A multi-layer complex network performance evaluation and resource planning method

Abstract

The application relates to the technical field of complex network evaluation and planning, and provides a multi-layer complex network performance evaluation and resource planning method, which comprises the following steps: constructing a double-layer evaluation framework, the double-layer evaluation framework combines a TOPSIS method and an importance-cost performance index to evaluate the capability attribute of a network node, and the node structure in a network structure is evaluated based on a complex network theory; network level performance evaluation results are calculated; the influence of network node failure on network system performance is analyzed; based on the analysis results, a resource planning multi-objective model considering network topology reconstruction triggered by network node failure is established by taking the condition that the overall task success rate of the network system is greater than or equal to a specified threshold as a constraint, and taking the minimum total investment cost and the minimum system total importance loss as targets; and the resource planning multi-objective model is solved by using an improved NSGA-II algorithm. The application effectively overcomes the shortcomings of traditional methods in decision-making of heterogeneous targets and multi-functional networks.

Description

Technical Field

[0001] This invention relates to the field of complex network evaluation and planning technology, and in particular to a method for performance evaluation and resource planning of multi-layer complex networks. Background Technology

[0002] As the core implementation of cyber-physical systems, the Internet of Things (IoT) typically consists of a perception layer (data acquisition), a decision-making layer (information processing and instruction generation), and an execution layer (action execution and function realization). This system exhibits high integration and real-time characteristics, meaning that the failure of any node can trigger a cascading effect through the network topology, leading to the interruption of the entire system's workflow. Therefore, accurate vulnerability assessment of IoT systems and the pre-formulation of targeted resource allocation schemes to enhance their resilience are of great significance. This raises two core questions: (1) how to construct a comprehensive capability assessment model that simultaneously reflects the attributes of system units and their topological position within the system; and (2) how to solve a nonlinear multi-objective programming problem under multiple constraints, minimizing maintenance costs while minimizing system performance degradation.

[0003] Current research on system network modeling focuses primarily on single network topology analysis, neglecting the functional differences between information flow and control flow. In node evaluation, it either separates attributes from structure or lacks effective methods for handling heterogeneous indicators across different categories of objectives. In resource planning, most studies simplify the decline in system performance to linear superposition, failing to fully consider the nonlinear effects brought about by the dynamic changes in network structure caused by multiple node failures. Summary of the Invention

[0004] The purpose of this invention is to solve at least one technical problem in the background art and to provide a method for performance evaluation and resource planning of multi-layer complex networks.

[0005] To achieve the above objectives, this invention provides a method for performance evaluation and resource planning of multi-layer complex networks, comprising: A two-layer evaluation framework is constructed to assess the capability attributes of network nodes and the importance of network structure in a network system. The two-layer evaluation framework combines the TOPSIS method with the importance-cost-performance ratio to evaluate the capability attributes of network nodes and evaluates the node structure in the network structure based on complex network theory. The network hierarchical performance evaluation results are calculated based on the evaluation results of capability attributes and node structure. Based on the evaluation results of capability attributes, node structure, and network hierarchy performance, the impact of network node failures on network system performance is analyzed. Based on the analysis results, with the overall task success rate of the network system being greater than or equal to a specified threshold as a constraint, and with the objectives of minimizing total investment cost and minimizing total system importance loss, a multi-objective resource planning model considering network topology reconfiguration caused by network node failures is established. An improved NSGA-II algorithm is used to solve the multi-objective model of resource planning.

[0006] According to one aspect of the present invention, the two-layer evaluation framework combines the TOPSIS method with an importance-cost-performance ratio to evaluate the capability attributes of network nodes, including: The TOPSIS method is used to evaluate the sub-categories of network nodes in the three types of network nodes in the perception layer, decision layer and execution layer of the network system to obtain the in-group evaluation value of the network nodes at each network level. The importance and maintenance cost of network nodes in the three types of network nodes in the network system—perception layer, decision layer, and execution layer—are evaluated to obtain the inter-group evaluation value of network nodes at each network layer. The attribute capability values ​​of network nodes are calculated based on the within-group evaluation values ​​and the between-group evaluation values. : ; in, This is the in-group evaluation value of the i-th network node within the k-th network layer; f represents the inter-group evaluation value of the i-th network node within the k-th network layer; k=1,2,3, representing the perception layer, decision layer, and execution layer, respectively; f represents and and The functional relationship.

[0007] According to one aspect of the present invention, the two-layer evaluation framework evaluates the node structure in a network structure based on complex network theory, comprising: To address the relationships between network nodes and the permissions involved in data transmission and retrieval between them, an information flow network diagram consisting of solid lines and a control flow network diagram consisting of dashed lines are constructed. Based on complex network theory, solid line network models and dashed line network models are established for the information flow network diagram and the control flow network diagram, respectively. Based on the solid line network model and the dashed line network model, the structural indices of network nodes in the solid line network model and the dashed line network model are obtained respectively. The node structure index is calculated based on the structural indices of network nodes in the realized network model and the structural indices of network nodes in the dashed line network model. : ; in, This represents the solid-line network model in the k-th network layer. The structural index of the i-th network node ; The dashed line represents the network model in the k-th network layer. The structural index of the i-th network node ; This is the output function.

[0008] According to one aspect of the present invention, the network hierarchical performance evaluation result calculated from the evaluation results based on capability attributes and node structure is as follows: ; in, F represents the performance index of the k-th network layer, where n is the number of network nodes; F represents... and and The functional relationship.

[0009] According to one aspect of the present invention, the multi-objective resource planning model, which considers network topology reconfiguration caused by network node failures and is constrained by an overall task success rate of the network system being greater than or equal to a specified threshold, and aims to minimize total investment cost and minimize total system importance loss, includes: (1) Decision variables: The resource planning scheme needs to consider four protection strategies for network nodes, using 0-1 decision variables x ij To indicate the protection plan: ; Where x represents the protection scheme matrix, i represents the network node, and j=1,2,3,4 represent four protection strategies: hot redundancy, full redundancy, partial redundancy, and no redundancy, respectively. Each protection strategy corresponds to the network node being fault-free, slightly faulty, moderately faulty, and severely faulty after protection. (2) Other variables: Let a k ρ represents the task guarantee rate threshold for the k-th network layer. j C represents the importance loss coefficient when the j-th protection strategy is adopted. ij Let represent the actual cost of implementing protection strategy j for network node i, and let importance be... i Cost represents the inherent importance of the i-th network node. i This represents the baseline maintenance cost of the i-th network node; (3) Constraints: 0-1 decision constraint: The same network node can only adopt one protection strategy, i.e., matrix [x] ijEach row contains exactly one non-zero value: ; System task guarantee rate constraint: The task guarantee rate of the perception layer, decision layer, and execution layer must be greater than or equal to a specified threshold. When network nodes adopt a non-redundant protection strategy, network nodes may be removed, and the network topology may change. The system's task assurance capability after protection needs to be calculated based on the new network structure, with the following constraints: ; in, This represents the network topology under the influence of protection scheme x; F represents a. k and and The functional relationship between them The attribute capability values ​​of network nodes in protection scheme x , Network topology under the influence of protection scheme x Node structure indicators ; (4) The objective function aims to minimize the total investment cost and the total importance loss of the system, while satisfying the system task guarantee rate. ; ; Let the objective function be the one that minimizes the total investment cost. Let be the objective function that aims to minimize the total importance loss of the system; (5) Multi-objective model of resource planning: To achieve the above objectives, the present invention also provides a multi-layer complex network performance evaluation and resource planning system, comprising: A two-layer evaluation framework construction module is used to construct a two-layer evaluation framework for evaluating the capability attributes of network nodes and the importance of network structure in a network system. The two-layer evaluation framework combines the TOPSIS method with the importance-cost-performance ratio index to evaluate the capability attributes of network nodes and evaluates the node structure in the network structure based on complex network theory. The network hierarchical performance evaluation result calculation module calculates the network hierarchical performance evaluation result based on the evaluation results of capability attributes and node structure. The resource planning multi-objective model construction module analyzes the impact of network node failures on network system performance based on the evaluation results of capability attributes, node structure, and network hierarchy effectiveness. Based on the analysis results, with the overall task success rate of the network system being greater than or equal to a specified threshold as a constraint, and with the objectives of minimizing total investment cost and minimizing the total importance loss of the system, a resource planning multi-objective model considering network topology reconfiguration caused by network node failures is established. The model solving module uses an improved NSGA-II algorithm to solve the multi-objective resource planning model.

