A method and system for identifying key nodes of highway network in plateau mountainous area

Abstract

The present invention relates to the field of traffic engineering and network optimization, and in particular to a method and system device for identifying key nodes in a plateau mountainous area highway network. The method comprises the following steps: first, constructing a topological structure model of a plateau mountainous area highway network, and abstractly representing nodes and edges in the network; then, establishing an importance evaluation index system for key nodes; then, calculating the comprehensive weight of each node by combining subjective weight and objective weight; then, based on an improved LeaderRank algorithm, by adding background nodes to the original network and establishing unidirectional connections with all other nodes, initializing the value of the node according to the comprehensive weight of the node, and obtaining a stable node LR value through iterative calculation, and then identifying and sorting the key nodes in the network according to the LR value; finally, performing simulation tests on the identified key nodes to verify their influence on the overall connectivity and stability of the highway network.

Description

Technical Field

[0001] The present invention relates to the fields of traffic engineering and network optimization, and in particular to a method and system device for identifying key nodes in a highway network in a plateau mountainous area. Background Art

[0002] With the rapid advancement of modernization, the national highway network has reached a certain scale, but the highway network in key areas such as those prone to natural disasters and geographical barriers still needs to be improved. As the key support for the sustained and stable development of the economy and society in plateau mountainous areas, the highway network plays a vital role in the transportation system of the region. However, due to the particularity of the topography and landforms of the plateau mountainous areas and the complexity of the road network structure, the failure of nodes usually has a significant impact on the local connectivity of the road network, and in severe cases even leads to the deterioration of the overall connectivity, resulting in a significant decline in transportation efficiency. Therefore, identifying key nodes in the highway network in plateau mountainous areas is of great significance for improving the stability and security of the entire network.

[0003] When studying and analyzing highway networks, scholars use complex network theory to model highway networks, abstract highway networks into topological network models, and then analyze the network topological structure characteristics. Liu Rui et al. used indicators such as betweenness centrality and network efficiency to analyze the network structure characteristics of my country's highways. Based on complex network theory, Zhang Xinyu et al. conducted a detailed study on the topological structure of highways in Guangxi Zhuang Autonomous Region, revealing the influence of degree distribution, clustering coefficient and network centrality on highway network connectivity. Cui Yang et al. constructed a topological structure network model of the highway network in the western region, and used complex network characteristic indicators such as degree distribution, average path length and network efficiency to quantitatively analyze the structural characteristics of the highway network in the region.

[0004] The highway network is a real traffic network. Not only is the network structure complex, but it is also affected by traffic attributes, such as highway grade, traffic capacity, and traffic flow. However, traditional models often ignore the traffic attributes in the highway network. Therefore, models and index analysis that consider the actual factors of the highway network have gradually become a research trend. In "Research on the Vulnerability of Highway Network Considering Traffic Weighting", Dai Hongna et al. established a traffic-weighted highway network model based on the traditional road network topology structure, and analyzed the vulnerability of the highway network through traffic attribute indicators such as travel efficiency and travel demand satisfaction rate. In "Research on the Resilience of Highway Network Based on Multivariate Weighted Central Characteristics", Lin Peiqun et al. established a highway weighted network by introducing passenger and freight traffic, and proposed a centrality index of the weighted network based on the multivariate characteristic gravity model to study the resilience of the highway network.

[0005] In recent years, many scholars have also carried out a large number of related studies on important nodes in highway networks. In "Reliability of Provincial Highway Network Connectivity: Case Analysis of Heilongjiang Province", Wu Lina et al. evaluated the importance of nodes in highway networks by combining key indicators such as network connectivity and reliability. In "Research on Evaluation Method of Traffic Network Node Importance Based on Clustering Algorithm", Wang Lingli et al. analyzed the applicability of random forest algorithm for node identification, and calculated the importance of weighted network nodes by constructing an undirected weighted network model of road traffic, combining indicators such as node traffic volume and PR value with improved random forest algorithm. In "Path Planning for Successive Congestion Evacuation of Urban Road Traffic Network Based on Comprehensive Node Importance", Zhang Guilan used entropy weight method to determine the weights of indicators such as node degree, point weight and proximity centrality, and combined grey system evaluation with hierarchical analysis method to comprehensively evaluate the importance of highway network nodes. In "Urban Traffic Perception and Road Network Key Node Identification Based on Trajectory Big Data", Feng Huifang et al. conducted research on identifying key points based on PageRank algorithm, a web page ranking method, by improving it to WNodeRank to be applicable to directed weighted networks.

