A rece causal network resilience multi-objective optimization method

Abstract

The application discloses a RECE causal network resilience multi-objective optimization method and belongs to the technical field of complex network data analysis. The steps comprise the following steps: constructing an index framework representing RECE and acquiring corresponding multi-source data; evaluating the causal relationship among RECE indexes by using a multi-space convergent cross mapping model, and determining the synergy / trade-off attribute of the causal relationship by using linear regression; performing link prediction by using a non-negative matrix factorization model containing PageRank and asymmetric link clustering information, taking the sum of network efficiency and edge weight increase / decrease as a target function, performing multi-objective optimization by using NSGA-II, and obtaining optimal network edge weight configuration and priority management path. The application quantitatively identifies the interaction relationship among RECEs and improves network function resilience, and provides technical support for RECE collaborative promotion and policy optimization.

Description

Technical Field

[0001] This invention relates to the field of data analysis technology for complex networks in sustainable development, and more specifically to a multi-objective optimization method for the resilience of RECE causal networks. Background Technology

[0002] Against the backdrop of rapid urbanization and global change, population agglomeration, industrial development, and high-intensity economic activity have significantly increased resource demand, while further exacerbating climate change and ecological environmental pressures. In other words, resources, economy, climate, ecology, and environmental factors (RECE) form a closely coupled relationship, becoming a key component of the human-land system.

[0003] Resource development and utilization can support economic growth, but may also lead to ecological degradation and increased carbon emissions; economic development can improve governance capabilities and technological levels, but may further intensify resource consumption and environmental pressures; climate change may exacerbate the complex interactions and coordination pressures within the RECE system by affecting hydrological processes, agricultural production, energy supply, and ecosystem functions. Therefore, accurately understanding the interactions among RECE is of great significance for promoting sustainable development.

[0004] Current research has identified the interactive relationships between specific departments and objectives related to RECE from the perspectives of correlation analysis, regression analysis, and network analysis. For example, network analysis methods can treat different departments or development objectives as nodes and represent the interactions between departments or objectives as edges, thereby characterizing the overall structure of the interactive system and identifying important nodes or key relationships. However, synergy and trade-offs are not inherent attributes of RECE-related objectives as nodes, but rather arise and are transmitted through the interactions between them as nodes. Existing interactive network analyses mostly focus on the static description of observed relationships and the identification of important nodes. Research on how to proactively adjust the relationships between nodes based on existing interactive networks, thereby enhancing synergy and weakening trade-offs to optimize resilience, remains insufficient.

[0005] Meanwhile, in actual governance, any measures that enhance or weaken synergy require corresponding resource investment, and the greater the intervention intensity, the higher the implementation cost. However, existing network resilience optimization methods usually focus more on improving system functional indicators such as network efficiency, while insufficiently considering the intervention costs required to achieve this improvement, resulting in excessive adjustment of edge weights and excessive resource investment.

[0006] Therefore, overcoming the above-mentioned shortcomings is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0007] In view of the above problems, this invention proposes a multi-objective optimization method for the resilience of RECE causal networks. The method aims to construct a RECE causal interaction network based on multi-source time series data, identify the trade-offs and synergies between RECEs, and determine the edge weight optimization scheme that improves synergy and weakens trade-offs under cost constraints by actively adjusting the synergistic and trade-off edges, thereby improving the overall network resilience. This provides technical support for the systematic governance and sustainable development decision-making of RECE.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] In a first aspect, embodiments of the present invention provide a multi-objective optimization method for the resilience of RECE causal networks, characterized in that the steps include: Establish a RECE indicator framework to characterize resources, economy, climate and ecology, and obtain corresponding multimodal time series data; Based on the RECE index framework and the multimodal time series data, an initial RECE causal interaction network is constructed using a multi-space convergent cross-mapping model and a linear regression model. Based on the positive and negative attributes of causal relationships, the initial RECE causal interaction network is split into a collaborative sub-network and a trade-off sub-network. A non-negative matrix factorization model that integrates local and global topological information is used to predict potential edges in the collaborative sub-network and the trade-off sub-network, respectively, to obtain a collaborative enhancement sub-network and a trade-off enhancement sub-network. The first objective function is to maximize the global efficiency of the collaborative enhancement subnetwork and minimize the total increase in edge weights. The second objective function is to minimize the global efficiency of the trade-off enhancement subnetwork and minimize the total decrease in edge weights. The first objective function and the second objective function are solved to determine the edge weight optimization scheme and obtain the optimized RECE causal network structure.

