A method for identifying a fragile key node of a supply chain network

Abstract

The application discloses a kind of supply chain network fragile key node identification method, realize the unified modeling and representation of heterogeneous multifunctional supply chain node, make model can complete capture the function dependence and collaborative relationship of supply chain network, the processing process of whole graph embedding vector makes that node embedding process no longer only rely on topological structure but is simultaneously fused with the multi-dimensional attribute information such as function type and function capacity of node, overcome the defect that only topological structure index is used to evaluate vulnerability in prior art, ignore supply chain core function logic, the node representation learned can also include supply chain business semantic information, can identify the bottleneck node on the low topological degree but in core business path, provide complete network state description for subsequent key node identification, obtain key node sequence in combination with the deep DQN network trained, convert key node identification into end-to-end automatic reasoning process, break through the local optimal limit problem caused by traditional static index, greedy sorting.

Description

Technical Field

[0001] This invention belongs to the field of graph embedding technology and relates to a method and system for identifying vulnerable critical nodes in a supply chain network. Background Technology

[0002] In the context of globalization and digital collaboration, modern supply chains have evolved from traditional chain structures into complex network systems with multiple nodes, levels, and functions, encompassing supply, production, warehousing, logistics, and distribution. These nodes are strongly interdependent through the flow of materials, information, and capital. The structural stability and functional continuity of the supply chain network directly determine enterprise production, industrial operations, and supply chain security. As supply chains expand in scale, node functions differentiate, and collaborative relationships become more complex, network vulnerability risks exhibit characteristics such as rapid transmission, high concealment, and prominent cascading failures. Outages at critical nodes and failures in localized links can trigger global supply disruptions, production stoppages, and soaring costs. Therefore, accurately quantifying supply chain vulnerability, automatically identifying critical bottleneck nodes, and optimizing network resilience have become core technological requirements for supply chain risk management and resilience optimization.

[0003] A key node identification method based on GraphSAGE and DQN. One of the closest existing technical solutions is the FINDER method proposed by Fan et al., which for the first time introduces deep reinforcement learning into the task of key node discovery in complex networks, transforming the network disintegration problem into a sequential decision-making process and achieving end-to-end key node identification. This method uses the network topology as the sole input, employs the GraphSAGE graph sampling aggregation model to learn the vector representation of nodes, generates node embeddings by aggregating the topological information of the node's neighborhood, and then inputs the node embeddings into a deep Q-network (DQN). The reward objective is to maximize the descent rate of the network's largest connected component. The trained agent sequentially selects nodes for removal, ultimately generating a ranking of node importance. This method ensures training stability through experience replay and the target network, achieving better disintegration performance than traditional degree-gree-gree-gree-gree-gree-gree-gree-greedy methods on homogeneous networks such as social networks, web networks, and communication networks.

[0004] The S2V-DQN combinatorial optimization method is based on Structure2Vec and DQN. A second similar technique is the S2V-DQN method proposed by Dai et al., a classic framework in graph structure combinatorial optimization. It combines Structure2Vec graph embedding with DQN to learn sequential decision policies on the graph, and can be used for optimization tasks such as node selection, network decomposition, and set coverage. This method learns the topological embedding representation of nodes through random walks and message passing mechanisms, mapping the graph structure to low-dimensional vectors. Then, it uses DQN to learn the optimal node selection policy, aiming to achieve maximum network structure disruption by minimizing the number of node removals. S2V-DQN has strong generalization ability on homogeneous graphs, can be trained on small-scale networks and transferred to large-scale networks, and solves the problem of traditional greedy methods relying on manual metrics.

[0005] A third similar technique is a meta-path and multi-index fusion evaluation method for heterogeneous networks. This type of method characterizes the relationships between nodes through meta-paths and uses topological indices such as fusion degree, betweenness, core number, and path reachability, such as TOPSIS, AHP, and entropy weighting, to rank node importance. This type of method can initially distinguish different types of nodes and capture the structural and semantic information of the network using multiple meta-paths, thus more closely reflecting the characteristics of heterogeneous networks than traditional homogeneous methods.

[0006] Therefore, existing methods generally employ approaches such as complex network topology analysis, homogeneous graph embedding, static index fusion, or general reinforcement learning for identifying critical network nodes and assessing vulnerabilities. However, these methods share common shortcomings in modeling mechanisms, feature learning, optimization objectives, and evaluation systems, leading to a series of inherent drawbacks when applied to supply chain networks.