[0006] At present, there are relatively few studies that effectively combine node importance evaluation and important node identification, and most identification methods still lack consideration of the comprehensive importance of nodes. Therefore, considering the network structure and traffic function of plateau mountain roads, a key node importance evaluation index system is established, and combined with the comprehensive weight determined based on subjective and objective combinations, the present invention proposes a plateau mountain road network key node identification method and system device to address the deficiencies of the existing technology. Summary of the invention

[0007] The purpose of the present invention is to overcome the deficiencies in the prior art in the identification of key nodes in plateau mountainous road networks, such as the traditional algorithms that do not adequately consider multi-dimensional factors such as terrain complexity and traffic flow, the existing key node identification methods that usually rely on a single network structure indicator or traffic attribute, and the determination of subjective weights and objective weights often lack scientificity and rationality. A method and system device for identifying key nodes in plateau mountainous road networks is provided, which introduces a multi-dimensional key node evaluation index system, combines the fuzzy analytic hierarchy process (FAHP) and the entropy-weighted improved CRITIC method to scientifically determine the subjective weights and objective weights, and optimizes the determination of the comprehensive weights through the game theory comprehensive weighting method, and finally improves the LeaderRank algorithm to achieve high-precision key node identification, thereby improving the overall connectivity and disaster resistance of the plateau mountainous road network.

[0008] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions:

[0009] A method for identifying key nodes of a plateau mountain highway network comprises the following steps:

[0010] S1. Construct a topological structure model of the plateau mountain highway network and abstract the nodes and edges in the network;

[0011] S2. Establish an importance evaluation index system for key nodes, including degree centrality, betweenness centrality, closeness centrality, travel time weight, and adjacent node travel time degree;

[0012] S3, combining subjective weight and objective weight, calculate the comprehensive weight of each node in the network;

[0013] S4. Identify and sort the key nodes in the network based on the comprehensive weight and the improved LeaderRank algorithm, specifically including:

[0014] S41, adding a background node in the network and establishing a bidirectional connection with all other nodes;

[0015] S42, initializing the value of the node according to the comprehensive weight of the node, and obtaining the node LR value through iterative calculation;

[0016] S43, identifying and sorting the nodes according to the LR values ​​to obtain key nodes;

[0017] S5. Perform simulation test on the identified key nodes.

[0018] Preferably, the network in step S1 is an undirected weighted network model, denoted as ,in Represents a set of nodes, n is the total number of nodes, represents the set of edges, m is the total number of edges, and the adjacency matrix represents the weight distribution of the weighted network, where is the weight of the edge between node i and node j. By modeling the highway network as an undirected weighted network model, the real relationship between nodes and edges in the network can be more accurately reflected, making the result of key node identification more consistent with the structure of the actual traffic network.

[0019] The degree centrality in step S2 The expression is

[0020]

[0021] in, It represents the number of other nodes directly connected to node i in the network. Using degree centrality as an evaluation indicator can effectively quantify the connection density of nodes in the network. The identification of highly central nodes can help determine the key nodes with high influence in the network, so as to better optimize and plan the network.

[0022] Betweenness Centrality The expression is

[0023]

[0024] Among them, s and t are two nodes in the network, and is the number of shortest paths from node s to node t; is the number of paths passing through node i in the shortest path from node s to node t. By using the betweenness centrality index, the present invention can evaluate the bridge role of nodes in connecting different parts of the network, help identify those nodes that play a key role in information circulation and traffic flow, and improve the scientificity and accuracy of the identification results.

[0025] Closeness Centrality The expression is

[0026]

[0027] in, is the shortest path length between node i and node j. The introduction of proximity centrality allows the distance between a node and other nodes to be quantified. This indicator helps to identify key nodes in the network that are geographically and traffic-centric, and further optimize network connectivity.

[0028] The travel time weight The expression is The travel time weight, as an evaluation index, can directly reflect the traffic function of a node. Through the application of this index, the present invention can more accurately evaluate the importance of a node in an actual highway network, thereby optimizing traffic flow management.

[0029] The adjacent node passability The expression is:

[0030]

[0031] in, is the travel time weight between node i and node j. The use of adjacent node travel time increases the consideration of traffic mobility around the node, making the importance assessment of the node more comprehensive, which helps to identify nodes that are critical to the operation of the entire network in a complex transportation network.

