Fuzzy hierarchical simulation-optimization-evaluation method for best management practices of non-point source pollution

Abstract

The application discloses a fuzzy hierarchical simulation-optimization-evaluation method for optimal management measures of non-point source pollution. The method builds a double-level intelligent algorithm model containing environmental and economic targets and corresponding constraint conditions, and couples with a hydrological model to form a hierarchical simulation-optimization algorithm. In the optimization calculation, the fuzzy expected value and fuzzy reliability are used to handle uncertainty, and the hierarchical iteration linkage optimization of sub-basins and whole basins is executed to obtain the Pareto optimal solution of the optimal management measure space configuration scheme. Then, the scheme attribute value is extracted to build a fuzzy decision matrix, the weight is calculated by combining the fuzzy maximum deviation method, and the relative closeness of each scheme is calculated by the fuzzy TOPSIS, and the optimal configuration scheme is output. The application solves the problems of long time consumption of dynamic link formed by existing effect simulation and spatial optimization of optimal management measures, and the problems of insufficient uncertainty processing, and improves the efficiency and comprehensive benefits of scientific control of basin non-point source pollution.

Description

Technical Field

[0001] This invention relates to the field of water resources and water environment, and in particular to a fuzzy hierarchical simulation-optimization-evaluation method for optimal management measures of non-point source pollution. Background Technology

[0002] Best Management Practices (BMPs) for non-point source pollution, such as vegetated filter strips, terraces, constructed wetlands, conservation tillage, partial substitution of chemical fertilizers with organic fertilizers, and agricultural water-saving measures, are effective measures for controlling non-point source pollution. Due to the spatial heterogeneity of climate, topography, and vegetation conditions, the spatial effectiveness of BMPs varies significantly. Furthermore, due to the complexity of pollution migration and transformation and the subjectivity of human decision-making, the configuration of BMPs is susceptible to uncertainty. Therefore, conducting multi-objective spatial optimization and scheme selection of BMPs under uncertain conditions is of great significance for the prevention and control of non-point source pollution in watersheds.

[0003] Common spatial optimization methods for Biomass Motion (BMPs) fall into two categories. One method uses a dynamic simulation-optimization link based on distributed hydrological models and intelligent optimization algorithms to generate a set of optimal spatial layout schemes for BMPs. This method reflects the physical processes, but the scenarios are complex, computationally expensive, and it lacks a comprehensive evaluation of the generated BMP spatial scheme set. The other method couples a database or surrogate model with the optimization algorithm to replace the direct simulation-optimization link. However, this method oversimplifies the hydrological cycle and pollutant migration processes in natural systems, fails to reflect the physical processes, and is unsuitable for areas where internal water flow significantly impacts pollutant transport. Regarding uncertainty handling in BMP spatial optimization, although a few researchers have addressed stochastic uncertainties in surrogate model-based BMP optimization methods, replacing distributed hydrological models with simplified surrogate models increases the uncertainty of simulation and optimization results. In summary, previous BMPs spatial optimization methods still have several shortcomings: First, existing BMPs spatial optimization methods that can reflect physical processes have complex scenarios and long computation times; second, previous BMPs simulation-optimization dynamic links have neglected the transmission and handling of uncertainties; and third, they have not conducted comprehensive evaluation and optimal selection of the generated BMPs spatial scheme set.

[0004] Therefore, a new simulation-optimization-evaluation method for uncertain BMPs is urgently needed to solve the simulation problem. This approach optimizes the low computational efficiency and neglected uncertainties of dynamic linking, and enables spatial layout optimization of BMPs and selection of optimal solutions across multiple dimensions, including economic, social, and environmental considerations. Summary of the Invention

[0005] The purpose of this invention is to overcome the technical problems of existing spatial optimization methods for optimal management measures of non-point source pollution, such as complex scenarios, long computation time, neglect of uncertainty handling in the simulation-optimization dynamic link, and failure to comprehensively evaluate and select the spatial scheme set. This invention provides a fuzzy hierarchical simulation-optimization-evaluation method for optimal management measures of non-point source pollution.

