A Multi-Objective Trade-Off Analysis with NSGA-II and Pareto Strategies for Total Phosphorus Load Allocation and Engineering Configuration in Yangcheng Lake Basin

Abstract

Yangcheng Lake, the third largest freshwater lake in the Taihu Plain (118.68 km²), serves critical functions in drinking water supply, aquaculture, and ecological regulation. This study aims to address the challenge of optimizing total phosphorus load allocation and engineering project configuration in the Yangcheng Lake basin by developing a multi-objective optimization model that integrates environmental, social, and economic dimensions with the goal of achieving three specific objectives: (1) maximizing ecological benefits, (2) minimizing life-cycle costs, and (3) minimizing the environmental Gini coefficient. The NSGA-II algorithm was used, with hyperparameters calibrated via orthogonal experiments and HV-GD evaluation. Under a normal flow year scenario, total phosphorus (TP) load allocation was optimized for an agricultural watershed where livestock manure contributes 86.5% of TP pollution. Five selection strategies (Economic Priority, Ecological Priority, Equity Priority, Ideal Point Method, Game Theory) were applied to the Pareto front. Results show synergy between ecological and equity objectives, both competing with economic cost. Optimal hyperparameters were a population size of 1000 and 1000 iterations. Among strategies, the Ideal Point Method achieved the best compromise (economic cost: 5772.7; Gini coefficient < 0.30). The proposed framework provides scientific support for pollution load allocation in plain river network regions, helping decision-makers balance economic development, ecological protection, and social equity.

1. Introduction

With the continuous acceleration of global urbanization and industrialization, the water quality of lakes and other water bodies is facing increasingly severe pollution challenges. To achieve sustainable water resource utilization and ecological restoration, the scientific allocation of pollution loads has become a core task in water environment management. Lakes often receive point and non-point source pollution inputs from surrounding areas; combined with weak hydrodynamic conditions and limited self-purification capacity, this leads to the easy accumulation of pollutants such as nitrogen and phosphorus, triggering ecological risks like eutrophication and algal blooms, which pose negative impacts on human life and the surrounding ecosystems [1,2]. Lake water bodies demand careful distribution of pollution loads, involving complicated physico-chemical reactions. This also requires the coordination of economic development, social equity, and ecological protection objectives.

Scholars at home and abroad have conducted extensive research on optimal pollution load allocation, proposing various analytical methods and solution techniques [3,4,5,6]. Among these, simulation methods that combine pollution load allocation with water quality response, along with optimal water resource allocation methods, represent an important direction in current research [7,8].

Among different allocation strategies, multi-objective programming and heuristic algorithm-based methods have received widespread attention due to their effectiveness in handling multi-stakeholder interest conflicts [9,10,11]. Existing studies typically establish decision models aimed at maximizing environmental benefits or minimizing treatment costs [12], and apply improved heuristic algorithms to find solutions under complex constraints. Wang et al. [13] integrated the Soil and Water Assessment Tool with NSGA-II (Non-dominated Sorting Genetic Algorithm II) to spatially optimize best management practices in the Jing River Basin, successfully balancing pollution reduction efficiency and implementation costs. Yang et al. [14] developed a multi-objective framework integrating XGBoost and NSGA-II for allocating saline farmlands and irrigation water in the Manas River Basin, achieving optimal trade-offs among cotton yield, soil salinity, and water productivity.

However, current research has two main limitations: (1) most models focus only on environment-economy trade-offs, ignoring equity and full life-cycle costs; (2) multi-objective algorithms often lack hyperparameter optimization, leading to poor Pareto front quality [13,14,15]. These gaps prevent accurate trade-off analysis and reduce decision reliability. The primary novelty of this work is the development of an “ecology-economy-equity” framework via the environmental Gini coefficient, supported by a systematic hyperparameter calibration of NSGA-II to ensure highly reliable optimization results.

This study addresses the identified research gaps by focusing on the Jiejing River basin, which is the main tributary of West Yangcheng Lake [16], developing an integrated framework for pollution load allocation and engineering configuration using NSGA-II [11,13,14,15]. The optimization objectives are: (1) maximizing ecological benefits, (2) minimizing life-cycle costs, and (3) minimizing the environmental Gini coefficient.

To ensure reliable optimization results, this study designs orthogonal experiments and uses Hypervolume (HV) and Generational Distance (GD) to analyze and tune the key parameters of NSGA-II [15]. Based on this, the study examines how ecological benefits, economic costs, and regional equity interact and compete during watershed management. The goal is to find the best pollution load allocation [17,18,19] and engineering layout [20] for the Jiejing River basin, balancing economic viability, environmental capacity, and social fairness. The findings can provide theoretical support and methodological tools for pollution load allocation in similar plain river network regions, though their practical application would require further validation with field data and consideration of local implementation conditions.

2. Methods

2.1. Overview of the Study Area

This study focuses on the Jiejing River—the primary inflowing river of West Yangcheng Lake—and its sub-watersheds, located in the plain river network region of the middle and lower reaches of the Yangtze River, China, to determine the optimal pollution load allocation. An overview of the study area is illustrated in Figure 1. Yangcheng Lake is located in the northeastern part of Suzhou City, Jiangsu Province (31°21′–31°30′ N, 120°39′–120°51′ E), spanning Xiangcheng District, Suzhou Industrial Park, and Kunshan City. It serves as the secondary water source for the Suzhou Industrial Park, a supplementary drinking water source for Kunshan City, and a national aquatic germplasm resource conservation area for the Chinese mitten crab [21,22]. Consequently, the water quality of Yangcheng Lake directly dictates the regional water supply security, as well as the safety of the aquatic ecology and environment. Since 2000, the water quality of Yangcheng Lake has improved significantly; according to the water quality monitoring data from 2000 to 2019, the concentration of TP (Total Phosphorus), a key indicator, showed an overall fluctuating downward trend. However, since 2015, the TP concentrations in all lake areas have increased to varying degrees, and in recent years, the water quality has stagnated at Class IV, with TP being the main influencing indicator [23]. From January to July 2024, water quality at the central Yangcheng Lake national monitoring section remained at Class IV, primarily limited by TP. The water quality shows no significant improvement and is notably worse in the west than in the east [24,25]. Therefore, controlling nutrient inputs from inflowing rivers is critical to resolving this issue.

Figure 1. Overview of Yangcheng Lake research area.