[0032] Preferably, the subjective weight combined in step S3 is determined by fuzzy hierarchical analysis method, which specifically includes constructing a decision hierarchy, establishing a fuzzy judgment matrix and performing a consistency test, and finally calculating the subjective weight of each indicator by fuzzy comprehensive evaluation; the objective weight is calculated by the CRITIC method improved by entropy weight, including data dimensionless, volatility analysis, conflict analysis, entropy value calculation and determination of objective weight, and finally the comprehensive weight of each node in the network is determined by combining the subjective weight and the objective weight through the game theory comprehensive weighting method. Combining fuzzy hierarchical analysis method and entropy weight improved CRITIC method to determine node weights can more scientifically and reasonably allocate the weights of each indicator, making key node identification more accurate, and effectively avoiding the problems of strong subjectivity or data distortion in traditional methods.

[0033] Preferably, the iterative calculation formula of the LeaderRank algorithm in step S4 is:

[0034]

[0035] in, is the LR value of node i at time t; is the out-degree of node i; Indicates the connection status between node i and node j in the network. When node i has an edge pointing to node i, is 1, otherwise it is 0;

[0036]

[0037] in, For node i The LR value that reaches the convergence state at the moment iteration; For background node g The LR value at the moment; the iterative calculation is performed until the LR value of the node reaches a convergence state. The iterative calculation is performed through the improved LeaderRank algorithm, and finally a stable LR value is obtained. This process ensures the stability and reliability of key node identification, making the identification result more credible.

[0038] Preferably, the present invention also provides a system device for identifying key nodes of resilience in a plateau mountainous area highway network based on improved LeaderRank, the system device comprising:

[0039] A network topology construction module is used to receive basic data of the plateau mountain highway network and construct it into an undirected weighted network model, wherein the network model includes a node set, an edge set and a weight matrix;

[0040] An index calculation module, used to calculate the importance evaluation index of each node based on the network model, wherein the index includes degree centrality, betweenness centrality, closeness centrality, travel time weight and adjacent node travel time degree;

[0041] The weight calculation module is used to determine the subjective weight using the fuzzy analytic hierarchy process, and calculate the objective weight using the CRITIC method improved by entropy weight, and finally determine the comprehensive weight of each node in combination with the game theory comprehensive weighting method;

[0042] A key node identification module is used to improve the LeaderRank algorithm based on the comprehensive weight to identify the key nodes in the plateau mountain road network. The improvement includes adding background nodes to the original network and establishing unidirectional connections with all other nodes, and iteratively calculating the LR value of the node until convergence;

[0043] The simulation test module is used to simulate the changes in network connectivity and stability when key nodes fail, so as to verify the impact of the identified key nodes on the overall performance of the highway network.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] The present invention introduces an improved LeaderRank algorithm, proposes a key node identification method suitable for plateau mountain road network, and effectively improves the accuracy of key node identification in plateau mountain road network. By constructing a topological structure model of plateau mountain road network and combining a multi-dimensional key node evaluation index system such as degree centrality, betweenness centrality, and proximity centrality, the importance of nodes can be evaluated more comprehensively and accurately, thereby accurately identifying key nodes that are crucial to network connectivity and stability. Combining subjective weights and objective weights, the comprehensive weight of each node is made more reasonable and objective. This not only avoids the limitation of relying on a single indicator for evaluation, but also improves the flexibility and accuracy of the identification process through the game theory comprehensive weighting method. By introducing background nodes to establish a two-way connection with all nodes, and combining the node's comprehensive weight initialization value, the LR value is iteratively calculated to achieve efficient sorting and identification of key nodes. The improved algorithm is more adaptable to the complex environment of plateau mountain road network, and improves the convergence speed and calculation efficiency of the algorithm. The identified key nodes are verified through simulation tests to evaluate their impact on the overall connectivity and disaster resistance of the network. This process not only improves the reliability of the results, but also provides a basis for decision-making in practical applications.

[0046] In general, the present invention effectively solves the problem of identifying key nodes in plateau mountain road networks, improves the connectivity management and fault recovery capabilities of the network, and has high practical value in complex terrain and special traffic environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a flow chart of a method for identifying key nodes in a plateau mountainous area highway network according to Embodiment 1 of the present invention;

[0048] Figure 2 This is a diagram of the key node evaluation index system of Example 2 of the present invention;

[0049] Figure 3 This is a graph showing changes in network efficiency according to Embodiment 3 of the present invention;

[0050] Figure 4 This is a graph showing changes in network connectivity rate according to Embodiment 3 of the present invention. DETAILED DESCRIPTION

[0051] The following is a further detailed description of a method and system device for identifying key nodes in a plateau mountainous road network provided by the present invention in conjunction with the accompanying drawings and specific embodiments. However, this should not be understood as the scope of the above-mentioned subject matter of the present invention being limited to the following embodiments, and all technologies implemented based on the content of the present invention belong to the scope of the present invention. Combined with the following description, the advantages and features of the present invention will become clearer. It should be noted that the drawings are all in a very simplified form and use non-precise proportions, which are only used to conveniently and clearly assist in explaining the purpose of the embodiments of the present invention.