[0006] In a first aspect, the present invention provides a fuzzy hierarchical simulation-optimization-evaluation method for optimal management measures of non-point source pollution, comprising the following steps: Acquire watershed data for the study area and input them into a preset watershed hydrological model. Perform simulation processing through the watershed hydrological model to output current pollution load data, which includes annual total nitrogen output load data, annual total phosphorus output load data, and annual sediment output data under different spatial scenarios. A two-level intelligent algorithm model is constructed, which includes a sub-basin-level optimization layer and a whole-basin-level optimization layer. In the two-level intelligent algorithm model, multiple objective functions including environmental objective functions and economic objective functions are configured, as well as constraint conditions including pollutant emission allowance constraints and optimal management measure scale constraints are configured. A hierarchical simulation optimization algorithm is established by coupling the watershed hydrological model and the two-level intelligent algorithm model. Comprehensive basic data, including the current pollution load data, preset optimal management measure cost parameters, and watershed spatial attribute data, are input into the hierarchical simulation optimization algorithm. The specific process is as follows: In the first-level sub-basin hierarchical optimization layer, an initial population of candidate schemes for optimal management measures in the sub-basin is generated; the watershed hydrological model is invoked to simulate the pollution reduction effect of each candidate scheme, and the objective function value of the multiple objective function is calculated in combination with the comprehensive basic data; during the calculation, the objective fuzzy number in the multiple objective function is processed by the fuzzy expectation method; based on the objective function value, the population is subjected to selection, crossover, and mutation operations to form a new generation population, and the watershed hydrological model is invoked again to evaluate the implementation effect. This process is repeated iteratively until the convergence condition is met, generating the Pareto front scheme for each sub-basin; In the second-level whole-basin hierarchical optimization layer, an initial population for the whole basin is generated based on the Pareto front schemes generated in each sub-basin. Based on the evaluation results of the Pareto front schemes in each sub-basin, the objective function values ​​of individual populations in the whole basin are calculated. During the calculation, the objective fuzzy number in the multiple objective function is processed using the fuzzy expectation method, and the constraint fuzzy parameters in the constraint conditions are processed using the fuzzy confidence constraint programming method. Based on the objective function values, the population undergoes selection, crossover, and mutation operations to form a new generation population. This process is iterated until convergence is achieved, outputting a set of optimal management measures space optimization schemes for the whole basin, containing multiple alternative configuration schemes. A fuzzy multi-criteria evaluation model is constructed for the set of spatial optimization schemes for the best management measures. The scheme attribute values ​​of the candidate configuration schemes in the set of spatial optimization schemes for the best management measures are extracted to construct a fuzzy decision matrix. The exact weight vector of each evaluation index is calculated based on the fuzzy decision matrix using the fuzzy maximum deviation method in the fuzzy multi-criteria evaluation model. The relative progress calculation of the set of spatial optimization schemes for the best management measures is performed using the fuzzy approximation ideal solution ranking method in the fuzzy multi-criteria evaluation model combined with the exact weight vector. The relative progress value of each candidate configuration scheme is output. The optimal spatial layout scheme of the best management measures for the target area source pollution is output based on the maximum relative progress value.

[0007] As an optional implementation of the first aspect of this application, configuring the environmental objective function and the economic objective function specifically includes: configuring the environmental objective function to minimize the normalized total pollution index of each sub-basin at the sub-basin level, and to minimize the normalized total pollution index of the entire basin at the whole basin level; constraining the expected value of the environmental objective fuzzy set corresponding to the environmental objective function to be equal to the minimum sum of the expected values ​​of the ratio of the annual total nitrogen output load fuzzy number to the current multi-year average total nitrogen output load, the ratio of the annual total phosphorus output load fuzzy number to the current multi-year average total phosphorus output load, and the ratio of the annual sediment output fuzzy number to the current multi-year average sediment output under each optimal management measure spatial configuration scenario. The economic objective function is configured to minimize the total investment cost of each sub-basin at the sub-basin level and the total investment cost of the entire basin at the whole basin level. The expected value of the economic objective fuzzy set corresponding to the economic objective function is constrained to be equal to the minimum sum of the cost fuzzy numbers of each hydrological response unit within each sub-basin implementing the optimal management measures. The cost fuzzy number of the optimal management measures is calculated by multiplying the area of ​​the hydrological response unit by a decision Boolean variable, the construction cost of the optimal management measures, and then by a discount correlation polynomial. The discount correlation polynomial is obtained through exponentiation and iterative summation based on a set discount rate, the maintenance and management cost ratio of the optimal management measures, and design cycle parameters.

[0008] As an optional implementation of the first aspect of this application, configuring the constraints specifically includes: configuring the pollutant allowable emission constraints as follows: the fuzzy set of the spatial scenario's multi-year total nitrogen reduction rate is greater than or equal to the confidence measure of the total nitrogen load reduction target, which is greater than or equal to a predefined confidence level; the fuzzy set of the spatial scenario's multi-year total phosphorus reduction rate is greater than or equal to the confidence measure of the total phosphorus load reduction target, which is greater than or equal to the predefined confidence level; and the fuzzy set of the spatial scenario's multi-year sediment reduction rate is greater than or equal to the confidence measure of the sediment load reduction target, which is greater than or equal to the predefined confidence level; configuring the optimal management measure scale constraints as follows: the area parameter for implementing optimal management measures for the target hydrological response unit within the corresponding sub-basin is less than or equal to the preset maximum implementable area threshold for optimal management measures within the corresponding sub-basin.

[0009] As an optional implementation of the first aspect of this application, the target fuzzy number in the multiple objective function is processed by the fuzzy expectation value method, and the constraint fuzzy parameters in the constraint conditions are processed by the fuzzy confidence constraint programming method. Specifically, this includes: defining a continuous membership function corresponding to the target convex fuzzy set contained in the multiple objective function using a combination of a continuously monotonically increasing function and a continuously monotonically decreasing function; determining the expectation interval of the target convex fuzzy set by calculating the integral limit of the continuous membership function; defining the midpoint value of the expectation interval as the fuzzy expectation value and using it to replace the target fuzzy number in the multiple objective function; wherein when the target convex fuzzy set is determined to be a trapezoidal fuzzy set, the sum of the values ​​of the four vertices associated with the trapezoidal fuzzy set is divided by 4 to obtain the fuzzy expectation value; obtaining a real number parameter with a value greater than 0.5 as the predefined confidence level; transforming the constraint fuzzy parameters determined by the triangular fuzzy number into deterministic constraint algebraic equations through a confidence measure; and using the extracted deterministic substitution parameters to replace the constraint fuzzy parameters in the constraint conditions to perform scheme optimization constraints based on deterministic boundaries.

