Forest ecological product value accounting method based on remote sensing and geographic information system
By building an integrated air-space-ground monitoring network and data fusion algorithm, and combining remote sensing with geographic information systems, we have achieved high-precision dynamic accounting and risk assessment of the value of individual trees in forest ecological products, solving the problems of insufficient accuracy and poor adaptability in traditional methods, and improving management efficiency and response speed.
Patent Information
- Application Number
- CN202510934967.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-08
- Publication Date
- 2025-09-16
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
Existing technologies make it difficult to achieve accurate spatiotemporal dynamic accounting of the value of forest ecological products at the scale of individual trees. This is limited by the insufficient accuracy of air-space-ground data fusion, poor regional adaptability of growth models, and the lack of multi-dimensional risk assessment. As a result, the accounting results are unable to accurately reflect the structural changes, value fluctuations, and potential risks of individual trees throughout their life cycle.
Construct a forest ecological product value accounting method based on remote sensing and geographic information systems, build an air-space-ground collection network through satellites, drones, and ground sensors, conduct intelligent cleaning and fusion of multimodal data, use LiDAR point cloud and hyperspectral data to collaboratively invert the three-dimensional structural parameters of single trees, combine spectral angle mapping to eliminate errors, build a digital twin model for dynamic simulation, and conduct spatial precise accounting and risk assessment through geographic information systems.
The accuracy of single-tree scale calculation has been improved to sub-meter level, solving the problem of capturing the temporal and spatial heterogeneity of growth. Through full life cycle risk prediction and intelligent decision-making, the management response time has been improved by more than 50%.
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Figure CN120655364A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of digital management of ecological resources, and more specifically, to a forest ecological product value accounting method based on remote sensing and geographic information system. Background Art
[0002] At present, from the precise implementation of the ecological compensation mechanism, to the scientific compilation of the forest resource balance sheet, to the standardized operation of the carbon sink trading market, all links have strict requirements on the accuracy and timeliness of the accounting system.
[0003] However, the current development of accounting technology has reached a bottleneck. As the core link in the refined management of forest resources, the accounting of the value of forest ecological products is currently facing the technical difficulty that traditional methods rely on ground sampling and static models, making it difficult to achieve accurate temporal and spatial dynamic accounting at the scale of individual trees.
[0004] Existing technologies are limited by the inaccuracy of air-space-ground data fusion, poor regional adaptability of growth models, and a lack of multi-dimensional risk assessment. Consequently, accounting results fail to accurately reflect the structural changes, value fluctuations, and potential risks of individual trees throughout their lifecycles, hindering the scientific validity of ecological compensation and the efficiency of resource optimization. This technological lag is increasingly evident when addressing dynamic challenges such as the frequent occurrence of extreme climate events and the intensification of forest pests and diseases. In light of this, we propose a method for calculating the value of forest ecological products based on remote sensing and geographic information systems. Summary of the Invention
[0005] The purpose of this invention is to provide a forest ecological product value accounting method based on remote sensing and geographic information system to solve the technical problems of low efficiency, insufficient data accuracy and difficulty in achieving dynamic monitoring and multi-dimensional value comprehensive evaluation of traditional accounting methods.
[0006] To solve the above technical problems, the present invention provides the following technical solution: a method for calculating the value of forest ecological products based on remote sensing and geographic information system, comprising the following steps: S1: Build an air-space-ground acquisition network using satellites, drones, and ground sensors to perform intelligent cleaning, registration, and standardized preprocessing of multimodal data; S2: Use multi-temporal remote sensing data to invert the three-dimensional structural parameters of the forest and construct a digital twin model to dynamically simulate its full-cycle growth process; S3: Use geographic information systems to accurately calculate the spatial distribution of single tree yields and establish a quality grading system based on spectral characteristics; S4: By building a dynamic model, we can accurately calculate the cost input and benefit output of each tree at each growth stage, and use risk assessment methods to predict potential economic risks; S5: Build a four-dimensional visualization platform covering time, space, value, and ecological indicators, integrate data analysis models, and provide intelligent decision-making support for the full life cycle management of individual trees.