[0010] To achieve the above objectives, the present invention also provides an electronic device, including a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the multi-layer complex network performance evaluation and resource planning method as described above.

[0011] To achieve the above objectives, the present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the multi-layer complex network performance evaluation and resource planning method as described above.

[0012] According to the present invention, the proposed two-layer evaluation framework systematically solves the key theoretical and technical problems in IoT performance evaluation and maintenance strategy planning, effectively overcoming the shortcomings of traditional methods in decision-making regarding heterogeneous targets and multifunctional networks. The present invention not only outputs reasonable performance index values ​​but also accurately locates critical nodes crucial to IoT stability. The proposed "two-layer evaluation model integrating attributes and structure" is an effective tool for quantifying system capabilities. In multi-objective optimization, the network reconstruction calculation system degradation rate is directly introduced, significantly improving the simulation accuracy of the strategy. The improved NSGA-II algorithm exhibits good convergence and distribution in this problem. The established "multi-objective programming model considering dynamic changes in network structure" and its solution algorithm can provide practical operators with a series of Pareto optimal solutions ranging from "economical" to "efficient". Attached Figure Description

[0013] Figure 1 A flowchart illustrating a method for performance evaluation and resource planning of multi-layer complex networks according to an embodiment of the present invention; Figure 2 A schematic diagram illustrating a cross-plot of an improved NSGA-II algorithm according to an embodiment of the present invention; Figure 3 A schematic diagram illustrating a variation of the improved NSGA-II algorithm according to one embodiment of the present invention; Figure 4This schematic diagram illustrates a solid-line network topology of the Internet of Things according to Verification Example 1 of the present invention; Figure 5 This schematic diagram illustrates the Internet of Things (IoT) network topology according to Verification Example 1 of the present invention. Figure 6 This is a schematic diagram illustrating the three types of network node attribute capability index bar charts according to Verification Example 1 of the present invention; Figure 7 This diagram illustrates the node hub centrality index according to Verification Example 1 of the present invention. Figure 8 This diagram illustrates the node proximity centrality index according to Verification Example 1 of the present invention. Figure 9 This diagram illustrates the node betweenness centrality index according to Verification Example 1 of the present invention. Figure 10 This diagram illustrates the node out-degree index according to Verification Example 1 of the present invention. Figure 11 This schematically illustrates a heatmap of the system descent rate under different faults at each node according to Verification Example 1 of the present invention. Figure 12 This schematic diagram illustrates the control flow network topology after removing a severe fault according to Verification Example 1 of the present invention. Figure 13 This schematic representation illustrates the Pareto front plot based on the improved NSGA-II algorithm according to Verification Example 1 of the present invention; Figure 14 The diagram schematically illustrates the convergence curve of the improved NSGA-II algorithm according to Verification Example 1 of the present invention. Detailed Implementation

[0014] The invention will now be discussed with reference to exemplary embodiments. It should be understood that the described embodiments are merely intended to enable those skilled in the art to better understand and thus implement the invention, and are not intended to imply any limitation on the scope of the invention.

[0015] As used herein, the term "comprising" and its variations are to be interpreted as open-ended terms meaning "including but not limited to". The term "based on" is to be interpreted as "at least partially based on". The terms "one embodiment" and "an embodiment" are to be interpreted as "at least one embodiment".

[0016] Figure 1 The flowchart schematically illustrates a method for performance evaluation and resource planning of multi-layered complex networks according to an embodiment of the present invention. Figure 1 As shown, in this embodiment, a method for performance evaluation and resource planning of multi-layer complex networks includes: A two-layer evaluation framework is constructed to assess the capability attributes of network nodes and the importance of network structure in a network system. The two-layer evaluation framework combines the TOPSIS method with the importance-cost-performance ratio to evaluate the capability attributes of network nodes and evaluates the node structure in the network structure based on complex network theory. The network hierarchical performance evaluation results are calculated based on the evaluation results of capability attributes and node structure. Based on the evaluation results of capability attributes, node structure, and network hierarchy performance, the impact of network node failures on network system performance is analyzed. Based on the analysis results, with the overall task success rate of the network system being greater than or equal to a specified threshold as a constraint, and with the objectives of minimizing total investment cost and minimizing total system importance loss, a multi-objective resource planning model considering network topology reconfiguration caused by network node failures is established. An improved NSGA-II algorithm is used to solve the multi-objective model of resource planning.

[0017] Furthermore, according to one embodiment of the present invention, regarding the capability attributes of nodes (network nodes), it is found that different network nodes exhibit characteristics of multiple types, multiple attributes, and heterogeneous indicators. Traditional evaluation methods such as entropy weight method and analytic hierarchy process (AHP) have low adaptability to this problem. Specifically, that is: 1. Multiple types: Nodes are divided into three major categories: perception layer, decision layer, and execution layer. Each major category is further divided into different subcategories. For example, perception layer nodes are subdivided into visual acquisition, environmental sensing, position and motion sensing, and state detectors. It is easy to see that the technical attributes of different subcategories have different applications and functions. Direct comparison and evaluation results are not ideal and have low interpretability. 2. Multiple attributes: Within the same subcategory, each target needs to be evaluated comprehensively through multiple attributes, such as the computing power, memory, network bandwidth, and processing latency of the computing platform, in order to make full use of the given data. 3. Heterogeneous metrics: Each node's attributes differ significantly in terms of dimensions and magnitude. For example, the number of connected devices on a terminal node is a dimensionless integer in the hundreds, while the communication delay is measured in milliseconds and its values ​​are concentrated in the tens. These metrics require standardization.