[0010] As a priority, the multimodal time series data is standardized, including uniformly mapping each indicator in the multimodal time series data using a target value-benchmark value linear transformation. The target value is determined based on a four-step decision tree, and the benchmark value is determined based on the bottom n% quantile of the historical data distribution, where n>0. Indicators exceeding the target value are assigned 100 points, and indicators below the benchmark value are assigned 0 points.

[0011] As a priority, an initial RECE causal interaction network is constructed using a multi-space convergent cross-mapping model and a linear regression model, including: using the multi-space convergent cross-mapping model to evaluate the causal relationship between RECE indicators, obtaining the causal direction and strength between RECE indicators, and using the linear regression model to determine the positive or negative direction of the causal relationship, obtaining the positive or negative attributes of the causal relationship between RECE indicators.

[0012] Preferably, the causal relationship between RECE indices is evaluated using a multi-space convergent cross-mapping model, including: The time series of RECE indicators from different regions are spliced ​​together to construct a multi-spatial time series sample; the causal relationship between RECE indicators is determined by running a convergent cross-mapping model, and the causal strength is characterized by the predictive power of the cross-mapping.

[0013] Preferably, determining the positive or negative direction of the causal relationship using a linear regression model includes: Based on the identified causal direction, a linear regression model is established with the index corresponding to the dependent variable as the explained variable and the SDG corresponding to the independent variable as the explanatory variable. When the regression coefficient is greater than 0, the causal relationship is determined to be a synergistic relationship; when the regression coefficient is less than 0, the causal relationship is determined to be a trade-off relationship.

[0014] Preferably, the initial RECE causal interaction network is a weighted directed network, wherein network nodes represent RECE indicators, network edges represent causal relationships between RECE indicators, the direction of the edge indicates the direction of causal action, the weight of the edge represents the causal strength, and the positive or negative attributes of the edge represent cooperative or trade-off relationships.

[0015] As a preferred approach, the nonnegative matrix factorization model that integrates local and global topological information has the following optimization objective function:

[0016] In the formula, Represents the basis matrix. Represents the coefficient matrix. Represents a nonnegative matrix. This represents the local optimization objective. This represents the global optimization objective. A positive parameter representing the contribution of control to global information. This represents a positive parameter to prevent overfitting, and F represents the Frobenius norm.

[0017] As a preferred approach, in the nonnegative matrix factorization model that integrates local and global topological information... The local optimization objective introduces an asymmetric link clustering coefficient; the asymmetric link clustering coefficient is obtained based on the observed similarity of link directions and the similarity of asymmetric link clustering coefficients. The global optimization objective introduces a node influence matrix; the node influence matrix is ​​obtained based on the PageRank algorithm.

[0018] As a priority, after predicting the potential edges, the following preliminary screening steps are performed: Remove potential edges whose absolute weight is lower than the minimum edge weight in the initial RECE causal interaction network; When both collaborative potential edges and trade-off potential edges exist for the same directed node pair, their absolute weights are compared, and the one with the higher absolute weight is retained. The absolute value of the difference between the two weights is used as the final edge weight of the current directed node pair, and the edge direction follows the positive or negative attribute corresponding to the one with the higher absolute weight value.

[0019] As a priority, the global efficiency is defined as the inverse mean of the shortest distances between all pairs of nodes in the corresponding sub-network, which is used to characterize the functional resilience of the RECE causal interaction network. The shortest distance is:

[0020]

[0021] In the formula, Let i be the shortest distance between nodes i and j. This represents the path from i to j, where u and v are paths. The nodes on This represents the path length from node u to node v. This indicates that the subsequent weights have been adjusted. The decision variables are determined based on the weight of each existing edge and the decision variables are either the amount of increase or decrease in edge weight.

[0022] As a priority, the decision variables satisfy the following in the collaborative enhancement subnetwork:

[0023] In the tradeoff-enhanced subnetwork, the following conditions are met:

[0024] In the formula, Let E represent the decision variables between node i and node j, and let E represent the set of edges in the subnetwork. This represents the original edge weight between node i and node j.

