f8 | f9 |
|---|---|---|---|---|---|---|---|---|---|---|
| Convergency value | ISSA | 0 | 0 | 0 | 0.000421 | 1.36×10−05 | − 12,569.49 | 0 | 4.44×10−16 | 0.000313 |
| SSA | 3.2×10−128 | 0 | 1.58×10−26 | 0.152665 | 0.002101 | −6,343.40 | 0 | 4.44×10−16 | 0.001253 | |
| WOA | 1.34×10−44 | 1.48×10−11 | 2.21×10−10 | 26.06157 | 9.11×10−05 | −7,527.69 | 0 | 4×10−15 | 0.000452 | |
| SMA | 0 | 0 | 1.4×10−231 | 27.79891 | 0.000104 | −8,588.84 | 0 | 4.44×10−16 | 0.000644 | |
| SOA | 0 | 2,912.023 | 8.64×10−98 | 0.075548 | 0.000266 | − 12569.49 | 0 | 4.44×10−16 | 0.000339 | |
| Run time | ISSA | 2.268861 | 5.557064 | 2.159638 | 2.211116 | 2.668569 | 2.090782 | 2.269535 | 2.446457 | 1.190155 |
| SSA | 2.092294 | 5.300575 | 2.138642 | 2.385022 | 2.334987 | 2.239941 | 2.358575 | 2.455433 | 1.166368 | |
| WOA | 4.692107 | 7.732886 | 4.540466 | 4.56091 | 5.363653 | 4.938326 | 4.84208 | 4.827091 | 1.24408 | |
| SMA | 7.790065 | 10.80751 | 7.719028 | 7.569109 | 8.672773 | 8.152447 | 7.830079 | 7.679462 | 1.99095 | |
| SOA | 2.135653 | 5.441 | 2.068386 | 2.162996 | 2.524568 | 2.180022 | 2.22072 | 2.472418 | 1.210997 | |
| Stable generation | ISSA | 194 | 258 | 332 | 302 | 739 | 994 | 17 | 36 | 567 |
| SSA | 72 | 538 | 261 | 800 | 602 | 989 | 224 | 422 | 277 | |
| WOA | 1,000 | 1,000 | 986 | 1,000 | 846 | 199 | 570 | 750 | 488 | |
| SMA | 878 | 926 | 1,000 | 1,000 | 758 | 1,000 | 516 | 446 | 1,000 | |
| SOA | 771 | 1,000 | 1,000 | 211 | 230 | 631 | 109 | 113 | 193 |
| Statistic | Algorithm | f1 | f2 | f3 | f4 | f5 | f6 | f7 | f8 | f9 |
|---|---|---|---|---|---|---|---|---|---|---|
| Convergency value | ISSA | 0 | 0 | 0 | 0.000421 | 1.36×10−05 | − 12,569.49 | 0 | 4.44×10−16 | 0.000313 |
| SSA | 3.2×10−128 | 0 | 1.58×10−26 | 0.152665 | 0.002101 | −6,343.40 | 0 | 4.44×10−16 | 0.001253 | |
| WOA | 1.34×10−44 | 1.48×10−11 | 2.21×10−10 | 26.06157 | 9.11×10−05 | −7,527.69 | 0 | 4×10−15 | 0.000452 | |
| SMA | 0 | 0 | 1.4×10−231 | 27.79891 | 0.000104 | −8,588.84 | 0 | 4.44×10−16 | 0.000644 | |
| SOA | 0 | 2,912.023 | 8.64×10−98 | 0.075548 | 0.000266 | − 12569.49 | 0 | 4.44×10−16 | 0.000339 | |
| Run time | ISSA | 2.268861 | 5.557064 | 2.159638 | 2.211116 | 2.668569 | 2.090782 | 2.269535 | 2.446457 | 1.190155 |
| SSA | 2.092294 | 5.300575 | 2.138642 | 2.385022 | 2.334987 | 2.239941 | 2.358575 | 2.455433 | 1.166368 | |
| WOA | 4.692107 | 7.732886 | 4.540466 | 4.56091 | 5.363653 | 4.938326 | 4.84208 | 4.827091 | 1.24408 | |
| SMA | 7.790065 | 10.80751 | 7.719028 | 7.569109 | 8.672773 | 8.152447 | 7.830079 | 7.679462 | 1.99095 | |
| SOA | 2.135653 | 5.441 | 2.068386 | 2.162996 | 2.524568 | 2.180022 | 2.22072 | 2.472418 | 1.210997 | |
| Stable generation | ISSA | 194 | 258 | 332 | 302 | 739 | 994 | 17 | 36 | 567 |
| SSA | 72 | 538 | 261 | 800 | 602 | 989 | 224 | 422 | 277 | |
| WOA | 1,000 | 1,000 | 986 | 1,000 | 846 | 199 | 570 | 750 | 488 | |
| SMA | 878 | 926 | 1,000 | 1,000 | 758 | 1,000 | 516 | 446 | 1,000 | |
| SOA | 771 | 1,000 | 1,000 | 211 | 230 | 631 | 109 | 113 | 193 |
Summary diagram of simulation curves.
In Figure 3, it can be seen in the plots of the fitness of the test functions 
and 
