A method for optimizing the layout of low-impact development facilities in coal ports considering underlying surface randomness

Abstract

The present invention belongs to the field of green port planning and operation, and discloses a method for optimizing the layout of low-impact development facilities in coal ports that takes into account the randomness of the underlying surface. The method comprises the following steps: collecting data; establishing a rainwater runoff model; constructing a response matrix; generating representative underlying surface scenarios; establishing a multi-objective optimization model; solving the optimization model; and determining the optimal layout plan. The method for optimizing the layout of low-impact development facilities in coal ports of the present invention provides a scientific basis for the planning and construction of rainwater collection facilities in coal ports, takes into account the randomness of the underlying surface types in coal ports, and improves the accuracy and adaptability of the layout plan of rainwater collection facilities. It helps to improve the efficiency of water resource utilization, reduce operating costs, and promote the construction of green ports.

Description

Technical Field

[0001] The present invention belongs to the field of green port planning and operation, relates to the layout optimization of rainwater collection facilities based on coal ports, and in particular to a method for optimizing the layout of low-impact development facilities in coal ports taking into account the randomness of the underlying surface. Background Art

[0002] As global water scarcity worsens, dust removal operations at ports, particularly coal ports, consume significant amounts of water, exacerbating regional water shortages. Currently, coal ports primarily utilize gray water systems such as sewers for rainwater recovery, which are unable to cope with the variability in runoff coefficients caused by operations within coal yards. Low-impact development (LID) facilities, with their decentralized layout and large-scale collection capabilities, are widely used in urban rainwater recovery and green city development. Their application in densely populated areas such as ports, chemical parks, and logistics parks is becoming a trend. Shuster et al.'s 2014 paper, "Residential Demolition and Its Impact on Vacant Lot Hydrology: Implications for the Management of Stormwater and Sewer System Overflows," noted that existing LID facility layout optimization methods often assume a fixed underlying surface type. Consequently, there is a lack of relevant technical support for the layout of LID facilities in coal ports, and failure to fully consider the randomness of the underlying surface in coal ports has resulted in poor practical application.

[0003] Therefore, a layout optimization method for port rainwater collection facilities that considers the randomness of the underlying surface is urgently needed to improve rainwater collection efficiency and reduce construction costs. Summary of the Invention

[0004] This paper aims to provide a method for optimizing the layout of low-impact development facilities at coal ports that considers the randomness of underlying surfaces. By incorporating random variations in underlying surface types and combining a multi-objective optimization model with a surrogate model, this method achieves efficient optimization of the layout of rainwater harvesting facilities at coal ports. A Nash bargaining solution is used to determine the optimal layout of low-impact development facilities at coal ports, targeting multiple objectives. The optimization method comprises four main stages: First, stormwater runoff at the coal port is simulated using SWMM. Based on this, a response matrix is ​​established as a surrogate model to improve computational efficiency. Second, a multi-objective stochastic optimization model for the layout of low-impact development facilities at the coal port is constructed, considering both port operator investment and rainfall runoff control. The runoff simulation results are then used to evaluate the impact of random underlying surface types on stormwater runoff. Based on a clustering algorithm, cluster analysis is performed on historical storage yard data to generate five representative underlying surface type scenarios. Finally, the NSGA-2 algorithm is used to identify trade-offs between two objective functions under representative surface types. The Nash bargaining solution is used to capture the interests of decision makers, thereby determining an appropriate layout of rainwater harvesting facilities on the Pareto front.

