Water network system balanced coordination optimization networking method and system

Abstract

The application discloses a water network system balanced coordination optimization networking method and system, adopts an improved meta-analysis method to screen water network system balanced state indexes and networking cost indexes, constructs a water network system balanced state initial index system, constructs a networking scheme set and inputs a pre-constructed system dynamics model to obtain water network system balanced state index values corresponding to each networking scheme; adopts a CNN-BP neural network coupling dimension reduction method to reduce dimensions of the water network system balanced state initial index system, obtains a water network system balanced state reduced dimension index system, and calculates water network system balanced state reduced dimension index values; inputs the water network system balanced state reduced dimension index values of each networking scheme into a pre-constructed water network system balanced state decision model to screen out an optimal networking scheme; and inputs the optimal networking scheme into a pre-constructed multi-objective optimization model to obtain a water network system balanced coordination optimization networking scheme. The application realizes efficient, safe and sustainable operation of the water network system.

Description

Technical Field

[0001] This invention relates to a balanced and coordinated optimization network design method for water network systems. Background Technology

[0002] The water network system is a comprehensive system based on natural rivers and lakes, with water diversion and drainage projects as channels, water storage projects as nodes, and intelligent regulation as a means. It integrates functions such as optimized allocation of water resources, flood control and disaster reduction in watersheds, and protection of aquatic ecosystems. It is an effective measure to solve the uneven spatial distribution of water resources, improve the water resource guarantee rate in water-receiving areas, alleviate the contradiction between water supply and demand in water-scarce areas, and achieve rational allocation of water resources. It is also an important way to promote economic development and comprehensive development and utilization of water resources in water-scarce areas.

[0003] Water network systems involve multiple processes, elements, and functions. Their networking problem is a massive, multidimensional, nonlinear, multi-objective, and complex constraint swarm intelligence optimization problem. However, existing research mainly focuses on optimization under independent boundary constraints of each subsystem, without fully considering the correlation between subsystems and their joint boundary constraints. Solving the multi-objective equilibrium collaborative optimization networking model of water network systems faces key technical challenges such as the "curse of dimensionality" and "multi-objective" issues, making most existing algorithms difficult to apply.

[0004] This invention proposes a balanced and collaborative optimization method and system for water network systems, which solves the above-mentioned problems, improves the intelligence level of water network construction, realizes deep interaction and integration of physical and digital water networks, takes into account the network benefits and construction and operation costs of water network systems, promotes the gradual development of various water conservancy projects from points to networks and from decentralized to systematic, and comprehensively enhances the systematicness, comprehensiveness and resilience of water networks. Summary of the Invention

[0005] Objective: To provide a balanced and coordinated optimization networking method for water network systems, thereby addressing the aforementioned problems in existing technologies. Furthermore, to provide a balanced and coordinated optimization networking system for water network systems.

[0006] Technical solution: A balanced and coordinated optimization networking method for water network systems, comprising the following steps:

[0007] Step S1: Use an improved meta-analysis method to screen the equilibrium state indicators and network cost indicators of the water network system, construct an initial indicator system for the equilibrium state of the water network system, construct a set of network schemes and input them into the pre-constructed system dynamics model to obtain the equilibrium state indicator values ​​of the water network system corresponding to each network scheme.

[0008] Step S2: Use the CNN-BP neural network coupled dimensionality reduction method to reduce the dimensionality of the initial index system of the equilibrium state of the water network system, and obtain the dimensionality reduction index system of the equilibrium state of the water network system. Based on the index values ​​of the equilibrium state of the water network system corresponding to each networking scheme, calculate the corresponding dimensionality reduction index values ​​of the equilibrium state of the water network system in sequence.

[0009] Step S3: Input the dimensionality reduction index value of the water network system equilibrium state of each networking scheme into the pre-constructed water network system equilibrium state decision model in turn, and select the optimal networking scheme.

[0010] Step S4: Input the selected optimal networking scheme into the pre-built multi-objective optimization model to obtain the optimized networking scheme, which is the water network system balanced collaborative optimization networking scheme.

[0011] According to one aspect of this application, step S1 is further comprising:

[0012] Step S11: Collect water network system data, use an improved meta-analysis method to screen and obtain water network system equilibrium state indicators and network cost indicators, and construct an initial indicator system for water network system equilibrium state.