that ISSA has the smallest initial fitness value compared with other algorithms, which can indicate that the elite chaotic inverse learning strategy can effectively improve the population diversity and reduce the initial fitness value. The fitness curve of the 
function in Figure 3 shows that the fitness curve of SSA remains unchanged after 400 iterations, while the curve of ISSA is still decreasing, which can indicate that the Cauchy–Gaussian mutation strategy can effectively prevent the stagnation of the convergence curve. Combining Figure 3 with Table 5 Simulation results, it can be seen that ISSA achieves the optimal value and on each test function, indicating that the introduction of Lévy flight strategy and the idea of sine cosine algorithm effectively improves the search ability.
STUDY AREA AND DATA SOURCE
Geographical map of Luanchuan County, Henan Province, China.
The main water sources in the study area include surface water, groundwater, and reclaimed water. The main water sectors are domesticity, industry, tertiary industry, agriculture, and ecology. Depending on the actual conditions in the study area, the values of some parameters in the model can be obtained: K = 1, I = 3, J = 5. Using 2019 as the base year, the water availability in the target year is projected using the trend line method, and the water demand in the target year is projected using the quota method at a guarantee rate of p = 75%, as shown in Table 6.
The volume (
) of water supply and demand
| Target year | 2025 | 2030 | |
|---|---|---|---|
| Water supply | Surface water | 6,985 | 7,071 |
| Groundwater | 997 | 1,014 | |
| Reclaimed | 450 | 757.5 | |
| Total | 8,432 | 8,843 | |
| Water demand | Domesticity | 1,151 | 1,229 |
| Industry | 3,024 | 3,229 | |
| Tertiary industry | 383 | 509 | |
| Agriculture | 3,402 | 3,144 | |
| Ecology | 632 | 712 | |
| Total | 8,592 | 8,822 |
| Target year | 2025 | 2030 | |
|---|---|---|---|
| Water supply | Surface water | 6,985 | 7,071 |
| Groundwater | 997 | 1,014 | |
| Reclaimed | 450 | 757.5 | |
| Total | 8,432 | 8,843 | |
| Water demand | Domesticity | 1,151 | 1,229 |
| Industry | 3,024 | 3,229 | |
| Tertiary industry | 383 | 509 | |
| Agriculture | 3,402 | 3,144 | |
| Ecology | 632 | 712 | |
| Total | 8,592 | 8,822 |
According to the actual situation and social development planning of the area, the order of water supply is determined as follows: surface water, groundwater, and reclaimed water. Determine the order of water consumption: domestic water, ecological water, industrial water, tertiary industry, agriculture. Based on the collected data and the actual plan, the other parameters in the water allocation model for the area were determined and the specific data on demand are shown in Table 7, where the emission concentration of pollutants is the sum of COD and ammonia nitrogen. There is only one parameter related to the water supply, 
, which are: 0.85, 0.10, and 0.05. Since the allocation of water resources greatly affects people's daily lives, this study prioritizes the satisfaction of water demand, i.e., social benefits, followed by economic, and ecological benefits. Therefore, the weight parameters 
are taken in the objective function of the comprehensive benefits.
