A method and system for optimizing design of a grey-green rainwater facility
By constructing a multi-objective optimization decision-making model and a comprehensive evaluation method, the problem of singularity in benefit evaluation in the design of gray-green stormwater facilities was solved, and the comprehensive optimization of economic, hydrological and environmental benefits was achieved, providing a scientific layout scheme.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHANDONG LUQIAO GROUP CO LTD
- Filing Date
- 2025-12-26
- Publication Date
- 2026-05-29
Smart Images
Figure CN122113556A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of gray-green rainwater facility technology, and in particular to an optimized design method and system for gray-green rainwater facilities. Background Technology
[0002] In recent years, with the acceleration of urbanization, changes in the nature of urban underlying surfaces have disrupted the natural water cycle system to some extent, thereby increasing the probability of urban flooding. Therefore, the concept of sponge city construction has received widespread attention as an important measure to effectively address urban flooding and water environment issues.
[0003] Green stormwater infrastructure is equivalent to low-impact development (LID) measures, such as green roofs, rain gardens, sunken green spaces, and permeable paving. Gray stormwater infrastructure refers to traditional drainage networks, retention facilities, and wastewater treatment facilities related to urban stormwater management. A scientific and rational layout of both green and gray stormwater infrastructure can effectively optimize urban stormwater management systems, improving stormwater control while also enhancing ecosystem and social benefits.
[0004] Coordinated optimization of gray and green rainwater facilities is the core technical path to realize the construction of sponge cities. Although the deployment of gray and green rainwater facilities can bring multiple benefits, the mutual constraints between various benefit objectives often cannot be satisfied at the same time during the construction process. Therefore, it is necessary to adopt multi-objective optimization methods to solve the problem and determine the optimal deployment scheme through comprehensive evaluation.
[0005] Several technical documents have proposed solutions, such as the gray-green sponge facility optimization design method based on urban stormwater model and NSGA-Ⅲ algorithm proposed in patent publication number CN115495914A. Although this method achieves optimization of gray-green sponge facilities, the final scheme selection is based solely on the principle of lowest construction standards and costs, and the judgment criteria are relatively singular. Another example is the sponge city optimization layout and comprehensive benefit evaluation method proposed in patent publication number CN112712268A. This method uses the analytic hierarchy process to evaluate the comprehensive benefits of sponge facilities from three aspects: total construction cost of LID facilities, annual comprehensive runoff coefficient of rainwater, and comprehensive pollutant control rate of LID system. However, the evaluation method still lacks objectivity and does not conduct a comprehensive evaluation from multiple benefit perspectives.
[0006] Therefore, how to provide an optimized design scheme for gray-green stormwater facilities that comprehensively considers economic, hydrological, and environmental benefits is an urgent problem to be solved. Summary of the Invention
[0007] This invention provides a method and system for optimizing the design of gray-green rainwater facilities to solve the aforementioned technical problems in the prior art.
[0008] According to a first aspect of the present invention, a method for optimizing the design of gray-green rainwater facilities is provided.
[0009] The optimized design method for gray-green rainwater facilities includes: A multi-objective optimization decision model for the economic, hydrological, and environmental benefits of gray-green stormwater facility layout schemes is constructed; and a multi-objective genetic algorithm is used to iteratively solve the multi-objective optimization decision model to obtain the non-dominated frontier solution set of the gray-green stormwater facility layout schemes. Based on the undominated front solution set, the initial decision matrix corresponding to each objective is constructed, and a weighted decision matrix is constructed according to the judgment index weight of each objective. Based on the weighted decision matrix, a single objective evaluation model for each objective is constructed, and the optimal and worst solutions of each single objective evaluation model are calculated. Based on the optimal and worst solutions, the relative similarity is obtained, and the relative ranking of the non-dominated solution gray-green rainwater facility layout schemes under different single objectives is determined. The relative ranking results under each objective are used as whitening values to construct a comprehensive effect measurement matrix and calculate the multi-objective comprehensive effect measurement. The multi-objective comprehensive effect measure is used as the comprehensive score of each gray-green rainwater facility layout scheme in the non-dominated solution set, and the gray-green rainwater facility layout scheme with the highest comprehensive score is the final optimized layout scheme.