[0052] Example 1

[0053] This embodiment provides a method for identifying key nodes in a plateau mountainous area highway network. The method steps are as follows: Figure 1 This method aims to more accurately identify key nodes in the plateau mountainous road network by improving the algorithm and evaluation index system.

[0054] 1. Constructing a topological structure model of the highway network in plateau mountainous areas

[0055] First, the plateau mountain road network in the target area is abstracted into an undirected weighted network model. ,in represents the set of nodes, n is the total number of nodes, represents the set of edges, m is the total number of edges, and the adjacency matrix represents the weight distribution of the weighted network, where is the weight of the edge between node i and node j.

[0056] 2. Establish an evaluation index system for the importance of key nodes

[0057] Based on this model, the degree centrality, betweenness centrality, closeness centrality, travel time weight and adjacent node travel time degree of each node are calculated.

[0058] Specifically, degree centrality The expression is

[0059]

[0060] in, Represents the number of other nodes directly connected to node i in the network.

[0061] Betweenness Centrality The expression is

[0062]

[0063] Among them, s and t are two nodes in the network, and is the number of shortest paths from node s to node t; is the number of paths passing through node i in the shortest path from node s to node t.

[0064] Closeness Centrality The expression is

[0065]

[0066] in, is the shortest path length between node i and node j.

[0067] The travel time weight The expression is .

[0068] The adjacent node passability The expression is:

[0069]

[0070] in, is the travel time weight between node i and node j.

[0071] 3. Combine subjective weight and objective weight to calculate comprehensive weight

[0072] (1) The fuzzy analytic hierarchy process (FAHP) is used to determine the subjective weight. By constructing a decision hierarchy and a fuzzy judgment matrix and performing a consistency test, the subjective weight of each indicator is obtained.

[0073] (2) The objective weights are determined using the CRITIC method improved by entropy weights. The subjective weights of each indicator are obtained through data dimensionlessness, volatility analysis, conflict analysis, and entropy value calculation.

[0074] (3) Combining subjective weights and objective weights, the comprehensive weight of each node is determined through the game theory comprehensive weighting method.

[0075] 4. Improved LeaderRank algorithm

[0076] Add background nodes to the constructed network model and establish unidirectional connections with all nodes of the original network, with the connection direction from the original network node to the background node.

[0077] Initialize the node value according to the comprehensive weight of each node, and calculate the LR value of each node through the following iterative formula:

[0078]

[0079] in, is the LR value of node i at time t; is the out-degree of node i; Indicates the connection status between node i and node j in the network. When node i has an edge pointing to node i, is 1, otherwise it is 0;

[0080]

[0081] in, For node i The LR value that reaches the convergence state at the moment iteration; For background node g The LR value at the moment; the iterative calculation is performed until the LR value of the node reaches a convergence state.

[0082] 5. Simulation test

[0083] (1) The identified key nodes are verified through simulation tests. The tests simulate node failures and evaluate the impact of node failures on the overall connectivity and efficiency of the highway network.

[0084] (2) The test results show that the recognition accuracy of key nodes is high. After deleting the key nodes, the connectivity and efficiency of the network are significantly reduced, which verifies the effectiveness and practicality of this method.

[0085] Through the above implementation steps, this embodiment successfully identified the key nodes in the plateau mountainous area highway network, and verified its important role in network stability through simulation, providing a reliable basis for the optimization management of the plateau mountainous area highway network.

[0086] Example 2

[0087] Based on Example 1, this Example 2 further optimizes the network model construction method and the evaluation indicators of key nodes, especially in terms of combining actual traffic data and terrain factors, so that the results of key node identification are more in line with actual application needs, and improves the applicability and accuracy of this method in complex plateau and mountainous environments.