As research shows, nitrogen and phosphorus from inflowing rivers are important sources of pollutants in Yangcheng Lake, and TN (Total Nitrogen) and TP are the key water quality control factors of the lake. Based on the BATHTUB model analysis, when the inflowing rivers of West Yangcheng Lake follow the nutrient salt control limits of TN 0.68~0.81 mg/L and TP 0.030–0.039 mg/L, the water quality of the lake area can meet the standard [26]. Moreover, field observation data shows that the average concentrations of TN and TP in Yangcheng Lake in 2016 were 1.15 mg/L and 0.088 mg/L respectively, exceeding the national Class III water quality standard, which makes the control of nutrient input from inflowing rivers more urgent [27,28].

In 2023, the water quality at the national assessment section in the center of Yangcheng Lake reached Class III for the first time, and TP concentration decreased by 13% year-on-year [29]. Nevertheless, to further improve the lake’s water environment, it remains imperative to carry out comprehensive remediation of the inflowing rivers and surrounding terrestrial areas. Recent studies show that the total pollutant flux directly entering the lake’s quasi-protection area has exceeded that from external sources over the past five years. To address this issue, we need to implement comprehensive water pollution load control measures. Drawing on Suzhou’s experience of investing over 12 billion yuan in four rounds of ecological optimization actions, we can enhance the water environment. These actions include projects such as the 10,679-acre aquatic vegetation planting pilot and the 130 million yuan shoreline ecological restoration in Yangcheng West Lake. Ultimately, we should execute integrated non-point source pollution management projects across the entire watershed [27].

Yangcheng Lake, located in the northeast of Suzhou, Jiangsu Province, has an average water depth of approximately 1.43 m and a storage capacity of about 170 million m³ [30]. The lake is naturally divided into three lake areas, West, Central, and East, by two ribbon-shaped sand ridges. Its annual water level fluctuation is obvious: the water level rises with the spring rain in April, reaches the highest in July and August, begins to decline after September, enters the dry season in November and December, and reaches the lowest in January and February of the next year. The historical highest water level is 4.62 m (recorded at Guajing on 25 August 1954), and the historical lowest water level is 2.17 m (recorded at Guajing on 29 February 1956) [31,32]. The normal water level is maintained between 2.6 and 2.9 m, and the annual water level fluctuation is less than 1.2 m. The lake features a total of 59 inflowing and outflowing river channels. The western and northern channels primarily receive inflows from Taihu Lake and western catchments; the eastern channels discharge into the Yangtze River via the Qiputang and Yanglintang rivers; and the southern channels connect to the Wusong River system via the Loujiang River.

The water flow is sluggish, with an average velocity of only 0.03–0.06 m/s, which facilitates the sedimentation of suspended solids and results in clear water. The hydrological dynamics are regulated by the water levels of Taihu Lake, exhibiting a gradient variation pattern of “Taihu Lake → river network → Yangcheng Lake.”

The basin of the Jiejing River, an inflow river to Yangcheng Lake, was divided into six sub-basins. Based on the statistical data from the Xiangcheng Yearbook (2024), and in conjunction with the rural and urban population densities of Xiangcheng District, the population, GDP (Gross Domestic Product), and land-use area of each sub-basin were estimated. The specific data are presented in Table 1.

Table 1. Zoning data and land use of Jiejing sub-basins.

No.	Population (Persons)	GDP /Million CNY	Land Area/km2	Agricultural Land/m2	Built-Up Land/m2	Water Area/m2	Forest Land/m2	Wetland/m2	Bare Land/m2
J-01	2621	19.9	1.12	0	951,000	172,900	0	0	0
J-02	6120	46.5	2.53	151,800	2,220,400	94,300	58,900	0	0
J-03	8541	64.9	5.59	630,400	3,098,800	1,852,300	1800	2600	92,500
J-04	8756	66.4	5.17	676,400	3,176,800	1,234,900	30,100	53,500	524,000
J-05	5207	39.6	3.42	366,000	1,889,300	831,700	116,400	2800	217,800
J-06	9554	72.6	11.16	3,705,800	3,466,100	3,860,100	129,500	330	0

Conflicts and trade-offs exist among diverse objectives, such as water environmental governance, watershed social development, and the construction and operational costs of engineering projects. Therefore, this study develops a multi-objective optimization model that balances ecological, economic, and equity objectives, providing a systematic approach for pollution load allocation in the Yangcheng Lake basin.

2.2. NSGA-II Multi Objective Optimization Algorithm

The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is the most popular multi-objective evolutionary algorithm (MOEA) and has been successfully applied to various water resource optimization problems [33,34,35]. Building upon the original non-dominated sorting genetic algorithm, it introduces a crowding distance mechanism that prioritizes the retention of individuals with a larger crowding distance, thereby ensuring an even distribution along the Pareto front. Concurrently, it adopts an elitist strategy by merging the parent and offspring populations, from which the best N individuals are selected to form the next generation population. This strategy helps preserve superior solutions across generations and accelerates convergence. By reducing computational complexity while maintaining the diversity of the solution set, NSGA-II has become one of the most widely applied algorithms in the field of multi-objective optimization.

NSGA-II evaluates the superiority of solutions based on Pareto dominance. For a multi-objective minimization problem, a solution u dominates a solution v if and only if: $\forall i\in 1,2,\dots ,M,f_i\left(u\right)\le f_i\left(v\right) and \exists j\in 1,2,\dots ,M,f_j\left(u\right)<f_j\left(v\right)$, where M is the number of objective functions. By simulating natural selection mechanisms, the algorithm utilizes genetic operations such as selection, crossover, and mutation to iteratively evolve the population, gradually approximating the Pareto optimal front.

To maintain the diversity of the Pareto front, NSGA-II introduces the concept of crowding distance. The crowding distance $d_i$ of an individual i is defined as the average distance between that individual and its adjacent individuals in the objective space:

$$d_i=\sum _{m=1}^M{\displaystyle \frac{f_m^{i+1}-f_m^{i-1}}{f_m^{max}-f_m^{min}}}$$

(1)

where $f_m^{max}$ and $f_m^{min}$ are the maximum and minimum values of the m-th objective function, respectively. During the selection operation, the algorithm prioritizes individuals with a lower non-domination rank; if individuals share the same rank, preference is given to those with a larger crowding distance. This guides the search toward sparser regions, ensuring a uniform distribution of the solution set.