[0010] The objective function of the multi-objective optimization decision model includes: ; ; ; ; ; ; ; ; In the formula, and These represent objective functions that minimize the total construction and maintenance costs of gray-green stormwater facilities within the study area, respectively. and Representing the first k Construction and maintenance costs per unit size of gray-green rainwater facilities; , and These represent the objective functions that maximize the total reduction of urban flooding, control of total runoff, and replenishment of groundwater in the gray-green stormwater facilities within the study area, respectively. , and These represent the relationship functions between the area of gray-green stormwater facilities and their reduction of urban flooding, total runoff control, and groundwater replenishment levels, respectively. , and These represent the objective functions that maximize the reduction of total SS load, COD load, and PM10 pollution level in the purified air by the gray-green rainwater facilities within the study area, respectively. , and These represent the relationship functions between the area of gray-green rainwater facilities and their reduction in SS load, COD load, and PM10 pollution level in purified air, respectively. Representing the k The scale of construction of gray-green rainwater facilities; The types of gray-green rainwater facilities represent the study area.
[0011] The constraints of the multi-objective optimization decision model include: ; ; In the formula: and Representing the first k The smallest and largest scale of gray-green rainwater facilities construction. The annual runoff control rate of gray-green stormwater facilities in the representative study area This represents the lower limit of the annual runoff volume control rate for the study area.
[0012] The multi-objective genetic algorithm is the NSGA-III algorithm.
[0013] Specifically, when constructing single-objective evaluation models for each objective based on a weighted decision matrix, the TOPSIS method is used to construct single-objective evaluation models for each objective based on the weighted decision matrix.
[0014] According to a second aspect of the present invention, a gray-green rainwater facility optimization design system is provided.
[0015] The gray-green rainwater facility optimization design system includes: A multi-objective construction module is used to construct a multi-objective optimization decision model for the economic, hydrological, and environmental benefits of gray-green stormwater facility layout schemes; and a multi-objective genetic algorithm is used to iteratively solve the multi-objective optimization decision model to obtain the non-dominated frontier solution set of the gray-green stormwater facility layout schemes. The decision matrix processing module is used to construct the initial decision matrix corresponding to each objective based on the non-dominated front solution set, and to construct the weighted decision matrix according to the judgment index weight of each objective; and based on the weighted decision matrix, to construct the single-objective evaluation model for each objective, and to calculate the optimal and worst solutions of each single-objective evaluation model. The comprehensive measurement calculation module is used to obtain the relative closeness based on the optimal and worst solutions, determine the relative ranking results of the gray-green rainwater facility layout schemes in the non-dominated solution set under different single objectives, and use the relative ranking results under each objective as whitening values to construct a comprehensive effect measurement matrix and calculate the comprehensive effect measurement of multiple objectives. The comprehensive scoring module is used to take the comprehensive effect measurement of multiple objectives as the comprehensive score of each gray-green rainwater facility layout scheme in the non-dominated solution set, and the gray-green rainwater facility layout scheme with the highest comprehensive score is the final optimized layout scheme.
[0016] The objective function of the multi-objective optimization decision model includes: ; ; ; ; ; ; ; ; In the formula, and These represent objective functions that minimize the total construction and maintenance costs of gray-green stormwater facilities within the study area, respectively. and Representing the first k Construction and maintenance costs per unit size of gray-green rainwater facilities; , and These represent the objective functions that maximize the total reduction of urban flooding, control of total runoff, and replenishment of groundwater in the gray-green stormwater facilities within the study area, respectively. , and These represent the relationship functions between the area of gray-green stormwater facilities and their reduction of urban flooding, total runoff control, and groundwater replenishment levels, respectively. , and These represent the objective functions that maximize the reduction of total SS load, COD load, and PM10 pollution level in the purified air by the gray-green rainwater facilities within the study area, respectively. , and These represent the relationship functions between the area of gray-green rainwater facilities and their reduction in SS load, COD load, and PM10 pollution level in purified air, respectively. Representing the k The scale of construction of gray-green rainwater facilities; The types of gray-green rainwater facilities represent the study area.
[0017] The constraints of the multi-objective optimization decision model include: ; ; In the formula: and Representing the first k The smallest and largest scale of gray-green rainwater facilities construction. The annual runoff control rate of gray-green stormwater facilities in the representative study area This represents the lower limit of the annual runoff volume control rate for the study area.