[0018] In summary, this invention employs an "within-group + between-group" evaluation method, including: The TOPSIS method is used to evaluate the sub-categories of network nodes in the three types of network nodes in the perception layer, decision layer and execution layer of the network system to obtain the in-group evaluation value of the network nodes at each network level. The importance and maintenance cost of network nodes in the three types of network nodes in the network system—perception layer, decision layer, and execution layer—are evaluated to obtain the inter-group evaluation value of network nodes at each network layer. The attribute capability values ​​of network nodes are calculated based on the within-group evaluation values ​​and the between-group evaluation values. : ; in, This is the in-group evaluation value of the i-th network node within the k-th network layer; f represents the inter-group evaluation value of the i-th network node within the k-th network layer; k=1,2,3, representing the perception layer, decision layer, and execution layer, respectively; f represents and and The functional relationship.

[0019] In this implementation, evaluations are conducted within the same category of objectives within a group. Common evaluation methods in academia include TOPSIS, entropy weighting, and analytic hierarchy process (AHP). However, entropy weighting relies on the degree of data variability, AHP requires the assumption that indicators are independent and cannot escape the subjective uncertainty of evaluation experts, and principal component analysis requires a large sample size. Therefore, to address the issues of multi-attribute and heterogeneous indicators, this invention selects TOPSIS for evaluation within each subcategory.

[0020] In this implementation, to address multiple types of problems, two common indicators exist among different categories of objectives: node importance and maintenance cost. Let importance be... (i) The cost represents the importance of the i-th network node in the hierarchy. (i) This represents the corresponding maintenance cost. To assess the attribute capabilities between groups, we define importance-cost-effectiveness: This concludes the TOPSIS evaluation score within the overall group. Inter-group cost-effectiveness index Define the target attribute capability index: Furthermore, according to one embodiment of the present invention, the two-layer evaluation framework evaluates the node structure in a network structure based on complex network theory, including: To address the relationships between network nodes and the permissions involved in data transmission and retrieval between them, an information flow network diagram consisting of solid lines and a control flow network diagram consisting of dashed lines are constructed. Based on complex network theory, solid line network models and dashed line network models are established for the information flow network diagram and the control flow network diagram, respectively. Based on the solid line network model and the dashed line network model, the structural indices of network nodes in the solid line network model and the dashed line network model are obtained respectively. The node structure index is calculated based on the structural indices of network nodes in the realized network model and the structural indices of network nodes in the dashed line network model. : ; in, This represents the solid-line network model in the k-th network layer. The structural index of the i-th network node ; The dashed line represents the network model in the k-th network layer. The structural index of the i-th network node ; This is the output function.

[0021] In this embodiment, considering the network node relationships and the permissions for data transmission and acquisition between network nodes, an information flow network diagram consisting of solid lines and a control flow network diagram consisting of dashed lines are constructed. Based on complex network theory, models (solid line network model and dashed line network model) are established for the two respectively.

[0022] Define the solid line diagram of the Internet of Things (i.e., the solid line network model). ,in, This represents the set of nodes that make up the solid-line information flow network. This represents the set of information transmission relationships between these nodes.

[0023] Define the Internet of Things (IoT) dashed line diagram (i.e., dashed line network model). ,in, This represents the set of nodes that make up the dashed control flow network. This represents the set of control relationships between these nodes.

[0024] In an Internet of Things (IoT) system, the core functions of the three layers—the perception layer, the decision-making layer, and the execution layer—are different. For example, the perception layer emphasizes the connectivity and transmission efficiency of information communication; the decision-making layer emphasizes information authority and global centrality; and the execution layer emphasizes the scope of task assignment and resource acceptance capabilities. Furthermore, within the same layer, there exists a solid-line information flow network G. r and dashed line control flow network G l The heterogeneity of network structures leads to different importance of the same node in different networks. Considering the different focuses of the three levels and the different importance of two network nodes, we abandon the single indicator and instead use an indicator that adapts to the hierarchical function and network structure for differentiated evaluation.

[0025] In this embodiment, different network characteristic indicators have different focuses in reflecting the importance of nodes. Therefore, five different static characteristic indicators (hub centrality, out-closeness centrality, betweenness centrality, out-degree index, and in-degree index) are selected and notated as follows. Let be the structural index of the i-th node in the k-th network layer. This represents the solid-line network model in the k-th network layer. The structural index of the i-th network node ; The dashed line represents the network model in the k-th network layer. The structural index of the i-th network node Node structure indicators It is composed of these two parts, denoted as .

[0026] Specifically, in this embodiment, the perception layer focuses on the efficiency of information flow in the target structure link and the hub status of target information transmission and reception. The Hub value reflects the importance of a node as a hub. In relation to practical problems, a higher value indicates that the node can transmit and receive information to multiple key nodes, reflecting the characteristic of the perception layer node as an information hub. Therefore, the Hub value is used as the perception layer's... Node structure indicators .

[0027] Similarly, this system emphasizes information transmission efficiency. In complex network theory, distance index and out-closeness centrality reflect the proximity of nodes to other nodes. Here, out-closeness centrality is chosen as the metric for this system. Structural indicators in High proximity centrality means that the target can quickly transmit information to other nodes in the network, which is in line with the characteristics of the perception layer of "early detection and rapid reporting".

[0028] The decision-making level makes significant differences between solid and dashed lines in the network, which is reflected in the network. In terms of content, it includes two types of targets: communication relay nodes and computing decision nodes, which constitute information flow, while the network... In terms of content, they only include one type of objective: computational processing and control flow. This is the most telling difference between the two networks. In this context, betweenness centrality, characterized by the number of shortest paths passing through a node, aligns with the goal of decision-makers in real-world problems, where nodes act as crucial conduits for information flow. Highly betweenness-centralized nodes are often located at the intersection of key information links, responsible for the "upstream and downstream" transmission of information. Therefore, betweenness centrality can be used as a measure of a decision-maker's importance. Node structure indicators .

[0029] Similarly, in control flow networks Because it only contains processing nodes and lacks communication hubs, the network has a tree-like structure. Therefore, it emphasizes hierarchical relationships and jurisdictional boundaries. This aligns with the out-degree metric in complex networks, which reflects the node's radiating capacity and direct influence. Thus, the out-degree metric is chosen as the decision-making metric for the network. Node structure indicators .

[0030] The network constructed above and In this context, the execution layer's objectives are based on reality, and its information flow and control flow are already integrated. Therefore, only one indicator needs to be selected. Simultaneously, the execution layer emphasizes the objective's task-receiving capability, i.e., receiving task instructions from multiple decision-making nodes to avoid service function loss due to a single-line failure. Therefore, the in-degree indicator from complex network theory is chosen as the execution layer's... and The node structure indicators in the data, and have This reflects the adaptability and versatility of the execution layer nodes.