Model parameters from the demand side
| User |  |  |  |  | |||
|---|---|---|---|---|---|---|---|
| 2025 | 2030 | 2025 | 2030 | 2025 | 2030 | ||
| Domesticity | 400 | 450 | 0.33 | 26.7 | 25.1 | 0.75 | 0.78 |
| Industry | 172 | 230 | 0.20 | 20.3 | 18.7 | 0.45 | 0.42 |
| Tertiary industry | 1,350 | 1,000 | 0.13 | 0 | 0 | 0 | 0 |
| Agriculture | 26 | 45 | 0.27 | 0 | 0 | 0 | 0 |
| Ecology | 400 | 450 | 0.07 | 0 | 0 | 0 | 0 |
| User | | | | | |||
|---|---|---|---|---|---|---|---|
| 2025 | 2030 | 2025 | 2030 | 2025 | 2030 | ||
| Domesticity | 400 | 450 | 0.33 | 26.7 | 25.1 | 0.75 | 0.78 |
| Industry | 172 | 230 | 0.20 | 20.3 | 18.7 | 0.45 | 0.42 |
| Tertiary industry | 1,350 | 1,000 | 0.13 | 0 | 0 | 0 | 0 |
| Agriculture | 26 | 45 | 0.27 | 0 | 0 | 0 | 0 |
| Ecology | 400 | 450 | 0.07 | 0 | 0 | 0 | 0 |
All data used in this paper are from the following three sources: (1) Henan Provincial Water Resources Bulletin (https://slt.henan.gov.cn/bmzl/szygl/szygb/), such as water demand in 2025 and 2030; (2) Henan Provincial Water Resources Department (https://slt.henan.gov.cn/), such as water supply in 2025 and 2030; (3) Henan Provincial Government Work Report (https://www.henan.gov.cn/zwgk/zfgzbg/), such as emission pollutant content and the unit water supply cost coefficient.
RESULTS
Based on the Section 3, the ISSA was applied to optimize the water allocation model for the region, and the experimental results are described specifically in this section.
Result of optimal allocation of water resources (
)
| Target year | Supplier | Domesticity | Industry | Tertiary industry | Agriculture | Ecology |
|---|---|---|---|---|---|---|
| 2025 | Surface water | 342.96 | 2,984.22 | 383 | 2,769.32 | 457.88 |
| Groundwater | 752.3 | 0 | 0 | 0 | 160.01 | |
| Reclaimed | 55.74 | 0 | 0 | 386.84 | 0 | |
| 2030 | Surface water | 937.7 | 2,479.98 | 422.88 | 2,934.9 | 254.59 |
| Groundwater | 80.77 | 741.96 | 67.44 | 4 | 89.19 | |
| Reclaimed | 210.53 | 2.05 | 0 | 0 | 355.29 |
| Target year | Supplier | Domesticity | Industry | Tertiary industry | Agriculture | Ecology |
|---|---|---|---|---|---|---|
| 2025 | Surface water | 342.96 | 2,984.22 | 383 | 2,769.32 | 457.88 |
| Groundwater | 752.3 | 0 | 0 | 0 | 160.01 | |
| Reclaimed | 55.74 | 0 | 0 | 386.84 | 0 | |
| 2030 | Surface water | 937.7 | 2,479.98 | 422.88 | 2,934.9 | 254.59 |
| Groundwater | 80.77 | 741.96 | 67.44 | 4 | 89.19 | |
| Reclaimed | 210.53 | 2.05 | 0 | 0 | 355.29 |
Iterative curves of ISSA based on 2025 data.