[0018] The multi-objective genetic algorithm is the NSGA-III algorithm.
[0019] Specifically, when constructing single-objective evaluation models for each objective based on a weighted decision matrix, the TOPSIS method is used to construct single-objective evaluation models for each objective based on the weighted decision matrix.
[0020] The technical solution provided by this invention may include the following beneficial effects: This invention comprehensively considers the economic, hydrological, and environmental benefits of gray-green stormwater facilities. It incorporates eight indicators, including the construction and maintenance costs of gray-green stormwater facilities, reduction of urban flooding, and control of total runoff, into a unified optimization framework and constructs a multi-objective optimization decision-making model to achieve Pareto optimality of the multi-dimensional comprehensive benefits of gray-green stormwater facilities.
[0021] Furthermore, by constructing the "TOPSIS-Gray Situation Decision" two-level comprehensive benefit evaluation model, compared with the traditional analytic hierarchy process, the judgment index weighting results are more realistic and objective, and can more comprehensively evaluate the layout scheme from multiple perspectives, thereby achieving scientific decision-making in the layout planning of gray-green rainwater facilities.
[0022] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description
[0023] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.
[0024] Figure 1 This is a schematic diagram illustrating a gray-green rainwater facility optimization design method according to an exemplary embodiment; Figure 2This is a structural block diagram illustrating an optimized design system for gray-green rainwater facilities according to an exemplary embodiment; Figure 3 This is a flowchart illustrating the construction system of a multi-objective optimization decision-making model for economic, hydrological, and environmental benefits, based on an exemplary embodiment. Figure 4 This is a schematic diagram of the structure of a computer device according to an exemplary embodiment. Detailed Implementation
[0025] Figure 1 An embodiment of the gray-green rainwater facility optimization design method of the present invention is shown.
[0026] In this optional embodiment, the gray-green rainwater facility optimization design method includes: Step S101: Construct a multi-objective optimization decision model for the economic, hydrological, and environmental benefits of the gray-green stormwater facility layout scheme; and use a multi-objective genetic algorithm to iteratively solve the multi-objective optimization decision model to obtain the non-dominated frontier solution set of the gray-green stormwater facility layout scheme. Step S102: Construct initial decision matrices for each objective based on the non-dominated front solution set, and construct weighted decision matrices according to the judgment index weights of each objective; and construct single-objective evaluation models for each objective based on the weighted decision matrices, and calculate the optimal and worst solutions of each single-objective evaluation model. Step S103: Based on the optimal and worst solutions, obtain the relative closeness and determine the relative ranking of the non-worsted solution gray-green rainwater facility layout schemes under different single objectives; and use the relative ranking results under each objective as whitening values to construct a comprehensive effect measurement matrix and calculate the multi-objective comprehensive effect measurement. Step S104: The multi-objective comprehensive effect measure is used as the comprehensive score of each gray-green rainwater facility layout scheme in the non-dominated solution set, and the gray-green rainwater facility layout scheme with the highest comprehensive score is the final optimized layout scheme.
[0027] Figure 2 An embodiment of a gray-green rainwater facility optimization design system of the present invention is shown.
[0028] In this optional embodiment, the gray-green rainwater facility optimization design system includes: The multi-objective construction module 201 is used to construct a multi-objective optimization decision model for the economic, hydrological, and environmental benefits of the gray-green stormwater facility layout scheme; and to use a multi-objective genetic algorithm to iteratively solve the multi-objective optimization decision model to obtain the non-dominated frontier solution set of the gray-green stormwater facility layout scheme. The decision matrix processing module 202 is used to construct the initial decision matrix corresponding to each objective based on the non-dominated front solution set, and to construct the weighted decision matrix according to the judgment index weight of each objective; and to construct the single objective evaluation model for each objective based on the weighted decision matrix, and to calculate the optimal solution and the worst solution of each single objective evaluation model. The comprehensive measurement calculation module 203 is used to obtain the relative closeness based on the optimal and worst solutions, determine the relative ranking results of the gray-green rainwater facility layout schemes in the non-dominant solution set under different single objectives, and use the relative ranking results under each objective as whitening values to construct a comprehensive effect measurement matrix and calculate the comprehensive effect measurement of multiple objectives. The comprehensive scoring module 204 is used to use the multi-objective comprehensive effect measurement as the comprehensive score of each gray-green rainwater facility layout scheme in the non-dominated solution set, and the gray-green rainwater facility layout scheme with the highest comprehensive score is the final optimized layout scheme.