[0007] First, existing technologies rely solely on network topology as the basis for analysis, using only topological features such as degree, betweenness, clustering coefficient, and connected component size. They fail to consider the clear functional divisions of supply chain nodes, such as supply, production, warehousing, logistics, and distribution, nor do they consider functional attributes such as node service capabilities, business load, and collaborative relationships. Therefore, they cannot effectively characterize heterogeneous nodes, nor can they distinguish the actual role of nodes in the closed loop of supply chain business. Consequently, vulnerability assessments heavily depend on connectivity, failing to identify the hidden risks of "topological connectivity but paralyzed supply chain functions," resulting in assessment results that are severely out of sync with actual supply capabilities.

[0008] Second, since existing technologies are all designed for homogeneous networks and adopt a unified graph embedding and message passing mechanism, they do not distinguish node types, are not aware of business attributes, and do not integrate functional capability information. Therefore, they cannot handle the large number of multifunctional composite nodes in the supply chain, nor can they capture the business link dependencies of supply, production, logistics, and distribution. As a result, the learned node representations only contain structural information and lack the core semantics of the supply chain. Key node identification can only find topological center nodes with high connectivity, and cannot locate bottleneck nodes with low topological connectivity but located on the core business path.

[0009] Third, because existing technologies generally adopt static index ranking or greedy strategies, they lack global sequential decision-making capabilities and rely on manually designed features and manually formulated rules. Therefore, the identification results are prone to getting trapped in local optima and cannot obtain the optimal node sequence that causes the supply chain function to decline rapidly through continuous interactive learning. At the same time, manual indicators are highly subjective and have poor generalization, and cannot adapt to supply chain networks of different structures, scales, and industries, resulting in weak model transferability and limited engineering applications.

[0010] Fourth, since existing technologies aim to disrupt network topology rather than paralyze supply chain business functions, their reward signals, loss functions, and evaluation indicators all revolve around topology destruction, which is misaligned with the actual needs of the supply chain to "ensure smooth operation, supply, and contract fulfillment." As a result, the identified key nodes cannot guide actual risk prevention and control, and the vulnerability analysis conclusions cannot be used to improve supply chain resilience and optimize resource allocation.

[0011] In summary, existing technologies, from modeling, learning, evaluation to decision-making, emphasize topology over functionality, homogeneity over heterogeneity, and statics over intelligence. In principle, they are not suitable for vulnerability identification and critical bottleneck node discovery tasks in supply chain networks. Summary of the Invention

[0012] The purpose of this invention is to solve the problems in the prior art and provide a method and system for identifying vulnerable critical nodes in a supply chain network.

[0013] To achieve the above objectives, the present invention employs the following technical solution: A method for identifying vulnerable critical nodes in a supply chain network includes the following steps: Obtain the topological connections, functional types, and capability values ​​of nodes in the actual supply chain network, and abstract the supply chain network into a heterogeneous graph containing nodes with multiple functional types. For each node in the heterogeneous graph, an initial feature vector is constructed. Based on the initial feature vector, feature mapping and attention weighting calculation are performed on neighboring nodes of different functional types. The topological structure information and functional capability information of neighboring nodes are aggregated to generate an updated node embedding vector. The node embedding vector is pooled to obtain the whole graph embedding vector representing the state of the entire supply chain network. Obtain the trained deep DQN network, input the whole image embedding vector as the current network state into the deep DQN network, and obtain the key node sequence.

[0014] A further improvement of the present invention is that: The heterogeneous graph is represented by the following formula:

[0015] in, A set of nodes, containing supply nodes. Production scheduling nodes Logistics and distribution nodes Three core functional categories; Let it be the set of edges; This is a node type mapping function used to identify the functional category to which a node belongs; , which are node capability vectors, representing the service capability strength of the node in the supply, production, and distribution stages, respectively.

[0016] The construction of an initial feature vector for each node in the heterogeneous graph includes: A heterogeneous graph attention embedding module is constructed, which integrates the topological features of the nodes themselves, the one-hot encoding of the node's functional type, and the node's capability values ​​in the three functions of supply, production, and distribution to obtain an initial feature vector.

[0017] The feature mapping of neighbor nodes of different functional types based on the initial feature vector includes: In each graph convolutional layer, the features are subjected to independent linear transformations based on the node function type:

[0018] in, For linear transformation matrices bound to node types, For nodes The embedding vector in the previous layer.

[0019] The attention-weighted calculation includes: Compute the basic attention weights between nodes, which are used to characterize the strength of dependencies in the topology; A similarity term for ability attributes is introduced to calculate the ability attention weight. The basic attention weight and the ability attention weight are then fused to obtain the final attention coefficient. The attention coefficient is then normalized to obtain the attention weight.