Iterative curves of ISSA based on 2030 data.
The Sankey diagram of water allocation in 2025.
The stacked column bar of supply side water allocation ratio in 2025.
The stacked column bar of demand side water allocation ratio in 2025.
For the perspective of the water supplier, see Figure 8. Surface water is the most abundant water supply object, containing water for five uses, with the highest proportion of water supplied to industry and agriculture, at 43.02 and 39.93%, respectively. Surface water is also the most abundant water resource, accounting for 82.83% of the total water volume. The supply of surface water and reclaimed water is relatively homogeneous. Surface water supplies domestic water and ecological water, of which the main supply is domestic water, with a proportion of 82.46%. Reclaimed water is supplied to agriculture and domestic use, with agriculture being the main supply, at 87.41%. It can be seen that the complexity of the water supply structure varies from one water source to another.
For the perspective of the water user, see Figure 9. The domestic water supply is the most abundant source, containing all three sources, with the main source being groundwater at 65.36%. The industrial and tertiary sectors have a single source of water supply and all rely on surface water supply. Water for agriculture is mainly supplied by surface water, with a proportion of 87.74%, and the remaining water is supplied by reclaimed water. 74.10% of the ecological water is supplied by surface water, and the remainder is supplied by reclaimed water. It can be clearly seen that surface water supplies all five water users and is the most important source of water in the Luan County area, especially supplying 100% of the water for industry and tertiary industries.
The Sankey diagram of water allocation in 2030.
The stacked column bar of supply side water allocation ratio in 2030.
The stacked column bar of demand side water allocation ratio in 2030.
From a supply perspective, there is little change in surface water. However, groundwater also supplies all five water sectors, with the largest proportion of supply becoming an industry, with a proportion of 75.45%. Reclaimed water is also mainly supplied to ecology and domestic water, and the proportion of water supplied to agriculture has decreased significantly. From a water use perspective, surface water is still the primary source of water for the vast majority of water-using sectors. Groundwater began to be supplied mainly for industrial and tertiary use. More reclaimed water is used to improve the ecological environment, with a percentage of 50.92. In summary, the 2030 water allocation scheme has an increased diversity of water supply and use compared to the 2025 scheme, and reclaimed water has a greater role in ecology, and groundwater is beginning to supply more areas.
DISCUSSION
Balance between supply and demand in different target years
| Target year | User | Water demand  ) | Water supply ( ) | Supply ratio (%) | Water deficit ( ) | Deficient ratio (%) |
|---|---|---|---|---|---|---|
| 2025 | Domesticity | 1,151 | 1,151 | 100 | 0.00 | 0.00 |
| Industry | 3,024 | 2,984.22 | 98.68 | 39.78 | 1.32 | |
| Tertiary industry | 383 | 383 | 100 | 0.00 | 0.00 | |
| Agriculture | 3,402 | 3,156.16 | 92.77 | 245.84 | 7.23 | |
| Ecology | 632 | 617.89 | 97.77 | 14.11 | 2.23 | |
| Total | 8,592 | 8,292.27 | 96.51 | 299.73 | 3.49 | |
| 2030 | Domesticity | 1,229 | 1,229 | 100 | 0.00 | 0.00 |
| Industry | 3,229 | 3,220.99 | 99.75 | 8.01 | 0.25 | |
| Tertiary industry | 509 | 490.32 | 96.33 | 16.68 | 3.67 | |
| Agriculture | 3,144 | 2,938.9 | 93.48 | 205.1 | 6.52 | |
| Ecology | 712 | 699.07 | 98.18 | 12.93 | 1.82 | |
| Total | 8,822 | 8,578.28 | 97.24 | 243.72 | 2.76 |
| Target year | User | Water demand ) | Water supply () | Supply ratio (%) | Water deficit () | Deficient ratio (%) |
|---|---|---|---|---|---|---|
| 2025 | Domesticity | 1,151 | 1,151 | 100 | 0.00 | 0.00 |
| Industry | 3,024 | 2,984.22 | 98.68 | 39.78 | 1.32 | |