[0029] In practical applications, when constructing a multi-objective optimization decision-making model for the economic, hydrological, and environmental benefits of green rainwater facility layout schemes in the above optional embodiments, the decision variable is the construction scale of various types of gray-green rainwater facilities in the study area. ), The classification is based on gray-green stormwater drainage systems. An objective function is constructed considering economic, hydrological, and environmental benefits.
[0030] For example, the types of grey-green stormwater facilities required for the study area are determined based on the higher-level planning and standards for the area. Assuming the grey-green stormwater facilities in the study area include one type of grey facility: a stormwater storage tank; and three types of green facilities: sunken green spaces, green roofs, and permeable paving, then the decision variable is the scale of the stormwater storage tank. Scale of sunken green spaces Green roof scale and the scale of permeable pavement .
[0031] From an economic perspective, the construction of gray-green rainwater facilities should minimize construction and maintenance costs. This is assessed using two indicators: the total construction cost and maintenance cost of the gray-green rainwater facilities. The specific objective function is as follows: (1) (2) In the formula: and These represent objective functions that minimize the total construction and maintenance costs of gray-green stormwater facilities within the study area, respectively. and Representing the first k Construction and maintenance costs per unit size of gray-green rainwater facilities; Representing the kThe scale of construction of gray-green rainwater facilities; The types of gray-green rainwater facilities represent the study area.
[0032] From a hydrological perspective, the deployment of gray-green stormwater facilities is required to improve water circulation and drainage within the study area. This is assessed based on three indicators: total reduction of urban flooding, control of total runoff, and groundwater replenishment. The specific objective function is as follows: (3) (4) (5) In the formula: , and These represent the objective functions that maximize the total reduction of urban flooding, control of total runoff, and replenishment of groundwater in the gray-green stormwater facilities within the study area, respectively. , and These represent the relationship functions between the area of gray-green stormwater facilities and their reduction of urban flooding, total runoff control, and groundwater replenishment levels, respectively. Representing the k The scale of construction of gray-green rainwater facilities; The types of gray-green rainwater facilities represent the study area.
[0033] From an environmental benefit perspective, the deployment of gray-green rainwater facilities is required to effectively reduce water and air pollution within the study area. This is assessed using three indicators: total SS (Suspended Solids Load Reduction) reduction, COD (Chemical Oxygen Demand Load Reduction) reduction, and PM10 (Particulate Matter 10) pollution level reduction. The specific objective function is as follows: (6) (7) (8) In the formula: , and These represent the objective functions that maximize the reduction of total SS load, COD load, and PM10 pollution level in the purified air by the gray-green rainwater facilities within the study area, respectively. , and These represent the relationship functions between the area of gray-green rainwater facilities and their reduction in SS load, COD load, and PM10 pollution level in purified air, respectively. Representing the k The scale of construction of gray-green rainwater facilities; The types of gray-green rainwater facilities represent the study area.
[0034] Furthermore, when constructing a multi-objective optimization decision-making model for the economic, hydrological, and environmental benefits of green rainwater facility layout schemes, the construction scale of various types of gray-green rainwater facilities and the annual runoff volume control rate are used as constraints. The specific constraints are as follows: (9) (10) In the formula: and Representing the first k The minimum and maximum scale of gray-green rainwater facilities construction, Equation (9) indicates that the construction scale of various gray-green rainwater facilities should be within the range; Representing the k The scale of construction of gray-green rainwater facilities; The annual runoff control rate of gray-green stormwater facilities in the representative study area This represents the lower limit of the annual runoff volume control rate for the study area.
[0035] The "Technical Guidelines for Sponge City Construction - Construction of Low Impact Development Rainwater Systems (Trial)" divides my country's land areas into five zones and specifies the annual runoff volume control rate for each zone. The minimum and maximum limits are as follows: Zone I (85% ≤ α ≤90%), Zone II (80%≤ α ≤85%), Zone III (75%≤ α ≤85%), Zone IV (70%≤ α ≤85%), V zone (60%≤ α (≤85%), this limit can be used as a reference to determine the annual runoff volume control rate for this study area.