[0010] As an optional implementation of the first aspect of this application, during the iterative calculation of the sub-basin hierarchical optimization layer and the whole-basin hierarchical optimization layer, the distance between the generated solution and the true reference solution is measured using the inverse generation distance to evaluate the convergence of the generated solution set, the spatial distribution of the generated solution set is evaluated using the diversity index, and the convergence and distribution of the generated solution set are comprehensively measured using the relative hypervolume index; the number of iterations of the sub-basin hierarchical optimization layer is set as a preset first iteration threshold, and the number of iterations of the whole-basin hierarchical optimization layer is set as a preset second iteration threshold. When the sub-basin hierarchical optimization layer completes iterations reaching the preset first iteration threshold number, and the whole-basin hierarchical optimization layer completes iterations reaching the preset second iteration threshold number, the convergent and stable Pareto optimal solution is output as the spatial optimization scheme set of the best management measures; the preset second iteration threshold is greater than the preset first iteration threshold.

[0011] As an optional implementation of the first aspect of this application, the exact weight vector of each evaluation index is calculated based on the fuzzy decision matrix using the fuzzy maximum deviation method in the fuzzy multi-criteria evaluation model. Specifically, this includes: obtaining the scheme attribute values ​​corresponding to the optimal management measure spatial optimization scheme set and performing triangular fuzzification representation to construct an initial fuzzy decision matrix; dividing the evaluation indexes into benefit-type indicators (where larger attributes are better) and cost-type indicators (where smaller attributes are better); and performing dimensionless processing on the initial fuzzy decision matrix to obtain a normalized decision matrix; wherein, the benefit-type indicators are calculated by dividing the corresponding attribute value by the maximum value among all schemes under the target attribute. The parameters are standardized by dividing the minimum parameter among all schemes under the target attribute by the corresponding attribute value. For each set evaluation index, the absolute Euclidean distance between the weighted attribute value of the benchmark reference scheme and the weighted attribute value of other comparative evaluation schemes is calculated as the corresponding local deviation. The local deviations of all participating schemes under the set evaluation index are summed to obtain the total deviation of the corresponding index. The total deviation of the corresponding index is divided by the sum of the total deviations of all evaluation indexes, and the resulting quotient ratio is used as the exact weight vector of the corresponding evaluation index and output.

[0012] As an optional implementation of the first aspect of this application, the fuzzy approximation ideal solution ranking method in the fuzzy multi-criteria evaluation model is combined with the exact weight vector to perform relative proximity calculation on the set of optimal management measures spatial optimization schemes. Specifically, this includes: multiplying each element in the normalized decision matrix with the corresponding element in the exact weight vector and performing weighted processing to output a weighted triangular fuzzy decision matrix; extracting the maximum value parameter component combination under each attribute dimension from the weighted triangular fuzzy decision matrix to form a positive ideal solution vector, and extracting the minimum value parameter component combination under each attribute dimension to form a negative ideal solution vector; calculating the first Euclidean geometric distance between the corresponding attribute of each alternative configuration scheme and the positive ideal solution vector, and calculating the second Euclidean geometric distance between the corresponding attribute of each alternative configuration scheme and the negative ideal solution vector; calculating the quotient result of dividing the second Euclidean geometric distance of each alternative configuration scheme by the sum of the first Euclidean geometric distance and the second Euclidean geometric distance, and outputting the quotient result as a relative proximity value reflecting the overall superiority or inferiority of the schemes.

[0013] In a second aspect, embodiments of this application provide an electronic device, which includes a processor, a memory, and a program or instructions stored in the memory and executable on the processor. When the program or instructions are executed by the processor, they implement the steps of the method described in the first aspect.

[0014] Thirdly, embodiments of this application provide a readable storage medium on which a program or instructions are stored, which, when executed by a processor, implement the steps of the method described in the first aspect.

[0015] Compared with the prior art, the present invention has the following beneficial effects: 1. Significantly improves the computational efficiency of large-scale spatial optimization based on physical processes. This invention cleverly decomposes complex spatial optimization problems into sub-basin level and whole-basin level processing. Through layered optimization by linking bottom-level parallel computing with top-level global iteration, it effectively simplifies the spatial scenario burden. While ensuring that the distribution and convergence of non-dominated solution sets are superior to traditional single-layer algorithms, it significantly shortens the spatial iteration time of the simulation-optimization link.

[0016] 2. This invention overcomes the bottleneck of uncertainty handling in the simulation-optimization-evaluation link. By introducing the fuzzy expectation method and fuzzy credibility-constrained programming theory, this invention deeply quantifies and transforms the data fluctuations caused by climate heterogeneity and management implementation, effectively ensuring the reliable transmission of uncertain information at each stage of the model and enhancing the anti-interference ability and robustness of the model's decision results.