[0013] Step S12: Construct a dynamic model of the water network system based on the initial index system of the equilibrium state of the water network system and calibrate the model parameters;

[0014] Step S13: Collect network schemes to construct a network scheme set, input the network scheme set into the water network system dynamic model, and obtain the initial index values ​​of the water network system equilibrium state corresponding to each network scheme.

[0015] According to one aspect of this application, step S2 is further comprising:

[0016] Step S21: Input the initial index of the equilibrium state of the water network system into the CNN and extract the corresponding spatial features;

[0017] Step S22: Train a BP neural network model based on the extracted spatial features;

[0018] Step S23: Use the trained BP neural network model to reduce the dimensionality of the initial index system of the equilibrium state of the water network system, and obtain the dimensionality-reduced index system of the equilibrium state of the water network system.

[0019] Step S24: Calculate the dimensionality reduction index value of the water network system equilibrium state corresponding to each networking scheme in sequence.

[0020] According to one aspect of this application, step S23 further comprises:

[0021] Step S23a: Using the initial index value of the equilibrium state of the water network system as the input vector, calculate the absolute and relative changes in the network output value;

[0022] Step S23b: Calculate the relative contribution rate of the change of each indicator to the network output value in turn;

[0023] Step S23c: Calculate the relative importance of each indicator in turn;

[0024] Step S23d: The product of relative contribution rate and relative importance is used as a comprehensive index to determine the initial index of the equilibrium state of the water network system in sequence. The initial index with a comprehensive index value lower than the average level is deleted to obtain the dimensionality reduction index system of the equilibrium state of the water network system.

[0025] According to one aspect of this application, step S3 further comprises:

[0026] Step S31: Construct a decision model for the equilibrium state of the water network system;

[0027] Step S32: Input the dimensionality reduction index value of the water network system equilibrium state of each networking scheme into the water network system equilibrium state decision model in sequence, calculate the comprehensive weight value of each networking scheme, sort them according to the size, and select the networking scheme with the largest comprehensive weight value as the optimal networking scheme.

[0028] According to one aspect of this application, step S31 further comprises:

[0029] Step S31a: Assign weights to the dimensionality reduction index of the equilibrium state of the water network system using both subjective and objective weighting methods.

[0030] Step S31b: Based on the subjective and objective weight values ​​of the water network system equilibrium state dimensionality reduction index, game theory is used to obtain the comprehensive weight value of the water network system equilibrium state dimensionality reduction index.

[0031] According to one aspect of this application, step S4 further comprises:

[0032] Step S41: Construct a multi-objective optimization model with the objective functions of minimizing construction costs, minimizing flood disaster losses, and maximizing GDP support. The constraints include pipeline flow constraints, water pressure constraints, and water quality limitations.

[0033] Step S42: Input the optimal networking scheme into the multi-objective optimization model, and use the NSGA-III algorithm, which integrates multiple crossover and mutation methods, to calculate the non-dominated solution set;

[0034] Step S43: Use grey relational analysis to make decisions on the non-dominated solution set and select the optimal solution as the balanced and coordinated optimization networking scheme for the water network system.

[0035] According to one aspect of this application, step S42 further comprises:

[0036] Step S42a: Obtain reference points based on the structured method, and calculate the number of reference points based on the number of targets and the number of equal parts in the target direction;

[0037] Step S42b: Randomly generate the parent population during the initialization process;

[0038] Step S42c: Generate a progeny population with the same size as the parent population using various crossover and mutation operations, and merge the progeny population with the parent population using an elitist strategy;

[0039] Step S42d: Perform fast non-dominated sorting on the merged population, and obtain a set of optimized solutions close to the reference point based on the reference point strategy;

[0040] Step S42e, repeat steps S42b to S42d until complete convergence, and take the current population as the final result. According to another aspect of this application, a water network system equilibrium cooperative optimization networking system is provided, comprising:

[0041] At least one processor; and

[0042] A memory communicatively connected to at least one of the processors; wherein,

[0043] The memory stores instructions that can be executed by the processor, which are used to implement the water network system balanced collaborative optimization networking method described in any of the above technical solutions.