| Tertiary industry | 383 | 383 | 100 | 0.00 | 0.00 | |
| Agriculture | 3,402 | 3,156.16 | 92.77 | 245.84 | 7.23 | |
| Ecology | 632 | 617.89 | 97.77 | 14.11 | 2.23 | |
| Total | 8,592 | 8,292.27 | 96.51 | 299.73 | 3.49 | |
| 2030 | Domesticity | 1,229 | 1,229 | 100 | 0.00 | 0.00 |
| Industry | 3,229 | 3,220.99 | 99.75 | 8.01 | 0.25 | |
| Tertiary industry | 509 | 490.32 | 96.33 | 16.68 | 3.67 | |
| Agriculture | 3,144 | 2,938.9 | 93.48 | 205.1 | 6.52 | |
| Ecology | 712 | 699.07 | 98.18 | 12.93 | 1.82 | |
| Total | 8,822 | 8,578.28 | 97.24 | 243.72 | 2.76 |
Plot of water deficient ratio in different target year (%).
Combining Table 9 with Figure 13, the results for 2025 are analyzed. First of all, the water supply for the tertiary sector can also be guaranteed with a 0% water shortage rate, provided that water for domestic use is guaranteed. Secondly, the water shortage rates for industrial and ecological water are also relatively low, at 1.32 and 2.23%, respectively. However, water shortage in agriculture is more serious, with a water shortage rate of 7.23%. According to the analysis, this should be due to the low economic efficiency of water use in agriculture (e.g., much lower than in the tertiary sector) and the low priority of water supply (e.g., lower than in domestic use). The overall water demand in 2025 is 
, while the overall water supply is 
. The overall water shortage rate reaches 3.49%, which is more serious considering the premise of 75% guarantee rate. The analysis of the water shortage in 2030 is as follows. First of all, only domestic water can guarantee 0% water shortage rate. Secondly, the industrial water shortage rate dropped from 1.32 to 0.25%, which can basically be considered as meeting the water demand. The water shortage rates for agriculture and ecological water also decreased, from 7.23 and 2.23% to 6.52 and 1.82%, respectively, but the water shortage rate for agriculture is still high. Then, it can be known that the tertiary industry is even more water stressed, rising from a 0% water shortage to 3.67%. However, the overall water deficit in 2030 decreases to 2.76% compared to 2025. Comparing the situation in 2025, the most significant change is that the tertiary industry begins to experience water shortages, while agricultural water shortages remain severe. In general, the local water shortage problem is more serious, and water shortage in the agricultural sector is more prominent.
Luanchuan County is currently at a faster stage of development, and economic development has led to an increase in demand for water resources, with overall water demand rising from 
in 2025 to 
, an increase in demand of 
, while the maximum water supply has increased from 
in 2025 to 
in 2030, an increase in the maximum supply of 
. As you can see, the water supply increases excess water demand, so the overall water shortage in Luanchuan County will be alleviated, but considering the 75% guarantee rate, the overall water shortage is more serious.
In 2025, the most serious part of water shortage in Luanchuan County is agriculture, and the rate of water shortage in agriculture is initially alleviated in 2030, probably because the local government strongly advocates the establishment of regional specialty agriculture. The increase in water shortage in the tertiary sector, the most economically efficient sector with little overall demand for water resources, may be due to the rapid growth of the tertiary sector, which has increased its demand for water resources by about 33%. The decline in the industrial water shortage rate indicates the importance the local government places on industrial development, especially the development of rich mineral resources. And while ecological water demand has increased, the rate of water shortage has decreased, indicating the need to develop a green economy locally. Overall, the most important direction of Luanchuan County's current work is to develop a green economy while trying to meet water demand and combining the advantages of local minerals and special agriculture.