[0017] 3. Achieved multi-dimensional integrated scientific management and evaluation. This invention couples the fuzzy maximum deviation method and the fuzzy TOPSIS method, realizing the dimensionless transformation and objective weight measurement of large-scale Pareto alternatives. It overcomes the limitations of relying solely on subjective human selection of solutions, and can accurately select the optimal spatial configuration of management measures under different preferences from multiple dimensions such as economy, society, and environment. It has extremely high application value for promoting watershed pollution prevention and control. Attached Figure Description

[0018] Figure 1 A flowchart illustrating a fuzzy hierarchical simulation-optimization-evaluation method for optimal management of non-point source pollution, provided in an embodiment of the present invention; Figure 2 This is a Pareto front plot showing the relationship between the normalized total pollution index and cost for the optimal spatial configuration scheme of management measures in a typical sub-basin layer in this invention embodiment; Figure 3 Pareto front plot of total pollution index versus cost for different confidence levels (λ) of the optimal spatial configuration scheme of management measures across the entire watershed layer in an embodiment of the present invention; Figure 4 This is a graph showing the convergence and distribution evaluation results of the fuzzy hierarchical simulation-optimization algorithm in an embodiment of the present invention. Detailed Implementation

[0019] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0020] The terms "first," "second," etc., used in the specification and claims of this application are used to distinguish similar objects and not to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that embodiments of this application can be implemented in orders other than those illustrated or described herein. Furthermore, in the specification and claims, "and / or" indicates at least one of the connected objects, and the character " / " generally indicates that the preceding and following objects are in an "or" relationship. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0021] Example This invention establishes a fuzzy hierarchical simulation-optimization-evaluation model for optimal management measures of non-point source pollution (BMPs) to optimize the spatial layout and select the best BMPs under uncertain conditions. In the model structure, the simulation module uses a non-point source pollution load simulation model, the optimization module uses a developed fuzzy two-level intelligent algorithm, and the evaluation module uses the fuzzy maximum deviation method and the fuzzy approximation ideal solution ranking method. A hierarchical intelligent algorithm is used to call cost accounting functions and hydrological models to form a dynamic link between simulation and optimization. Fuzzy expectation value method and fuzzy confidence constraints are introduced to handle the uncertainties in the simulation-optimization link, establishing a fuzzy hierarchical simulation-optimization model for BMPs. Through hierarchical optimization from sub-basin to whole-basin, a set of BMP spatial layout schemes is obtained. Finally, a fuzzy multi-criteria evaluation model is coupled to select the optimal spatial layout of BMPs under different economic, social, and environmental dimensions. The specific methodological framework is as follows: Figure 1 As shown, the core process of this invention includes the following steps: Step 1: Obtain watershed data for the study area and input it into a preset watershed hydrological model. Perform simulation processing through the watershed hydrological model to output current pollution load data, which includes annual total nitrogen output load data, annual total phosphorus output load data, and annual sediment output data under different spatial scenarios.

[0022] In this embodiment, the preset watershed hydrological model is specifically the SWAT (Soil and Water Assessment Tool) model. The SWAT model is a distributed watershed hydrological model used to simulate hydrological and ecological processes such as sediment and nutrient transport, vegetation and crop growth, and has been widely applied in academic research, engineering construction, and government departments. The SWAT model divides the study area into sub-watersheds based on gravity- and elevation-driven land surface hydrological flow paths. It can further divide the sub-watersheds into Hydrological Response Units (HRUs) based on land use, slope, and soil properties. After acquiring the watershed data input for the study area, the SWAT model can generate HRUs, as well as daily, monthly, and yearly simulation outputs at the sub-watershed and full watershed scales. This reflects the impact of different crops and management practices on the spatiotemporal distribution of different factors in the hydrological cycle, revealing the impact of set land use and BMPs scenarios on current pollution loads such as non-point source TN (total nitrogen) and TP (total phosphorus) at the HRU scale.

[0023] Furthermore, this method uses the SUF12 algorithm in the SWAT-CUP software to calibrate and validate the distributed hydrological model SWAT through iterative calculations. The calibration and validation order is runoff, sediment, non-point source TN, and TP load. The degree of agreement between the model simulation results and the measured values ​​reflects the applicability of the model in the study area. This invention uses the Nash-Sutcliffe efficiency coefficient (NSE) and the deterministic coefficient (R²). 2To determine the applicability of the distributed hydrological model SWAT; if R 2 If NSE is greater than 0.5, the SWAT model meets the accuracy requirements and can simulate runoff, sediment, total nitrogen, and total phosphorus well.

[0024] Step 2: Construct a two-level intelligent algorithm model, which includes a sub-basin level optimization layer and a whole-basin level optimization layer. In the two-level intelligent algorithm model, multiple objective functions including environmental objective functions and economic objective functions are configured, as well as constraint conditions including pollutant emission allowance constraints and optimal management measure scale constraints are configured.

[0025] In this embodiment, the two-level intelligent algorithm model is specifically a multi-algorithm genetically adaptive multi-objective (AMALGAM) algorithm that hierarchically progresses from sub-basin to the entire basin. This method combines non-dominated sorting genetic algorithm, particle swarm optimization algorithm, differential algorithm, and adaptive Metropolis evolutionary algorithm. It can simultaneously use multiple methods for searching and adaptively generate offspring to ensure that the multi-objective optimization problem is solved quickly, reliably, and efficiently.

[0026] The environmental objective function is configured to minimize the normalized total pollution index (TPI) for both the sub-basin and the entire basin. Local soil erosion causes significant non-point source pollution; therefore, the environmental objective is to minimize the sum of the ratios of total nitrogen (TN) load, total phosphorus (TP) load, and sediment yield to the pollution load under the current scenario. Due to differences in rainfall and hydrological conditions across different years, the annual load exhibits uncertainty under the same BMPs spatial scenario, represented as a fuzzy number. The environmental objective function is configured as follows: in, Spatial scenario combinations for different hydrological response units; TN represents the annual output load under different spatial scenarios, and is the triangular fuzzy number in kg; TP output load under different spatial scenarios, denoted as the triangular fuzzy number, in kg; Let be the annual sediment output under different spatial scenarios, and be the triangular fuzzy number, in kg; The current multi-year average TN output load is in kg; The current average TP output load over many years is in kg; The current average annual sediment output is expressed in kg. , , The fuzzy set parameters are determined by the minimum, average, and maximum values ​​of the output TN, TP, and annual sediment load, respectively.