[0007] This invention addresses the problems of low spatial resolution and poor temporal continuity in traditional methods by constructing an integrated air-space-ground monitoring network, combining spatiotemporal data fusion algorithms to achieve high-frequency and high-precision data acquisition, collaboratively inverting the three-dimensional structural parameters of individual trees through LiDAR point clouds and hyperspectral data, and using spectral angle mapping to eliminate error data, thereby improving the accuracy of individual tree scale calculation to sub-meter level, effectively solving the problem of capturing the spatiotemporal heterogeneity of individual tree growth.
[0008] Preferably, step S1 specifically includes the following steps: S101: Construction of a satellite-UAV-ground IoT trinity monitoring network; Among them, satellites use Sentinel-2 and PlanetScope constellations to acquire multi-band data, drones are equipped with hyperspectral cameras to obtain high-resolution images, and smart monitoring stations are deployed on the ground to collect environmental data; S102: Spatiotemporal registration and intelligent fusion of multi-source heterogeneous data, including deep learning-based image registration and spatiotemporal data fusion algorithms, and data quality control through spectral angle mapping algorithms.
[0009] Preferably, the spatiotemporal data fusion adopts the STARFM algorithm, and the formula is: ; Where, For the target moment image, As the reference time image, and is the weight coefficient, and They represent the number of images at the reference moment involved in the fusion and the number of reflectivity changes, For the The reflectivity is arrive The amount of change at a moment.
[0010] Preferably, step S2 specifically includes the following steps: S201: Utilize LiDAR point cloud and hyperspectral data to collaboratively extract individual tree parameters, and apply algorithms to accurately invert and deeply analyze individual tree parameters; S202: Utilize plant physiological and ecological principles and combine environmental variables to construct a digital twin model of single tree growth.
[0011] Preferably, the digital twin model of single tree growth consists of three parts: light energy utilization model, carbon allocation model and spatial heterogeneity correction. The spatial heterogeneity correction is based on regional geographical differences to accurately calibrate the spatial dimension of single tree ecological value accounting.
[0012] Preferably, the single tree parameters include tree height 、Crown width and ground diameter ; tree height : , where is the canopy height model, is the coefficient of determination, is the root mean square error; Crown width : , where is the crown projection area; Ground diameter : , where is the red edge band reflectivity.
[0013] Preferably, step S3 specifically includes the following steps: S301: Three-dimensional spatial interpolation and administrative unit output allocation; S302: Quality grading and market value assessment based on spectral characteristics; Spectral feature extraction: extract spectral parameters; Gradient boosting tree classification: establish a quality grading model, use 10-fold cross validation, and achieve a classification accuracy of ≥88%; Market value assessment: Establishing a value assessment model: ; Where, For quality grade, the impact of ground diameter, tree height and quality grade on value is comprehensively considered.
[0014] Preferably, the step S301 specifically includes the following steps: The biomass distribution map was generated by using collaborative Kriging interpolation. The observed biomass values of the sampling points in the region were set to , the auxiliary variable observation value is , for the point to be estimated , its biomass Cokriging estimate of It can be expressed as: ; Where, and are the weight coefficients of biomass observations and auxiliary variable observations, is the biomass, is an auxiliary variable; And construct a weight distribution model based on topography, soil and management level.
[0015] Preferably, step S4 specifically includes the following steps: S401: Establish direct cost dynamic model and indirect cost dynamic model and use Monte Carlo simulation to analyze the sensitivity index of each cost factor; S402: Predict future market price trends based on the SARIMA model and generate regional price distribution through kernel density estimation. The formula is: ; Where, is the price density, It is The coordinates of the observation points, is the number of observation points, is the bandwidth, is the kernel function.
[0016] Preferably, step S5 specifically includes the following steps: S501: Space-time cube construction and virtual reality expression; Construct and store value data cubes containing space and time; Develop interactive 3D maps that support multi-scale browsing, attribute query, and historical backtracking; Develop a mobile AR application based on Unity3D to achieve real-time acquisition of individual tree value information through on-site scanning; S502: Eco-compensation decision-making adopts a multi-objective optimization model: ; Where, 、 、 is the weight coefficient, For ecological benefits, For economic benefits, For social benefits; The NSGA-II algorithm is used to solve the Pareto optimal solution set.