[0044] Beneficial effects: By adopting the balanced and coordinated optimization networking method for water network systems, efficient management and operational optimization of water network systems can be achieved, further improving the overall performance and level of water network systems. Attached Figure Description

[0045] Figure 1 This is a flowchart of the present invention.

[0046] Figure 2 This is a flowchart of step S1 of the present invention.

[0047] Figure 3 This is a flowchart of step S2 of the present invention.

[0048] Figure 4 This is a flowchart of step S3 of the present invention.

[0049] Figure 5 This is a flowchart of step S4 of the present invention. Detailed Implementation

[0050] like Figure 1 As shown, the following technical solution is proposed. According to one aspect of this application, a method for balanced and coordinated optimization of a water network system is provided, characterized by comprising the following steps:

[0051] Step S1: Use an improved meta-analysis method to screen the equilibrium state indicators and network cost indicators of the water network system, construct an initial indicator system for the equilibrium state of the water network system, construct a set of network schemes and input them into the pre-constructed system dynamics model to obtain the equilibrium state indicator values ​​of the water network system corresponding to each network scheme.

[0052] Step S2: Use the CNN-BP neural network coupled dimensionality reduction method to reduce the dimensionality of the initial index system of the equilibrium state of the water network system, and obtain the dimensionality reduction index system of the equilibrium state of the water network system. Based on the index values ​​of the equilibrium state of the water network system corresponding to each networking scheme, calculate the corresponding dimensionality reduction index values ​​of the equilibrium state of the water network system in sequence.

[0053] Step S3: Input the dimensionality reduction index value of the water network system equilibrium state of each networking scheme into the pre-constructed water network system equilibrium state decision model in turn, and select the optimal networking scheme.

[0054] Step S4: Input the selected optimal networking scheme into the pre-built multi-objective optimization model to obtain the optimized networking scheme, which is the water network system balanced collaborative optimization networking scheme.

[0055] According to one aspect of this application, step S1 is further comprising:

[0056] Step S11: Collect water network system data, use an improved meta-analysis method to screen and obtain water network system equilibrium state indicators and network cost indicators, and construct an initial indicator system for water network system equilibrium state.

[0057] Meta-analysis is a systematic and comprehensive research method that integrates, summarizes, and analyzes the results of multiple independent studies to arrive at more comprehensive and objective conclusions. It helps to resolve contradictions in research results, assess the size and consistency of effects, and reveal potential causal relationships.

[0058] Traditional meta-analysis methods suffer from heterogeneity, publication bias, data quality issues, and model selection limitations. Therefore, in this embodiment, the effectiveness and reliability of the results are enhanced by improving the meta-analysis method, specifically as follows:

[0059] Heterogeneity was addressed through sensitivity analysis, subgroup analysis, and meta-regression analysis.

[0060] The system searches all relevant research, including unpublished research and grey literature, visualizes the review and analysis of research to identify publication bias, and makes adjustments to address the issue of publication bias.

[0061] Use consistent tools to evaluate the quality of included studies, ensure the reliability of results, and assess and compare the methodological quality of each study before inclusion in the meta-analysis.

[0062] We employ advanced statistical methods to improve study inclusion criteria, implement prospective registration, and utilize machine learning and data mining to enhance meta-analysis.

[0063] In this embodiment, an improved meta-analysis method is used to screen initial indicators. This method can integrate the results of multiple independent studies, consolidate and statistically analyze the data from different studies, and help reduce the bias of individual studies and the influence of human intervention factors on indicator selection. It can also quantitatively analyze the data from different studies and summarize and compare them through statistical methods. This can help researchers more objectively evaluate the effectiveness and importance of each indicator, while improving research efficiency and saving time and costs.

[0064] Step S12: Construct a dynamic model of the water network system based on the initial index system of the equilibrium state of the water network system and calibrate the model parameters;

[0065] Step S13: Collect network schemes to construct a network scheme set, input the network scheme set into the water network system dynamic model, and obtain the initial index values ​​of the water network system equilibrium state corresponding to each network scheme.