[0025] As a priority, the first objective function and the second objective function are solved, including: The NSGA-II multi-objective evolutionary algorithm is used to solve the problem. Through population initialization, crossover, mutation, non-dominated sorting, and crowding distance selection, the Pareto front solution sets of the cooperative enhancement subnetwork and the tradeoff enhancement subnetwork are obtained. In the target space, an ideal point is set, and the Euclidean distance between each solution in the Pareto front solution set and the ideal point is calculated. The solution with the smallest distance is selected as the optimal edge weight configuration scheme.

[0026] The coordinates of the ideal point are composed of the maximum theoretical value of the global efficiency of the cooperative subnetwork and the minimum theoretical value that balances the global efficiency of the subnetwork.

[0027] In a second aspect, embodiments of the present invention provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a RECE causal network resilience multi-objective optimization method as described in any of the preceding claims.

[0028] This invention provides a multi-objective optimization method for the resilience of RECE causal networks, addressing the difficulty in proactively adjusting the cooperative and trade-off relationships between RECEs in existing technologies. Specifically, it constructs a standardized time-series dataset, identifies the causal direction, strength, and positive / negative attributes between RECEs, and builds an enhanced causal interaction network through link prediction. Furthermore, it performs multi-objective optimization on the cooperative sub-network and the trade-off sub-network respectively, thereby determining the edge weight optimization scheme for the enhanced RECE causal interaction network.

[0029] Compared with existing technologies, the beneficial effects include at least the following: 1. This invention constructs a standardized time-series dataset based on multi-source time-series data, which can unify raster data and statistical data into a data foundation that can be used for RECE causal relationship identification; 2. This invention utilizes a multi-space convergent cross-mapping model to evaluate the causal relationships among SDGs, enabling the acquisition of causal direction and strength among RECE indicators. By combining a linear regression model to determine the positive and negative attributes of causal relationships, it can distinguish between synergistic and trade-off relationships among RECE indicators and construct an initial RECE causal interaction network with direction, strength, and positive / negative attributes.

[0030] 3. This invention splits the initial RECE causal interaction network into a cooperative sub-network and a trade-off sub-network, and performs link prediction on each, thereby constructing an enhanced RECE causal interaction network.

[0031] 4. This invention performs multi-objective optimization on the enhanced collaborative subnetwork and the trade-off subnetwork, respectively. The increase in collaborative edge weights and the decrease in trade-off edge weights are used as decision variables. The NSGA-II algorithm is employed to obtain the Pareto optimal solution set, and the ideal solution is selected by Euclidean distance from a preset ideal point. This allows for the determination of the edge weight optimization scheme for the enhanced SDG causal interaction network. The multi-objective optimization in this application can simultaneously consider both performance improvement and cost control, constraining the total amount of edge weight adjustment while enhancing collaboration and weakening trade-offs, thus better meeting the actual decision-making needs of RECE system governance. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0033] Figure 1 This is a flowchart of the RECE causal network resilience multi-objective optimization method provided in this embodiment of the invention; Figure 2 The RECE initial causal network, link prediction results, and enhanced causal network graph provided in this embodiment of the invention; Figure 3 This is a diagram showing the optimized RECE causal network results provided in an embodiment of the present invention. Detailed Implementation

[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0035] Specifically, in view of the lack of technical process in the existing technology that combines causal network construction, potential relationship completion and network resilience optimization based on multi-source time series data, this invention discloses a RECE causal network resilience multi-objective optimization method to determine the edge weight configuration scheme of synergistic enhancement and trade-off weakening under the condition of limited input.

[0036] Example 1: like Figure 1 As shown in this embodiment, a multi-objective optimization method for the resilience of RECE causal networks includes the following steps: S1, RECE data collection and preprocessing; Establish a RECE indicator framework to characterize resources, economy, climate and ecology, and obtain corresponding multimodal time series data; S2, RECE causal relationship identification; Based on the RECE index framework and the multimodal time series data, an initial RECE causal interaction network is constructed using a multi-space convergent cross-mapping model and a linear regression model. S3, Completion of potential interactive relationships; Based on the positive and negative attributes of causal relationships, the initial RECE causal interaction network is split into a collaborative sub-network and a trade-off sub-network. A non-negative matrix factorization model that integrates local and global topological information is used to predict potential edges in the collaborative sub-network and the trade-off sub-network, respectively, to obtain a collaborative enhancement sub-network and a trade-off enhancement sub-network. S4, RECE causal network multi-objective optimization; The first objective function is to maximize the global efficiency of the collaborative enhancement subnetwork and minimize the total increase in edge weights. The second objective function is to minimize the global efficiency of the trade-off enhancement subnetwork and minimize the total decrease in edge weights. The first objective function and the second objective function are solved to determine the edge weight optimization scheme and obtain the optimized RECE causal network structure.