[0031] Furthermore, in this embodiment, after selecting the aforementioned differentiated indicators, the next step is to couple the structural indicators of the two-layer network within the same system based on these indicators. Specifically, it means defining the function h. k Considering the heterogeneity of node metrics—specifically, some nodes exist in two networks, while others only appear in the solid line network— In the latter case, only indicators exist. Furthermore, the node metrics may differ in magnitude; therefore, the calculated raw metrics are preprocessed here. Preprocessing includes: Step 1, Indicator Extension: Address indicator heterogeneity and ensure the two types of indicators , In the output function h k Having the same dimensions, for Perform an extension assignment, ensuring that the value exists only in the original text. Middle node ,Right now This operation ensures consistency across the input dimensions for the assigned values. In subsequent calculations, it will be mapped to the value 1, which will be reflected in step 2.

[0032] Step 2, Linear Normalization: To avoid potential differences in the magnitude of the indicators, the five static feature indicators mentioned above need to be mapped to the same interval [1, 10]. Here, a linear mapping function is chosen: ; By setting α=1 and β=9, the original index values ​​are mapped to [1, 10], and the lower limit of the index is restricted to 1. This ensures that the calculation will not result in extreme values ​​due to approaching 0, thus guaranteeing the rationality of the values.

[0033] Through preprocessing, normalized indices are obtained. , Based on this, using the function h k Coupled node structure indices under different systems : 1. Perception layer, k=1: 2. Decision-making level, k=2: 3. Execution layer, k=3: Furthermore, according to one embodiment of the present invention, the network hierarchical performance evaluation result is calculated based on the evaluation results of capability attributes and node structure as follows: in, F represents the performance index of the k-th network layer, where n is the number of network nodes; F represents... and and The functional relationship.

[0034] Furthermore, according to one embodiment of the present invention, the analysis of the impact of network node failures on network system performance based on the evaluation results of capability attributes, the evaluation results of node structure, and the evaluation results of network hierarchy performance includes: To analyze the impact of node failures on system performance in an IoT system, the degradation rate of performance indicators was calculated for three levels: light, medium, and severe failures. Based on the impact of different node failure levels on attribute capabilities, when the node failure level is light or medium, some node attribute capabilities are reduced, while the network topology remains unchanged. In this case, it is only necessary to re-evaluate the node attribute capability indicators. When a node's failure level is severe, it can be considered removed from the network, meaning the node is directly deleted (all edges connecting it to the node are directly broken). The corresponding network topology changes directly, requiring recalculation of node attribute capability indices. Furthermore, a new network model should be established, and new node structure indices should be calculated. Continuing with the notation system above, let's denote the task assurance capability of the k-th level after the i-th node suffers the t-th type of failure as . Let t=1, 2, and 3 represent minor, moderate, and severe faults, respectively. Let the total rate of decline in mission assurance capability for the three levels be denoted as t=1, 2, and 3. k=1, 2, 3, representing the decline rate of the perception layer, decision-making layer, and execution layer, respectively.

[0035] The evaluation matrix T is constructed from the data of each subcategory, then x ij This represents the j-th (j=1, 2, ..., m) indicator of the i-th (i=1, 2, ..., n) node within each subcategory, combined with the capability reduction coefficient θ of the node. j The new evaluation matrix for all nodes under mild to moderate faults was calculated. The element value is: ; The new evaluation matrix cannot be used directly. The evaluation should be conducted according to the TOPSIS evaluation model in Question 1, because the new node attribute capability evaluation data required is obtained under the premise that only a single node is slightly or moderately damaged, and the new evaluation matrix... Each row in the table represents the index values ​​for all nodes after the data has been damaged. If a TOPSIS evaluation is performed, the evaluation results will not change. Therefore, a new evaluation matrix should be used for each node. The original data matrix is ​​used to construct the corresponding evaluation matrix, and the evaluation matrix is ​​then evaluated accordingly. Finally, TOPSIS is evaluated based on the model from Problem 1.

[0036] Given the attribute capability index in the model The calculation uses node importance and maintenance cost. Node importance and maintenance cost decrease with different failure levels, thus introducing new node importance. New maintenance costs ,in The node importance coefficient represents the node of the l-th node at the t-th level of failure. This represents the maintenance cost coefficient of the l-th node at the t-th level of failure.

[0037] Thus, utilizing , and Calculate the indicators for the corresponding fault severity to obtain the hierarchical task assurance capability under this condition. Define the formula for the rate of decline: Further, calculate the rate at which the i-th node causes a decrease in the mission assurance capability at the k-th level under the t-th level of failure. .

[0038] Severe node failures can be considered as direct removal, requiring network model reconstruction. A two-layer network model is reconstructed for the removed i-th node. Calculate the new node structure index of the network. Further, the hierarchical task assurance capability value under this condition is obtained. The i-th node under the third type of failure, and the rate of decline in the mission assurance capability at the k-th level. : Furthermore, according to one embodiment of the present invention, based on the above-mentioned evaluation indicators, in the resource planning of an industrial Internet of Things (IoT) system, a multi-objective optimization problem is established with the constraint that the task assurance capabilities of the three levels—perception layer, decision layer, and execution layer—are not lower than a specified threshold, and with the objectives of minimizing the total system maintenance cost and minimizing the total system importance loss. Mild to moderate failures only cause a reduction in attribute capabilities, while severe failures of nodes lead to changes in the network structure. The calculation of its indicators is closely related to the network structure; therefore, this planning is a complex nonlinear problem. Intelligent optimization algorithms, such as genetic algorithms, are used to solve nonlinear programming problems. These algorithms do not depend on the linearity and differentiability of the problem and can overcome the difficulties of network structure changes and node nonlinear indicators, achieving a balance between solution accuracy and computation time. In addition, Pareto optimality analysis is performed, in conjunction with academic approaches to multi-objective programming.

[0039] Specifically, in this embodiment, a multi-objective resource planning model is established, considering network topology reconfiguration caused by network node failures, with the constraint that the overall task success rate of the network system is greater than or equal to a specified threshold, and with the objectives of minimizing total investment cost and minimizing the total system importance loss. This model includes: (1) Decision variables: The resource planning scheme needs to consider four protection strategies for network nodes, using 0-1 decision variables x ij To indicate the protection plan: Where x represents the protection scheme matrix, i represents the network node, and j=1,2,3,4 represent four protection strategies: hot redundancy, full redundancy, partial redundancy, and no redundancy, respectively. Each protection strategy corresponds to the network node being fault-free, slightly faulty, moderately faulty, and severely faulty after protection. (2) Other variables: Let a k ρ represents the task guarantee rate threshold for the k-th network layer. j C represents the importance loss coefficient when the j-th protection strategy is adopted.ij Let represent the actual cost of implementing protection strategy j for network node i, and let importance be... i Cost represents the inherent importance of the i-th network node. i This represents the baseline maintenance cost of the i-th network node; (3) Constraints: 0-1 decision constraint: The same network node can only adopt one protection strategy, i.e., matrix [x] ij Each row contains exactly one non-zero value: ; System task guarantee rate constraint: The task guarantee rate of the perception layer, decision layer, and execution layer must be greater than or equal to a specified threshold. When network nodes adopt a non-redundant protection strategy, network nodes may be removed, and the network topology may change. The system's task assurance capability after protection needs to be calculated based on the new network structure, with the following constraints: in, This represents the network topology under the influence of protection scheme x; F represents a. k and and The functional relationship between them The attribute capability values ​​of network nodes in protection scheme x , Network topology under the influence of protection scheme x Node structure indicators ; (4) The objective function aims to minimize the total investment cost and the total importance loss of the system, while satisfying the system task guarantee rate. ; ; Let the objective function be the one that minimizes the total investment cost. Let be the objective function that aims to minimize the total importance loss of the system; (5) Multi-objective model of resource planning: Furthermore, according to one embodiment of the present invention, the complex planning problem is solved from the algorithmic solution level. Currently, heuristic algorithms are mostly used to solve nonlinear problems. For nonlinear multi-objective planning problems, the non-dominated sorting genetic algorithm II has significant advantages. Therefore, the present invention also uses this algorithm to solve the problem and perform Pareto analysis.