[0088] 1.1 Network topology model construction

[0089] It is an important research method to transform the highway network topology of plateau mountainous areas into a complex network model, and the main technical methods to achieve the transformation goal include Space-L, Space-R and Space-P. The core idea of ​​Space-L is to map and build a model based on the actual relationship between nodes and sections in the highway network. The result of this abstract mapping can intuitively reflect the positional relationship and spatial structure of nodes in the actual road network, which is more in line with the general spatial cognition. Its advantage is that it can directly perform structural topological modeling based on the geographic information of the actual road network, thereby deeply analyzing the topological structure of the highway transportation system under the framework of complex network theory, thereby revealing key nodes, important sections and the overall spatial layout, which helps to deeply understand the infrastructure of the transportation network and the actual connection between nodes. Therefore, in order to study the importance of each traffic node in the highway network, the present invention will adopt the Space-L method to construct a topological model of the highway network in plateau mountainous areas.

[0090] First, the plateau mountain road network in the target area is abstracted into an undirected weighted network model. ,in Represents a set of nodes, n is the total number of nodes, represents the set of edges, m is the total number of edges, and the adjacency matrix represents the weight distribution of the weighted network, where is the weight of the edge between node i and node j.

[0091] 1.2 Complex Network Theory

[0092] As a typical real-world complex system, the highway network in plateau mountainous areas presents multi-level complexity in system structure and function. From the perspective of system structure, the highway transportation system has a large and intricate road network; from the perspective of system function, there are complex interactions between materials, information, and traffic in the highway network. Complex network theory provides a powerful tool for in-depth understanding of the structure and function of the highway transportation system in plateau mountainous areas.

[0093] 1.2.1 Degree and degree distribution

[0094] In complex network theory, the degree of a node is one of the key indicators to measure the properties of a node. It reflects the influence of a node in the network in a simple and intuitive way, so it is also called the node degree. Indicates the connection status between node i and node j in the network. When node i has an edge pointing to node i, is 1, otherwise it is 0. The number of other nodes directly connected to node i in the network is the degree of the node, which is represented by The formula is expressed as follows:

[0095]

[0096] The degree distribution is a probability distribution of node degrees, which has different forms in different types of networks. For example, the node degree distribution of regular networks usually satisfies the Delta distribution, while the degree distribution of random networks conforms to the Poisson distribution.

[0097] 1.2.2 Clustering coefficient

[0098] The clustering coefficient can effectively reflect the degree of local clustering of nodes in the network by describing the connection status between a node and its adjacent nodes. is the number of nodes connected to node i in the network The ratio of the actual number of edges between neighbor nodes to the maximum number of edges that may exist:

[0099]

[0100] Where: is the node j The actual number of edges between neighbor nodes; is the maximum number of possible edges.

[0101] 1.2.3 Average path length

[0102] Shortest path length It refers to the number of edges contained in the shortest path between node i and node j. Its reciprocal It is called the efficiency between node i and node j The average path length is usually expressed as the average of the shortest path lengths between all node pairs in the network, denoted by L:

[0103]

[0104] Where: is the shortest path length between node i and node j.

[0105] Key node identification

[0106] 2.1 Establishment of key node evaluation index system

[0107] Based on the comprehensive consideration of the evaluation index selection principles and the characteristics of the plateau mountainous road network, the evaluation index system of key nodes is mainly constructed from two aspects: network topology and traffic attributes. The results of the construction of the evaluation index system of key nodes in the plateau mountainous road network are shown in Figure 2 .

[0108] In the network topology analysis, in order to comprehensively consider the importance of nodes, three indicators, degree centrality, betweenness centrality and closeness centrality, are introduced; and in terms of traffic attributes, two indicators, the travel time weight of the node and the travel time degree of the adjacent node, are selected to more accurately reflect the role of the node in the traffic flow.

[0109] 2.1.1 Degree Centrality

[0110] The degree centrality of a node directly quantifies the connection density of the node. Nodes with higher degree values ​​are generally considered to have higher centrality because they have direct connections with multiple nodes in the network. The degree centrality expression of node i is shown as follows:

[0111]

[0112] 2.1.2 Betweenness Centrality

[0113] Betweenness centrality is an indicator that focuses on evaluating the ability of a node to connect different parts of the network from the perspective of the overall network structure. It is an indicator of the critical degree of a node as an intermediary in the transmission and circulation of network information, reflecting the frequency and degree of a node connecting different parts of the network. The expression of betweenness centrality of node i is as follows:

[0114]

[0115] Among them, s and t are two nodes in the network, and is the number of shortest paths from node s to node t; is the number of paths passing through node i in the shortest path from node s to node t.