[0037] It should be noted that the step numbers above are for descriptive convenience only and do not constitute a strict limitation on the order of step execution. In some implementations, some steps can be executed in parallel or their order can be adjusted in an equivalent manner.

[0038] In one alternative implementation, step S1 first establishes a RECE indicator framework; in some implementations, the Sustainable Development Goals (SDGs) are used as RECE proxies, and the official and specific target definitions in the SDG framework are mapped to the resource (water, energy, food), economic, climate, and ecological sectors to construct the RECE indicator framework.

[0039] Then, multi-source time-series data corresponding to the aforementioned indicator framework are collected, and preprocessed, imputed for missing values, and standardized to obtain a standardized time-series dataset. The multi-source data includes raster data and statistical data, with the raster data including land use data and remote sensing imagery. Preprocessing includes: projection transformation, cropping, and zonal statistical processing of the raster data; converting the raster data into panel data according to the administrative units and years of the study area; and matching the panel data with the statistical data to form a unified region-year-indicator dataset.

[0040] In some implementations, the standardization process includes applying a target-to-benchmark linear transformation to map all index values ​​in the multimodal time-series data to the 0-100 range, thereby mitigating the potential impact of data distribution skew on the standardization results; the formula is expressed as:

[0041] In the formula, These are the raw data values ​​for each indicator. It is a score normalized to the range of 0-100. , These are the benchmark and target values ​​for the indicator.

[0042] In this embodiment, the setting of the target value and the baseline value follows the following principles: The target values ​​are determined based on a four-step decision tree, meaning that if the condition in the previous step is met, all subsequent steps are skipped. First, the same upper limit is used for indicators used in the 2018 Sustainable Development Goals Indices and dashboard reports; second, for indicators with clear theoretical boundaries or normative optimal values, their ideal values ​​are directly adopted as the optimal values; third, if there is no explicit upper limit, the "leaving no one behind" principle is used to determine the upper limit for indicators related to basic infrastructure and public service coverage; fourth, the upper limit for all other indicators is set as the average of the five best-performing values ​​among all observations of that indicator.

[0043] The benchmark value is determined based on the bottom n% quantile of the historical data distribution, where n>0; for example, the benchmark value is set as the 2.5% quantile value in a single ranked index sequence.

[0044] Based on this, indicators that exceed the target value are assigned 100 points, and indicators that fall below the benchmark value are assigned 0 points, in order to ensure the consistency of dimensions and the stability of calculation among indicators. The data of each indicator are summarized according to the arithmetic mean to form standardized data for causal inference.

[0045] Each indicator is aggregated with equal weights under the same specific SDG objective to form standardized panel data for causal modeling, which is then used as the indicators and data for RECE analysis.

[0046] In an optional implementation, step S2 involves using the RECE index framework and the multimodal time series data to evaluate the causal relationship between RECE indices using a multi-space convergent cross-mapping model, obtaining the causal direction and strength between RECE indices, and using a linear regression model to determine the positive or negative direction of the causal relationship, thereby obtaining the positive or negative attributes of the causal relationship between RECE indices and constructing an initial RECE causal interaction network. Some implementations utilize multispatial convergent cross-mapping models to evaluate the causal relationships between RECE metrics. This includes running the multispatialCCM package in R to determine the causal relationships between RECE metrics. The specific steps are as follows: The RECE index time series from different regions are concatenated into a single vector, with the interval between time series represented by NA, to construct a multi-spatial time series sample. Use the function SSR_pred_boot to find the optimal embedding dimension that maximizes predictive power. The function SSR_check_signal is used to detect whether there is a non-linear signal in the data that is not dominated by noise. Use the function ccm_boot to run the convergent cross-mapping algorithm; If the effectiveness of the convergent cross mapping continuously increases with the length of the library, and converges to a stable level significantly greater than 0 under a large library length, it is considered that there is a definite causal relationship between the variables, and the effectiveness of the convergent cross mapping is used as the weight of the causal relationship.

[0047] In some implementations, to distinguish the positive or negative nature of causal relationships among identified indicators, a linear regression model is used to determine the direction of each causal relationship. This includes: For each confirmed causal direction, a regression model is constructed with the affected variable as the dependent variable and the variable exerting the effect as the independent variable. To eliminate the influence of fixed effects, a double mean removal process is adopted, subtracting the mean of the region and year from each variable to obtain the series after removing fixed effects.