[0020] The aggregation of neighboring node topology and functional capabilities generates an updated node embedding vector. This node embedding vector is then pooled to obtain a graph embedding vector representing the overall supply chain network state, including: Obtain basic structure messages based on attention weights and node features; The node capability vector is mapped to weights, and the neighbor features are weighted and enhanced to obtain the capability enhancement message; By integrating infrastructure messages and capability enhancement messages, information transmitted by neighboring nodes can be obtained. By integrating the information transmitted by all neighboring nodes, we obtain the node embedding vector. Then, we perform pooling on the node embedding vector to obtain the whole graph embedding vector representing the state of the entire supply chain network.

[0021] A system for identifying vulnerable critical nodes in a supply chain network, comprising: The heterogeneous graph construction module is used to obtain the topological connection relationship of nodes in the actual supply chain network, the functional type of nodes, and the capability value of nodes in each function, and to abstract the supply chain network into a heterogeneous graph containing nodes with multiple functional types. The whole graph embedding vector acquisition module is used to construct an initial feature vector for each node in the heterogeneous graph. Based on the initial feature vector, feature mapping and attention weighting calculation are performed on neighboring nodes of different functional types. The topological structure information and functional capability information of neighboring nodes are aggregated to generate an updated node embedding vector. The node embedding vector is pooled to obtain the whole graph embedding vector representing the state of the entire supply chain network. The key node identification module is used to obtain the trained deep DQN network. It inputs the whole image embedding vector as the current network state into the deep DQN network to obtain the key node sequence.

[0022] A computer program product includes a computer program that, when executed by a processor, implements any one of the methods described.

[0023] A terminal device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of any of the methods described above.

[0024] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of any of the methods described herein.

[0025] Compared with the prior art, the present invention has the following beneficial effects: This invention discloses a method for identifying vulnerable critical nodes in a supply chain network. It constructs a heterogeneous graph that abstracts the supply chain network into nodes with multiple functional types, achieving unified modeling and representation of heterogeneous, multifunctional supply chain nodes. This solves the problem that existing homogeneous graph models cannot distinguish node functional types or represent multifunctional composite nodes, enabling the model to fully capture the functional dependencies and collaborative relationships of the supply chain network. The whole-graph embedding vector processing process ensures that the node embedding process no longer relies solely on topology but also integrates multi-dimensional attribute information such as node functional type and capabilities. This overcomes the shortcomings of existing technologies that only evaluate vulnerability based on topology indicators and ignore the core functional logic of the supply chain. The learned node representation can also include supply chain business semantic information, identifying bottleneck nodes with low topological degree but located on core business paths, providing a complete network state description for subsequent critical node identification. Finally, the method combines a trained deep DQN network to obtain a sequence of critical nodes, transforming critical node identification into an end-to-end automatic reasoning process. This overcomes the limitations of local optima caused by traditional static indicators and greedy sorting, transforming vulnerable node identification into a sequential decision-making problem, removing the optimal node removal sequence when supply chain functionality rapidly declines, and improving the effectiveness and efficiency of critical bottleneck identification. Attached Figure Description

[0026] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is a message passing architecture diagram disclosed in an embodiment of the present invention; Figure 2 This is a sample graph node embedding effect diagram disclosed in an embodiment of the present invention; Figure 3 This is a diagram of the overall training architecture disclosed in an embodiment of the present invention; Figure 4 This is an example diagram illustrating the meaning of AUDC as disclosed in an embodiment of the present invention; Figure 5 The diagrams show a comparison of the disintegration effects and the greedy method (where a represents a comparison of B-type network disintegration strategies; b represents a comparison of SD-type network disintegration strategies; c represents a comparison of RM-type network disintegration strategies; and d represents a comparison of HC-type network disintegration strategies). Figure 6The following are comparative diagrams of the methods disclosed in the embodiments of the present invention (where a represents a comparative diagram of B-type network disintegration strategies; b represents a comparative diagram of SD-type network disintegration strategies; c represents a comparative diagram of RM-type network disintegration strategies; and d represents a comparative diagram of HC-type network disintegration strategies). Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0029] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0030] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0031] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper," "lower," "horizontal," or "inner" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of the invention is in use, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. Furthermore, terms such as "first" and "second" are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0032] Furthermore, the use of the term "horizontal" does not imply that the component must be absolutely horizontal, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0033] In the description of the embodiments of the present invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention according to the specific circumstances.