NSGA-II employs an elitism mechanism to ensure that superior individuals are preserved. Specifically, the parent population $P_t$ and the offspring population $Q_t$ are merged to form a new population $R_t$ of size 2N. After performing fast non-dominated sorting and calculating the crowding distance for $R_t$, the best N individuals are selected to advance to the next generation based on their sorting rank and crowding distance. This strategy effectively enhances the convergence speed and stability of the algorithm. Figure 2 presents a simplified schematic of the multi-objective genetic algorithm process, primarily illustrating the relationships between core operations such as population initialization, fast non-dominated sorting, crowding distance evaluation, elitism, crossover, and mutation.

Figure 2. Simplified schematic of the core process and principles of the NSGA-II algorithm. The left boxes and arrows show the NSGA-II workflow; the colored boxes on the right distinguish different individuals, and the dashed boxes indicate genetic-operation regions.

2.3. Entropy Weight Method

To objectively quantify the ecological contribution weights of the seven categories of pollution-reduction engineering measures in the Jiejing River Basin, a standardized entropy weight method was adopted for weighting and comprehensive evaluation. A two-level evaluation indicator system was constructed, including five criterion-level dimensions—directness, timeliness, durability, stability, and ecological risk—with two specific indicators under each dimension (detailed in Table 2). The physical interpretations and quantitative calculation formulas of each indicator are presented as follows:

Table 2. Ecological contribution indicator system for reduction projects.

Target Layer	Criterion Layer	Indicator Name	Calculation Formula
Maximization of ecological contribution of pollution load reduction engineering measures	Directness	Pollution source interception efficiency	(Influent pollutant flux—Effluent pollutant flux)/Influent pollutant flux × 100%
		Spatial coverage	Engineering control area (or river reach length)/Total pollution contribution area of the basin (or total length of transmission pathway) × 100%
	Timeliness	Period of effect manifestation	1/Effect response rate constant
		Construction period coefficient	Critical time window for watershed governance/Actual construction period
	Durability	Design service life	1/Annual efficiency decay rate
		Annual average maintenance cost ratio	(Total maintenance cost over full life cycle/Design service life)/Annual average pollution reduction benefit
	Stability	Coefficient of variation in treatment efficiency	Standard deviation of treatment efficiency/Average removal efficiency
		Compliance guarantee rate	Cumulative compliance time/Total operation time × 100%
	Ecological risk	Ecological risk index	Σ (Weight of each risk factor × Score of each risk factor)
		Secondary pollution risk index	(Total amount of residual substances/Total flux of treated substances) + (Output of residual products/Annual treated water volume)

Based on the aforementioned theoretical framework and indicator system, this study employs the standardized entropy weight method to conduct a quantitative analysis of the ecological contribution weights for seven categories of engineering measures [36]. The specific calculation steps are as follows:

Step 1: Construction of the standardized scoring matrix

Assume that the evaluation system comprises $m$ evaluation dimensions and $n$ types of engineering measures to be evaluated. After calibrating the indicator parameters and applying the extreme value method to map the original quantitative indicators onto a unified scale, a standardized scoring matrix is formed:

$${\mathbf{R}}^{*}={\left[r_{ij}^{*}\right]}_{n\times m},r_{ij}^{*}\in \left[1,9\right]$$

(2)

where $r_{ij}^{*}$ denotes the standardized score of the i-th engineering type on the j-th dimensional indicator, thereby eliminating the influence of dimensional discrepancies on weight estimation.

Step 2: Column-wise normalization to obtain the proportion matrix

Normalize ${\mathbf{R}}^{*}$ column-wise:

$$p_{ij}={\displaystyle \frac{r_{ij}^{*}}{{\displaystyle {\sum }_{i=1}^n}{r}_{ij}^{*}}},{\displaystyle \sum _{i=1}^n}{p}_{ij}=1$$

(3)

$p_{ij}$ reflects the relative contribution share of different engineering measures under a given indicator j.

Step 3: Calculation of information entropy

Calculate the information entropy of each indicator based on Shannon entropy:

$$E_j=-k{\displaystyle \sum _{i=1}^n}{p}_{ij}\mathrm{l}\mathrm{n}{p}_{ij},k={\displaystyle \frac{1}{\ln n}}$$

(4)

It is stipulated that when $p_{ij}=0$, $p_{ij}\mathrm{l}\mathrm{n}(p_{ij})=0$ to ensure mathematical consistency. $E_j\in [0,1]$, and a larger value indicates smaller differences among the engineering measures for that indicator and thus a lower amount of effective information provided.

Step 4: Calculation of indicator weights

From the degree of divergence (redundancy) $d_j=1-E_j$, the indicator weights are calculated as:

$$w_j^{*}={\displaystyle \frac{d_j}{{\displaystyle {\sum }_{j=1}^m}{d}_j}}={\displaystyle \frac{1-E_j}{{\displaystyle {\sum }_{j=1}^m}(1-E_j)}}$$

(5)

This achieves objective weighting based on the “contribution of discriminability”: the more significant the differences (i.e., the smaller the entropy), the higher the assigned weight.

Step 5: Calculation of composite scores and ecological contribution weights

The composite score for each engineering measure is obtained by a weighted sum of the standardized scores:

$$s_i={\displaystyle \sum _{j=1}^m}{w}_j^{*}\hspace{0.17em}{r}_{ij}^{*}$$

(6)

The composite scores are then normalized to derive the final ecological contribution weights:

$$w_i={\displaystyle \frac{s_i}{\underset{1\le i\le n}{\mathit{max}\left(s_i\right)}}}={\displaystyle \frac{{\displaystyle {\sum }_{j=1}^m}{w}_j^{*}\hspace{0.17em}{r}_{ij}^{*}}{\underset{1\le i\le n}{\mathit{max}\left({\displaystyle {\sum }_{j=1}^m}{w}_j^{*}\hspace{0.17em}{r}_{ij}^{*}\right)}}}$$

(7)

These weights satisfy $0\le w_i\le 1$ and $max\left(w_i\right)=1$. A larger numerical value indicates a superior comprehensive performance of the corresponding engineering type under the multi-dimensional criteria of ecological contribution, and it should therefore be assigned a higher priority in subsequent optimal allocation.

2.4. Construction of the Pollution Load Allocation Model

2.4.1. Objective Functions

Considering the ecological environment, economic costs, and regional equity, the following three objective functions are constructed.