[0017] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention addresses the problems of low spatial resolution and poor temporal continuity in traditional methods by constructing an integrated air-space-ground monitoring network. It combines a spatiotemporal data fusion algorithm to achieve high-frequency, high-precision data acquisition, collaboratively inverts the three-dimensional structural parameters of individual trees through LiDAR point clouds and hyperspectral data, and uses spectral angle mapping to eliminate error data, thereby improving the accuracy of individual tree scale calculations to sub-meter levels, effectively solving the problem of capturing the spatiotemporal heterogeneity of individual tree growth.
[0018] 2. The present invention also constructs a regional adaptive growth simulation and value calibration system based on high-precision calculation results at the single-tree scale to address the defect of existing models that are insufficiently adaptable to geographical differences. It quantifies the photosynthetic process through the light energy utilization model and the carbon allocation model, introduces the terrain moisture index, solar radiation index and management level index, uses co-kriging interpolation to generate a high-resolution biomass distribution map, and corrects the growth simulation deviations of different terrains and forest types, further reducing the regional-scale value calculation error.
[0019] 3. This invention also establishes a closed loop of risk prediction and intelligent decision-making throughout the entire lifecycle. Monte Carlo simulation quantifies the sensitivity index of cost factors such as fertilizer and labor, combines it with the SARIMA model to predict market price trends, and uses kernel density estimation to generate regional price distributions. Based on a four-dimensional visualization platform, a multi-objective optimization model is integrated to seek a Pareto optimal solution among ecological benefits, economic benefits, and social stability. This enables intelligent decision-making throughout the entire chain of "data collection - growth simulation - risk warning - optimization," improving management response time by over 50%. BRIEF DESCRIPTION OF THE DRAWINGS
[0020] Figure 1 It is a structural schematic diagram of the present invention. DETAILED DESCRIPTION
[0021] like Figure 1 As shown, the present invention relates to a forest ecological product value accounting method based on remote sensing and geographic information system, comprising the following steps: S1: Build an air-space-ground acquisition network using satellites, drones, and ground sensors to perform intelligent cleaning, registration, and standardized preprocessing of multimodal data; In an embodiment of the present invention, step S1 specifically includes the following steps: S101: Construction of a satellite-UAV-ground IoT trinity monitoring network; Satellite remote sensing data collection: Deployment of the Sentinel-2 (10m resolution) and PlanetScope (3m resolution) satellite constellations provides full-coverage monitoring every five days, acquiring data in five wavelength bands: blue (490nm, used for preliminary identification of water bodies and vegetation cover), green (560nm, reflecting vegetation growth status), red (665nm, related to chlorophyll absorption characteristics), red-edge (705nm, sensitive to vegetation health), and near-infrared (842nm, used for estimating vegetation biomass). UAV hyperspectral data acquisition: A fixed-wing UAV equipped with a Headwall Nano-Hyperspec camera was used to acquire hyperspectral images with a spectral range of 400-1000nm and a spatial resolution of 0.1m. The flight altitude was 300m (balancing coverage and resolution), and the revisit period was 15 days (to meet the needs of dynamic monitoring of individual tree growth cycles). Ground IoT deployment: 50 smart monitoring stations were deployed in typical sample plots, equipped with soil moisture sensors (EC-5, real-time monitoring of soil moisture content), light intensity sensors (PAR-LITE, obtaining photosynthetically active radiation), and air temperature and pressure sensors (BME280, recording ambient temperature, humidity, and air pressure). Data collection frequency was once an hour (to ensure the continuity of environmental data). S102: Spatiotemporal registration and intelligent fusion of multi-source heterogeneous data; Image registration based on deep learning: The U-Net++ model is used to automatically register images of different phases and resolutions, with a registration accuracy of <0.5 pixels (ensuring data spatial consistency); Spatiotemporal data fusion: Apply the STARFM (Spatial and Temporal Adaptive Reflectance Fusion Model) algorithm to generate a spatiotemporally continuous high-resolution dataset. The core formula of the STARFM algorithm is as follows: ; Where, For the target moment image, As the reference time image, and is the weight coefficient (dynamically adjusted according to data relevance), and They represent the number of images at the reference moment involved in the fusion and the number of reflectivity changes, For the The reflectivity is arrive The amount of change at a moment; Data quality control: Outlier detection is performed using the spectral angle