[0034] The present invention will now be described in further detail with reference to the accompanying drawings: See Figure 1 To address the inherent shortcomings of existing technologies, such as relying solely on topology, detaching from the essential functions of the supply chain, failing to handle node heterogeneity, depending on static greedy strategies, and struggling to achieve globally optimal decisions, which cannot meet the practical needs of accurate vulnerability assessment and key bottleneck node identification in real supply chain networks, this invention discloses a method and system for identifying vulnerable key nodes in supply chain networks. By constructing a function-oriented vulnerability measurement system, a heterogeneous graph modeling method, and an intelligent reinforcement learning identification framework, it achieves high-precision, high-efficiency, and highly practical supply chain network vulnerability analysis, thus overcoming the core deficiencies of existing technologies.

[0035] This embodiment mainly includes the following: First, we will build a function-oriented supply chain vulnerability assessment system to overcome the shortcomings of existing technologies that only evaluate vulnerability based on topological indicators such as connectivity and maximum connected branches, which are detached from the closed loop of supply chain business. We will establish quantitative indicators based on the complete fulfillment link and node service capabilities to achieve accurate measurement of the actual operational capabilities and damage level of the supply chain.

[0036] Second, to achieve unified modeling and representation of heterogeneous multifunctional supply chain nodes, addressing the problem that existing homogeneous graph models cannot distinguish node functional types or represent multifunctional composite nodes, we construct a heterogeneous graph model for the supply chain and design a feature embedding method that integrates node type, functional capabilities, and topology. This enables the model to fully capture the functional dependencies and collaborative relationships of the supply chain network, improving the accuracy and applicability of feature representation.

[0037] Third, a superior intelligent identification method for critical vulnerable nodes is proposed to overcome the limitations of local optima caused by traditional static indicators and greedy sorting. It transforms vulnerable node identification into a sequential decision problem and uses deep reinforcement learning to achieve end-to-end global optimization. It automatically learns the optimal node removal sequence that can cause the supply chain function to decline rapidly, thereby improving the effectiveness and efficiency of critical bottleneck identification.

[0038] Fourth, it accurately identifies hidden bottleneck nodes that are secondary in topology but critical in function, overcoming the shortcomings of existing methods that can only identify explicit topology nodes with high degree of connectivity and large betweenness. Through a function-aware feature learning and decision-making mechanism, it accurately locates those hidden critical nodes that have low connectivity but are located in the core performance chain and play a decisive role in supply capacity, thereby improving the comprehensiveness of risk identification.

[0039] Fifth, it provides an engineering-ready intelligent vulnerability analysis method to build an end-to-end intelligent learning framework that does not require manual indicator design or parameter tuning. It can adapt to supply chain networks of different sizes, structures, and types, and realize full-process automation from network data input to vulnerability assessment and key node output. It provides stable, reliable, and directly implementable technical support for supply chain resilience design, risk prevention and control, and resource optimization.

[0040] Specifically, the following steps are included: Step 1: Embedding Heterogeneous Supply Chain Network Modern supply chain networks exhibit significant heterogeneity, with different nodes performing differentiated functions such as supply, production scheduling, and logistics distribution, and many nodes possessing multifunctional composite attributes. To accurately characterize this feature, this invention abstracts the supply chain network as a type of point-weighted heterogeneous graph, represented as: .

[0041] in, A set of nodes, containing supply nodes. Production scheduling nodes Logistics and distribution nodes Three core functional categories; Let it be a set of edges, representing the relationships of material flow, information transmission, and collaborative operations between nodes; This is a node type mapping function used to identify the functional category to which a node belongs; , which are node capability vectors, representing the service capability strength of the node in the supply, production, and distribution stages, respectively.

[0042] To accommodate both single-function and multi-functional composite nodes, this invention employs an idempotent mechanism to uniformly model node functions, allowing nodes to possess multiple functions simultaneously, thus better reflecting the operational mode of real supply chain systems. Based on this modeling, the functional dependencies, business link structure, and differences in node contributions within the supply chain network can be fully expressed, providing a foundation for subsequent high-quality graph embedding.

[0043] Furthermore, this embodiment discloses an overall framework for heterogeneous graph attention embedding: To achieve effective representation of supply chain networks, this invention designs a Heterogeneous Graph Attention (HGA) embedding module, which fuses multi-dimensional information such as topology, node type, and functional capabilities into a low-dimensional, dense, and learnable vector representation. This framework overcomes the limitation of traditional homogeneous graph embeddings in distinguishing node functions. It differentiates the information contributions of nodes with different functions through a type-aware dynamic attention mechanism and strengthens the role of functional capabilities in feature learning through an attribute-aware message passing mechanism. Ultimately, it generates node embeddings and whole-graph embeddings that simultaneously contain structural information and business semantics, providing accurate state representations for subsequent reinforcement learning decisions.