[0036] When using a multi-objective genetic algorithm to iteratively solve a multi-objective optimization decision model and obtain the non-dominated frontier solution set of the gray-green stormwater facility layout scheme, the NSGA-III (Non-dominated Sorting Genetic Algorithm III) algorithm can be used to iteratively solve the multi-objective optimization decision model. Specifically, the population size of the NSGA-III algorithm is set as follows: N Maximum number of generations G Crossover probability Pc Probability of mutation Pm By solving for relevant parameters, the non-dominated solution set under eight judgment indicators for the gray-green rainwater facility deployment scheme in the study area is obtained. .
[0037] When constructing the initial decision matrix corresponding to each objective based on the non-dominated front solution set, and constructing the weighted decision matrix according to the weight of the judgment index of each objective, the eight judgment indexes corresponding to the economic, hydrological and environmental benefit objectives are as follows: construction cost of gray-green rainwater facilities, maintenance cost of gray-green rainwater facilities, reduction of urban flooding, total runoff control, replenishment of groundwater, reduction of SS load, reduction of COD load, and purification of PM10 pollution in the air.
[0038] Non-inferior solution set The CCP m There are 10 optimization schemes, each containing the values of the above 8 judgment indicators, and initial decision matrices are constructed for the three objectives of economic, hydrological, and environmental benefits. , , Together they form .
[0039] (11) In the formula: Representative optimization scheme i of j Determine the value corresponding to the indicator.
[0040] To make the indicators more accurate, before constructing the weighted decision matrix based on the weights of the judgment indicators for each objective, the indicators can be standardized. Specifically, the following steps are taken: First, the indicators are categorized into positive and negative indicators based on their meanings, and then standardized using the range standardization method, as shown in equations (12) and (13): For positive indicators: (12) For negative indicators: (13) In the formula: For the standardized solution i of j Determine the value of the indicator.
[0041] The indicators are standardized by unifying the dimensions of each judgment indicator, resulting in a standardized matrix. As shown in equation (14): (14) In the formula: Representative proposal i of jThe judgment index is determined after standardization.
[0042] Calculation scheme i of j Judgment indicator value accounts for j Weight of the indicator As shown in equation (15): (15) Calculate judgment indicators j entropy value As shown in equation (16): (16) Calculate the coefficient of variation for each judgment indicator. As shown in equation (17): (17) Calculate the entropy weight of each judgment indicator As shown in equation (18): (18) Standardized matrix With each entropy weight The weight matrix formed W Multiply to establish a weighted decision matrix. , For the plan i of j The weighted values of the judgment index are shown in equation (19): (19) Furthermore, in practical applications, when constructing single-objective evaluation models for each objective based on a weighted decision matrix and calculating the optimal and worst solutions for each single-objective evaluation model, the TOPSIS method can be used to construct single-objective evaluation models for each objective separately, calculate the optimal and worst solutions for each single-objective evaluation model, and thus obtain the relative closeness based on the optimal and worst solutions, determining the relative ranking of the non-dominated solution set of gray-green rainwater facility layout schemes under different single objectives. Specifically: The TOPSIS method was used to construct single-objective evaluation models for the economic, hydrological, and environmental benefits of gray-green stormwater facilities. First, the distances between each optimized scheme and the optimal and worst solutions were determined. (Matrix) ， The maximum values of each judgment indicator constitute the positive ideal solution. The minimum value forms the negative ideal solution. Based on this, the economic, hydrological, and environmental benefits of the proposed scheme can be calculated. i index vector to positive ideal solution distance and the negative ideal solution distance As shown in equations (20), (21), and (22): (20) (twenty one) (twenty two) In the formula: for j The matrix of positive ideal solutions composed of the maximum values of the judgment indicators; for j The minimum values of the judgment indicators form the negative ideal solution matrix; The schemes represent the economic, hydrological, and environmental benefit objectives, respectively. i index vector to positive ideal solution distance; The schemes represent the economic, hydrological, and environmental benefit objectives, respectively. i index vector to negative ideal solution distance.
[0043] By comparing the solutions i The degree of closeness between the index vector and the optimal solution Determine the relative order of the various options. The larger the value in the formula, the better the solution. As shown in equation (23): (twenty three) Ultimately, the non-dominated solution set is obtained under the objectives of economic, hydrological, and environmental benefits. Relative ranking results of each scheme , in order , , The solution with the largest value in the relative ranking results is the optimal solution under single-objective evaluation.