[0040] In this embodiment, frequent changes to the network structure significantly increase the complexity of the problem. This invention solves the planning problem based on the Non-Dominated Sorting Genetic Algorithm II (NSGA-II). NSGA-II is a classic multi-objective optimization algorithm that effectively solves the Pareto optimal solution set search problem in multi-objective optimization problems through non-dominated sorting and crowding distance calculation. Compared to the traditional Non-Dominated Sorting Genetic Algorithm (NSGA), NSGA-II has the following main advantages: Computational efficiency has been greatly improved; NSGA uses the original non-dominated sort, with a computational complexity of O(n log n). (M is the number of objective functions, and N is the population size) NSGA-II introduced a fast non-dominated sorting algorithm, reducing the complexity to .

[0041] A better mechanism for maintaining diversity; NSGA requires manual parameter specification. Shared functions are parameter-sensitive and difficult to configure.

[0042] NSGA-II proposes crowding degree and crowding degree comparison operators that can automatically generate a more uniform Pareto front without requiring key parameters.

[0043] An elite retention strategy was introduced; NSGA does not have an explicit mechanism for preserving elite solutions, so excellent solutions may be lost.

[0044] NSGA-II significantly improves the convergence performance of the algorithm through elite retention.

[0045] Furthermore, in this embodiment, the improved NSGA-II algorithm specifically includes: Chromosome coding method: The 0-1 integers in the problem constitute one-hot codes. The chromosome uses binary one-hot codes, which naturally satisfy the mutual exclusion condition, making it highly feasible. The search space is flat and connected, and the Hamming distance is constant, but custom crossover and mutation operations are required.

[0046] Crossover, mutation, and selection operations: The NSGA-II algorithm uses the same crossover, mutation, and selection operations as GA. However, to ensure the validity of the offspring solutions, it employs special crossover and mutation methods. The crossover operation selects one of the corresponding four bits from the two parent chromosomes with equal probability, while the mutation operation changes the selected four one-hot bits to one of the other three states with equal probability. (See diagram below.) Figure 2 and Figure 3 As shown.

[0047] Non-dominant level determination: Regarding this question: in For a feasible solution, it must always dominate an infeasible solution. If two solutions are both infeasible, then their overall constraint violation degrees are compared. The solution with the lower constraint violation degree dominates the solution with the higher constraint violation degree. The constraint violation degree is calculated based on the three system capability degradation rates that the attack plan must satisfy, and is defined as follows: The traditional Pareto dominance relation is used for comparison only when both solutions are feasible or have the same degree of constraint violation, i.e., solution x1 dominates solution x2 (denoted as...). If and only if: ; If no other solution dominates a solution, it is a non-dominated solution, and the Pareto solution set is the set of all non-dominated solutions.

[0048] Select operation: In genetic algorithms (GA), tournament selection involves randomly selecting a tournament group T of size τ and then probabilistically selecting the optimal individual. ; Here, f represents the fitness function. However, the NSGA-II algorithm considers two metrics when selecting operations: First, select individuals with a higher non-dominant level; When the non-dominance levels are the same, select the individual with the higher crowding level; Formation of a new paternal generation At this time, an elite retention strategy is adopted, that is, the best n individuals of the current generation are retained. To the next generation: ; Crowding calculation: Crowding distance measures the distribution density of solutions in their frontier: ; in, It is the value of the i-th individual on the m-th objective function; and These are the maximum and minimum values ​​of the m-th objective function; The crowding degree of boundary individuals is set to infinity.

[0049] Improved Quick Non-Dominated Sort: Fast non-dominated sort initializes the "dominance pressure" n of all individuals through a single pairwise comparison. p and "Dominion" S pThen, the iterative process of finding the layer with current pressure of 0 and reducing the pressure of the individuals dominated by it is repeated to divide the population into multiple non-dominated layers. This method avoids the tedious process of repeatedly scanning the entire population required in the original NSGA and is the key to improving the algorithm's performance.

[0050] The complexity of standard quick nondominated sort is However, this remains a performance bottleneck when the population size N is very large. Considering that only a small number of individuals are typically updated during iteration, it's more efficient to update only the dominance relationships of the solutions affected by the new individuals, rather than reordering the entire new population. When a new individual joins, it is only compared with the existing population, and its rank and the ranks of the individuals it dominates are updated; when an old individual is removed, only the dominance counts of the individuals it previously dominated are updated.

[0051] According to the above-described scheme of the present invention, the present invention proposes a two-layer evaluation framework that integrates node attributes and network structure. It solves the problem of network attribute evaluation by "intra-group TOPSIS + inter-group importance-cost-effectiveness", and solves the problem of network structure evaluation by "dual network + three-level" differentiated indicators.

[0052] For the system resource planning problem, this invention constructs a multi-objective planning model that considers the dynamic changes in network structure, which is more in line with the actual situation of "node failure causing system cascade failure".

[0053] This invention employs an improved NSGA-II algorithm to efficiently solve this complex nonlinear problem through incremental nondominated sorting and other methods.

[0054] Furthermore, to achieve the above objectives, the present invention also provides a multi-layer complex network performance evaluation and resource planning system, comprising: A two-layer evaluation framework construction module is used to construct a two-layer evaluation framework for evaluating the capability attributes of network nodes and the importance of network structure in a network system. The two-layer evaluation framework combines the TOPSIS method with the importance-cost-performance ratio index to evaluate the capability attributes of network nodes and evaluates the node structure in the network structure based on complex network theory. The network hierarchical performance evaluation result calculation module calculates the network hierarchical performance evaluation result based on the evaluation results of capability attributes and node structure. The resource planning multi-objective model construction module analyzes the impact of network node failures on network system performance based on the evaluation results of capability attributes, node structure, and network hierarchy effectiveness. Based on the analysis results, with the overall task success rate of the network system being greater than or equal to a specified threshold as a constraint, and with the objectives of minimizing total investment cost and minimizing the total importance loss of the system, a resource planning multi-objective model considering network topology reconfiguration caused by network node failures is established. The model solving module uses an improved NSGA-II algorithm to solve the multi-objective resource planning model.

[0055] The multi-layer complex network performance evaluation and resource planning system according to the present invention can realize the above-mentioned multi-layer complex network performance evaluation and resource planning method, and the specific process steps will not be repeated.