(1)

Environmental and ecological objective. The objective is to maximize the ecological benefits of various pollution load reduction projects, expressed as follows:

$$\max f_1=\sum _{i=1}^7{R}_i·w_i$$

(8)

where $f_1$ is the objective function value, $R_i$ is the pollution load reduction amount of the $i$-th type of project, and $w_i$ is the ecological contribution weight of the $i$-th type of project.

(2)

Economic cost objective of engineering measures

The objective is to minimize the total annualized cost over the full life cycle, covering construction investment and operation and maintenance (O&M) costs:

$$\mathit{min}{f}_2=\sum _{k=1}^K\sum _{j=1}^J\left(C_{k,j}^{cap}·s_{k,j}+C_{k,j}^{op}·R_{k,j}\right)$$

(9)

where $s_{k,j}$ is the construction scale of the $j$-th type of engineering measure in the $k$-th sub-basin; $C_{k,j}^{cap}$ is the annualized construction cost per unit scale converted based on the project lifespan; and $C_{k,j}^{op}$ is the operation and maintenance cost per unit scale.

(3)

Watershed management equity objective

To prevent the excessive concentration of reduction tasks in specific sub-basins and the neglect of regional development differences, this study introduces the environmental Gini coefficient as a metric for allocation equity. The equity objective is constructed as follows:

$$\mathit{min}{f}_3=\sum _{m\in M}{\omega }_m·G_m$$

(10)

where $M$ is the set of evaluation indicators, including pollution load allocation and socio-economic indicators such as regional GDP, population, built-up area, and sub-basin area; $G_m$ is the environmental Gini coefficient calculated based on the $m$-th indicator; and ${\omega }_m$ is the weight coefficient of the respective indicator. The Gini coefficient is determined by calculating the area under the curve using the trapezoidal method:

$$G_m=1-{\displaystyle \sum _{k=1}^n}\left(X_k^{\left(m\right)}-X_{k-1}^{\left(m\right)}\right)·\left(Y_k^{\left(m\right)}+Y_{k-1}^{\left(m\right)}\right)$$

(11)

Sub-basins are first sorted in ascending order according to the m-th indicator, then, $X_k^{\left(m\right)}$ is defined as the cumulative proportion of the indicator for the first $k$ sub-basins after sorting by the $m$-th indicator in ascending order; $Y_k^{\left(m\right)}$ is the cumulative proportion of the pollution load reduction for the corresponding sub-basins; and it is defined that $X_0^{\left(m\right)}=Y_0^{\left(m\right)}=0$. The value of $G_m$ ranges from [0, 1], where a smaller value indicates a fairer allocation of the pollution load.

2.4.2. Decision Variables

In response to the systemic characteristics of the integrated “source-plant-network-river-lake” governance in the Jiejing River basin, this study constructs a decision variable system comprising seven types of pollution reduction projects. Based on pollution transmission pathways, this system categorizes the engineering measures into five major categories: “source”: non-point source LID (Low Impact Development) control projects, “network”: pipe network rehabilitation projects, “plant”: constructed wetland projects for wastewater treatment plant effluent, “river”: estuary pre-treatment projects, river ecological buffer zones, and “lake”: sediment solidification projects, tannin flocculation and algae removal projects. The load reduction amount of each engineering type serves as a decision variable in the optimization model, and its value is determined through an optimization search within the range satisfying engineering feasibility constraints.

The optimization search needs to find a feasible descent direction that meets both feasibility and descent conditions, and conduct constrained one-dimensional search to determine the step size. For example, methods like the gradient projection method can be used to project the negative gradient direction of the objective function onto the constraint surface when it does not meet the feasibility condition to obtain the search direction; meanwhile, we can also use penalty function methods such as the interior point penalty function method and exterior point penalty function method to transform the constrained optimization problem into an unconstrained one for iterative solution until the optimal value is found within the feasible range [37,38].

Among them, the decision variables for “source” and “network” projects are established at the sub-basin level, involving a total of six sub-basins (J-01 to J-06), with the reduction amounts of these two project types in each sub-basin acting as independent decision variables. The “plant-river-lake” projects are established as overall watershed decision variables, with their reduction amounts serving as unified decision variables at the watershed level. The definitions of the decision variables are presented in Table 3.

Table 3. Definitions and units of decision variables.

Variable	Meaning	Unit
$R_1={\sum }_{j=1}^6{x}_j$	Reduction by non-point source LID control	kg/a
$R_2={\sum }_{j=1}^6{x}_{j+6}$	Reduction by pipe network rehabilitation	kg/a
$R_3=x_{13}$	Reduction by constructed wetland for wastewater treatment plant effluent	kg/a
$R_4=x_{14}$	Reduction by river ecological buffer zone	kg/a
$R_5=x_{15}$	Reduction by estuary pre-treatment project	kg/a
$R_6=x_{16}$	Reduction by sediment solidification project	kg/a
$R_7=x_{17}$	Reduction by tannin flocculation and algae removal technology	kg/a

2.4.3. Constraints

• Total pollution load control constraint

To ensure that the total annual total phosphorus (TP) reduction in the Jiejing River basin meets the water quality compliance target, the expression for total pollution load control is:

$$\sum _{k=1}^K\sum _{j=1}^J{R}_{k,j}\ge W_{target}$$

(12)

where $W_{target}$ is the target annual TP reduction amount for the Jiejing River basin, t/a.

2.

Upper limit constraint on engineering reduction capacity, expressed as follows:

$$\begin{array}{c}0\le R_{k,j}\le R_{k,j}^{max}\end{array}$$

(13)

where $R_{k,j}^{max}$ is the upper limit of the reduction capacity for the $j$-th type of project in the $k$-th sub-basin.

3.

Environmental Gini coefficient constraint

To ensure that the optimized reduction and engineering schemes for each sub-basin are not inferior to the current level and remain at a relatively equitable level, the environmental Gini coefficient constraint is as follows:

$$G_m\le \mathit{min}\left(G_m^{\left(0\right)},0.4\right)$$

(14)

where $G_m$ is the environmental Gini coefficient of the $m$-th indicator after optimized allocation; $G_m^{\left(0\right)}$ is the current environmental Gini coefficient of the $m$-th indicator; $M$ is the set of evaluation indicators, including population, GDP, built-up area, sub-basin area, etc. An environmental Gini coefficient of less than 0.4 is considered a relatively equitable allocation.

4.