[0066] According to one aspect of this application, step S2 is further comprising:

[0067] Step S21: Input the initial index of the equilibrium state of the water network system into the CNN and extract the corresponding spatial features;

[0068] Step S22: Train a BP neural network model based on the extracted spatial features;

[0069] Step S23: Use the trained BP neural network model to reduce the dimensionality of the initial index system of the equilibrium state of the water network system, and obtain the dimensionality-reduced index system of the equilibrium state of the water network system.

[0070] Step S24: Calculate the dimensionality reduction index value of the water network system equilibrium state corresponding to each networking scheme in sequence.

[0071] CNN is a deep learning model specifically designed for processing data with network structures. Its basic components include convolutional layers, pooling layers, activation functions, and fully connected layers. The convolutional layer is the core of the CNN. Through convolution operations, the neural network can effectively identify spatial patterns in images. The convolutional layer uses filters to perform convolution operations on the input data to extract features. Convolution operations can reduce the number of parameters and preserve the spatial structure of the input data. The pooling layer is used for downsampling, reducing the dimensionality of the feature map, reducing the amount of computation, and retaining the main features. The activation function introduces non-linearity, allowing the network to learn complex patterns. The fully connected layer unfolds the features extracted by the convolutional and pooling layers and connects them to the final output layer.

[0072] Backpropagation (BP) neural networks are artificial neural network models consisting of an input layer, hidden layers, and an output layer. BP neural networks are multi-layer feedforward artificial neural networks that use the backpropagation algorithm for network training. They can establish a highly nonlinear mapping between the input and output layers, exhibiting strong robustness, adaptability, and parallel processing capabilities. They are currently widely used artificial neural network models. BP neural networks store and transform information through the network connection weights between nodes in each layer. After training, the network connection weights essentially reflect the amount of information introduced into the neural network from the input data, thus indirectly characterizing the importance of the input data to the network output.

[0073] The CNN-BP neural network coupled dimensionality reduction method combines the feature extraction capability of CNN with the dimensionality reduction learning capability of BP neural network. Compared with using either method alone for indicator data, it can effectively reduce the dimensionality of indicator data and extract the most critical feature information in the data. Therefore, in this embodiment, the CNN-BP neural network coupled dimensionality reduction method is selected to reduce the dimensionality of the initial indicator system of the water network system equilibrium state, and obtain the dimensionality-reduced indicator system of the water network system equilibrium state.

[0074] In one embodiment, specifically:

[0075] CNN is used to extract features from the original indicator data, and spatial features in the data are extracted through convolutional layers and pooling layers;

[0076] The features extracted by the CNN are used as input to the BP neural network to train the model for dimensionality reduction.

[0077] Using a CNN as a feature extractor, only the last fully connected layer is retained, and its output is used as the input layer of a BP neural network.

[0078] The mean squared error is set as the loss function;

[0079] Cross-validation was used to adjust the structure and hyperparameters of the BP neural network.

[0080] According to one aspect of this application, step S23 further comprises:

[0081] Step S23a: Using the initial index value of the equilibrium state of the water network system as the input vector, calculate the absolute and relative changes in the network output value;

[0082] Step S23b: Calculate the relative contribution rate of the change of each indicator to the network output value in turn;

[0083] Step S23c: Calculate the relative importance of each indicator in turn;

[0084] Step S23d: The product of relative contribution rate and relative importance is used as a comprehensive index to determine the initial index of the equilibrium state of the water network system in sequence. The initial index with a comprehensive index value lower than the average level is deleted to obtain the dimensionality reduction index system of the equilibrium state of the water network system.

[0085] The storage and transformation of information in a BP neural network is reflected in the network connection weights of the neurons in each layer. For a well-trained neural network, the relative importance information of each input neuron can be extracted from the network connection weights, and indicators can be selected accordingly.

[0086] The higher the relative importance value, the more significant the role of the indicator in multi-attribute decision-making for flood control scheduling, and the more important its position in the original indicator system.

[0087] The relative contribution rate quantitatively assesses the impact of changes in various indicators on multi-attribute decision-making. The larger the value, the more sensitive the decision outcome is to that indicator.