[0056] Furthermore, to achieve the above objectives, the present invention also provides an electronic device, including a processor, a memory, and a computer program stored in the memory and executable on the processor. When the computer program is executed by the processor, it implements the multi-layer complex network performance evaluation and resource planning method as described above.

[0057] Furthermore, to achieve the above objectives, the present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the multi-layer complex network performance evaluation and resource planning method described above.

[0058] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described and verified in detail below with reference to the accompanying drawings and verification examples. It should be understood that the specific verification examples described herein are only used to explain and verify this invention and do not limit the scope of protection of this invention.

[0059] Verification Example 1 To verify the above method, we will analyze a complex IoT system containing 176 nodes (26 sensing nodes, 100 decision-making nodes, and 50 execution nodes) and establish a network. Figure 4 This represents a solid-line information diagram (solid-line network model) for the Internet of Things. Figure 5 This represents a dashed line control diagram (dashed line network model) for the Internet of Things (IoT). Figure 4 The points at both ends of the red line are decision nodes, the points at the non-overlapping ends of the green line are perception nodes, and the points at the ends of the yellowish line that do not overlap with the red line are execution nodes.

[0060] Hierarchical performance evaluation results Through calculation, all node attribute capability indicators are as follows: Figure 6 As shown, the evaluation model has strong practical significance when comprehensively considering the attributes and capabilities of "within-group + between-group".

[0061] Using graph and network-related algorithms in MATLAB software, the node network indices of the "dual network + three system" were calculated sequentially.

[0062] Based on the preceding analysis, in a solid-line information flow network In this study, the hub centrality (Hub value) of a node was calculated. This metric reflects a node's ability to act as an information hub, i.e., the degree to which it connects other important nodes during information transmission. The visualization results are shown below. Figure 7 As shown in the diagram, the depth of a node's color is positively correlated with its Hub value; a darker color indicates a stronger hub role in information flow. Analysis reveals that perception nodes 1 and 2 have significantly higher hub centrality than other nodes. Combined with the network structure diagram, it can be seen that these two nodes are not only directly connected to each other but also connected to multiple computing centers through short paths, placing them at the core of information aggregation and distribution. Therefore, their high hub centrality plays a crucial role in improving the overall network's information transmission efficiency.

[0063] In the dotted information flow network Furthermore, the outward proximity centrality Cout of the nodes was calculated. This metric measures how easily a node can reach other nodes; a higher value indicates that the node can more easily and quickly spread information throughout the network. The visualization results are shown below. Figure 8 As shown, the darker the node color, the higher its proximity centrality.

[0064] Figure 9 Showing The betweenness centrality (CB) index of nodes. This index measures a node's ability to control the flow of information in a network. Nodes with high betweenness centrality are often located on multiple shortest paths and have a controlling effect on information transmission. As shown in the figure, decision nodes 74 and 76 have significantly higher betweenness centrality than other nodes. Combined with network topology analysis, these nodes occupy a critical position in the communication link, directly connecting to the decision nodes and forming essential nodes in the communication path. Therefore, they act as "bridges" in information transmission; their failure will significantly affect network connectivity and information transmission efficiency.

[0065] Figure 10 Showing The out-degree (dout) metric of a node reflects its ability to send information to other nodes. A larger node area indicates a higher out-degree. In the decision-making layer, nodes with higher out-degrees are decision nodes 1 and 2. These nodes occupy a core position in data processing and information distribution; their high out-degree indicates strong control capabilities within the network, enabling them to transmit instructions and information to multiple lower-level nodes and providing crucial support for the overall operation of the system.

[0066] in-degree d of a node in The metrics reflect a node's ability to receive information. Execution layer nodes generally have low in-degree values, indicating that their role in information reception is relatively weak.

[0067] In summary, the above analysis reveals the functions and roles of each node in the system in information flow and task coordination from multiple dimensions. Nodes with high hub centrality and high out-degree centrality are mainly concentrated in the perception layer, reflecting their key role in information convergence and dissemination; nodes with high intermediary centrality are mainly distributed in the decision-making layer, highlighting their bridging role in information transmission paths; while out-degree and in-degree indicators further reveal the information sending and receiving characteristics of each node in the decision-making and execution layers, providing important reference for system architecture analysis to a certain extent.

[0068] For the comprehensive capability index of the i-th node in the hierarchy This metric integrates a node's attribute capabilities with network structure characteristics, reflecting the comprehensive functional and structural importance of a node within the system. All scores were calculated using MATLAB. The performance indices at three levels were calculated, as shown in Table 1. The hierarchical performance index V defined in this verification example... k Essentially, it refers to the attribute capabilities of all nodes within a hierarchy. Network structure metrics The sum of the products reflects the overall contribution of different levels in its IoT system.

[0069] Table 1 Results of Hierarchical Performance Indicators Analyzing the numerical results, the execution layer efficiency index (14211) is significantly higher than the other two systems. This can be explained by the high importance of its nodes, cost-effectiveness, and structural characteristics. As mentioned earlier, multiple nodes in the execution layer have high in-degree values, exhibiting a "many-to-one" correspondence, which enhances its network structure index. Generally higher. Furthermore, thanks to their high cost-effectiveness, these nodes also offer superior attribute capabilities. The value of this aspect is also high, and the product effect of the two leads to a significant improvement in its overall index.

[0070] The decision-making level efficiency index (4399.8) falls between the two, which is closely related to the high betweenness centrality of its nodes in the network. Combining complex network theory, the efficiency of key nodes (such as control centers and communication hubs) in this system... The value is relatively large. Although the number of nodes is relatively small, the contribution of each node is high. A deeper analysis reveals that the efficiency index of the decision-making level is much lower than that of the execution level because all nodes at the decision-making level have low cost-effectiveness.

[0071] The perception layer performance index (3827.5) is relatively low, reflecting that although its information aggregation function in the network is important, the small number of nodes (only 26) limits its utilization of V.k The results calculated by the formula are relatively low.

[0072] Node failure impact analysis Based on the evaluation results, the impact of node failures under light, medium, and severe conditions on the hierarchy was further analyzed, and the decline rate of hierarchy performance indicators was calculated. .

[0073] Single target node failure From the perspective of node importance, when a single node fails, the three-level calculation results are visualized, such as... Figure 11 The diagram clearly shows the top 10 performance indicators at three different levels when nodes experience various failures, intuitively illustrating the degraded effect of critical node failure on the overall IoT system. This reveals the following key conclusions: Main Conclusions: 1. "Critical nodes" reflect system vulnerability: Analyzing the same failure scenarios and multiple targets, the top ten ranking chart shows that node importance is concentrated in a few high-value critical nodes. Under the same conditions, the first-ranked decline rate is more than three times that of the tenth-ranked decline rate. (Thermal) Figure 11 In this study, the number of targets causing high degradation rates in each system does not exceed 30%. This indicates that the IoT system is a network composed of a few "hubs" and a large number of "ordinary nodes," dominated by the state of a few core nodes. Once a core node fails, it will lead to a significant drop in system performance.