[0116] 2.1.3 Closeness Centrality

[0117] Closeness centrality is often used to quantify the distance between a node and other nodes in the network. It reveals the relative position of the node in the network topology. The expression of closeness centrality of node i is as follows:

[0118]

[0119] 2.1.4 Travel time weight

[0120] The travel time weight is the weight information of the network edge transferred to the node, which is defined as the node weight, which can reflect the important position of the node in the network structure and the actual highway. The travel time weight of node i is The calculation formula is as follows:

[0121]

[0122] 2.1.5 Adjacent Node Travel Time

[0123] When studying the highway network in plateau mountainous areas, due to the frequent traffic flow connections between nodes, the importance of a node is not only restricted by its own characteristics, but also affected by its adjacent nodes. In order to more effectively evaluate the importance of nodes in the highway network in plateau mountainous areas, the role of nodes in their neighborhoods is fully considered, and the concept of adjacent node travel time degree is proposed in combination with the dynamic characteristics of highway network traffic flow to evaluate the importance of nodes in the highway network in plateau mountainous areas. The expression is:

[0124]

[0125] in, is the travel time weight between node i and node j.

[0126] 2.2 Calculation of weights of key node evaluation indicators

[0127] 2.2.1 Subjective weight calculation

[0128] The subjective weight is determined by the FAHP method, which introduces the concept of fuzzy numbers on the basis of the traditional AHP method. Fuzzy numbers are used to replace the determined values ​​of the judgment matrix in the traditional AHP method. The weight calculation has the following steps:

[0129] (1) Constructing a decision-making hierarchy

[0130] In the fuzzy hierarchical analysis method, the first step is to divide the hierarchical structure and divide the numerous indicators and criteria of complex decision-making problems into multiple levels, including the target level, criterion level and indicator level.

[0131] (2) Constructing a judgment matrix

[0132] The relative importance of each indicator under the same criterion layer is compared in pairs, and the indicators are scored according to the "1-9 scale method". A simplified triangular fuzzy judgment matrix is ​​constructed based on the scores, as shown in the following formula.

[0133]

[0134] Where: is a simplified triangular fuzzy judgment matrix; the matrix elements is a simplified triangular fuzzy number.

[0135] (3) Consistency test

[0136] The consistency test is used to ensure that the decision maker's pairwise comparison judgment is logically consistent. When the consistency is below a certain threshold, it indicates that the decision maker's judgment is logically consistent; otherwise, it needs to be readjusted.

[0137] (4) Solving the fuzzy comprehensive degree

[0138] After the simplified triangular fuzzy judgment matrix passes the consistency test, the triangular fuzzy numbers are used to replace the simplified fuzzy numbers accordingly to construct a complete judgment matrix containing only triangular fuzzy numbers, as shown in the following formula:

[0139]

[0140] Where: is a triangular fuzzy judgment matrix; is a triangular fuzzy number; Triangular fuzzy numbers The minimum, median, and maximum values ​​of .

[0141] According to the constructed triangular fuzzy number judgment matrix, the fuzzy comprehensive degree of the evaluation judgment given by the experts is calculated and recorded as , its value can be calculated using the following formula:

[0142]

[0143] (5) Determination of subjective weight

[0144] According to the comprehensive fuzziness , determine the normalized weight of the i-th indicator in the same level, and the weights of each indicator together form the final subjective weight vector , as shown in the following formula:

[0145]

[0146] Where: is the weight of the i-th indicator before normalization; is the weight of the ith indicator after normalization.

[0147] 2.2.2 Objective weight calculation

[0148] Although the CRITIC method comprehensively considers the interrelationships between evaluation indicators, it ignores the discreteness of the data of evaluation indicators in actual decision-making problems. Introducing the entropy weight method into the CRITIC method can effectively measure the degree of data discreteness, thereby making the determination of objective weights more scientific. The specific calculation steps for determining objective weights using the entropy weight-improved CRITIC method are as follows:

[0149] (1) Dimensionless data

[0150] Given that the dimensions of different indicators are quite different, there are logical obstacles to directly comparing the relative size of the information contained in each indicator. Therefore, the data set needs to be normalized first to ensure that the indicators are comparable. The normalization formula is as follows:

[0151]

[0152] Where: is the index value after normalization; is the value of the jth index of the ith node.

[0153] (2) Volatility analysis

[0154] Volatility refers to the difference in the value of the same indicator in different evaluation nodes, which helps to determine the sensitivity of the indicator to the node, thus affecting its position in the weight distribution. The volatility of the indicator is usually expressed by standard deviation calculation:

[0155]

[0156] Where: is the mean value of the jth indicator data after standardization; is the standard deviation of the j-th indicator.