[0044] Furthermore, this invention employs the grey situation decision-making method to establish a comprehensive benefit evaluation model for grey-green stormwater facilities. Specifically, the relative ranking results of the obtained economic, hydrological, and environmental benefits as single objectives are used as whitening values to construct a comprehensive effect measurement matrix. , is used to represent the effect measure of each optimization scheme and each relative ranking result under each benefit objective, as shown in equation (24): (twenty four) In the formula: The results are ranked relative to the single objective of economic, hydrological, and environmental benefits; The resulting comprehensive effect measurement matrix; The scheme after single-objective evaluation i of j Values to be selected under the benefit objectives.
[0045] Based on the effect measurement matrix, the comprehensive effect measurement of each optimization scheme and each relative ranking result under each benefit objective is calculated. As shown in equation (25). Based on this, a multi-objective comprehensive effect measurement matrix R is established, as shown in equation (26): (25) (26) Calculate the multi-objective comprehensive effect measure matrix R The scheme in i A unified comprehensive effect measure, as a set of non-dominated solutions. The comprehensive score of each scheme is shown in Equation (27).
[0046] (27) In the formula: For the plan i The corresponding unified comprehensive effect measurement result, i.e., the scheme i The overall score.
[0047] Corresponding non-dominated solution set The optimal solution with the highest overall score is the best layout of gray-green facilities that takes into account economic, hydrological, and environmental benefits.
[0048] Figure 4 An embodiment of a computer device according to the present invention is shown. The computer device may be a server, and includes a processor, memory, and a network interface connected via a system bus. The processor of the computer device provides computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The database of the computer device stores static and dynamic information data. The network interface of the computer device is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements the steps in the above method embodiment.
[0049] Those skilled in the art will understand that Figure 4 The structure shown is merely a block diagram of a portion of the structure related to the present invention and does not constitute a limitation on the computer device to which the present invention is applied. A specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.
[0050] In addition, the present invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above method embodiments.
[0051] In addition, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the above method embodiments.
[0052] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. Any references to memory, storage, databases, or other media used in the embodiments provided by this invention can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.
Claims
1. A method for optimizing the design of gray-green rainwater facilities, characterized in that, include: Construct a multi-objective optimization decision-making model for the economic, hydrological, and environmental benefits of gray-green stormwater facility layout schemes; A multi-objective genetic algorithm was used to iteratively solve the multi-objective optimization decision model, and the non-dominated front solution set of the gray-green rainwater facility layout scheme was obtained. Based on the undominated front solution set, the initial decision matrix corresponding to each objective is constructed, and a weighted decision matrix is constructed according to the judgment index weight of each objective. Based on the weighted decision matrix, a single objective evaluation model for each objective is constructed, and the optimal and worst solutions of each single objective evaluation model are calculated. Based on the relative similarity between the optimal and worst solutions, the relative ranking of the non-dominated solution centralized gray-green rainwater facility layout schemes under different single objectives is determined. The relative ranking results under each objective are used as whitening values to construct a comprehensive effect measurement matrix and calculate the comprehensive effect measurement of multiple objectives. The multi-objective comprehensive effect measure is used as the comprehensive score of each gray-green rainwater facility layout scheme in the non-dominated solution set, and the gray-green rainwater facility layout scheme with the highest comprehensive score is the final optimized layout scheme.
2. The gray-green rainwater facility optimization design method according to claim 1, characterized in that, The objective function of the multi-objective optimization decision model includes: ； ； ； ； ； ； ； ； In the formula, and These represent objective functions that minimize the total construction and maintenance costs of gray-green stormwater facilities within the study area, respectively. and Representing the first k Construction and maintenance costs per unit size of gray-green rainwater facilities; , and These represent the objective functions that maximize the total reduction of urban flooding, control of total runoff, and replenishment of groundwater in the gray-green stormwater facilities within the study area, respectively. , and These represent the relationship functions between the area of gray-green stormwater facilities and their reduction of urban flooding, total runoff control, and groundwater replenishment levels, respectively. , and These represent the objective functions that maximize the reduction of total SS load, COD load, and PM10 pollution level in the purified air by the gray-green rainwater facilities within the study area, respectively. , and These represent the relationship functions between the area of gray-green rainwater facilities and their reduction in SS load, COD load, and PM10 pollution level in purified air, respectively. Representing the k The scale of construction of gray-green rainwater facilities; The types of gray-green rainwater facilities represent the study area.