mapping (SAM) algorithm, and samples with errors > 5% are eliminated to ensure data reliability; S2: Utilize multi-temporal remote sensing data to invert three-dimensional structural parameters such as individual tree crown width, tree height, and branch volume, and construct a digital twin model to dynamically simulate its full growth cycle; In an embodiment of the present invention, step S2 specifically includes the following steps: S201: Extraction of single tree parameters using LiDAR point cloud and hyperspectral data; Point cloud preprocessing: Use the Cloth Simulation Filter (CSF) algorithm to separate ground points from vegetation points. Parameter settings: cloth resolution = 0.5m (controls filter fineness), maximum number of iterations = 100 (avoids excessive iterations), classification accuracy ≥ 98% (ensures accuracy of vegetation point extraction); Single tree segmentation: Combine the watershed algorithm and the graph-cut algorithm to achieve single tree segmentation, energy function The expression is: , where is a data item used to measure pixels Similarity to the target, is a smoothing term used to constrain adjacent pixels and consistency, represents the set of all adjacent pixel pairs; Structural parameter inversion: Use algorithms to accurately invert and deeply analyze single wood parameters; In the embodiment of the present invention, the single tree parameters include tree height 、Crown width and ground diameter ; tree height : , where is the canopy height model, is the coefficient of determination, indicating that the model explains 91% of the variation in tree height. is the root mean square error, indicating that the average error between the model prediction value and the actual value is 0.32 meters; Crown width : , where is the crown projection area, is the coefficient of determination, indicating that the model can explain 87% of the crown width variation. is the root mean square error, indicating that the predicted value differs from the actual value by an average of 0.25 meters; Ground diameter : , where is the red edge band reflectivity, is the coefficient of determination, indicating that the model can explain 83% of the variation in ground diameter; S202: Using plant physiological and ecological principles and combining environmental variables, construct a digital twin model of single tree growth; In an embodiment of the present invention, the digital twin model of single tree growth consists of three parts: light energy utilization model, carbon allocation model and spatial heterogeneity correction. By quantifying key ecological processes, it achieves accurate simulation of single tree growth.
[0022] Light energy utilization model: , where is the light energy conversion efficiency, is photosynthetically active radiation, 、 、 are temperature, water, and carbon dioxide stress factors (reflecting environmental limitations on photosynthesis); Carbon allocation model: , where To maintain respiration (carbon consumed by plants to maintain life activities), respiration for growth (carbon consumption for growth); Spatial heterogeneity correction: Based on regional geographical differences, the spatial dimension of the ecological value accounting of individual trees is accurately calibrated: Topographic Wetness Index: , where is the upslope catchment area per unit contour length, is the slope; Solar radiation index: , where is the solar incidence angle, is the distance from the sun; S3: Use geographic information systems to accurately calculate the spatial distribution of individual tree yields and establish a quality grading system based on spectral characteristics to achieve scientific assessment of yield and quality; In an embodiment of the present invention, step S3 specifically includes the following steps: S301: Three-dimensional spatial interpolation and administrative unit output allocation; Co-Kriging interpolation: Using the tree height and remote sensing spectral features extracted by LiDAR, co-Kriging interpolation is used to generate a 10m resolution biomass distribution map. The biomass observation value of the sampling points in the area is set to , the auxiliary variable observation value is ( ), for the point to be estimated , its biomass Cokriging estimate of It can be expressed as: ; Where, and are the weight coefficients of biomass observations and auxiliary variable observations, respectively, which are obtained by solving the Kriging equations to minimize the estimated variance. is the biomass, Auxiliary variables (such as NDVI Normalized Vegetation Index and EVI Enhanced Vegetation Index, which help improve interpolation accuracy); Weight distribution model: Construct a weight distribution model based on topography, soil, and management level, and regional weight The calculation formula is: , where is the topographic wetness index, is the solar radiation index, is the management level index (determined by remote sensing identification of irrigation facilities, fertilization frequency, etc.), 、 、 is the weight coefficient, determined by analytic hierarchy process or regression analysis; S302: Quality grading and market value assessment based on spectral characteristics; Spectral feature extraction: Extract 12 spectral parameters including red edge position (REP, reflecting the physiological