[0048] Based on this, the regression coefficients of Y on X are estimated at the regional level, and the estimation results from each region are averaged to obtain the overall regression coefficient. When the regression coefficients... When the regression coefficient is greater than 0, the causal relationship is determined to be a cooperative relationship; when the regression coefficient is greater than 0, the causal relationship is determined to be a cooperative relationship. When the value is less than 0, the causal relationship is determined to be a trade-off relationship.

[0049] In one specific embodiment, the regression model is represented as follows:

[0050] In the formula, 't' represents the region, and 't' represents the year. It is the explained variable (target variable). It is an explanatory variable. It is a region Fixed effects (controlling for long-term differences between regions). It is the year The fixed effect (controlling the overall trend in each year). This indicates the overall direction (positive or negative) of the influence of X on Y. This is the residual term.

[0051] Ultimately, the initial RECE causal interaction network constructed in this embodiment is a weighted directed network, where network nodes represent RECE indicators, network directed edges represent causal relationships between RECE indicators, the direction of the edge indicates the direction of causal action, the weight of the edge represents the causal strength, and the positive or negative attributes of the edge represent cooperative or trade-off relationships, that is, promoting relationships correspond to positive edges, and inhibiting relationships correspond to negative edges.

[0052] In an optional implementation, step S3 involves splitting the initial RECE causal interaction network into a collaborative sub-network and a trade-off sub-network based on the positive or negative attributes of the causal relationship; and using a non-negative matrix factorization model to predict potential edges in the collaborative sub-network and the trade-off sub-network, respectively.

[0053] This embodiment employs nonnegative matrix factorization. By minimizing the Frobenius norm error between the original matrix A and its low-rank approximation under nonnegative constraints, it achieves a dimensionality reduction representation and structural approximation of A, as shown in the following formula:

[0054]

[0055] In the formula, A is the original subnetwork. As a basis matrix, The coefficient matrix, Let K be the set of nonnegative real numbers, n be the number of nodes in the original subnetwork, K be the latent dimension, and T denote the transpose. Let F be the objective function of nonnegative matrix decomposition, i.e., the reconstruction error, and let F denote the Frobenius norm.

[0056] Furthermore, the nonnegative matrix factorization model in this embodiment incorporates both local and global topological information.

[0057] In a preferred implementation, local information of the network is mined through observed link directions and asymmetric link clustering coefficients. Specifically, the final asymmetric link clustering coefficient is calculated from the observed link direction similarity and the similarity of the asymmetric link clustering coefficients, denoted as S. This S is then incorporated into the non-negative matrix factorization objective function to obtain an optimization objective that considers local information, as shown in the following formula:

[0058]

[0059] In the formula, S represents the asymmetric link clustering coefficient matrix. This represents the observed link direction similarity matrix. This represents the similarity matrix of asymmetric link clustering coefficients. This represents the local optimization objective. Parameters used to control the degree of participation of local information.

[0060] Among them, the observed link direction similarity matrix Asymmetric link clustering coefficient similarity matrix The elements in the code are obtained through the following steps: Define B as the unweighted adjacency matrix of the network, i.e., if there exists a link from i to j, then ,on the contrary ,but:

[0061]

[0062]

[0063]

[0064]

[0065] In the formula, It is the observed link direction similarity between nodes i and j. This represents the unweighted connection vector between nodes i and j. , , Let represent the asymmetric clustering coefficient similarity from node i to z, i to j, and j to i, respectively. Let i be the set of the in-neighbors of node i. Let z be the set of out neighbors. Let z be the out-degree of node z. Let nodes i and j be common neighbors. , Let be the set of incoming neighbors of node j.

[0066] In a preferred implementation, a node influence matrix is ​​introduced to obtain global topology information; in this implementation, the node influence matrix is ​​determined based on the PageRank algorithm. Furthermore, in order to fully utilize global information, Mapping to a low-dimensional latent space The loss function is minimized, and the formula is as follows:

[0067] In the formula, This represents the global optimization objective. Represents the basis matrix. It is a non-negative matrix, a basis matrix Each line in It can be viewed as a low-dimensional latent representation of nodes, with W providing degrees of freedom to make the decomposition more accurate; This represents the node influence matrix, whose elements... Influence score representing node i [0,1];

[0068]

[0069] Where p is the damping coefficient, set to 0.5, and N is the total number of nodes. It is the out-degree of node j. This represents the influence score of node j. It is the node influence score matrix. It is the unweighted adjacency matrix of nodes.