3. The gray-green rainwater facility optimization design method according to claim 1, characterized in that, The constraints of the multi-objective optimization decision model include: ； ； In the formula: and Representing the first k The smallest and largest scale of gray-green rainwater facilities construction. The annual runoff control rate of gray-green stormwater facilities in the representative study area This represents the lower limit of the annual runoff volume control rate for the study area.
4. The gray-green rainwater facility optimization design method according to claim 1, characterized in that, The multi-objective genetic algorithm is the NSGA-III algorithm.
5. The gray-green rainwater facility optimization design method according to claim 1, characterized in that, When constructing single-objective evaluation models for each objective based on a weighted decision matrix, the TOPSIS method is used to construct single-objective evaluation models for each objective based on the weighted decision matrix.
6. A gray-green rainwater facility optimization design system, characterized in that, include: A multi-objective construction module is used to build a multi-objective optimization decision-making model for the economic, hydrological, and environmental benefits of gray-green stormwater facility layout schemes. A multi-objective genetic algorithm was used to iteratively solve the multi-objective optimization decision model, and the non-dominated front solution set of the gray-green rainwater facility layout scheme was obtained. The decision matrix processing module is used to construct the initial decision matrix corresponding to each objective based on the non-dominated front solution set, and to construct the weighted decision matrix according to the judgment index weight of each objective; and based on the weighted decision matrix, to construct the single-objective evaluation model for each objective, and to calculate the optimal and worst solutions of each single-objective evaluation model. The comprehensive measurement and calculation module is used to obtain the relative closeness based on the optimal and worst solutions, and to determine the relative ranking of the non-dominated solution gray-green rainwater facility layout schemes under different single objectives. The relative ranking results under each objective are used as whitening values to construct a comprehensive effect measurement matrix and calculate the comprehensive effect measurement of multiple objectives. The comprehensive scoring module is used to take the comprehensive effect measurement of multiple objectives as the comprehensive score of each gray-green rainwater facility layout scheme in the non-dominated solution set, and the gray-green rainwater facility layout scheme with the highest comprehensive score is the final optimized layout scheme.
7. The gray-green rainwater facility optimization design system according to claim 6, characterized in that, The objective function of the multi-objective optimization decision model includes: ； ； ； ； ； ； ； ； In the formula, and These represent objective functions that minimize the total construction and maintenance costs of gray-green stormwater facilities within the study area, respectively. and Representing the first k Construction and maintenance costs per unit size of gray-green rainwater facilities; , and These represent the objective functions that maximize the total reduction of urban flooding, control of total runoff, and replenishment of groundwater in the gray-green stormwater facilities within the study area, respectively. , and These represent the relationship functions between the area of gray-green stormwater facilities and their reduction of urban flooding, total runoff control, and groundwater replenishment levels, respectively. , and These represent the objective functions that maximize the reduction of total SS load, COD load, and PM10 pollution level in the purified air by the gray-green rainwater facilities within the study area, respectively. , and These represent the relationship functions between the area of gray-green rainwater facilities and their reduction in SS load, COD load, and PM10 pollution level in purified air, respectively. Representing the k The scale of construction of gray-green rainwater facilities; The types of gray-green rainwater facilities represent the study area.
8. The gray-green rainwater facility optimization design system according to claim 6, characterized in that, The constraints of the multi-objective optimization decision model include: ； ； In the formula: and Representing the first k The smallest and largest scale of gray-green rainwater facilities construction. The annual runoff control rate of gray-green stormwater facilities in the representative study area This represents the lower limit of the annual runoff volume control rate for the study area.
9. The gray-green rainwater facility optimization design system according to claim 6, characterized in that, The multi-objective genetic algorithm is the NSGA-III algorithm.
10. The gray-green rainwater facility optimization design system according to claim 6, characterized in that, When constructing single-objective evaluation models for each objective based on a weighted decision matrix, the TOPSIS method is used to construct single-objective evaluation models for each objective based on the weighted decision matrix.