state of vegetation), chlorophyll index (CIred-edge, quantifying chlorophyll content), and nitrogen reflectance index (NRI, assessing nitrogen nutrition level); Gradient boosting tree classification: Establish a quality grading model, use 10-fold cross validation, and achieve a classification accuracy of ≥88% (to ensure the reliability of quality grading); Market valuation: establishing a valuation model , taking into account the ground diameter ( , unit: cm), tree height ( , unit: m) and quality grade ( , 1-5 levels) on value; S4: By building a dynamic model, we can accurately calculate the cost input and benefit output of each tree at each growth stage, and use risk assessment methods to predict potential economic risks; In an embodiment of the present invention, step S4 specifically includes the following steps: S401: Spatiotemporal dynamic cost accounting and sensitivity analysis; Direct cost dynamic model: , where is the number of saplings, is the fertilizer efficiency index, is the labor cost index, The amount of pesticide used, is the planting area; Indirect cost dynamic model: , where is the location coefficient, is the pest risk index, The cost of ecological restoration; Sensitivity analysis: Monte Carlo simulation is used to analyze the sensitivity index of each cost factor. To measure the The degree of influence of each cost factor on the total cost is calculated as follows: , where It is because of The change in total cost caused by the change of each cost factor is is the original total cost, It is The change in the cost factor, No. The original value of each cost element; S402: Market value intelligent prediction and risk assessment; Time series analysis: Predict market price trends for the next three years based on the SARIMA model. The general expression of the SARIMA model is: , where is the price series, is the backshift operator, For seasonal cycles, and is an autoregressive polynomial, and is the moving average polynomial, and are seasonal and non-seasonal difference orders, respectively. is a white noise sequence; Spatial price surface: Generate regional price distribution through kernel density estimation (KDE), the formula is: ; Where, is the price density, It is The coordinates of the observation points, is the number of observation points, is the bandwidth, is the kernel function; S5: Build a four-dimensional visualization platform covering time, space, value, and ecological indicators, integrate data analysis models, and provide intelligent decision-making support for the full life cycle management of individual trees; In an embodiment of the present invention, step S5 specifically includes the following steps: S501: Space-time cube construction and virtual reality expression; Four-dimensional data model: Constructs a value data cube containing space (x, y, z) and time (t), and stores it in HDF5 format (efficiently processing massive multidimensional data); WebGL 3D visualization: Develop interactive 3D maps that support multi-scale browsing, attribute query, and historical backtracking, with a frame rate of ≥30fps (to ensure smooth visualization); Augmented Reality (AR) Application: Develop a mobile AR application based on Unity3D to enable real-time scanning and acquisition of individual tree value information; S502: Multi-objective optimization decision-making model for ecological compensation; Multi-objective optimization: , where 、 、 is the weight coefficient, For ecological benefits, For economic benefits, For social benefits; Pareto optimal solution set: Solved using the NSGA-II algorithm, population size = 100, number of iterations = 200 (balancing computational efficiency and optimization effect).
[0023] The embodiments disclosed in the present invention are preferred embodiments, but are not limited to them. Ordinary technicians in this field can easily understand the spirit of the present invention based on the above embodiments and make different extensions and changes. As long as they do not deviate from the spirit of the present invention, they are all within the scope of protection of the present invention.
Claims
1. A method for calculating the value of forest ecological products based on remote sensing and geographic information system, characterized in that: The following steps are involved: S1: Build an air-space-ground acquisition network using satellites, drones, and ground sensors to perform intelligent cleaning, registration, and standardized preprocessing of multimodal data; S2: Use multi-temporal remote sensing data to invert the three-dimensional structural parameters of the forest and construct a digital twin model to dynamically simulate its full-cycle growth process; S3: Use geographic information systems to accurately calculate the spatial distribution of single tree yields and establish a quality grading system based on spectral characteristics; S4: By building a dynamic model, we can accurately calculate the cost input and benefit output of each tree at each growth stage, and use risk assessment methods to predict potential economic risks; S5: Build a four-dimensional visualization platform covering time, space, value, and ecological indicators, integrate data analysis models, and provide intelligent decision-making support for the full life cycle management of individual trees.