Non-negativity constraint of decision vectors, expressed as follows:

$$\begin{array}{c}{R}_{k,j}\ge 0\end{array}$$

(15)

where $R_{k,j}$ is the decision vector for the allocated amount of each type of engineering project.

2.5. Other Tools

During the preparation of this manuscript, ChatGPT (OpenAI, GPT-4 and 5, January 2026) was primarily used to write parts of the Python code for the NSGA-II (form pymoo 0.6.1.3) genetic algorithm. When processing optimization data results and generating related images, Origin 2024, ArcGIS Pro 3.1.6, and Python 3.12.6 were mainly used for image visualization.

3. Results

3.1. Hyperparameter Sensitivity Analysis

To achieve optimal optimization performance, a sensitivity analysis of the model’s hyperparameters is required. Ideally, the obtained non-dominated solutions should lie on the true Pareto front and be uniformly distributed along it. Generational Distance (GD) and Hypervolume (HV) are employed to measure the convergence and distribution of the model, respectively. GD characterizes the proximity of the approximate Pareto solution set to the true front, with a smaller value indicating better convergence; HV represents the coverage and distribution uniformity of the solution set within the objective space, with a larger value indicating better distribution.

This study designed an orthogonal experimental scheme as shown in Table 4. Four key hyperparameters of the genetic algorithm were selected for this test, namely population size, maximum number of iterations, crossover probability, and mutation probability. Four gradient levels were set for each parameter to cover the interactive effects among the parameters with a minimum number of trials.

Table 4. Orthogonal experimental scheme for hyperparameter tuning.

Hyperparameters	Level 1	Level 2	Level 3	Level 4
Population size	100	200	500	1000
Maximum iterations	200	500	1000	2000
Crossover probability	0.5	0.6	0.7	0.8
Mutation probability	0.05	0.1	0.2	0.3

The results of the orthogonal experiment for the hyperparameters of the model-solving algorithm are shown in Figure 3 and Table 5, illustrating the effects of hyperparameter levels on HV and GD, respectively. The degree of influence of each parameter on the algorithm’s convergence metric, in descending order, is: maximum number of iterations > population size > mutation probability > crossover probability. Among these, the maximum number of iterations has the most significant effect on convergence. The GD value decreases rapidly as the number of iterations increases; when the iterations reach 1000, the GD metric drops to an extremely low level, indicating that the number of iterations is the core variable determining whether the algorithm can effectively approximate the true Pareto front. Population size also exerts a significant impact on convergence but exhibits nonlinear characteristics. Moderately expanding the population can significantly reduce the GD, whereas an excessively large population size may lead to diminishing marginal returns in convergence efficiency due to computational redundancy.

Figure 3. Effects of hyperparameter levels on HV and GD.

Table 5. Orthogonal test results for hyperparameter sensitivity.

No.	Parameter Combination				HV	GD
	Population Size	Maximum Iterations	Crossover Probability	Mutation Probability
1	100	200	0.5	0.05	4.21 × 106	646.24
2	100	500	0.6	0.1	8.14 × 106	131.45
3	100	1000	0.7	0.2	8.48 × 106	35.62
4	100	2000	0.8	0.3	8.99 × 106	25.56
5	200	200	0.6	0.2	7.74 × 106	2787.96
6	200	500	0.5	0.3	1.70 × 107	574.78
7	200	1000	0.8	0.05	1.77 × 107	254.60
8	200	2000	0.7	0.1	1.84 × 107	149.84
9	500	200	0.7	0.3	1.11 × 107	1185.64
10	500	500	0.8	0.2	3.93 × 107	178.79
11	500	1000	0.5	0.1	4.48 × 107	17.86
12	500	2000	0.6	0.05	4.60 × 107	8.70
13	1000	200	0.8	0.1	1.97 × 107	2049.17
14	1000	500	0.7	0.05	6.70 × 107	417.92
15	1000	1000	0.6	0.3	8.83 × 107	13.04
16	1000	2000	0.5	0.2	8.33 × 107	1.12

In terms of their impact on the hypervolume (HV) metric, parameter sensitivity is ranked as follows: population size > maximum number of iterations > crossover probability > mutation probability. Population size is the dominant factor affecting HV. Its normalized value rises from 0.04 at level 1 to 0.73 at level 4, indicating that enlarging the population can substantially expand the search space and improve the coverage of the solution set. The maximum number of iterations also exerts a notable influence on HV. As the iteration count increases, HV continues to grow, although the growth rate gradually slows. This suggests that the iteration count mainly addresses convergence, whereas population size primarily governs distribution.

Overall, the algorithm shows clear parameter-coupling behavior. Emphasizing convergence alone often compromises solution-set distribution, while overemphasizing distribution can lead to insufficient convergence accuracy. Therefore, parameter settings should balance convergence and distribution to achieve robust overall performance.

As shown in Figure 4, performance differences across parameter combinations are substantial. When population size is small (100) or the maximum number of iterations is low (200), most scatter points cluster in the lower-right region, corresponding to lower HV and higher GD values. This pattern indicates weak convergence and limited diversity of the solution set. As population size and iteration count increase, the scatter points progressively shift toward the upper-left region, suggesting clear improvements in both convergence and solution distribution. In particular, when population size reaches 500 or 1000 and the number of iterations is 1000 or higher, HV increases markedly while GD decreases significantly. These results indicate that a larger population and more sufficient iterations can effectively improve the search capability of NSGA-II and the quality of the obtained solution set.

Figure 4. HV-GD distribution relationship across different parameter combinations.

A further comparison shows that some parameter settings perform well on both metrics. Most notably, Parameter Combination 15 (population size = 1000, maximum iterations = 1000, crossover probability = 0.6, mutation probability = 0.3) is located near the upper-left region of the plot. Its HV reaches $8.83\times {10}^7$, and its GD is only 13.04, indicating excellent overall performance among all tested combinations, with strong distribution and convergence characteristics. Although a few other combinations perform slightly better in GD, their HV values are relatively lower, resulting in weaker overall performance than Combination 15. Therefore, Combination 15 is identified as the optimal parameter configuration.