[0027] Simultaneously, the economic objective function is configured to minimize the total investment cost for both sub-basins and the entire basin. For engineering-type BMPs, the cost generally consists of three parts: land cost, construction cost, and subsequent maintenance cost. In this embodiment, land cost is not considered. By discounting the costs within the planning period to their final values ​​and summing the costs of hydrological response unit BMPs within each sub-basin, the final economic objective function is obtained. This function depends on the calculation of the discounting correlation polynomial: , in Types of BMPs; For sub-basins; For sub-basins HRU inside; For the basin Hydrological response unit within The j The cost of planting BMP is a fuzzy number, in yuan / hm. 2 ; For sub-basins Hydrological response unit within area, hm 2 ; 0-1 variables; This indicates a hydrological response unit where the land use type is cultivated land; Construction cost, yuan / hm 2 ; The discount rate; The percentage of maintenance and management costs for BMPs; For the first j The design cycle of a type of BMP; in SWAT, each HRU corresponds to a specific combination of BMPs.

[0028] The specific logic for configuring the constraints includes: (1) Constraints on permissible pollutant emissions: in , and These are the targets for reducing TN, TP, and sediment load in the watershed, respectively. For credibility measurement; For a predefined level of credibility; For spatial context Fuzzy set of multi-year TN reduction rates, % For spatial context Fuzzy set of multi-year TP reduction rates, % For spatial context Fuzzy set of multi-year sediment reduction rate, % For spatial context exist TN reduction rate in 2018, % for Annual current TN load output, kg; For spatial context exist Annual TN load output, kg; For spatial context exist Annual TP reduction rate, % for Annual current TP load output, kg; For spatial context exist Annual TP load output, kg; For spatial context exist annual sediment reduction rate, % for Annual current sediment load output, kg; For spatial context exist Annual sediment load output, kg; , and In The minimum, average, and maximum values ​​within the year respectively constitute... , and The three parameters of the triangular fuzzy set.

[0029] (2) Scale constraints of optimal management measures: , in For sub-basins The maximum feasible area of ​​the j-th type of BMP, hm 2 .

[0030] Step 3: Couple the watershed hydrological model and the two-level intelligent algorithm model to establish a hierarchical simulation optimization algorithm. Input the comprehensive basic data, including the current pollution load data, the preset optimal management measure cost parameters, and the watershed spatial attribute data, into the hierarchical simulation optimization algorithm.

[0031] This step processes the fuzzy numbers in the multiple objective function using fuzzy expectation values. Assume the continuous membership function of the target convex fuzzy set ξ can be defined as: in , , and are real numbers, and , It is a continuously monotonically increasing function. It is a continuously monotonically decreasing function.

[0032] The expected interval of the fuzzy set ξ is represented as: Define the midpoint of the expected interval as the fuzzy expected value. When the target convex fuzzy set is determined to be a trapezoidal fuzzy set, the values ​​of its four associated vertices are ( The sum of these two values ​​divided by 4 is used as the fuzzy expectation value. When the target convex fuzzy set is determined to be a triangular fuzzy set... .

[0033] The fuzzy parameters in the constraints are handled using the fuzzy confidence constraint programming method. The confidence constraint formula can be transformed into a deterministic constraint using confidence measures. Assume a fuzzy set... Determined by triangular fuzzy numbers and , From triangular fuzzy numbers Determined and . The credibility is: Real numbers greater than 0.5 are used as meaningful predefined confidence levels, and the intelligent optimization algorithm is constrained by the parameters on the left-hand side. and the parameters on the right Replace each and This is transformed into a constraint for optimizing a solution based on a deterministic boundary: Subsequently, the set of spatial optimization schemes for BMPs at the sub-basin to whole-basin scales is calculated. An initial population size is set, and the BMPs spatial scenario is first simulated and optimized at the first-level sub-basin level, with parallel computation to obtain the Pareto optimal solution set for BMPs configuration schemes in different sub-basins. Figure 2Specifically, the AMALGAM algorithm is used to generate an initial population of BMPs candidate schemes for each sub-basin. A hydrological model is then used to simulate the pollution load of each individual in the population, thereby calculating the economic and environmental objective functions at the sub-basin level. Based on the objective function values ​​of the individual populations, a non-dominated ranking is performed, and the crowding distance of each individual is calculated. A tournament selection process is then conducted based on the calculation results, followed by crossover and mutation operations to generate a new generation of offspring populations. This simulation and optimization process is repeated until the sub-basin level convergence condition is met. Finally, the Pareto front of the normalized total pollution index versus cost for each sub-basin BMP spatial configuration scheme is generated.

[0034] Then, a global linkage iteration is performed at the second-level whole-basin hierarchical optimization layer to obtain the Pareto optimal solution set of BMPs spatial configuration under different confidence levels (λ) across the whole basin. Figure 3 Specifically, based on the BMPs schemes on the Pareto front of each sub-basin, an initial population of BMPs candidates for the entire basin is generated using the AMALGAM algorithm. The economic and environmental objective functions for each individual are calculated for the entire basin. Based on the objective function values ​​of the individuals in the population, a non-dominated ranking is performed, and the crowding distance of each individual is calculated. A tournament selection process is then conducted based on the calculation results, followed by crossover and mutation operations to generate a new generation of offspring. This process is repeated until the convergence condition for the entire basin level is met. Finally, the Pareto front of the normalized total pollution index and cost of the spatial configuration schemes for BMPs across the entire basin is generated.