[0088] Relative importance and relative contribution rate quantitatively characterize the relative importance and sensitivity of each indicator, providing a reference for decision-makers to select indicators. However, in the actual indicator selection process, there is still considerable subjective arbitrariness and fuzzy uncertainty in deciding which indicators to delete and retain. In order to more effectively combine relative importance and relative contribution rate information for indicator selection, a comprehensive indicator that can take into account both of the magnitudes is defined as the product of relative importance and relative contribution rate.

[0089] When both relative importance and relative contribution rate are large, the comprehensive index value is also large; when one of relative importance and relative contribution rate is large and the other is small, the comprehensive index value is moderate; when both relative importance and relative contribution rate are small, the comprehensive index value is small. Therefore, the order of index deletion can be determined based on the comprehensive index value of each index. That is, the smaller the comprehensive index value, the earlier the index should be considered for deletion. When the comprehensive index value of an index is more than one order of magnitude smaller than the average comprehensive index value of all indicators, it is considered that the relative importance and relative contribution rate of the index are significantly lower than the average level of all indicators, and the index can be deleted. In this embodiment, the index screening process is transformed from a subjective analysis and judgment process to a quantitative calculation process.

[0090] According to one aspect of this application, step S3 further comprises:

[0091] Step S31: Construct a water network system equilibrium state decision model;

[0092] Step S32: Input the dimensionality reduction index value of the water network system equilibrium state of each networking scheme into the water network system equilibrium state decision model in sequence, calculate the comprehensive weight value of each networking scheme, sort them according to the size, and select the networking scheme with the largest comprehensive weight value as the optimal networking scheme.

[0093] According to one aspect of this application, step S31 further comprises:

[0094] Step S31a: Assign weights to the dimensionality reduction index of the equilibrium state of the water network system using both subjective and objective weighting methods.

[0095] Step S31b: Based on the subjective and objective weight values ​​of the water network system equilibrium state dimensionality reduction index, game theory is used to obtain the comprehensive weight value of the water network system equilibrium state dimensionality reduction index.

[0096] According to one aspect of this application, step S4 further comprises:

[0097] Step S41: Construct a multi-objective optimization model with the objective functions of minimizing construction costs, minimizing flood disaster losses, and maximizing GDP support. The constraints include pipeline flow constraints, water pressure constraints, and water quality limitations.

[0098] Step S42: Input the optimal networking scheme into the multi-objective optimization model, and use the NSGA-III algorithm, which integrates multiple crossover and mutation methods, to calculate the non-dominated solution set;

[0099] Step S43: Use grey relational analysis to make decisions on the non-dominated solution set and select the optimal solution as the balanced and coordinated optimization networking scheme for the water network system.

[0100] According to one aspect of this application, step S42 further comprises:

[0101] Step S42a: Obtain reference points based on the structured method, and calculate the number of reference points based on the number of targets and the number of equal parts in the target direction;

[0102] Step S42b: Randomly generate the parent population during the initialization process;

[0103] Step S42c: Generate a progeny population with the same size as the parent population using various crossover and mutation operations, and merge the progeny population with the parent population using an elitist strategy;

[0104] Step S42d: Perform fast non-dominated sorting on the merged population, and obtain a set of optimized solutions close to the reference point based on the reference point strategy;

[0105] Step S42e, repeat steps S42b to S42d until complete convergence, and take the current population as the final result.

[0106] The NSGA-III algorithm is based on the NSGA-II algorithm. It introduces the reference point method to enhance the diversity of the population and overcomes the shortcoming of the previous generation algorithm, which is that the crowding distance is not suitable for high-dimensional spaces. This makes the algorithm perform better in high-dimensional optimization problems.

[0107] Crossover and mutation are key genetic operations in genetic algorithms, used to generate new individuals and increase population diversity. The crossover operation generates one or more offspring individuals by combining the genetic information of two parent individuals. Common crossover methods include single-point crossover, multi-point crossover, and uniform crossover. The mutation operation is used to randomly change a part of the genes of an individual to increase genetic diversity and avoid premature convergence.

[0108] Incorporating crossover methods during the crossover process can improve population diversity, avoid early convergence, and enhance the algorithm's global search capability. Using different combinations and adjustments based on specific application requirements can optimize the performance of the genetic algorithm.