3.2. Optimal Allocation Results for a Typical Year

The total pollution reduction target for the Jiejing River basin was determined based on its water environmental capacity. This capacity was calculated with the goal of achieving Class III water quality for Total Phosphorus at the control point of the estuary mixing zone. Under a typical normal flow year scenario, the water environmental capacity was found to be 13.59 t/a, while the actual estimated TP flux was 21.79 t/a. Considering a safety margin of 10% applied to the environmental capacity, the required total annual TP reduction was derived as 9.56 t/a. These values formed the essential total load control constraint for the subsequent multi-objective optimization model. Following this, the year 2024 was selected as a representative normal-flow year for the JieJing River, and optimal allocation and engineering configuration were conducted at the annual scale. Based on the sensitivity analysis, NSGA-II adopted the parameter set of Combination 15 as the model’s operational parameters, with a population size of 1000, a maximum of 1000 iterations, a crossover probability of 0.6, and a mutation probability of 0.3. The resulting configuration scheme is as follows.

As shown in Figure 5, across all optimal configuration results, the ecological-environmental objective ranged from a maximum of 6853.8 to a minimum of 4388.14; the economic cost ranged from a maximum of 99.537 million CNY to a minimum of 45.846 million CNY; and the environmental Gini coefficient ranged from a maximum of 0.50 to a minimum of 0.218.

Figure 5. Three-dimensional space of Pareto frontier solutions.

To further analyze the trade-off relationships among the economic cost of engineering construction, the contribution to the ecological health of the lake water environment, and the allocation equity among sub-basins during the optimal configuration process, the Pareto frontier scatter plot was projected onto the two-dimensional planes corresponding to each coordinate axis, as shown in Figure 6, Figure 7 and Figure 8.

Figure 6. Two-dimensional frontier plot of the Gini coefficient and economic cost.

Figure 7. Two-dimensional frontier plot of the ecological environment and the Gini coefficient.

Figure 8. Two-dimensional frontier plot of the ecological environment and economic cost.

As can be seen from Figure 6, when the ecological-environmental benefit is fixed, a decrease in the Gini coefficient is accompanied by a marked increase in economic cost. Specifically, as the Gini coefficient decreases from its maximum value of 0.50 to its minimum value of 0.218, the economic cost increases from its minimum value of 45.846 million CNY to its maximum value of 99.537 million CNY. Therefore, there is a clear trade-off between the economic cost objective and the equity objective.

As shown in Figure 7, when the economic cost is fixed, the environmental Gini coefficient exhibits a clear decreasing trend as ecological-environmental benefits increase. Specifically, as the ecological-environmental benefit increases from its minimum value of 4388.14 to its maximum value of 6853.8, the environmental Gini coefficient decreases from its maximum value of 0.50 to its minimum value of 0.218. Therefore, there is an evident synergistic relationship between the ecological-environmental objective and the equity objective.

As can be seen from Figure 8, when the Gini coefficient is fixed, the economic cost shows a clear increasing trend as ecological-environmental benefits increase. Specifically, as the ecological-environmental benefit increases from its minimum value of 4388.14 to its maximum value of 6853.8, the economic cost increases from its minimum value of million CNY to its maximum value of 99.537 million CNY. Therefore, there is a clear trade-off between the ecological-environmental objective and the economic cost objective.

4. Discussion

To comprehensively analyze the Pareto frontier solution set and identify optimal schemes suited to different decision-making preferences, this study established two categories comprising five selection strategies. The first category is the single-objective priority strategy (economic priority, equity priority, and ecological-environmental priority), which aims to identify the extreme optimal boundary for each dimension. The second category is the multi-criteria compromise strategy (the Ideal Point Method [11,39] and the game theory method [9,39,40]), which seeks a balanced solution for overall system benefits. Through the coordinated analysis of these strategies, a complete spectrum of schemes ranging from single-focus preferences to comprehensive trade-offs can be provided for decision-makers. The specific strategies are as follows:

4.1. Selection Strategies

The Pareto frontier solution set contains numerous feasible non-dominated solutions. To identify compromise solutions from this set, this study proposes five different selection strategies. First, three preferred schemes are selected according to the priority of each of the three different objectives. In addition, the game theory method and the Ideal Point Method are applied for solution selection.

• Single-objective priority method.

Taking equity, economic cost, and ecological-environmental objectives as the order of priority, the optimal solution is selected independently for each objective. The mathematical expression of this process is:

$$X_k^{*}=\arg \underset{X\in \mathsf{\Omega }}{\max f_k\left(X\right)}\hspace{1em}\mathrm{or}\hspace{1em}{X}_k^{*}=\arg \underset{X\in \mathsf{\Omega }}{\min f_k\left(X\right)}$$

(16)

where $\mathsf{\Omega }$ is the Pareto non-dominated solution set; $f_k\left(X\right)$ is the value of the $k$-th objective function; $\mathrm{a}\mathrm{r}\mathrm{g} \mathrm{m}\mathrm{a}\mathrm{x}$ is used for objective maximization; and $\mathrm{a}\mathrm{r}\mathrm{g} \mathrm{m}\mathrm{i}\mathrm{n}$ is used for objective minimization.

2.

Ideal Point Method.

The Ideal Point Method is a commonly used multi-criteria decision analysis technique in the field of systems engineering, particularly suitable for multi-objective decision-making under a finite number of alternatives. The main steps of the Ideal Point Method include determining the reference point, calculating the Euclidean distance from each candidate scheme to the reference point, and computing the relative fitness.

First, the objective function values are standardized to eliminate the influence of dimensionality, and a weighted standardized decision matrix $V=(v_{ij}{)}_{n\times m}$ is constructed, where $v_{ij}$ denotes the weighted standardized value of scheme $i$ under objective $j$. The positive ideal solution $Z^{+}$ and the negative ideal solution $Z^{-}$ are then determined. For benefit-type objectives (the larger, the better), the positive ideal solution is the maximum value of that objective among all schemes, while the negative ideal solution is the minimum; for cost-type objectives (the smaller, the better), the opposite applies. Specifically, they are defined as follows:

$$\left\{\begin{array}{c}\mathrm{P}\mathrm{o}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} Z^{+}=\left(\mathrm{m}\mathrm{a}\mathrm{x} z_{1j},\mathrm{m}\mathrm{a}\mathrm{x} z_{2j},\dots ,\mathrm{m}\mathrm{a}\mathrm{x} z_{nj}\right)\\ \mathrm{N}\mathrm{e}\mathrm{g}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{s}\mathrm{o}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} Z^{-}=\left(\mathrm{m}\mathrm{i}\mathrm{n} z_{1j},\mathrm{m}\mathrm{i}\mathrm{n} z_{2j},\dots ,\mathrm{m}\mathrm{i}\mathrm{n} z_{nj}\right)\end{array}\right.$$