[0157] (3) Conflict Analysis

[0158] Conflict refers to the correlation between different indicators, which is usually calculated using the correlation coefficient. Although the correlation coefficient can be positive or negative, for correlation coefficients with the same absolute value, the correlation strength between indicators should be equal. Therefore, when calculating the comparison strength between indicators, the correlation coefficient is used. Instead of the original method Better for:

[0159]

[0160] When calculating the conflict between indicators, the Spearman correlation coefficient, which has lower data requirements, is introduced to replace the Pearson correlation coefficient to calculate the correlation between indicators, so as to enhance the applicability of the CRITIC method in processing a wider range of indicator data sets.

[0161] (4) Entropy calculation

[0162] According to the information entropy theory, the lower the entropy value of an indicator, the greater the amount of information it contains, and thus it has a greater contribution and importance in the allocation of indicator weights, and vice versa. Therefore, the calculation formula for the entropy value is:

[0163]

[0164] Where: is the proportion of the i-th node data in the j-th index; is the entropy value of the jth indicator, Represents the total number of edges connected to each node i when calculating information entropy.

[0165] (5) Determination of objective weights

[0166] The objective weight calculation method of the jth indicator is shown in the following formula, and finally the objective weight vector determined by the entropy weight improved CRITIC method is composed of the objective weights of each indicator: .

[0167]

[0168] Where: is the objective weight of the jth indicator calculated by the improved CRITIC method based on entropy weight; Improve the information content of the entropy value of the jth indicator.

[0169] 2.2.3 Objective weight calculation

[0170] The core idea of ​​the game theory comprehensive weighting method is to coordinate the weight differences between subjective and objective weighting methods through the framework of game theory to obtain a compromise solution. This method aims to retain the original information of subjective and objective weights to the greatest extent possible, and to achieve a reasonable distribution of indicator weights by minimizing the deviation between subjective and objective weights.

[0171] (1) Constructing a linear combination optimization model

[0172] According to the framework of game theory, it is necessary to clearly define the multiple weights involved in the game and the decision variables and objective functions between them, so a linear combination model that weighs the relationship between the weights is constructed:

[0173] ,

[0174] Where: is the comprehensive weight; is the subjective weight; is the objective weight; and is the linear combination coefficient.

[0175] Drawing on the idea of ​​solving Nash equilibrium points in game theory, we optimize the linear combination coefficients to minimize the gap between subjective and objective weights, and construct an objective function based on this criterion:

[0176]

[0177] (2) Solving the linear combination optimization model

[0178] According to the matrix differential theory, in order to obtain the optimal solution of the linear combination optimization model, it is necessary to construct a linear equation system with first-order derivative conditions as shown below:

[0179]

[0180] (3) Calculate the final comprehensive weight

[0181] According to the optimal linear combination coefficient and , and finally obtain the comprehensive weight of the index system .

[0182]

[0183] 2.3 Key Node Identification Based on Improved LeaderRank Algorithm

[0184] The LeaderRank algorithm is an improvement on the PageRank algorithm. The algorithm replaces the PR value in the PageRank algorithm with the proposed LR value, achieving the purpose of not relying on subjective parameters and expressing the results in a more rigorous form.

[0185] An extra node is added to the original network structure, called the background node, and a bidirectional connection is established between the node and all nodes in the original network to build a new network. The original network node is given an initial LR value of 1, and the background node is given an initial LR value of 0. The LR of each node except the background node is evenly transferred to the node it points to, and a jump matrix is ​​established. The matrix is ​​calculated by repeated iterations until the LR values ​​of all nodes in the network no longer change, that is, the network is recognized to have reached a steady state. At this time, the final LR value of each node is used as the node importance. The specific calculation formula is as follows:

[0186]

[0187] Where: is the LR value of node i at time t; is the out-degree of node i; Indicates the connection status between node i and node j in the network. When node i has an edge pointing to node i, is 1 if the value is true, otherwise it is 0.

[0188]

[0189] Where: For node i The LR value that reaches the convergence state at the moment iteration; For background node g The LR value at the time is iterated and calculated until the LR value of the node reaches a convergence state.

[0190] The plateau mountain road network of the present invention is constructed as an undirected weighted network model, and in order to comprehensively consider the network structure and traffic characteristics of key nodes, the LeaderRank algorithm is improved based on the comprehensive weight of the nodes, so that it is more suitable for the plateau mountain road network. The improved parts of the improved LeaderRank algorithm mainly include: the connection between the background node and the original network node is a one-way connection, and the connection direction is from the original network node to the background node; the node's out-degree is replaced by the node's degree value; the comprehensive importance value of the plateau mountain road network node is used as the initial LR value of the original network node, and the comprehensive importance value of the node is also involved in the iterative calculation. The specific steps are as follows:

[0191] (1) Initialization parameters. According to the plateau mountain highway network model and index weights, the adjacency matrix and node comprehensive importance are obtained. . Set the background node At the initial time, it is 0, and the initial time of node i is Value is .