[0035] Three metrics are used to evaluate the algorithm: Inverse Generation Distance (IGD) measures the distance between the generated solution and the true solution (reference solution) to evaluate convergence; Delte measures the distribution; and Relative Hypervolume (RHV) is used for a comprehensive metric. The smaller the values ​​of these three metrics, the better the algorithm's performance. Figure 4 The evaluation results of the algorithms were compared. Under the same number of iterations, the performance indicators of the two-layer algorithm were all lower than those of the single-layer algorithm, indicating that the two-layer algorithm is superior to the single-layer algorithm in terms of distribution and convergence. Tests revealed that when the first layer is set to a preset first iteration threshold (e.g., 100 iterations) and the second layer is set to a preset second iteration threshold (e.g., 1000 iterations), the algorithm with two-layer iterations not only exhibits good convergence and distribution but also reduces the iteration time by approximately 1 / 10 under the same computing power. Therefore, when the sub-basin and the entire basin reach their respective preset iteration thresholds, the convergent and stably distributed non-dominated optimal Pareto front solution set is output as the set of optimal management measures spatial optimization schemes.

[0036] Step 4: Obtain the fuzzy multi-criteria evaluation model constructed for the set of spatial optimization schemes for the best management measures, extract the scheme attribute values ​​of the alternative configuration schemes to construct the fuzzy decision matrix, calculate the exact weight vector by the fuzzy maximum deviation method, and perform relative progress calculation by the fuzzy approximation ideal solution ranking method, and output the optimal spatial layout scheme of the best management measures for the target area source pollution.

[0037] First, an evaluation index system for the BMPs spatial optimization scheme set is established, selecting three dimensions for evaluation: economic cost, social resources, and ecological environment. These are divided into benefit-type indicators where the larger the attribute, the better, and cost-type indicators where the smaller the attribute, the better.

[0038] The fuzzy maximum deviation method is used to determine the weights (the larger the deviation, the more important the attribute, and the greater the weight). The extracted attribute values ​​of the alternatives are triangularly fuzzified to construct the initial fuzzy decision matrix. Let... , For any two triangular fuzzy numbers, then it is said that: when At that time, The modulus is: Fuzzy Number and The distance is: For a decision problem where the weight information is unknown and the attribute value is a triangular fuzzy number, let the solution set be... The attribute set is The weight vector is , ,and .plan property Triangular fuzzy number Thus, a fuzzy decision matrix is ​​formed. The most common attribute types are generally divided into benefit-based and cost-based. Benefit-based indicators refer to attributes where a higher value is better, and are sets... I 1; Cost-related indicators are attributes where smaller is better, and are a set. I 2. First, all attributes are dimensionless, and the normalized decision matrix is: Where m represents the number of attributes and n represents the total number of solutions. The specific standardization method is as follows: in, , .

[0039] The weighted normalized matrix is According to the distance formula, for attributes... ,plan Weighted attribute values The deviation from the attribute values ​​of other schemes is defined as: The total deviation of all decision options from other options is: The weights are: Subsequently, the fuzzy approximation ideal solution ranking method (i.e., the fuzzy TOPSIS method) is used to rank the solutions. First, the triangular fuzzy numbers are normalized, and the normalized decision matrix is ​​as follows: The normalized triangular fuzzy matrix is ​​weighted to obtain the weighted triangular fuzzy decision matrix: The ideal solution to the scheme is: The negative ideal solution is: Distance from the ideal solution: Distance from the negative ideal solution: Calculate relative tracking progress: Finally, based on the maximum relative proximity value, the optimal spatial layout scheme for the best management measures of the target area source pollution is output.

[0040] It should be noted that the method of the present invention can provide watershed managers with different economic and environmental goals or preferences with the optimal spatial layout of non-point source pollution BMPs (such as vegetation filter strips, terraces, constructed wetlands, conservation tillage, partial substitution of chemical fertilizers with organic fertilizers, agricultural water-saving measures, etc.) to achieve multiple objectives such as TN and TP load reduction, cost savings, and sediment yield reduction, which is of great significance to the improvement of watershed water quality and the sustainable development of social economy.

[0041] Optionally, embodiments of this application also provide an electronic device, including a processor, a memory, and a program or instructions stored in the memory and executable on the processor. When the program or instructions are executed by the processor, they implement the various processes of the above-described fuzzy hierarchical simulation-optimization-evaluation method embodiment for optimal management of non-point source pollution, and can achieve the same technical effect. To avoid repetition, they will not be described again here.

[0042] This application also provides a readable storage medium storing a program or instructions. When the program or instructions are executed by a processor, they implement the various processes of the above-described embodiment of a fuzzy hierarchical simulation-optimization-evaluation method for optimal management of non-point source pollution, and achieve the same technical effect. To avoid repetition, they will not be described again here.

[0043] The processor is the processor in the electronic device described in the above embodiments. The readable storage medium includes computer-readable storage media, such as computer read-only memory (ROM), random access memory (RAM), magnetic disk, or optical disk.