[0005] The technical solution of the present invention:

[0006] A method for optimizing the layout of low-impact development facilities at coal ports considering the randomness of the underlying surface is proposed. The steps are as follows:

[0007] Step 1: Data collection and preprocessing;

[0008] (1) Collect geographical information of the coal port, including topographic maps of the port and functional division maps of different areas;

[0009] (2) Collect meteorological data, including rainfall amount, rainfall intensity and rainfall duration over many years;

[0010] (3) Obtain a layout diagram of the stormwater pipe network, including the distribution, pipe diameter, and slope of the existing stormwater pipe network within the port;

[0011] (4) Collect runoff coefficient data for different underlying surface types, including coal piles, concrete floors, soil, and green areas under different rainfall conditions;

[0012] (5) Collect data on the construction costs and annual operating costs of low-impact development facilities, including green roofs, grass-lined trenches, and permeable pavement;

[0013] (6) Collect historical data on coal port yard storage, i.e., the stacking and unloading operations of various types of cargo in the yard;

[0014] (7) Collecting actual observation data on historical rainwater runoff at coal ports;

[0015] Organize and analyze the collected data and check the completeness and accuracy of the data;

[0016] Step 2: Establish a rainwater runoff model;

[0017] The stormwater management model (SWMM) was used to dynamically simulate rainfall runoff processes and the hydrological performance of low-impact development facilities. Based on the collected geographic information of the coal port, meteorological data, stormwater network layout diagrams, and runoff coefficient data for different underlying surface types, an input file for the stormwater management model was established, including the division of subcatchments, rainfall patterns and durations, stormwater network connectivity, and the configuration of different underlying surface types.

[0018] Verify the effectiveness of the stormwater management model by comparing it with the actual observation data of historical stormwater runoff at the coal port obtained in step 1, and adjust the parameters of the stormwater management model so that the stormwater management model accurately simulates the changes in stormwater runoff at the coal port under different rainfall scenarios;

[0019] Step 3: Construct the response matrix;

[0020] Run the stormwater management model to simulate several low-impact development facility layout schemes, including type, location, and capacity. The model then calculates the runoff flow rates for different subcatchments under each low-impact development facility layout scheme, under various rainfall scenarios and underlying surface types. A response matrix is ​​constructed, in which rows represent different low-impact development facility layout schemes, and columns represent different combinations of subcatchment surface types and rainfall scenarios. The matrix elements represent the runoff flow rates for the subcatchments under each low-impact development facility layout scheme and rainfall scenario. The total runoff volume under any low-impact development facility layout scheme is calculated using the response matrix.

[0021] The steps to construct the response matrix are as follows:

[0022] (1) For each low-impact development facility layout plan, a stormwater management model is required to be run once in the coal port study area to simulate runoff;

[0023] (2) For any low-impact development facility layout and rainfall scenario, a response matrix is ​​constructed, where the elements along the diagonal are the runoff of each subcatchment. ;

[0024] (3) Construct a decision vector for each low-impact development facility layout plan , where the elements are the area fractions allocated to each low-impact development in the subcatchment;

[0025] (4) Based on the input data of each subcatchment area, the subcatchment area matrix A is obtained;

[0026] (5) Construct a connectivity matrix , describing the upstream and downstream relationships of all subcatchments; if subcatchment j is located upstream of subcatchment i, then the off-diagonal elements in the connectivity matrix is equal to 1, otherwise it is zero, and specifies the diagonal elements ;

[0027] (6) Estimate the stormwater runoff flow at the outlet of each subcatchment by summing the runoff from each subcatchment and the stormwater runoff flow from all upstream sources:

[0028]

[0029] in, Indicates that the vector parameters are converted into a diagonal matrix, as in the above formula, the vector parameters and Perform diagonal matrix transformation, the diagonal elements in the diagonal matrix are ; is the correction factor for the low-impact development facility layout plan; is the duration of stormwater runoff simulation;

[0030] Step 4: Generate representative underlying surface type scenarios;

[0031] The K-medoids clustering algorithm was used to analyze the historical data of the coal port yard collected in step 1. The number of clusters generated by the clustering algorithm was set to 5. The sum of the distances between the underlying surface type data points and the centroid of the data set was searched and calculated, and the data points were divided into 5 clusters. The 5 real data centroids generated by the clustering operation are representative underlying surface type scenarios.