[0074] 2. The decline rate exhibits "multiplicative amplification": When analyzing different fault levels of individual nodes, both graphs show that as the fault level increases from mild to severe, the decline rate of critical nodes increases significantly. For example, the decline rate of the core control node under mild fault increases from 0.0271 to 0.1234 under severe fault, an increase of about 4.5 times. This reflects the maintenance strategy of "better to cut off one finger than to injure all ten fingers." It is better to focus on ensuring critical nodes than to maintain a large number of ordinary nodes.

[0075] 3. The IoT system highly conforms to complex network theory: Analysis of the entire network shows a strong correlation between node decline rate data and node importance in complex network theory. This further confirms the significant role of node importance analysis in IoT system research, enabling the establishment of a more scientific maintenance priority ranking.

[0076] Multi-node failure impact analysis A typical maintenance scheme was selected, with 58 nodes experiencing minor, 38 moderate, and 22 severe faults. The two-layer network of the industrial IoT system was reconstructed and analyzed. After the faults, a total of 154 nodes were retained. The topology of the reconstructed industrial IoT system control flow network is visualized as follows: Figure 12 As shown.

[0077] The decline rate formula is used to calculate the decline rate of network structure indicators of each node in a damaged two-layer network. The overall decline rate of the system's three task assurance capabilities under multi-node failure was obtained. =(39.11%,31.74%,40.97%), k= 1, 2,3, representing the perception layer, decision-making layer, and execution layer, respectively.

[0078] The calculation results are analyzed from a data perspective. First, most of the severely faulty nodes are directly related to the execution layer, such as production lines and robotic arms. The failure of these nodes directly weakens the control and operational capabilities of the execution layer, which is the most significant reason for its overall decline rate. Second, while the perception layer has fewer severely faulty nodes, it involves some key nodes, such as sensor control stations. Their severe failures not only affect the station itself but also the sensors associated with it. Therefore, this invention argues that the perception layer has a smaller number of nodes, and only some nodes have redundancy, which explains its slightly lower overall decline rate, but is similar to that of the execution layer. Finally, this invention believes that the result shows the lowest decline rate for the decision layer because the decision layer has more redundant nodes, and the severely faulty nodes have lower importance (not involving many high-level control centers), thus resulting in the lowest calculated decline rate.

[0079] Pareto Analysis of Resource Planning To solve the multi-objective programming problem of resource planning in IoT systems, a program was written in MATLAB to solve the optimization problem. The main parameter settings of the NSGA-II algorithm are listed in Table 2.

[0080] Table 2 NSGA-II Algorithm Parameter Settings Running the program yielded 200 solutions for the first front. The Pareto front and convergence curve are shown below. Figure 13 and Figure 14 As shown. From a mathematical model perspective, the graph is found to consist of discrete, non-dominated solution sets, rather than a continuous curve. This precisely reflects the core characteristic of NSGA-II as a population-based metaheuristic algorithm. The algorithm's random initialization, crossover, and mutation operations enable it to explore a broad solution space and converge to multiple approximate points of the global Pareto front. The final solution distribution clusters around a clear curve, proving the algorithm's good convergence in solving this problem.

[0081] Figure 14The horizontal axis represents the total investment cost of the system (Obj1), and the vertical axis represents the loss of system importance (Obj2). This frontier basically shows a decreasing trend, which effectively demonstrates the conflicting relationship between the two objective functions. To reduce the loss of system importance, it is necessary to increase the investment cost. This accurately reveals the core characteristics of Pareto optimality in multi-objective programming.

[0082] From the perspective of resource planning strategies, Figure 14 The system offers a variety of solutions for system maintenance, ranging from "economical," "high-security," to "balanced": The left side of the image shows a solution that achieves limited retention of system importance with a lower investment cost, suitable for scenarios with tight budgets or limited maintenance resources; the right side of the image shows that a higher investment cost is required to achieve a high retention rate of system importance, suitable for critical scenarios with extremely high system reliability requirements; the solution in the middle is a compromise solution based on cost-benefit balance, which can be used as a recommended solution for most industrial scenarios.

[0083] Based on system requirements, namely minimizing system importance loss while minimizing investment costs, the most cost-effective solution was selected from among many cutting-edge solutions as the final resource planning scheme, as shown in Table 3. The total investment cost of this scheme is 2241, and the system importance loss is 3238. It has achieved good maintenance results and presents a clear concept of "prioritizing key nodes".

[0084] Table 3 Protection Plan As can be seen from the above, the two-layer evaluation framework proposed in this invention systematically solves the key theoretical and technical problems in IoT performance evaluation and maintenance strategy planning, effectively overcoming the shortcomings of traditional methods in decision-making regarding heterogeneous targets and multifunctional networks. Example verification shows that the solution of this invention not only outputs reasonable performance index values ​​but also accurately locates key nodes crucial to IoT stability. The proposed "two-layer evaluation model integrating attributes and structure" is an effective tool for quantifying system capabilities. In multi-objective optimization, directly introducing the network reconstruction computational system degradation rate increases computational complexity but significantly improves the simulation accuracy of the strategy. The improved NSGA-II algorithm exhibits good convergence and distribution in this problem. The established "multi-objective programming model considering dynamic changes in network structure" and its solution algorithm can provide practical operators with a series of Pareto optimal solutions ranging from "economical" to "efficient".

[0085] Those skilled in the art will recognize that the modules and algorithm steps described in conjunction with the embodiments disclosed herein can be implemented using electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0086] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the above-described apparatus and equipment can be referred to the corresponding process in the foregoing method implementation, and will not be repeated here.

[0087] In the embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or modules may be electrical, mechanical, or other forms.

[0088] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical modules; that is, they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the objectives of the embodiments of the present invention, depending on actual needs.

[0089] In addition, the functional modules in the embodiments of the present invention can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0090] If the aforementioned functions are implemented as software functional modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the sending / receiving methods of various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, ROM, RAM, magnetic disks, or optical disks.

[0091] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in this application.

[0092] It should be understood that the sequence number of each step in the invention and its embodiments does not absolutely imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