[0044] Step 1.1: Initial node feature construction: Before graph embedding, initial features are constructed for each supply chain node, fusing structural, type, and capability information. The initial node features consist of three parts: the node's own topological structure features, the one-hot encoding of the node's functional type, and the node's capability values ​​in supply, production, and distribution functions. The initial features can be represented as:

[0045] in, These are the basic structural features of nodes. Encode the function type. This is a capability vector. In this way, the initial representation of each node simultaneously contains three types of information: structure, type, and capability, providing sufficient input for subsequent aggregation of heterogeneous information.

[0046] Step 1.2: Type-Aware Dynamic Attention Mechanism In heterogeneous supply chain networks, different functional nodes contribute significantly differently to the business chain; therefore, node types must be distinguished during information aggregation. This invention performs independent linear transformations on features based on node functional types in each graph convolution layer, ensuring that different types of nodes have independent feature spaces.

[0047] in, For linear transformation matrices bound to node types, For nodes The embedding vector in the previous layer.

[0048] Based on this, the basic attention scores between nodes are calculated to characterize the strength of dependencies in the topology:

[0049] Meanwhile, to highlight the impact of functional capabilities on the importance of nodes, a capability attribute similarity term is introduced. This approach assigns higher attention weights to nodes with similar capabilities and close business collaboration. It integrates basic attention with capability-based attention to obtain the final attention coefficient, which is then normalized using LeakyReLU and softmax to arrive at the final attention weight.

[0050]

[0051] This attention mechanism can automatically learn the contribution levels of different neighboring nodes to the central node, making the embedding more aligned with the actual business logic of the supply chain. See Table 1 for the overall graph embedding calculation process.

[0052]

[0053] Step 1.3: Attribute-Aware Message Passing and Aggregated Updates See Figure 1 During the message passing phase, this invention simultaneously aggregates topological structure information and functional capability information, achieving deep fusion of heterogeneous information. Each message consists of a basic structure message and a capability enhancement message, representing topological contribution and functional contribution, respectively. The basic message is composed solely of attention weights and node features.

[0054] Capability enhancement messages map node capability vectors to weights, thus weighting and enhancing neighbor features:

[0055] The final message is obtained by combining the two messages:

[0056] in, This is the capability enhancement coefficient, used to adjust the strength of the influence of functional attributes in embedding learning.

[0057] Then, all neighbor messages are aggregated to obtain the aggregated embedding representation of the node:

[0058] Finally, the node embedding is updated using linear transformation, residual connections, and nonlinear activation functions.

[0059] Through multi-level iteration, node embedding can gradually integrate multi-hop neighbor information, achieving a unified representation of global structural and functional information.

[0060] Step 1.4: Graph Reconstruction and Comparative Learning Constraints To improve the stability, discriminativeness, and generalization ability of embedding, this invention introduces graph reconstruction contrastive learning loss to optimize the embedding effect from two levels: graph structure and node type.

[0061] At the graph level, two enhanced views of the same network are generated through random node masks and edge perturbations, making similar views as close as possible in the embedding space and views from different graphs as far apart as possible, thereby improving the consistency of structural representation:

[0062] At the node level, a type contrast loss is introduced to make nodes with similar functions closer together in the embedding space and nodes with different functions more dispersed, thereby improving the embedding's ability to distinguish between function types.

[0063] in The average similarity of nodes of the same type. This represents the average similarity between dissimilar nodes. See Table 2 for the pseudocode for calculating the node-level contrastive loss.

[0064] Table 2. Calculation process of learning loss

[0065] The final graph embedding loss is a weighted combination of two parts:

[0066] See Figure 2 This loss can effectively improve the quality of the embedding, making subsequent reinforcement learning strategies more stable and efficient.

[0067] Step 1.5: Full Image Embedding Generation and Output After completing node embedding learning, this invention obtains the whole graph embedding through global average pooling, which is used to represent the functional and structural state of the entire supply chain network.

[0068]

[0069] The final output graph embedding contains information such as topological connectivity, node functional distribution, and overall service capabilities, which can be directly used as the state input of the reinforcement learning model, providing a unified and high-quality feature representation for subsequent vulnerability assessment and key node identification.

[0070] Step 2: Reinforcement Learning Method Training See Figure 3 DQN is a classic algorithm that combines deep learning methods with reinforcement learning. It is roughly divided into the agent collecting samples and the neural network updating stage.

[0071] Step 3.1: Agent collects samples. In this step, the agent uses a certain strategy... Interacting within an environment typically involves the following methods: Strategy:

[0072] By exploring the strategies described above, its motion trajectory can be obtained.