[0070] By fusing local and global information, the objective function of the link prediction model is obtained: The formula is as follows:

[0071] In the formula, Represents the basis matrix. Represents the coefficient matrix. Represents a nonnegative matrix. This represents the local optimization objective. This represents the global optimization objective. A parameter representing the degree of participation of local information. A positive parameter representing the contribution of control to global information. This represents a positive parameter to prevent overfitting.

[0072] Furthermore, let = The final matrix is ​​obtained through the following update rules:

[0073]

[0074]

[0075] In the formula, It is the Hadamard product. Among the parameters, =4, =0.05, =0.1. Repeat the above rule until the maximum number of iterations (40 times) is reached.

[0076] In a preferred embodiment, the obtained collaborative and tradeoff potential edges are filtered, removing potential edges whose absolute weights are lower than the smallest edge weight in the initial RECE causal interaction network. When both collaborative and tradeoff potential edges exist for the same directed node pair, the potential edge with the larger absolute weight is retained, and the absolute value of the difference between their weights is used as the weight of that potential edge. This ultimately yields an enhanced causal network.

[0077] In one alternative implementation, step S4 involves performing multi-objective optimization on both the collaborative enhancement subnetwork and the trade-off enhancement subnetwork.

[0078] For each subnetwork, first define Define the weight of each existing edge and the decision variables. In the cooperative subnetwork, the increase in cooperative edge weights is used as the decision variable; in the trade-off subnetwork, the decrease in trade-off edge weights is used as the decision variable. Since edge weights in the network represent the strength of causal relationships, the adjusted edge weights are defined... The boundary still belongs to [0,1], as shown in the following formula:

[0079]

[0080] in, This represents the adjusted edge weight between node i and node j. This represents the original edge weight between node i and node j. This represents the decision variables between node i and node j.

[0081] Simultaneously, decision variable constraints are set for both positive and negative networks. Specifically, in a collaborative network, the total increase cannot exceed its overall upside potential; that is, the sum of the newly added weights on each edge cannot exceed the remaining capacity of its initial weights within a 1-degree radius of the upper bound. In a tradeoff network, the total decrease cannot exceed its overall downside potential; that is, the sum of the decreased weights on each edge cannot exceed the sum of the network's own weights, as shown in the following formula:

[0082]

[0083] In the formula, E represents the set of edges in the subnetwork.

[0084] Furthermore, this embodiment uses maximizing the global efficiency of the collaborative enhancement subnetwork and minimizing the total increase in edge weights as the first objective function, and minimizing the global efficiency of the trade-off enhancement subnetwork and minimizing the total decrease in edge weights as the second objective function. This aims to maximize the transmission of positive effects in the causal network and minimize the diffusion of negative effects. Simultaneously, in reality, adjusting the causal paths between RECEs requires intervention costs, and the overall intervention intensity is constrained by budget. Therefore, for the subnetwork, it is also desirable to minimize the total intervention amount, i.e., the sum of the increased or decreased edge weights. Finally, from a resilience perspective, the optimization of the edges of the collaborative and trade-off subnetworks can be transformed into two multi-objective optimization problems, as shown in the following formulas:

[0085]

[0086] Here, This represents the global efficiency of the network and is used to characterize the functional resilience of RECE causal interaction networks. The number of nodes in the network. The shortest distance between nodes i and j is expressed as:

[0087] in, This represents the path from i to j, where u and v are paths. The nodes on This represents the path length from node u to v. Edges with higher weights have shorter lengths, as shown below:

[0088] In the formula, This indicates that the weights following the adjustment will be changed.

[0089] In a preferred implementation, the NSGA-II multi-objective evolutionary algorithm is used to solve each optimization problem. Specifically, based on the DEAP framework, it obtains Pareto front solution sets for the cooperative reinforcement sub-network and the tradeoff reinforcement sub-network through population initialization, crossover, mutation, non-dominated sorting, and crowding distance selection. Furthermore, an ideal point (i.e., the theoretical limit of optimal efficiency and minimum input) is defined, and the solution with the minimum Euclidean distance to this ideal point is selected from the Pareto solution set as the representative RECE interaction network edge weight optimization scheme, ultimately outputting the optimized RECE causal network structure.