[0044] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element. Furthermore, it should be noted that the scope of the methods and apparatuses in the embodiments of this application is not limited to performing functions in the order shown or discussed, but may also include performing functions substantially simultaneously or in the reverse order, depending on the functions involved. For example, the described methods may be performed in a different order than described, and various steps may be added, omitted, or combined. Additionally, features described with reference to certain examples may be combined in other examples.

[0045] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of this application.

[0046] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of this application.

Claims

1. A fuzzy hierarchical simulation-optimization-evaluation method for optimal management of non-point source pollution, characterized in that, Includes the following steps: Acquire watershed data for the study area and input them into a preset watershed hydrological model. Perform simulation processing through the watershed hydrological model to output current pollution load data, which includes annual total nitrogen output load data, annual total phosphorus output load data, and annual sediment output data under different spatial scenarios. A two-level intelligent algorithm model is constructed, which includes a sub-basin-level optimization layer and a whole-basin-level optimization layer. In the two-level intelligent algorithm model, multiple objective functions including environmental objective functions and economic objective functions are configured, as well as constraint conditions including pollutant emission allowance constraints and optimal management measure scale constraints are configured. A hierarchical simulation optimization algorithm is established by coupling the watershed hydrological model and the two-level intelligent algorithm model. Comprehensive basic data, including the current pollution load data, preset optimal management measure cost parameters, and watershed spatial attribute data, are input into the hierarchical simulation optimization algorithm. The specific process is as follows: In the first-level sub-basin hierarchical optimization layer, an initial population of candidate schemes for optimal management measures in the sub-basin is generated; the watershed hydrological model is invoked to simulate the pollution reduction effect of each candidate scheme, and the objective function value of the multi-objective function is calculated in combination with the comprehensive basic data; In the calculation, the target fuzzy number in the multiple objective function is processed by the fuzzy expectation method; the population is selected, crossover and mutated according to the objective function value to form a new generation population, and the watershed hydrological model is called again to evaluate the implementation effect. This process is repeated until the convergence condition is reached, and the Pareto front scheme for each sub-watershed is generated. In the second-level whole-basin hierarchical optimization layer, the initial population of the whole basin is generated based on the Pareto front scheme generated in each sub-basin. Based on the evaluation results of the Pareto front schemes for each sub-basin, the objective function values ​​of individuals in the entire basin population are calculated. In the calculation, the target fuzzy number in the multiple objective function is processed by the fuzzy expectation value method, and the constraint fuzzy parameter in the constraint condition is processed by the fuzzy confidence constraint programming method. Based on the objective function value, the population is selected, crossover and mutation operations are performed to form a new generation population. This process is repeated until the convergence condition is reached, and the output is a set of spatial optimization schemes for the best management measures in the whole watershed containing multiple alternative configuration schemes. A fuzzy multi-criteria evaluation model is constructed for the set of spatial optimization schemes for the best management measures. The scheme attribute values ​​of the candidate configuration schemes in the set of spatial optimization schemes for the best management measures are extracted to construct a fuzzy decision matrix. The exact weight vector of each evaluation index is calculated based on the fuzzy decision matrix using the fuzzy maximum deviation method in the fuzzy multi-criteria evaluation model. The relative progress calculation of the set of spatial optimization schemes for the best management measures is performed using the fuzzy approximation ideal solution ranking method in the fuzzy multi-criteria evaluation model combined with the exact weight vector. The relative progress value of each candidate configuration scheme is output. The optimal spatial layout scheme of the best management measures for the target area source pollution is output based on the maximum relative progress value.

2. The method according to claim 1, characterized in that, Configuring the environmental objective function and the economic objective function specifically includes: The environmental objective function is configured to minimize the normalized total pollution index of each sub-basin at the sub-basin level and minimize the normalized total pollution index of the entire basin at the whole basin level. The expected value of the environmental objective fuzzy set corresponding to the environmental objective function is constrained to be equal to the minimum value of the sum of the expected values ​​of the ratio of the annual total nitrogen output load fuzzy number to the current multi-year average total nitrogen output load, the ratio of the annual total phosphorus output load fuzzy number to the current multi-year average total phosphorus output load, and the ratio of the annual sediment output fuzzy number to the current multi-year average sediment output under each optimal management measure spatial configuration scenario. The economic objective function is configured to minimize the total investment cost of each sub-basin at the sub-basin level and the total investment cost of the entire basin at the whole basin level. The expected value of the economic objective fuzzy set corresponding to the economic objective function is constrained to be equal to the minimum sum of the cost fuzzy numbers of each hydrological response unit within each sub-basin for implementing the optimal management measures. The cost fuzzy number of the optimal management measures is calculated by multiplying the area of ​​the hydrological response unit by a decision Boolean variable, the construction cost of the optimal management measures, and then by a discount correlation polynomial. The discount correlation polynomial is obtained through exponentiation and iterative summation based on a set discount rate, the maintenance and management cost ratio of the optimal management measures, and design cycle parameters.

3. The method according to claim 2, characterized in that, Configuring the constraints specifically includes: The pollutant emission allowance constraints are configured as follows: the fuzzy set of the multi-year total nitrogen reduction rate in the spatial scenario is greater than or equal to the confidence measure of the total nitrogen load reduction target, which is greater than or equal to a predefined confidence level; the fuzzy set of the multi-year total phosphorus reduction rate in the spatial scenario is greater than or equal to the confidence measure of the total phosphorus load reduction target, which is greater than or equal to the predefined confidence level; and the fuzzy set of the multi-year sediment reduction rate in the spatial scenario is greater than or equal to the confidence measure of the sediment load reduction target, which is greater than or equal to the predefined confidence level. The configuration of the optimal management measures scale constraints includes: the area parameter for implementing the optimal management measures in the target hydrological response unit within the corresponding sub-basin is less than or equal to the preset maximum implementable area threshold of the optimal management measures within the corresponding sub-basin.