[0032] Step 5: Establish a multi-objective planning model;

[0033] The total investment cost of low-impact development facilities is used as objective function 1, including fixed costs, low-impact development facility construction costs, and operating costs throughout the entire life cycle. Considering the impact of different low-impact development facility types, locations, and areas on the total investment cost, the total runoff control rate of the coal port is used as objective function 2 to maximize the rainwater collection and control effect and reduce the impact of rainwater runoff on port operations and the surrounding environment. This is connected with the response matrix constructed in step 3 to form a multi-objective planning model based on the response matrix. The randomness of the underlying surface type is used as a constraint condition of the multi-objective planning model to ensure that the optimization results are feasible and effective under different underlying surface type scenarios. The objective function and constraints of the multi-objective planning model are expressed as follows:

[0034] (1) Objective function 1:

[0035]

[0036] in, The construction cost per unit area of ​​the lth type of low-impact development facility at the candidate location j in the ith subcatchment; The fixed cost required to deploy the lth low-impact development facility at candidate location j in the ith subcatchment; The operating cost per unit area required to deploy the lth type of low-impact development facility at candidate location j in the ith subcatchment; is the area of ​​the lth type of low-impact development facility to be arranged at the candidate location j in the ith subcatchment; is a 0-1 variable, representing whether the l-th type of low-impact development facility is arranged at the candidate location j of the i-th subcatchment; Life cycle of a Type 1 low-impact development facility; is the discount rate;

[0037] (2) Objective function 2:

[0038]

[0039] in, Representative Planting surface type scenario, Representative The probability of occurrence under the planting surface type scenario, represents the total runoff of subcatchment i when no low-impact development facilities are deployed, represents the total runoff of subcatchment i after the deployment of low-impact development facilities; t represents the simulation time step;

[0040]

[0041] The above formula calculates the total runoff of subcatchment i before the construction of the low-impact development facility;

[0042] in, and is the slope function and roughness coefficient function under the kth underlying surface type scenario; is the area of ​​subcatchment i; is the equivalent width of subcatchment i; For the rainfall scenarios;

[0043]

[0044] The above formula represents the total runoff of subcatchment i after the construction of low-impact development facilities;

[0045]

[0046] The above formula defines the functional expression of the runoff of subcatchment i in time step t;

[0047] in, is the slope of subcatchment i, is the roughness coefficient of subcatchment i;

[0048]

[0049]

[0050] The above formula represents the relationship between slope, roughness coefficient and surface type, where u represents the u-th surface type; represents the slope; represents the roughness coefficient;

[0051] (3) Constraints:

[0052] (3.1) Regional area constraints:

[0053]

[0054]

[0055]

[0056]

[0057]

[0058] They are the relationship constraints between the layout area of ​​low-impact facilities, the layout area of ​​low-impact development facilities and the area of ​​sub-catchment; is the area occupied by u land surface types at candidate location j in the ith subcatchment;

[0059] (3.2) Low-impact development facility type constraints:

[0060]

[0061]

[0062] Require that the type of rainwater collection facilities match the type of ground surface; Indicates whether there are areas of u surface types at the candidate location j of the i-th subcatchment;

[0063] (3.3) Flow Constraints:

[0064]

[0065] Ensure that the runoff of each subcatchment at each time step is within a safe range, and are the lower and upper limits of runoff;

[0066]

[0067] Define the relationship between peak runoff and runoff at each time step, where is the peak runoff of the ith subcatchment;

[0068] (3.4) Logical constraints:

[0069]

[0070] Ensure that area values ​​for each low-impact development facility are obtained only after the facility is built at the candidate location. A number representing infinity;

[0071] Step 6: Solve the optimization model;

[0072] NSGA-2 was used as the optimization algorithm. The algorithm parameters were set, NSGA-2 was run, and the multi-objective optimization model was solved to obtain the Pareto frontier under different underlying surface types, that is, a set of low-impact development facility layout plans that achieved a balance between total investment cost and total runoff control rate of the coal port.