[0109] During the mutation process, combining different mutation methods can increase gene diversity and improve search capabilities. First, an individual is subjected to a certain mutation, and then another mutation is applied as a follow-up treatment to achieve more complex mutation effects.

[0110] Therefore, in this embodiment, the NSGA-III algorithm, which integrates multiple crossover and mutation methods to improve the model, can obtain a more comprehensive set of non-dominated solutions.

[0111] After obtaining the non-dominated solution set, grey relational analysis is used to make decisions based on it. Grey relational analysis is a method for analyzing and evaluating the relationship between multiple variables. It is mainly applied in situations of uncertainty and insufficient information, and can effectively handle decision problems with incomplete or ambiguous information. Through decision-making, the differences between alternatives can be systematically evaluated, and a choice that meets the decision objective can be made. In this embodiment, specifically:

[0112] The objective is to select the optimal solution, and qualitative indicators are determined.

[0113] Collect the index values ​​corresponding to each scheme in the non-dominated solution set and normalize them;

[0114] Select a superior solution from the set of non-dominated solutions as a reference solution and calculate the correlation coefficient of each solution based on the coefficient formula;

[0115] The correlation coefficient is the absolute difference between each alternative and the reference alternative;

[0116] Based on the correlation coefficient, the comprehensive correlation degree of each scheme is calculated, and each scheme is ranked. The scheme with the highest correlation degree is selected as the decision result.

[0117] The decision result, i.e. the optimal solution, serves as the balanced and coordinated optimization network scheme for the water network system.

[0118] According to another aspect of this application, a water network system with balanced and coordinated optimization is provided, characterized in that it includes:

[0119] At least one processor; and

[0120] A memory communicatively connected to at least one of the processors; wherein,

[0121] The memory stores instructions that can be executed by the processor to implement the water network system balanced collaborative optimization networking method described above.