For the current status of water resources in Luanchuan County, the following recommendations are made.
- (1)
Plan for the long term and enrich the allocation options. For Luanchuan County, the current water shortage is relatively serious, and the most important task at present is the rational allocation of water resources to obtain the maximum comprehensive benefits. An important approach is to plan ahead and set aside sufficient water resources reasonably based on long-term planning, such as a 33% increase in water demand in the tertiary sector from 2025 to 2030 causing an increase in water shortage. For the allocation of water resources, it is necessary to enrich the diversity of water supply to avoid the problem of water shortage caused by too homogeneous water supply. If there is a drought and surface water cannot meet the needs of industry and tertiary industry, water resources from other sources can be used as a supplement, forming a water allocation scheme with diversity.
- (2)
Develop virtual water resources to encourage lower water consumption. Virtual water is not consumed by people who actually consume water, it is the water consumed in the process of producing products and providing services. For Luanchuan County, you can encourage the production of low water-consuming products and import high water-consuming products to reduce water consumption in various ways. Specific measures such as higher taxes for local high water-consuming enterprises and policy incentives for low water-consuming enterprises, such as tax rebates. Establish a tiered water price to encourage businesses and people to develop the habit of water conservation.
- (3)
Vigorously develop reclaimed water and pay attention to ecological protection. For the agricultural and industry, normal production generates large amounts of wastewater. If some of this wastewater can be treated to obtain recycled water that meets the process requirements, then this recycled water can again be put to use in some sectors that meet the requirements at best, in order to reduce the use of non-renewable resources such as groundwater. In parallel, as the direct discharge of wastewater is reduced, the local ecological environment will be effectively improved, and water resources (mostly surface water) that could not be used due to environmental pollution can be used again. A healthy cycle of water use will be formed.
CONCLUSION
This study considered social, economic, and ecological objectives and constructed a comprehensive objective based on this to form a regional water resources optimal allocation model, and the proposed ISSA to solve the model. Luanchuan County in Henan Province, China, was selected as the study area, and the corresponding water allocation scheme was obtained based on the relevant data for 2025 and 2030.
For the benchmark SSA, we introduce four improvement points: the elite chaotic reverse learning strategy, the Lévy flight strategy, the sine cosine algorithm idea, and the Cauchy–Gaussian mutation strategy. The superiority of ISSA performance is demonstrated by comparing ISSA with four benchmark algorithms and applying it to the solution problem of water resources allocation, and the rapid rise of the fitness curve reflects its fast convergence ability.
Next, by analyzing the current situation of water resources in Luanchuan County, the water sources in the region are divided into three categories: surface water, groundwater, and reclaimed water. Then, according to the current situation of local development, the water users are divided into domesticity, industry, tertiary industry, agriculture, and ecology. Subsequently, the optimal water allocation scheme is solved based on the relevant data for 2025 and 2030. Lastly, the water resources allocation plan is discussed with the situation of water resources in Luanchuan County. The discussion shows that there is a more serious shortage of water resources in Luanchuan County at present and the water allocation scheme proposed in this study has good comprehensive benefits.
To summarize, this research shows that the proposed ISSA-based regional multi-objective water allocation model is effective and the obtained water allocation scheme is reasonable. However, this study has some limitations, for example, only a single region water allocation problem is considered, and the problem of multi-regional water co-allocation is not analyzed. Only one region was analyzed, and the applicability of the model was not verified. In order to solve the above problems, we will continue to explore some new methods in our future research.
ACKNOWLEDGEMENT
It was supported by the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research (grant No. IWHR-SKL-201905).
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.
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