[0073] Step 7: Determine the optimal low-impact development facility layout plan;

[0074] Select the optimal layout plan on the Pareto front through Nash bargaining solution; set the distance parameter of Nash bargaining solution , find the point on the Pareto front that is closest to the ideal solution, which is the optimal layout solution;

[0075] The Nash bargaining theory is used to simulate the negotiation process between stakeholders and select a final solution from a set of non-dominant solutions, which is expressed as the following formula:

[0076]

[0077]

[0078] in, is the distance function; is the distance parameter; and To arrange the plan, that is, the solution; and The meaning of is the two objective functions in the model; is a set on the Pareto frontier. Given A certain value of , the point closest to the ideal point, is the Nash bargaining solution; if ,exist In the case of , the two objectives have the same weight; if ,exist , targets with larger deviations have greater weights.

[0079] The system of the present invention includes a data processing module, a model building module, a scenario generation module, a response matrix construction module, an optimization model solving module and a layout scheme determination module. The modules work together to optimize the layout of rainwater collection facilities in coal ports.

[0080] Beneficial effects of the present invention:

[0081] 1. The randomness of the underlying surface type of the coal port is taken into account, which improves the accuracy and adaptability of the layout plan of rainwater collection facilities.

[0082] 2. The response matrix improves the computational efficiency of the multi-objective optimization model, and a reasonable layout solution can be obtained in a shorter time.

[0083] 3. Use Nash bargaining solution to balance the goals of different stakeholders, making the final layout plan more feasible and acceptable.

[0084] 4. The method and system of the present invention provide a scientific basis for the planning and construction of rainwater collection facilities in coal ports, which helps to improve water resource utilization efficiency, reduce operating costs, and promote green port construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] Figure 1 It is a flow chart of the low-impact development layout optimization model for coal ports.

[0086] Figure 2 It is a schematic diagram of each functional area in the study area.

[0087] Figure 3 This is a schematic diagram of the sub-catchment division of the study area. DETAILED DESCRIPTION

[0088] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0089] Taking the optimization of rainwater collection facilities layout at a large coal port in northern China as an example, the optimization model is divided into five steps. Figure 1 shown.

[0090] Step 1: Data collection and preprocessing

[0091] We collected geographic information for the case coal port (including topographic maps of the port and functional zoning maps of different areas), meteorological data (including rainfall, rainfall intensity, and rainfall duration over multiple years), stormwater network layouts, runoff coefficient data for different underlying surface types (coal piles, concrete floors, bare soil, and green areas), and historical coal port yard storage data. We collated and analyzed the collected historical data, checking its completeness and accuracy, and addressing any missing or abnormal data to ensure data quality.

[0092] The study area includes the first and second phases of the case coal port project, covering an area of ​​approximately 20 km 2 The research area is divided into three parts: coal terminal front area, coal yard area and coal terminal auxiliary area. Each functional area in the research area is as follows Figure 2 As shown. 1 represents soil; 2 represents green space; 3 represents concrete ground; 4 represents main road; 5 represents roof; 6 represents coal pile; 7 represents auxiliary operation area; 8 represents yard area; 9 represents dock front operation area. The layout map and rainwater pipe network map of the study area were obtained as the basic data for regional rainwater runoff simulation. The study area was divided into sub-catchment areas. The sub-catchment area division topographic map is shown as follows Figure 3 The areas of the 12 coal storage areas are shown in Table 1 below, and the historical runoff coefficient data for different area types are shown in Table 2 below:

[0093] Table 1 Area data of coal yard area

[0094]

[0095] Table 2 Historical runoff coefficient data for different regional types in the study area

[0096]

[0097] The rainfall is designed to have a return period of 1 year, 5 years, 10 years, 50 years and 100 years, and a duration of 2 hours, which matches the average operation time of a single stacking or reclaiming task in the coal yard. The rainstorm intensity duration-frequency formula in the study area is:

[0098]

[0099] where q is the rainfall intensity (mm / min), P is the rainfall return period (years), and t is the rainfall duration (minutes).