Claims

1. A method for performance evaluation and resource planning of multi-layer complex networks, characterized in that, include: A two-layer evaluation framework is constructed to assess the capability attributes of network nodes and the importance of network structure in a network system. The two-layer evaluation framework combines the TOPSIS method with the importance-cost-performance ratio to evaluate the capability attributes of network nodes and evaluates the node structure in the network structure based on complex network theory. The network hierarchical performance evaluation results are calculated based on the evaluation results of capability attributes and node structure. Based on the evaluation results of capability attributes, node structure, and network hierarchy performance, the impact of network node failures on network system performance is analyzed. Based on the analysis results, with the overall task success rate of the network system being greater than or equal to a specified threshold as a constraint, and with the objectives of minimizing total investment cost and minimizing total system importance loss, a multi-objective resource planning model considering network topology reconfiguration caused by network node failures is established. An improved NSGA-II algorithm is used to solve the multi-objective model of resource planning; The two-layer evaluation framework combines the TOPSIS method with the importance-cost-performance ratio to evaluate the capability attributes of network nodes, including: The TOPSIS method is used to evaluate the sub-categories of network nodes in the three types of network nodes in the perception layer, decision layer and execution layer of the network system to obtain the in-group evaluation value of the network nodes at each network level. The importance and maintenance cost of network nodes in the three types of network nodes in the network system—perception layer, decision layer, and execution layer—are evaluated to obtain the inter-group evaluation value of network nodes at each network layer. The attribute capability values ​​of network nodes are calculated based on the within-group evaluation values ​​and the between-group evaluation values. : ； in, This is the in-group evaluation value of the i-th network node within the k-th network layer; f represents the inter-group evaluation value of the i-th network node within the k-th network layer; k=1,2,3, representing the perception layer, decision layer, and execution layer, respectively; f represents and and The functional relationship; The two-layer evaluation framework evaluates the node structure in a network based on complex network theory, including: To address the relationships between network nodes and the permissions involved in data transmission and retrieval between them, an information flow network diagram consisting of solid lines and a control flow network diagram consisting of dashed lines are constructed. Based on complex network theory, solid line network models and dashed line network models are established for the information flow network diagram and the control flow network diagram, respectively. Based on the solid line network model and the dashed line network model, the structural indices of network nodes in the solid line network model and the dashed line network model are obtained respectively. The node structure index is calculated based on the structural indices of network nodes in the realized network model and the structural indices of network nodes in the dashed line network model. : ； in, This represents the solid-line network model in the k-th network layer. The structural index of the i-th network node ; The dashed line represents the network model in the k-th network layer. The structural index of the i-th network node ; This is the output function; The network hierarchical performance evaluation result is calculated from the evaluation results based on capability attributes and node structure as follows: ； in, F represents the performance index of the k-th network layer, where n is the number of network nodes; F represents... and and The functional relationship; The aforementioned multi-objective resource planning model, constrained by an overall task success rate of the network system being greater than or equal to a specified threshold, and aiming to minimize total investment cost and total system importance loss, considers network topology reconfiguration caused by network node failures. This model includes: (1) Decision variables: The resource planning scheme needs to consider four protection strategies for network nodes, using 0-1 decision variables x ij To indicate the protection plan: ； Where x represents the protection scheme matrix, i represents the network node, and j=1,2,3,4 represent four protection strategies: hot redundancy, full redundancy, partial redundancy, and no redundancy, respectively. Each protection strategy corresponds to the network node being fault-free, slightly faulty, moderately faulty, and severely faulty after protection. (2) Other variables: Let a k ρ represents the task guarantee rate threshold for the k-th network layer. j C represents the importance loss coefficient when the j-th protection strategy is adopted. ij Let represent the actual cost of implementing protection strategy j for network node i, and let importance be... i Cost represents the inherent importance of the i-th network node. i This represents the baseline maintenance cost of the i-th network node; (3) Constraints: 0-1 decision constraint: The same network node can only adopt one protection strategy, i.e., matrix [x] ij Each row contains exactly one non-zero value: ; System task guarantee rate constraint: The task guarantee rate of the perception layer, decision layer, and execution layer must be greater than or equal to a specified threshold. When network nodes adopt a non-redundant protection strategy, network nodes may be removed, and the network topology may change. The system's task assurance capability after protection needs to be calculated based on the new network structure, with the following constraints: ； in, This represents the network topology under the influence of protection scheme x; F represents a. k and and The functional relationship between them The attribute capability values ​​of network nodes in protection scheme x , Network topology under the influence of protection scheme x Node structure indicators ; (4) The objective function aims to minimize the total investment cost and the total importance loss of the system, while satisfying the system task guarantee rate. ； ； Let the objective function be the one that minimizes the total investment cost. Let be the objective function that aims to minimize the total importance loss of the system; (5) Multi-objective model of resource planning: ； The improved NSGA-II algorithm includes: Chromosome encoding method: The integers 0-1 in the problem constitute a one-hot code, and the chromosome uses a binary one-hot code; Crossover, mutation, and selection operations: The crossover operation selects one of the four corresponding bits from the two parent chromosomes with equal probability and retains it; the mutation operation changes the four selected one-hot bits to one of the other three states with equal probability. Non-dominant level determination: Regarding this question: in For a feasible solution, it must be determined that a feasible solution always dominates an infeasible solution. If two solutions are both infeasible, then their overall constraint violation degrees are compared. The solution with a smaller constraint violation degree dominates the solution with a larger constraint violation degree. The constraint violation degree is calculated based on the three system capability reduction rates that the attack scheme must satisfy, and is defined as follows: Pareto dominance is used for comparison only when both solutions are feasible or have the same degree of constraint violation, i.e., solution x1 dominates solution x2 (denoted as x1 + x2 + x3). If and only if: ； If no other solution dominates a solution, it is a non-dominated solution, and the Pareto solution set is the set of all non-dominated solutions. Select operation: First, select individuals with a higher non-dominant level; When the non-dominance levels are the same, select the individual with the higher crowding level; Formation of a new paternal generation At this time, an elite retention strategy is adopted, that is, the best n individuals of the current generation are retained. To the next generation: ； Crowding calculation: Crowding distance measures the distribution density of solutions in their frontier: ； in, It is the value of the i-th individual on the m-th objective function; and These are the maximum and minimum values ​​of the m-th objective function; The crowding degree of boundary individuals is set to infinity; Improved Quick Non-Dominated Sort: Fast non-dominated sort initializes the dominance pressure n of all individuals through a single pairwise comparison. p and the scope of control S p Then, the iterations of finding the layer with current pressure of 0 and reducing the pressure of the individuals dominated by it are repeated to divide the layer into multiple non-dominated layers.

2. A system for evaluating the performance and resource planning of multi-layer complex networks, implementing the method for performance evaluation and resource planning of multi-layer complex networks as described in claim 1, characterized in that: include: A two-layer evaluation framework construction module is used to construct a two-layer evaluation framework for evaluating the capability attributes of network nodes and the importance of network structure in a network system. The two-layer evaluation framework combines the TOPSIS method with the importance-cost-performance ratio index to evaluate the capability attributes of network nodes and evaluates the node structure in the network structure based on complex network theory. The network hierarchical performance evaluation result calculation module calculates the network hierarchical performance evaluation result based on the evaluation results of capability attributes and node structure. The resource planning multi-objective model construction module analyzes the impact of network node failures on network system performance based on the evaluation results of capability attributes, node structure, and network hierarchy effectiveness. Based on the analysis results, with the overall task success rate of the network system being greater than or equal to a specified threshold as a constraint, and with the objectives of minimizing total investment cost and minimizing the total importance loss of the system, a resource planning multi-objective model considering network topology reconfiguration caused by network node failures is established. The model solving module uses an improved NSGA-II algorithm to solve the multi-objective resource planning model.

3. An electronic device, characterized in that, It includes a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the multilayer complex network performance evaluation and resource planning method as described in claim 1.

4. A computer-readable storage medium, characterized in that, A computer program is stored on the computer-readable storage medium, which, when executed by a processor, implements the multilayer complex network performance evaluation and resource planning method as described in claim 1.

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