4. The method according to claim 3, characterized in that, The objective fuzzy number in the multiple objective function is processed by the fuzzy expectation method, and the constraint fuzzy parameters in the constraint conditions are processed by the fuzzy confidence constraint programming method, specifically including: A continuous membership function corresponding to the target convex fuzzy set included in the multi-objective function is defined by combining a continuously monotonically increasing function and a continuously monotonically decreasing function. The expected interval of the target convex fuzzy set is determined by calculating the integral limit of the continuous membership function. The midpoint value of the expected interval is defined as the fuzzy expected value and used to replace the target fuzzy number in the multi-objective function. When the target convex fuzzy set is determined to be a trapezoidal fuzzy set, the sum of the values ​​of the four vertices associated with the trapezoidal fuzzy set is divided by 4 to obtain the fuzzy expected value. A real number parameter with a value greater than 0.5 is obtained as the predefined confidence level. The constraint fuzzy parameters determined by the triangular fuzzy number are transformed into deterministic constraint algebraic equations through the confidence measure. The extracted deterministic substitution parameters are used to replace the constraint fuzzy parameters in the constraint conditions to perform scheme optimization constraints based on deterministic boundaries.

5. The method according to claim 1, characterized in that, During the iterative calculation of the sub-basin hierarchical optimization layer and the whole-basin hierarchical optimization layer, the distance between the generated solution and the true reference solution is measured by the inverse generation distance to evaluate the convergence of the generated solution set. The spatial distribution of the generated solution set is evaluated by the diversity index, and the convergence and distribution of the generated solution set are comprehensively measured by the relative hypervolume index. The number of iterations of the sub-basin-level optimization layer is set as a preset first iteration threshold, and the number of iterations of the whole-basin-level optimization layer is set as a preset second iteration threshold. When the sub-basin-level optimization layer completes iterations reaching the preset first iteration threshold and the whole-basin-level optimization layer completes iterations reaching the preset second iteration threshold, the convergent and stable Pareto optimal solution is taken as the set of optimal management measures spatial optimization schemes and output. The preset second iteration threshold is greater than the preset first iteration threshold.

6. The method according to claim 1, characterized in that, The exact weight vector of each evaluation index is calculated based on the fuzzy decision matrix using the fuzzy maximum deviation method in the fuzzy multi-criteria evaluation model, specifically including: The attribute values ​​corresponding to the optimal management measure spatial optimization scheme set are obtained and represented by triangular fuzzy representation to construct an initial fuzzy decision matrix. The evaluation indicators are divided into benefit indicators (the larger the attribute, the better) and cost indicators (the smaller the attribute, the better). The initial fuzzy decision matrix is ​​then subjected to dimensionless processing to obtain a normalized decision matrix. Specifically, the benefit indicators are normalized by dividing the corresponding attribute value by the maximum value parameter among all schemes under the target attribute, and the cost indicators are normalized by dividing the minimum value parameter among all schemes under the target attribute by the corresponding attribute value. For each set evaluation index, the absolute Euclidean distance between the weighted attribute values ​​of the benchmark reference scheme and the weighted attribute values ​​of other comparative evaluation schemes is calculated as the corresponding local deviation. The total deviation of the corresponding indicator is obtained by summing the local deviations of all participating schemes under the set evaluation indicators. The total deviation of the corresponding indicator is divided by the sum of the total deviations of all indicators corresponding to all evaluation indicators. The resulting quotient ratio is used as the exact weight vector of the corresponding evaluation indicator and output.

7. The method according to claim 6, characterized in that, Using the fuzzy approximation ideal solution ranking method in the fuzzy multi-criteria evaluation model, combined with the exact weight vector, to perform relative progress calculations on the optimal management measure space optimization scheme set, specifically including: The elements in the normalized decision matrix are multiplied by the corresponding elements in the exact weight vector and then weighted to output the weighted triangular fuzzy decision matrix. The maximum value parameter components under each attribute dimension are extracted from the weighted triangular fuzzy decision matrix to form a positive ideal solution vector, and the minimum value parameter components under each attribute dimension are extracted to form a negative ideal solution vector. Calculate the first Euclidean geometric distance between the corresponding attribute of each alternative configuration scheme and the positive ideal solution vector, and calculate the second Euclidean geometric distance between the corresponding attribute of each alternative configuration scheme and the negative ideal solution vector; Calculate the quotient of the second Euclidean geometric distance corresponding to each alternative configuration scheme divided by the sum of the first Euclidean geometric distance and the second Euclidean geometric distance. Output the quotient as a relative closeness value reflecting the overall superiority or inferiority of the schemes.

8. An electronic device, characterized in that, The method includes a processor, a memory, and a program or instructions stored in the memory and executable on the processor. When the program or instructions are executed by the processor, they implement the steps of a fuzzy hierarchical simulation-optimization-evaluation method for optimal management of non-point source pollution as described in any one of claims 1-7.

9. A readable storage medium, characterized in that, The program or instructions stored on the readable storage medium, when executed by a processor, implement the steps of a fuzzy hierarchical simulation-optimization-evaluation method for optimal management of non-point source pollution as described in any one of claims 1-7.

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