[0100] The port operator derived runoff coefficients for specific subsets of the study area based on previous intermittent rainfall runoff monitoring data, which are shown in Table 3 below.

[0101] Table 3 Runoff coefficients of some subsets of the study area

[0102]

[0103] Step 2: Establishing a stormwater runoff model and response matrix

[0104] A stormwater management model was used to simulate the coal port's stormwater runoff under different underlying surface scenarios. The model used collected geographic information, meteorological data, and a stormwater network layout diagram as input, including subcatchment delineation, stormwater network connections, and the configuration of different underlying surface types. The model parameters were adjusted based on comparisons with actual stormwater runoff observations at the coal port.

[0105] A sub-catchment was selected and three low-impact development facilities were used to verify the effectiveness of the response matrix proxy model. Under a 1-year 2-hour design rainfall, the effectiveness of the proxy model was checked without any facility arrangement. The relationship between the flow of the sub-catchment and the area of ​​a single low-impact development facility was nearly linear, and R 2 A value > 0.95 indicates that the response matrix effectively simulates the outcomes of low-impact development facilities during rainfall events. The effectiveness of the surrogate model was verified in scenarios involving multiple facility placements. For all low-impact development facility combinations, the Nash-Sutcliffe efficiency coefficients were close to 1, indicating that the response matrix is ​​effective.

[0106] Step 3: Generate representative underlying surface scenarios

[0107] A clustering algorithm was used to analyze historical storage data for the coal port yard, classifying similar underlying surface types into the same category and generating five representative underlying surface scenarios. The clustering algorithm was used to select key watersheds and observe representative water levels within each water level interval. The clustering results for all subset domain hydrographs are shown in Table 4 below.

[0108] Table 4 Clustering results of all subset domain process lines in the study area

[0109]

[0110] By changing the proportion of the stockpile area occupied by the coal pile, the impact of the underlying surface changes on the coal port's rainwater runoff, i.e., the utilization rate of the stockpile area, was analyzed, and the rainwater runoff process of the stockpile was simulated. Under a 1-year 2-hour design storm, 11 utilization rate scenarios were established, ranging from 0% to 100%, with equal intervals (10%). As the coal stockpile increased, the total runoff volume decreased significantly, and the area under the discharge curve gradually decreased. The incremental accumulation of coal in the stockpile caused the total runoff volume to increase from 48,000 m 3 Reduced to 14,100 m 3Based on a historical dataset of coal port yard operations in 2019, a clustering approach was used to generate representative scenarios for the yard's underlying surface types. The clustering method identified the five most likely coal and concrete underlying surface scenarios across the entire study area, as shown in Table 5. Scenario 4, which occurs more frequently, suggests that port operators can optimize the layout of rainwater collection facilities under this scenario. Therefore, Scenario 4 serves as a benchmark for discussing the necessity of considering the stochastic nature of the underlying surface.

[0111] Table 5 Representative scenarios of the underlying surface types of the storage yard (percentage of impermeability)

[0112]

[0113] Step 4: Establish and solve the multi-objective optimization model

[0114] Establish a multi-objective optimization model:

[0115] (1) Objective function setting

[0116] (1.1) Minimization of total investment cost: Calculate the total cost of low-impact development facilities, including construction costs, operation and maintenance costs, etc., taking into account the impact of factors such as different facility types, layout locations, and area on costs. The formula is:

[0117]

[0118] (1.2) Maximization of total runoff control rate: This aims to maximize the effect of rainwater collection and control, and reduce the impact of rainwater runoff on port operations and the surrounding environment. The formula is:

[0119]

[0120] (2) Constraint setting:

[0121] (2.1) Area Constraints: Ensure that the area of ​​low-impact development facilities does not exceed the available space.

[0122] (2.2) Facility type and underlying surface matching constraint: Ensure that the low-impact development facility type matches the underlying surface type.

[0123] (2.3) Flow constraint: Ensure that the runoff volume is within a safe range.