(17)

where $z_{ij}$ represents the weighted standardized value. Next, the Euclidean distances $D_i^{+}$ and $D_i^{-}$ from each scheme $i$ to the positive and negative ideal solutions are calculated as follows:

$$D_i^{+}=\sqrt{{\displaystyle \sum _{j=1}^m}(v_{ij}-Z_j^{+}{)}^2},D_i^{-}=\sqrt{{\displaystyle \sum _{j=1}^m}(v_{ij}-Z_j^{-}{)}^2}$$

(18)

Finally, the relative closeness $C_i$ of each scheme (i.e., the fitness value) is calculated:

$$C_i={\displaystyle \frac{D_i^{-}}{D_i^{+}+D_i^{-}}},0\le C_i\le 1$$

(19)

The closer $C_i$ is to 1, the closer the scheme is to the ideal optimal state. In this study, all non-dominated solutions are ranked in descending order according to $C_i$, and the scheme with the largest $C_i$ is selected as the final optimal compromise solution.

3.

Game theory method.

The selection strategy based on the Nash equilibrium solution in game theory is a decision-making method that treats multiple objectives as game participants. The core idea is to regard each objective (ecology, equity, and cost) as a virtual decision-making agent, representing the environmental protection department, management department, and economic department, respectively, with utility functions corresponding to the objective function values. The solution process constructs a non-cooperative game model, determines the strategy set and payoff function of each participant, and then identifies the equilibrium solution by maximizing the Nash product.

$$u_i\left(x\right)={\displaystyle \frac{F_i^{\mathrm{m}\mathrm{a}\mathrm{x}}-F_i\left(x\right)}{F_i^{\mathrm{m}\mathrm{a}\mathrm{x}}-F_i^{\mathrm{m}\mathrm{i}\mathrm{n}}}},i=1,2,3$$

(20)

where $F_i\left(x\right)$ is the original value of the $i$-th objective (cost, ecology, or equity), and $F_i^{\mathrm{m}\mathrm{a}\mathrm{x}}$ and $F_i^{\mathrm{m}\mathrm{i}\mathrm{n}}$ are the maximum and minimum values on the Pareto frontier, respectively. The final allocation scheme $x^{*}$ is then given by:

$$x^{*}=\arg \underset{x\in \mathcal{X}}{\max {\displaystyle \prod _{i=1}^3}{u}_i\left(x\right)}$$

(21)

where $\mathcal{X}$ is the Pareto-optimal solution set, and $\mathrm{a}\mathrm{r}\mathrm{g} \mathrm{m}\mathrm{a}\mathrm{x}$ denotes the solution that maximizes the product.

4.2. Preferred Results of Optimal Configuration

In this study, five optimal solutions were selected based on the five selection strategies described above: Scheme A was obtained using the ecological-priority method, Scheme B using the economic-priority method, Scheme C using the equity-priority method, Scheme D using the Ideal Point Method, and Scheme E using the game theory method. These schemes were also compared with the current actual engineering configuration in the Jiejing River Basin of Lake Yangcheng, as shown in Table 6.

Table 6. Comparison of current configuration results and optimization schemes.

Preferential Strategy	Ecological Contribution	Economic Cost/Million CNY	Environmental Gini Coefficient
Current situation	4522.09	71.4767	0.4338
Strategy A	6853.78	99.3603	0.2187
Strategy B	4388.14	45.8460	0.4648
Strategy C	6113.55	91.8398	0.2180
Strategy D	4677.00	57.7273	0.2848
Strategy E	6517.02	68.3698	0.4869

From an economic perspective, as shown in Figure 9, all solutions exhibit diminishing marginal returns. Solution B achieves the lowest cost at 45.85 million CNY, well below the current level of 71.48 million CNY. However, Solution A, which prioritizes ecological benefits, and Solution C, which emphasizes fairness, require higher investments at 99.36 and 91.84 million CNY, respectively. Solution D (Ideal Point Method) performs best in cost control at 57.73 million CNY, balancing all indicators while significantly reducing current expenditure.

Figure 9. Economic cost comparison between the current situation and the optimization schemes.

Regarding ecological contribution (Figure 10), Solution A delivers the strongest governance effect with an ecological value of 6853.8, about 51.6% higher than the current status. This highlights the potential of an ecology-first approach. Solution E (game theory method) also maintains relatively high ecological output at 6517.02. In contrast, Solution B yields only 4388.1—slightly below the current level—due to its excessive focus on cost reduction, revealing the limitations of single-objective optimization.

Figure 10. Comparison of ecological contribution between current situation and optimization schemes.

In terms of fairness (Gini coefficient, Figure 11), notable differences emerge in resource allocation balance. Solutions C and A reduce the Gini coefficient to 0.2180 and 0.2187, respectively, much lower than the current 0.4338. This suggests that prioritizing ecology or fairness leads to more equitable resource distribution. However, Solution E shows a high Gini coefficient of 0.4869. Despite strong ecological performance, its game-based process may concentrate resources in advantaged areas, compromising overall fairness.

Figure 11. Comparison of environmental Gini coefficient between current situation and optimization schemes.

In summary, the five strategies each have distinct strengths and weaknesses, reflecting typical multi-objective trade-offs. Solution D achieves a reasonable compromise among ecological improvement, cost savings, and fairness, making it a promising pathway for comprehensive basin management. Meanwhile, Solutions A and C offer valuable references for scenarios prioritizing extreme ecological restoration or social equity.

Figure 12 presents the allocation results of initial-rainfall non-point source control projects under five optimization schemes. Clear spatial differences in LID deployment are observed among the schemes. Scheme B has the lowest overall reduction intensity, with most measures concentrated in Sub-basin 1 and only limited deployment elsewhere, showing a strong cost-priority orientation. By contrast, Schemes C and D show higher reduction intensity, with larger allocations in Sub-basins 5, 1, and 3, indicating a stronger ecological focus. Schemes A and E fall between these two extremes and show a more balanced distribution across sub-basins. Overall, LID measures are mainly assigned to sub-basins with higher non-point source loads and greater influence on inflow water quality. Notably, Schemes A, C, and D consistently prioritize Sub-basins 5 and 1, where larger agricultural areas and higher livestock populations are closely linked to heavier non-point source pollution in the Jiejing River Basin.