[0090] Example 2: Based on Example 1, the following specific implementation method is provided. Referring to the definitions of official targets and specific targets in the United Nations Sustainable Development Goals framework, for the Beijing-Tianjin-Hebei urban agglomeration, 43 indicators from 7 SDGs and their 36 specific targets for assessing RECE are selected, and annual data for these indicators from 13 cities in the Beijing-Tianjin-Hebei region from 2000 to 2023 are collected. This embodiment uses the 36 SDG specific targets as proxy indicators for RECE analysis, as detailed in Table 1. Table 1 RECE Evaluation Index Framework

[0091] Furthermore, the multi-source time-series data is preprocessed; an initial RECE causal interaction network is constructed using a multi-spatial convergent cross-mapping model and a linear regression model. For example, in this embodiment, the RECE index scores of each city from 2000 to 2023 obtained in step S1 are used as input, and the multi-spatial convergent cross-mapping model is run according to the specific objective. For the identified directed causal relationships, the RECE index scores of each city from 2000 to 2023 are also used as input, and linear regression is run to obtain the positive and negative attributes of the causal relationship. An initial interaction network is constructed through the causal relationships between RECEs, where nodes are RECE indices, causal relationships are edges, and causal strength is the edge weight.

[0092] To supplement potential interactions not identified by the multi-space convergent cross-mapping model, the initial causal network is split into positive and negative sub-networks, and a non-negative matrix factorization model is used to predict links in the cooperative and tradeoff sub-networks. For example, as... Figure 2 As shown, Figure 2 Figure a illustrates the initial causal relationship network identified based on the multi-space convergent cross-mapping model in this embodiment. Figure 2 In the diagram, b represents the potential causal network obtained based on the link prediction algorithm. Figure 2 In the middle, c represents the final causal network after integrating both. The edge colors, from red to blue, represent negative (trade-off) and positive (synergistic) relationships, respectively, and the intensity of the color indicates the strength of the causal influence.

[0093] In this embodiment, the external policy input is ultimately viewed as an adjustment to the edge weights in the causal network, and the NSGA-II algorithm is used to perform multi-objective optimization in the trade-off and cooperative subnetworks, respectively. For example, Figure 3 The multi-objective optimization results of the RECE causal network provided in this embodiment are shown. Among them, Figure 3 In this context, 'a' represents the cooperative subnetwork before optimization. Figure 3 In this context, 'b' represents the optimized collaborative subnetwork; Figure 3 In the middle, 'c' represents the trade-off subnetwork before optimization. Figure 3 In this context, d represents the optimized collaborative subnetwork.

[0094] In the actual operation of this embodiment, the weights of positive edges in the network were increased, while the weights of negative edges were decreased. The results show that the resilience of the optimized collaborative network was improved by 51%, while the resilience of the negative network was decreased by 53%.

[0095] The embodiments of the present invention have been described in detail above, and the principles and implementation methods of the present invention have been explained. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of the present invention. Those skilled in the art should understand that the embodiments of the present invention can be provided as methods, computer software program products, or electronic devices, etc. For example, a computer-readable storage medium storing a computer program that, when executed by a processor, implements a RECE causal network resilience multi-objective optimization method as described in any of the above claims. That is, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of one or more storage media (including but not limited to disk storage, CDs) containing computer-usable program code. The form of a computer program product implemented on ROM, optical memory, etc. Content or technical means not mentioned in the embodiments of this invention can be obtained by referring to the prior art; this disclosure does not limit the scope of the invention, and therefore will not be elaborated further.

[0096] It should be noted that the word "comprising" does not exclude the presence of components or steps not listed in the claims. The words "a" or "an" preceding a component do not exclude the presence of a plurality of such components. This invention can be implemented by means of hardware comprising several different components and by means of a suitably programmed computer.