[0124] (2.4) Logical constraint: Ensure that the facility area has value only after construction is confirmed.

[0125] NSGA-2 was used to solve the multi-objective optimization model. The algorithm parameters were set as follows: population size of 100, maximum number of iterations of 300, crossover probability of 0.9, and mutation probability of 0.1. NSGA-2 was run to obtain the Pareto front for different underlying surface scenarios.

[0126] NSGA-2 was coded in Python 3.10, with parameters set to a maximum iteration size of 300, a crossover rate of 0.9, and a mutation rate of 0.1. Under a 1-year, 2-hour design storm, a 10% increase in runoff control before the inflection point increases the total cost by approximately RMB 2,302,950,000, while a 10% increase in runoff control after the inflection point increases the total cost by approximately RMB 6,092,930,000. Under scenario 4, port operators tend to choose a rainwater harvesting facility layout near the inflection point, with a total cost of approximately RMB 1.8 billion.

[0127] By combining five representative scenarios with the proposed model and method, corresponding Pareto fronts were generated. The following data were obtained: the solution sets for each scenario had consistent characteristics, with an inflection point in the Pareto front occurring between 48% and 50%, and a significant change in the relationship between cost and runoff control ratio before and after the inflection point; the total cost of low-impact development layout options changed across the five scenarios as the runoff control ratio ranged from 40% to 50%, with the inflection point also occurring between 48% and 50%; and the total runoff control ratio changed across the five scenarios as the total cost of low-impact development facilities ranged from RMB 500 million to RMB 3 billion.

[0128] Step 5: Determine the optimal layout solution

[0129] The optimal layout solution is selected on the Pareto front using a Nash bargaining solution. The distance parameter λ of the Nash bargaining solution is set and adjusted based on the level of concern expressed by different stakeholders, such as the coal port management and the government, regarding cost and runoff control. The optimal layout solution is the point on the Pareto front that is closest to the ideal solution.

[0130] A Nash bargaining solution is identified based on the distance parameter λ, balancing the total runoff control rate and the total cost of rainwater harvesting facilities. The resulting Pareto frontier and layout scheme are more cost-effective, as the investment cost is lower than that in scenario 4 for most rainwater harvesting rates. For example, at a 49% rainwater harvesting rate, the savings are approximately 100 million RMB. The Pareto frontier lies within its fluctuation range. Purple dots represent Nash bargaining solutions selected for different values ​​of λ, which exhibit similar characteristics and lie within the same fluctuation range. For example, the Pareto frontier for a one-year design rainfall and considering the randomness of the storage yard's underlying surface type yields a total runoff control rate of 50.98% and a total cost of low-impact development facilities of 1.636 billion RMB, respectively, when 3.1 ≤ λ ≤ 5.0. This solution demonstrates that, considering a representative scenario of the storage yard's underlying surface type, the expected values ​​of the total runoff control rate and cost overrun are 50.98% and 1.636 billion RMB, respectively.