Figure 12. Allocation results of initial rainfall runoff reduction projects under five different optimization schemes. The blue dendritic lines represent the Jiejing River and its tributaries.

Figure 13 shows the configuration results of pipeline network rehabilitation projects under the same five schemes. Compared with LID allocation, pipeline rehabilitation is more spatially concentrated. Scheme A assigns relatively high rehabilitation tasks across all sub-basins, especially Sub-basins 2, 3, and 4, reflecting a systematic remediation strategy consistent with its ecology-priority orientation. Scheme B has the lowest rehabilitation intensity, with only small allocations in a few sub-basins, which matches its economy-priority preference. Schemes C and D mainly focus on Sub-basin 3 while also covering Sub-basins 1 and 5, suggesting a preference for areas with dense pipeline networks and high infiltration risk. Scheme E shows a moderate pattern, balancing targeted rehabilitation and cost control. Across all schemes, Sub-basin 6 consistently receives the lowest rehabilitation allocation, likely because it is dominated by built-up land and already has relatively mature urban drainage infrastructure. These differences in LID and pipeline allocation highlight the need to tailor engineering measures to the pollution-source characteristics and infrastructure conditions of each sub-basin.

Figure 13. Allocation results of pipeline network rehabilitation projects under five different optimization schemes. The blue dendritic lines represent the Jiejing River and its tributaries.

The project configuration results obtained using the Ideal Point Method are summarized in Table 7. In the Jiejing River watershed of Lake Yangcheng, the Chengyang Wastewater Treatment Plant is the only wastewater treatment facility, with a treatment capacity of 25,000 m³/d. The optimal configuration includes an effluent wetland designed to fully accommodate the plant effluent, providing an additional TP reduction of 1281.87 kg/a after wastewater treatment. For in-river pollution control, a 4 km ecological buffer is proposed along the reach from the Chengyang Wastewater Treatment Plant to the lake estuary. Aquatic vegetation planted within the channel and along both riverbanks is expected to reduce the TP load by 569.18 kg/a. Given the large flow volume and navigation function of the Jiejing River, an enhanced estuarine pretreatment project with an area of approximately 18 hm² is recommended at the river mouth. This project, which may include a sedimentation basin and surface-flow wetlands on both sides of the estuary, is expected to reduce TP by 1492.83 kg/a, with an estimated investment of 17.76 million CNY.

Table 7. Ideal Point Method project configuration results.

Reduction Project Name	Project Scale	Annual Reduction	Estimated Investment
Initial Rainwater Runoff Control (LID) Project	Optimized at sub-basin level	3098.64 kg/a	4.2856 million CNY
Sewer Network Rehabilitation Project	Optimized at sub-basin level	252.39 kg/a	5.9647 million CNY
Wastewater Treatment Plant Effluent Wetland Project	25,000 m3/d	1281.87 kg/a	10.3824 million CNY
Riverine Ecological Buffer Project	4 km	569.18 kg/a	7.1268 million CNY
Estuarine Pretreatment Project	180,000 m2	1492.83 kg/a	17.7635 million CNY
Sediment Solidification Project	3.35 km2	2672.87 kg/a	9.4183 million CNY
Flocculation and Aeration Project	4,507,000 t	245.96 kg/a	2.7860 million CNY

For internal load control, sediment solidification is identified as the preferred measure, with a treatment area of 3.35 km² in northern West Lake Yangcheng, where sediment P release is relatively high. This measure is expected to reduce sediment-derived TP release by 2672.87 kg/a. In addition, to mitigate TP loads associated with cyanobacterial blooms, treatment of 4,507,000 t of water using tannin-based flocculation combined with micro/nano-aeration is recommended, with an estimated TP reduction of 245.96 kg/a. Overall, the Ideal Point Method was selected as the preferred solution from the Pareto frontier, and the corresponding engineering measures, project scales, and estimated investments provide a practical basis for pollution load allocation and engineering planning in the Lake Yangcheng watershed.

4.3. Limitations and Future Perspectives

Although this study provides a systematic optimization approach for pollution load allocation, several limitations should be noted. First, the current optimization relies on static data from a typical flow year, which overlooks the hydrological variability associated with wet or dry seasons and extreme weather events. Second, the ecological objective primarily focuses on the total amount of phosphorus reduction, without coupling a high-resolution hydrodynamic-water quality model to dynamically simulate the complex physical and chemical responses within the lake.

Future research should expand this framework into a dynamic one by integrating climate change scenarios and coupling it with advanced mechanistic water quality models. Additionally, scaling the model to the entire Yangcheng Lake basin and utilizing real-time monitoring data will further enhance the adaptive management and real-world applicability of the proposed engineering configurations.

5. Conclusions

Focusing on the Jiejing River basin of Yangcheng Lake, this study constructed a multi-objective optimization allocation model for pollution load based on the NSGA-II algorithm, integrating ecological environment, economic cost, and regional equity. The main conclusions are as follows:

(1)

Trade-off patterns among the three objectives are clearly identified: Significant competitive and synergistic relationships exist among economic cost, ecological benefit, and regional equity. Specifically, ecological benefit and equity exhibit a synergistic relationship, where a higher ecological contribution corresponds to a lower Gini coefficient. In contrast, both ecological benefit and equity are in competition with economic cost, as pursuing higher ecological contributions or improved equity requires a substantial increase in economic investment.

(2)

Hyperparameter sensitivity analysis effectively enhances algorithm performance: Through orthogonal experiments and HV-GD dual-indicator evaluation, the optimal parameter combination for the NSGA-II algorithm was determined as a population size of 1000, maximum iterations of 1000, a crossover probability of 0.6, and a mutation probability of 0.3. Under these parameters, the algorithm’s convergence and solution set distribution reached optimal levels, with the GD value dropping to 13.04 and the HV value reaching 8.83 × 10⁷.

(3)

Selection strategies reveal scheme characteristics under different decision orientations: Among the five selection strategies, the Ideal Point Method achieved the best balance among economic cost, ecological contribution, and Gini coefficient, making it the recommended scheme for integrated watershed management. The Ecological Priority and Equity Priority methods performed best under ecological restoration and social equity objectives, respectively, providing a scientific basis for specific policy scenarios. Although the Economic Priority method has the lowest cost, its ecological contribution is lower than current levels. The Game Theory method showed strong ecological performance but resulted in a Gini coefficient as high as 0.4869 due to resource concentration, thereby sacrificing allocation equity.