[0073] This motion trajectory can be separated into several quadruplet training data. , as training samples for the neural network.

[0074] Step 3.2: Update the neural network. Randomly select a training sample of a quadruple. Inputting into DQN yields:

[0075] Calculate the TD target and its current estimate. The difference in TD error

[0076] Next, we calculate the parameter gradient and update the parameter gradient using inverse gradient descent.

[0077]

[0078] in, This represents the learning rate. The two processes described above can occur simultaneously: the agent interacts with the environment to collect training data while the DQN network updates.

[0079] See Figure 4 This embodiment further defines quantitative indicators for supply chain network functionality and quantitative indicators for vulnerability.

[0080] This invention abstracts the actual supply chain system into a heterogeneous graph structure with multi-level, multi-entity, and multi-functional characteristics, represented as: The set of nodes It includes three types of core functional nodes, namely raw material supply nodes. Production scheduling nodes and logistics distribution nodes To ensure the integrity and computational efficiency of the supply chain business loop, a path that sequentially passes through the supply chain, production scheduling, and logistics distribution stages, and whose path length does not exceed 6 and the number of nodes in each stage does not exceed 2, is defined as an efficient supply chain path. All efficient supply chain paths in the network that meet the above conditions constitute a set. This is used for quantitative calculations of the overall functions of the subsequent supply chain.

[0081] For any efficient supply chain path Let the set of nodes that perform supply, production, and distribution functions be respectively... , , The capacity of a single supply chain path is then defined as:

[0082] in, , , Representing nodes respectively Capabilities in supply, production, and distribution functions. For path The number of nodes.

[0083] The overall fulfillment and operational capabilities of a supply chain network are supported by all efficient supply chain routes within the network. Therefore, summing the capabilities of all efficient supply chain routes yields the overall functional capability of the network.

[0084] To improve numerical stability and avoid training anomalies caused by excessively large index amplitudes, the functional capabilities of logarithmic networks are further defined:

[0085] in, It is a very small positive number that approaches 0, used to ensure the validity of logarithmic operations.

[0086] When a supply chain network is disrupted by node failures, interruptions, or removals, the degree to which the remaining network retains its functionality can be measured by its relative functional residual value. Let the network after node removal be... The relative functional residual value is

[0087] The range of values ​​for this indicator is: The closer the value is to 0, the more severe the network function impairment.

[0088] To comprehensively measure the changing vulnerability trends of the supply chain network during the gradual failure of nodes, the percentage of node removal is used as the metric. The x-axis represents the relative remaining functionality at the corresponding removal ratio. Using the vertical axis as the ordinate, construct a functional breakdown curve, and use the area under the breakdown curve (AUDC) as a quantitative indicator of vulnerability:

[0089] The smaller the AUDC value, the faster the supply chain function declines and the higher the overall vulnerability of the network.

[0090] To transform vulnerability optimization into a solvable objective function, given a node removal sequence... Define the cumulative regularization performance metric: , This invention minimizes the objective function The optimization goal is to reduce the functionality of the supply chain network as quickly as possible, thereby enabling the accurate identification of critical vulnerable nodes.

[0091] See Figure 5 The effectiveness of the method disclosed in this invention (HGA-DQN) was verified in four different types of supply chain networks with varying functional ratios. The specific configurations of the four types of supply chain networks are as follows: In a balanced (B) network, the ratio of single-function nodes (supply, production scheduling, and logistics distribution) is 0.25, the ratio of dual-function nodes is 0.08, and the ratio of triple-function nodes is 0.01, resulting in a balanced distribution of functional nodes.

[0092] The Single Dominant (SD) network is dominated by supply nodes, accounting for 0.50%, production scheduling nodes account for 0.20%, logistics and distribution nodes account for 0.15%, and multi-functional nodes account for a relatively low proportion.

[0093] Rare Multi (RM) networks are dominated by single-function nodes, with supply and production scheduling nodes each accounting for 0.35%, logistics and distribution nodes accounting for 0.28%, and multi-function nodes accounting for a very low percentage. Among them, S_I and D_I nodes account for only 0.005%, and there are no three-function nodes.

[0094] High Complexity (HC) networks are dominated by composite functional nodes. The proportion of each of the three types of single-functional nodes is only 0.10, the proportion of each of the three types of dual-functional nodes is 0.20, and the proportion of triple-functional nodes is 0.10, making the node functional composition the most complex.