Claims

1. A method for optimizing the layout of low-impact development facilities at a coal port considering the randomness of the underlying surface, characterized in that: Here are the steps: Step 1: Data collection and preprocessing; Collect geographic information, meteorological data, stormwater pipe network layout maps, runoff coefficient data for different underlying surface types, construction costs and annual operating costs of low-impact development facilities, historical data on coal port yard storage, and actual observation data on historical stormwater runoff at the coal port; Step 2: Establish a rainwater runoff model; The stormwater management model (SWMM) was used to dynamically simulate rainfall runoff processes and the hydrological performance of low-impact development facilities. Based on the collected geographic information of the coal port, meteorological data, stormwater network layout diagrams, and runoff coefficient data for different underlying surface types, an input file for the stormwater management model was established, including the division of subcatchments, rainfall patterns and durations, stormwater network connectivity, and the configuration of different underlying surface types. Step 3: Construct the response matrix; The stormwater management model was run to simulate several low-impact development (LID) layout scenarios, including type, location, and capacity. The runoff flow rates of different subcatchments under each LID layout scenario were obtained for each rainfall scenario and underlying surface type. A response matrix was constructed, in which rows represented different LID layout scenarios and columns represented different combinations of subcatchment surface types and rainfall scenarios. The elements in the matrix represented the runoff flow rates of the subcatchments under each LID layout scenario and rainfall scenario. The total runoff under any low-impact development facility layout plan is calculated through the response matrix; Step 4: Generate representative underlying surface type scenarios; The K-medoids clustering algorithm was used to analyze the historical data of the coal port yard collected in step 1. The number of clusters generated by the clustering algorithm was set to 5. The sum of the distances between the underlying surface type data points and the centroid of the data set was searched and calculated, and the data points were divided into 5 clusters. The 5 real data centroids generated by the clustering operation are representative underlying surface type scenarios. Step 5: Establish a multi-objective planning model; The total investment cost of low-impact development facilities is used as objective function 1, including fixed costs, low-impact development facility construction costs, and operating costs throughout the entire life cycle. The impact of different low-impact development facility types, locations, and areas on the total investment cost is considered. The total runoff control rate of the coal port is used as objective function 2 to maximize the rainwater collection and control effect and reduce the impact of rainwater runoff on port operations and the surrounding environment. Connecting with the response matrix constructed in step 3, a multi-objective planning model based on the response matrix is ​​formed. The randomness of the underlying surface type is used as a constraint condition of the multi-objective planning model to ensure that the optimization results are feasible and effective under different underlying surface type scenarios. Step 6: Solve the optimization model; NSGA-2 was used as the optimization algorithm. The algorithm parameters were set, NSGA-2 was run, and the multi-objective optimization model was solved to obtain the Pareto frontier under different underlying surface types, that is, a set of low-impact development facility layout plans that achieved a balance between total investment cost and total runoff control rate of the coal port. Step 7: Determine the optimal low-impact development facility layout plan; Select the optimal layout plan on the Pareto front through Nash bargaining solution; set the distance parameter of Nash bargaining solution , find the point on the Pareto front that is closest to the ideal solution, which is the optimal layout solution.

2. The method for optimizing the layout of low-impact development facilities at a coal port considering the randomness of the underlying surface according to claim 1 is characterized in that: (1) Collect geographical information of the coal port, including topographic maps of the port and functional division maps of different areas; (2) Collect meteorological data, including rainfall amount, rainfall intensity and rainfall duration over many years; (3) Obtain a layout diagram of the stormwater pipe network, including the distribution, pipe diameter, and slope of the existing stormwater pipe network within the port; (4) Collect runoff coefficient data for different underlying surface types, including coal piles, concrete floors, soil, and green areas under different rainfall conditions; (5) Collect data on the construction costs and annual operating costs of low-impact development facilities, including green roofs, grass-lined trenches, and permeable pavement; (6) Collect historical data on coal port yard storage, i.e., the stacking and unloading operations of various types of cargo in the yard; (7) Collecting actual observation data on historical rainwater runoff at coal ports; Organize and analyze the collected data and check the completeness and accuracy of the data.

3. The method for optimizing the layout of low-impact development facilities at a coal port considering the randomness of the underlying surface according to claim 2 is characterized in that: The steps to construct the response matrix are as follows: (1) For each low-impact development facility layout plan, a stormwater management model is required to be run once in the coal port study area to simulate runoff; (2) For any low-impact development facility layout and rainfall scenario, a response matrix is ​​constructed, where the elements along the diagonal are the runoff of each subcatchment. ; (3) Construct a decision vector for each low-impact development facility layout plan , where the elements are the area fractions allocated to each low-impact development in the subcatchment; (4) Based on the input data of each subcatchment area, the subcatchment area matrix A is obtained; (5) Construct a connectivity matrix , describing the upstream and downstream relationships of all subcatchments; if subcatchment j is located upstream of subcatchment i, then the off-diagonal elements in the connectivity matrix is equal to 1, otherwise it is zero, and specifies the diagonal elements ; (6) Estimate the stormwater runoff flow at the outlet of each subcatchment by summing the runoff from each subcatchment and the stormwater runoff flow from all upstream sources: ,in, Indicates that the vector parameters are converted into a diagonal matrix, as in the above formula, the vector parameters and Perform diagonal matrix transformation, the diagonal elements in the diagonal matrix are ; is the correction factor for the low-impact development facility layout plan; is the duration of the stormwater runoff simulation.