[0097] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0098] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-objective optimization method for the resilience of RECE causal networks, characterized by the following steps: include: Establish a RECE indicator framework to characterize resources, economy, climate and ecology, and obtain corresponding multimodal time series data; Based on the RECE index framework and the multimodal time series data, an initial RECE causal interaction network is constructed using a multi-space convergent cross-mapping model and a linear regression model. Based on the positive and negative attributes of causal relationships, the initial RECE causal interaction network is split into a collaborative sub-network and a trade-off sub-network. A non-negative matrix factorization model that integrates local and global topological information is used to predict potential edges in the collaborative sub-network and the trade-off sub-network, respectively, to obtain a collaborative enhancement sub-network and a trade-off enhancement sub-network. The first objective function is to maximize the global efficiency of the collaborative enhancement subnetwork and minimize the total increase in edge weights. The second objective function is to minimize the global efficiency of the trade-off enhancement subnetwork and minimize the total decrease in edge weights. The first objective function and the second objective function are solved to determine the edge weight optimization scheme and obtain the optimized RECE causal network structure.

2. The RECE causal network resilience multi-objective optimization method as described in claim 1, characterized in that, The multimodal time series data is first standardized, including a unified mapping of each indicator in the multimodal time series data using a target value-benchmark value linear transformation. The target value is determined based on a four-step decision tree, and the benchmark value is determined based on the bottom n% quantile of the historical data distribution, where n>0. Indicators exceeding the target value are assigned 100 points, and indicators below the benchmark value are assigned 0 points.

3. The RECE causal network resilience multi-objective optimization method as described in claim 1, characterized in that, An initial RECE causal interaction network is constructed using a multi-space convergent cross-mapping model and a linear regression model, including: using the multi-space convergent cross-mapping model to evaluate the causal relationship between RECE indicators, obtaining the causal direction and strength between RECE indicators, and using the linear regression model to determine the positive or negative direction of the causal relationship, obtaining the positive or negative attributes of the causal relationship between RECE indicators.

4. The RECE causal network resilience multi-objective optimization method as described in claim 1, characterized in that, The objective function of the nonnegative matrix factorization model that integrates local and global topological information is expressed as follows: In the formula, Represents the basis matrix. Represents the coefficient matrix. Represents a nonnegative matrix. This represents the local optimization objective. This represents the global optimization objective. A positive parameter representing the contribution of control to global information. This represents a positive parameter to prevent overfitting, and F represents the Frobenius norm.

5. A multi-objective optimization method for the resilience of RECE causal networks as described in claim 1 or 4, characterized in that, In the nonnegative matrix factorization model that integrates local and global topological information The local optimization objective introduces an asymmetric link clustering coefficient; the asymmetric link clustering coefficient is obtained based on the observed similarity of link directions and the similarity of asymmetric link clustering coefficients. The global optimization objective introduces a node influence matrix; the node influence matrix is ​​obtained based on the PageRank algorithm.

6. The RECE causal network resilience multi-objective optimization method as described in claim 1, characterized in that, After predicting the potential edges, the following preliminary screening steps are performed: Remove potential edges whose absolute weight is lower than the minimum edge weight in the initial RECE causal interaction network; When both collaborative potential edges and trade-off potential edges exist for the same directed node pair, their absolute weights are compared, and the one with the higher absolute weight is retained. The absolute value of the difference between the two weights is used as the final edge weight of the current directed node pair, and the edge direction follows the positive or negative attribute corresponding to the one with the higher absolute weight value.

7. The RECE causal network resilience multi-objective optimization method as described in claim 1, characterized in that, The global efficiency is defined as the reciprocal mean of the shortest distances between all pairs of nodes in the corresponding sub-network; The shortest distance is: In the formula, Let i be the shortest distance between nodes i and j. This represents the path from i to j, where u and v are paths. The nodes on This represents the path length from node u to node v. This indicates that the weights after adjustment are determined based on the weights of each existing edge and the decision variables, where the decision variables are the amount by which the edge weights are increased or decreased.

8. The RECE causal network resilience multi-objective optimization method as described in claim 7, characterized in that, The decision variables satisfy the following in the collaborative enhancement subnetwork: In the tradeoff-enhanced subnetwork, the following conditions are met: In the formula, Let E represent the decision variables between node i and node j, and let E represent the set of edges in the subnetwork. This represents the original edge weight between node i and node j.

9. The RECE causal network resilience multi-objective optimization method as described in claim 1, characterized in that, Solving the first objective function and the second objective function includes: The NSGA-II multi-objective evolutionary algorithm is used to solve the problem and obtain the Pareto front solution set. In the target space, an ideal point is set, and the Euclidean distance between each solution in the Pareto front solution set and the ideal point is calculated. The solution with the smallest distance is selected as the optimal edge weight configuration scheme.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements a RECE causal network resilience multi-objective optimization method as described in any one of claims 1 to 9.

Images