[0095] See Figure 6In the same test supply chain network environment, the functional index change curves in the figure clearly demonstrate that the vulnerability identification and network disintegration strategy constructed by the method of this invention has significant advantages. In the initial stage of strategy execution, although the supply chain network functional indexes show a rapid downward trend, the advantage difference between algorithms is not yet prominent. As node removal and disintegration steps continue, the network functional disintegration effect of this invention is significantly better than various traditional greedy methods. It can achieve a substantial decay of the core functions of the supply chain network in fewer iterations, and the AUDC index corresponding to the functional residual value decline curve is significantly smaller. Quantitatively, this verifies that the strategy of this invention has higher efficiency in disintegrating supply chain network functions and more accurate identification of vulnerable nodes.

[0096] In contrast, the vulnerability assessment and network disintegration performance of various traditional greedy algorithms did not show significant differentiation. Regardless of whether high-topology nodes, high-between-number nodes, or locally structurally critical nodes were prioritized, the AUDC values ​​of various greedy algorithms showed minimal differences in four different supply chain network test scenarios with varying functional ratios, and the network function degradation effects tended to be consistent. This result fully demonstrates that the identification and disintegration strategy generated in this invention is more in line with the business operation mechanism and dynamic functional evolution law of heterogeneous supply chain networks. It can quickly identify core vulnerable nodes and disintegrate the overall fulfillment capability of the supply chain with less node intervention cost, providing more practical theoretical methods and technical support for supply chain risk prevention and control, critical node protection, and network resilience optimization.

[0097] Meanwhile, to highlight the adaptability and superiority of the method in this invention for supply chain networks with node functional attributes, its performance is compared with two classic homogeneous graph disintegration algorithms, S2V-DQN and FINDER. Both algorithms employ a core framework combining graph embedding and reinforcement learning, but are essentially designed for homogeneous graphs without functional attributes. S2V-DQN explores the graph structure based on a random walk mechanism, performs graph embedding, and generates low-dimensional embedding vectors by capturing the local topological relationships of nodes; its decision-making is limited to network topological connection features. FINDER, on the other hand, uses the GraphSAGE graph embedding method, constructing a graph representation by aggregating the topological information of node neighbors, similarly without considering the coupling relationship between the node's own functional attributes and the global network function.

[0098] Using the four previously defined typical supply chain networks as the test environment, and unifying key experimental parameters such as network size, initial functional threshold, and upper limit of disintegration steps, only the core algorithm was changed. The resulting curves showing the decline in supply chain network functional indicators for each method are shown in the figure. The experimental results clearly demonstrate that when these two algorithms, which performed well in homogeneous graph disintegration tasks, are transferred to heterogeneous supply chain networks, their performance remains significantly weaker than the method proposed in this invention.

[0099] The core reason for this comparison is that S2V-DQN and FINDER rely solely on topology information for decision-making, failing to identify key nodes in the supply chain network that have low topological importance but high functional contribution, causing the disintegration strategy to deviate from the core of network function.

[0100] This invention also discloses a system for identifying vulnerable critical nodes in a supply chain network, comprising: The heterogeneous graph construction module is used to obtain the topological connection relationship of nodes in the actual supply chain network, the functional type of nodes, and the capability value of nodes in each function, and to abstract the supply chain network into a heterogeneous graph containing nodes with multiple functional types. The whole graph embedding vector acquisition module is used to construct an initial feature vector for each node in the heterogeneous graph. Based on the initial feature vector, feature mapping and attention weighting calculation are performed on neighboring nodes of different functional types. The topological structure information and functional capability information of neighboring nodes are aggregated to generate an updated node embedding vector. The node embedding vector is pooled to obtain the whole graph embedding vector representing the state of the entire supply chain network. The key node identification module is used to obtain the trained deep DQN network. It inputs the whole image embedding vector as the current network state into the deep DQN network to obtain the key node sequence.

[0101] This invention utilizes a technical approach of precisely locating vulnerable links in the supply chain network and combines an end-to-end deep learning framework to automate the process from data input to output. The entire process requires no manual intervention or feature construction, thus offering advantages such as high efficiency, low error, and strong stability.

[0102] This invention employs a multi-dimensional feature fusion mechanism, which can simultaneously extract network topology, node attributes, functional relationships, and dynamic change information, avoiding the one-sidedness caused by a single indicator. Therefore, it has the advantages of comprehensive evaluation, objective results, and wide applicability.

[0103] The model and method proposed in this invention are characterized by strong versatility, scalability, and reusability. They do not depend on specific scenarios or data formats and can be directly applied to various supply chain vulnerability assessment scenarios. Therefore, they have the advantages of strong industrial applicability and high promotion value.

[0104] A schematic diagram of a terminal device according to an embodiment of the present invention. The terminal device of this embodiment includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps in the various method embodiments described above. Alternatively, when the processor executes the computer program, it implements the functions of each module / unit in the various device embodiments described above.