4. The method for optimizing the layout of low-impact development facilities at a coal port considering the randomness of the underlying surface according to claim 3 is characterized in that: The objective function of the multi-objective programming model is expressed as: (1) Objective function 1: ,in, The construction cost per unit area of ​​the lth type of low-impact development facility at the candidate location j in the ith subcatchment; The fixed cost required to deploy the lth low-impact development facility at candidate location j in the ith subcatchment; The operating cost per unit area required to deploy the lth type of low-impact development facility at candidate location j in the ith subcatchment; is the area of ​​the lth type of low-impact development facility to be arranged at the candidate location j in the ith subcatchment; is a 0-1 variable, representing whether the l-th type of low-impact development facility is arranged at the candidate location j of the i-th subcatchment; Life cycle of a Type 1 low-impact development facility; is the discount rate; (2) Objective function 2: ,in, Representative Planting surface type scenario, Representative The probability of occurrence under the planting surface type scenario, represents the total runoff of subcatchment i when no low-impact development facilities are deployed, represents the total runoff of subcatchment i after the deployment of low-impact development facilities; t represents the simulation time step; , the above formula calculates the total runoff of subcatchment i before the construction of low-impact development facilities; in, and is the slope function and roughness coefficient function under the kth underlying surface type scenario; is the area of ​​subcatchment i; is the equivalent width of subcatchment i; For the rainfall scenarios; , the above formula represents the total runoff of subcatchment i after the construction of low-impact development facilities; , the above formula defines the functional expression of the runoff of subcatchment i in time step t; in, is the slope of subcatchment i, is the roughness coefficient of subcatchment i; , the above formula represents the relationship between slope, roughness coefficient and surface type, where u represents the u-th surface type; represents the slope; Represents the roughness coefficient.

5. The method for optimizing the layout of low-impact development facilities at a coal port considering the randomness of the underlying surface according to claim 4 is characterized in that: The constraints of the multi-objective programming model are expressed as: (1) Regional area constraints: ， ， ， ， , are the relationship constraints among the layout area of ​​low-impact facilities, the layout area of ​​low-impact development facilities and the area of ​​sub-catchment; is the area occupied by u types of land surface at candidate location j in the ith subcatchment; (2) Constraints on low-impact development facility types: ， , requiring the type of rainwater collection facilities to match the surface type; Indicates whether there are areas of u surface types at the candidate location j of the i-th subcatchment; (3) Traffic constraints: , ensuring that the runoff of each subcatchment at each time step is within a safe range, and are the lower and upper limits of runoff; , defines the relationship between peak runoff and runoff at each time step, where is the peak runoff of the ith subcatchment; (4) Logical constraints: , ensuring that the area value for each facility is obtained only after the low-impact development facility is built at the candidate location, A number representing infinity.

6. The method for optimizing the layout of low-impact development facilities at a coal port considering the randomness of the underlying surface according to claim 5 is characterized in that: The Nash bargaining theory is used to simulate the negotiation process between stakeholders and select a final solution from a set of non-dominant solutions, which is expressed as the following formula: ， ,in, is the distance function; is the distance parameter; and To arrange the plan, that is, the solution; and The meaning of is the two objective functions in the model; is a set on the Pareto frontier; given A certain value of , the point closest to the ideal point, is the Nash bargaining solution; if ,exist In the case of , the two objectives have the same weight; if ,exist , targets with larger deviations have greater weights.

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