2. The forest ecological product value accounting method based on remote sensing and geographic information system according to claim 1 is characterized in that: Step S1 specifically includes the following steps: S101: Construction of a satellite-UAV-ground IoT trinity monitoring network; Among them, satellites use Sentinel-2 and PlanetScope constellations to acquire multi-band data, drones are equipped with hyperspectral cameras to obtain high-resolution images, and smart monitoring stations are deployed on the ground to collect environmental data; S102: Spatiotemporal registration and intelligent fusion of multi-source heterogeneous data, including deep learning-based image registration and spatiotemporal data fusion algorithms, and data quality control through spectral angle mapping algorithms.
3. The forest ecological product value accounting method based on remote sensing and geographic information system according to claim 2 is characterized in that: The spatiotemporal data fusion adopts the STARFM algorithm, and the formula is: ; Where, For the target moment image, As the reference time image, and is the weight coefficient, and They represent the number of images at the reference moment involved in the fusion and the number of reflectivity changes, For the The reflectivity is arrive The amount of change at a moment.
4. The forest ecological product value accounting method based on remote sensing and geographic information system according to claim 1 is characterized in that: Step S2 specifically includes the following steps: S201: Utilize LiDAR point cloud and hyperspectral data to collaboratively extract individual tree parameters, and apply algorithms to accurately invert and deeply analyze individual tree parameters; S202: Utilize plant physiological and ecological principles and combine environmental variables to construct a digital twin model of single tree growth.
5. The forest ecological product value accounting method based on remote sensing and geographic information system according to claim 4 is characterized in that: The digital twin model of single tree growth consists of three parts: light energy utilization model, carbon allocation model and spatial heterogeneity correction. The spatial heterogeneity correction is based on regional geographical differences to accurately calibrate the spatial dimension of single tree ecological value accounting.
6. The forest ecological product value accounting method based on remote sensing and geographic information system according to claim 5 is characterized in that: The single tree parameters include tree height 、Crown width and ground diameter ; tree height : , where is the canopy height model, is the coefficient of determination, is the root mean square error; Crown width : , where is the crown projection area; Ground diameter : , where is the red edge band reflectivity.
7. The forest ecological product value accounting method based on remote sensing and geographic information system according to claim 1 is characterized in that: Step S3 specifically includes the following steps: S301: Three-dimensional spatial interpolation and administrative unit output allocation; S302: Quality grading and market value assessment based on spectral characteristics; Spectral feature extraction: extract spectral parameters; Gradient boosting tree classification: establish a quality grading model, use 10-fold cross validation, and achieve a classification accuracy of ≥88%; Market value assessment: Establishing a value assessment model: ; Where, For quality grade, the impact of ground diameter, tree height and quality grade on value is comprehensively considered.
8. The forest ecological product value accounting method based on remote sensing and geographic information system according to claim 7 is characterized in that: The step S301 specifically includes the following steps: The biomass distribution map was generated by using collaborative Kriging interpolation. The observed biomass values of the sampling points in the region were set to , the auxiliary variable observation value is , for the point to be estimated , its biomass Cokriging estimate of It can be expressed as: ; Where, and are the weight coefficients of biomass observations and auxiliary variable observations, is the biomass, is an auxiliary variable; And construct a weight distribution model based on topography, soil and management level.
9. The forest ecological product value accounting method based on remote sensing and geographic information system according to claim 1 is characterized in that: Step S4 specifically includes the following steps: S401: Establish direct cost dynamic model and indirect cost dynamic model and use Monte Carlo simulation to analyze the sensitivity index of each cost factor; S402: Predict future market price trends based on the SARIMA model and generate regional price distribution through kernel density estimation. The formula is: ; Where, is the price density, It is The coordinates of the observation points, is the number of observation points, is the bandwidth, is the kernel function.
10. The forest ecological product value accounting method based on remote sensing and geographic information system according to claim 1 is characterized in that: Step S5 specifically includes the following steps: S501: Space-time cube construction and virtual reality expression; Construct and store value data cubes containing space and time; Develop interactive 3D maps that support multi-scale browsing, attribute query, and historical backtracking; Develop a mobile AR application based on Unity3D to achieve real-time acquisition of individual tree value information through on-site scanning; S502: Eco-compensation decision-making adopts a multi-objective optimization model: ; Where, 、 、 is the weight coefficient, For ecological benefits, For economic benefits, For social benefits; The NSGA-II algorithm is used to solve the Pareto optimal solution set.