[0105] The computer program can be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention.

[0106] The terminal device can be a desktop computer, laptop computer, cloud server, or other device with strong computing power. The terminal device may include, but is not limited to, a processor and memory.

[0107] The optimal choice for the processor is a multi-core high-speed central processing unit (CPU).

[0108] The memory can be used to store the computer program and / or module. The processor implements various functions of the terminal device by running or executing the computer program and / or module stored in the memory and calling the data stored in the memory.

[0109] If the modules / units integrated into the terminal device are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0110] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for identifying vulnerable critical nodes in a supply chain network, characterized in that, Includes the following steps: Obtain the topological connections, functional types, and capability values ​​of nodes in the actual supply chain network, and abstract the supply chain network into a heterogeneous graph containing nodes with multiple functional types. For each node in the heterogeneous graph, an initial feature vector is constructed. Based on the initial feature vector, feature mapping and attention weighting calculation are performed on neighboring nodes of different functional types. The topological structure information and functional capability information of neighboring nodes are aggregated to generate an updated node embedding vector. The node embedding vector is pooled to obtain the whole graph embedding vector representing the state of the entire supply chain network. Obtain the trained deep DQN network, input the whole image embedding vector as the current network state into the deep DQN network, and obtain the key node sequence.

2. The method for identifying vulnerable critical nodes in a supply chain network according to claim 1, characterized in that, The heterogeneous graph is represented by the following formula: in, A set of nodes, containing supply nodes. Production scheduling nodes Logistics and distribution nodes Three core functional categories; Let it be the set of edges; This is a node type mapping function used to identify the functional category to which a node belongs; , which are node capability vectors, representing the service capability strength of the node in the supply, production, and distribution stages, respectively.

3. The method for identifying vulnerable critical nodes in a supply chain network according to claim 1, characterized in that, The construction of an initial feature vector for each node in the heterogeneous graph includes: A heterogeneous graph attention embedding module is constructed, which integrates the topological features of the nodes themselves, the one-hot encoding of the node's functional type, and the node's capability values ​​in the three functions of supply, production, and distribution to obtain an initial feature vector.

4. The method for identifying vulnerable critical nodes in a supply chain network according to claim 3, characterized in that, The feature mapping of neighbor nodes of different functional types based on the initial feature vector includes: In each graph convolutional layer, the features are subjected to independent linear transformations based on the node function type: in, For linear transformation matrices bound to node types, For nodes The embedding vector in the previous layer.

5. The method for identifying vulnerable critical nodes in a supply chain network according to claim 4, characterized in that, The attention-weighted calculation includes: Compute the basic attention weights between nodes, which are used to characterize the strength of dependencies in the topology; A similarity term for ability attributes is introduced to calculate the ability attention weight. The basic attention weight and the ability attention weight are then fused to obtain the final attention coefficient. The attention coefficient is then normalized to obtain the attention weight.

6. The method for identifying vulnerable critical nodes in a supply chain network according to claim 1, characterized in that, The aggregation of neighboring node topology and functional capabilities generates an updated node embedding vector. This node embedding vector is then pooled to obtain a graph embedding vector representing the overall supply chain network state, including: Obtain basic structure messages based on attention weights and node features; The node capability vector is mapped to weights, and the neighbor features are weighted and enhanced to obtain the capability enhancement message; By integrating infrastructure messages and capability enhancement messages, information transmitted by neighboring nodes can be obtained. By integrating the information transmitted by all neighboring nodes, we obtain the node embedding vector. Then, we perform pooling on the node embedding vector to obtain the whole graph embedding vector representing the state of the entire supply chain network.

7. A system for identifying vulnerable critical nodes in a supply chain network, characterized in that, include: The heterogeneous graph construction module is used to obtain the topological connection relationship of nodes in the actual supply chain network, the functional type of nodes, and the capability value of nodes in each function, and to abstract the supply chain network into a heterogeneous graph containing nodes with multiple functional types. The whole graph embedding vector acquisition module is used to construct an initial feature vector for each node in the heterogeneous graph. Based on the initial feature vector, feature mapping and attention weighting calculation are performed on neighboring nodes of different functional types. The topological structure information and functional capability information of neighboring nodes are aggregated to generate an updated node embedding vector. The node embedding vector is pooled to obtain the whole graph embedding vector representing the state of the entire supply chain network. The key node identification module is used to obtain the trained deep DQN network. It inputs the whole image embedding vector as the current network state into the deep DQN network to obtain the key node sequence.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1-6.

9. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1-6.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1-6.

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