[0122] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A water network system balanced collaborative optimization networking method, characterized in that, Includes the following steps: Step S1: Use an improved meta-analysis method to screen the equilibrium state indicators and network cost indicators of the water network system, construct an initial indicator system for the equilibrium state of the water network system, construct a set of network schemes and input them into the pre-constructed dynamic model of the water network system to obtain the equilibrium state indicator values ​​of the water network system corresponding to each network scheme. Step S2: Use the CNN-BP neural network coupled dimensionality reduction method to reduce the dimensionality of the initial index system of the equilibrium state of the water network system, and obtain the dimensionality reduction index system of the equilibrium state of the water network system. Based on the index values ​​of the equilibrium state of the water network system corresponding to each networking scheme, calculate the corresponding dimensionality reduction index values ​​of the equilibrium state of the water network system in sequence. Step S3: Input the dimensionality reduction index value of the water network system equilibrium state of each networking scheme into the pre-constructed water network system equilibrium state decision model in turn, and select the optimal networking scheme. Step S4: Input the selected optimal networking scheme into the pre-built multi-objective optimization model to obtain the optimized networking scheme, which is the balanced and coordinated optimization networking scheme of the water network system. Step S1 further comprises: Step S11: Collect water network system data, use an improved meta-analysis method to screen and obtain water network system equilibrium state indicators and network cost indicators, and construct an initial indicator system for water network system equilibrium state. Step S12: Construct a dynamic model of the water network system based on the initial index system of the equilibrium state of the water network system and calibrate the model parameters; Step S13: Collect network schemes to construct a network scheme set, input the network scheme set into the water network system dynamic model, and obtain the initial index values ​​of the water network system equilibrium state corresponding to each network scheme. Step S2 further comprises: Step S21: Input the initial index of the equilibrium state of the water network system into the CNN and extract the corresponding spatial features; Step S22: Train a BP neural network model based on the extracted spatial features; Step S23: Use the trained BP neural network model to reduce the dimensionality of the initial index system of the equilibrium state of the water network system, and obtain the dimensionality-reduced index system of the equilibrium state of the water network system. Step S24: Calculate the dimensionality reduction index value of the water network system equilibrium state corresponding to each networking scheme in turn; Step S23 further comprises: Step S23a: Using the initial index value of the equilibrium state of the water network system as the input vector, calculate the absolute and relative changes in the network output value; Step S23b: Calculate the relative contribution rate of the change of each indicator to the network output value in turn; Step S23c: Calculate the relative importance of each indicator in turn; Step S23d: Use the product of relative contribution rate and relative importance as a comprehensive index to determine the initial index of the equilibrium state of the water network system in sequence, delete the initial index with a comprehensive index value lower than the average level, and obtain the dimensionality reduction index system of the equilibrium state of the water network system. The improved meta-analysis method specifically includes: Heterogeneity was addressed through sensitivity analysis, subgroup analysis, and meta-regression analysis. The system searches all relevant research, including unpublished research and grey literature, visualizes the review and analysis of research to identify publication bias, and makes adjustments to address the issue of publication bias. Use consistent tools to evaluate the quality of included studies, ensure the reliability of results, and assess and compare the methodological quality of each study before inclusion in the meta-analysis. We employ statistical methods to improve study inclusion criteria and implement prospective registration, and utilize machine learning and data mining to improve meta-analysis. Step S4 further comprises: Step S41: Construct a multi-objective optimization model with the objective functions of minimizing construction costs, minimizing flood disaster losses, and maximizing GDP support. The constraints include pipeline flow constraints, water pressure constraints, and water quality limitations. Step S42: Input the optimal networking scheme into the multi-objective optimization model, and use the NSGA-III algorithm, which integrates multiple crossover and mutation methods, to calculate the non-dominated solution set; Step S43: Use grey relational analysis to make decisions on the non-dominated solution set and select the optimal solution as the balanced and coordinated optimization network scheme for the water network system. In step S42, the non-dominated solution set calculated using the NSGA-III algorithm, which incorporates multiple crossover and mutation methods, is further described as follows: Step S42a: Obtain reference points based on the structured method, and calculate the number of reference points based on the number of targets and the number of equal parts in the target direction; Step S42b: Randomly generate the parent population during the initialization process; Step S42c: Generate a progeny population with the same size as the parent population using various crossover and mutation operations, and merge the progeny population with the parent population using an elitist strategy; Step S42d: Perform fast non-dominated sorting on the merged population, and obtain a set of optimized solutions close to the reference point based on the reference point strategy; Step S42e, repeat steps S42b to S42d until complete convergence, and use the current population as the final result; After obtaining the set of non-dominated solutions, grey relational analysis is used to make decisions about the set of non-dominated solutions, specifically as follows: The objective is to select the optimal solution, and qualitative indicators are determined. Collect the index values ​​corresponding to each scheme in the non-dominated solution set and normalize them; Select a superior solution from the set of non-dominated solutions as a reference solution and calculate the correlation coefficient of each solution based on the coefficient formula; The correlation coefficient is the absolute difference between each alternative and the reference alternative; Based on the correlation coefficient, the comprehensive correlation degree of each scheme is calculated, and each scheme is ranked. The scheme with the highest correlation degree is selected as the decision result, and the decision result, i.e. the optimal scheme, is the balanced and coordinated optimization network scheme of the water network system.

2. The water network system balanced collaborative optimization networking method as described in claim 1, characterized in that, Step S3 further comprises: Step S31: Construct a decision model for the equilibrium state of the water network system; Step S32: Input the dimensionality reduction index value of the water network system equilibrium state of each networking scheme into the water network system equilibrium state decision model in sequence, calculate the comprehensive weight value of each networking scheme, sort them according to the size, and select the networking scheme with the largest comprehensive weight value as the optimal networking scheme.

3. The water network system balanced collaborative optimization networking method as described in claim 2, characterized in that, Step S31 further comprises: Step S31a: Assign weights to the dimensionality reduction index of the equilibrium state of the water network system using both subjective and objective weighting methods. Step S31b: Based on the subjective and objective weight values ​​of the water network system equilibrium state dimensionality reduction index, game theory is used to obtain the comprehensive weight value of the water network system equilibrium state dimensionality reduction index.

4. A water network system with balanced and coordinated optimization, characterized in that: include: At least one processor; as well as A memory communicatively connected to at least one of the processors; wherein, The memory stores instructions that can be executed by the processor to implement the water network system balanced collaborative optimization networking method according to any one of claims 1 to 3.

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