[0192]

[0193] (2) Iterative loop calculation. Calculate the ILR value of each node in the network at time t. When the ILR of all nodes in the network remains unchanged, it is considered that convergence has been reached and the iteration is stopped:

[0194]

[0195] Where: is the improved LR value of node i at time t; is the weight of node i.

[0196] (3) Node importance ranking. After reaching stability, calculate the importance ILR value of each node and rank the nodes according to the ILR value:

[0197]

[0198] Where: For node i The improved LR value that reaches convergence state at the moment iteration.

[0199] Example 3

[0200] Since the traffic functions of plateau mountain roads are frequently disturbed by geological disasters and extreme climate events, strengthening the management of key nodes is of great significance for ensuring the structural safety and function of the entire highway network. Based on complex network theory, a key node evaluation index system considering the topological structure and traffic function of the highway network is established. Combined with the comprehensive weight of the node index, this embodiment 3 proposes to improve the LeaderRank algorithm to identify the key nodes of the highway network. Taking the highway network in the plateau mountainous area of ​​western Sichuan as an example, an empirical analysis is carried out, the importance of 236 nodes in the network is ranked and analyzed, and the effect of the method of the present invention is analyzed through node attack simulation experiments.

[0201] 1.1 Construction of the highway network model in the mountainous area of ​​western Sichuan Plateau

[0202] Sichuan is an important transportation center in the southwest region, and its highway network extends deep into the plateau and mountainous areas in western Sichuan. The western plateau and mountainous areas of Sichuan were selected as the research area, and the highway network consisting of expressways and national highways mainly in corridors such as Yingxiu to Maerkang G317, Ya'an to Kangding G318 and Ya'an to Xichang G108 was selected as the research object.

[0203] The highway network topology of the mountainous area of ​​western Sichuan Plateau was transformed into an undirected weighted network model. After simplification, 236 nodes and 255 edges were extracted. The names and serial numbers of some nodes are shown in Table 1.

[0204] Table 1 Highway network node number table (partial)

[0205]

[0206] The map API is used to obtain the travel time data of each path in the regional road network. This method is based on the travel time prediction results of the real path and road condition information of the Internet big data platform. According to the perception of different travel times by traffic users, and considering the disadvantage that the weights cannot reflect the differences due to similar values, the travel time of each path is divided into sections as shown in Table 2 and assigned different weights.

[0207] Table 2 Travel time weight values

[0208]

[0209] Based on the node and edge information, the topological model of the mountainous highway network in the western Sichuan plateau was generated, and the topological map of the model was drawn using the complex network visualization tool Gephi software. In order to make the plateau mountainous highway network more beautiful and convenient for observation and analysis after visualization, the layout of the network model was displayed using the FruchtermanReingold (FR) algorithm instead of the geographic coordinates of the nodes.

[0210] 1.2 Analysis of highway network characteristics in the mountainous area of ​​western Sichuan Plateau

[0211] Among the 236 nodes in the mountainous highway network of the western Sichuan Plateau, the number of nodes with a degree value of 2 is the largest, with a total of 166, accounting for 70.3% of the total number of nodes. The highest degree value is 5 and the lowest degree value is 1. The average degree value of the highway network is 2.18, that is, each node is connected to 2 to 3 nodes on average.

[0212] The average clustering coefficient of the highway network in the mountainous area of ​​western Sichuan Plateau is about 0.009, which is at a relatively low level, indicating that the connection between nodes is loose and the overall network structure is relatively simple. The average path length of the highway network in the mountainous area of ​​western Sichuan Plateau is 19.433, and the network diameter is 53, which means that in actual traffic activities, starting from any node of the highway network, it takes an average of 19 to 20 nodes to reach the destination, and there are 53 nodes on the longest path.

[0213] 1.3 Identification of key nodes of highway network in the mountainous area of ​​western Sichuan Plateau

[0214] 1.3.1 Numerical calculation of key node indicators

[0215] Based on the constructed highway network model of the western Sichuan plateau mountainous area, the specific values ​​of the five evaluation indicators of 236 nodes can be calculated. Table 3 lists the indicator values ​​of some nodes.

[0216] Table 3 Node evaluation index value table (partial)

[0217]

[0218] 1.3.2 Calculation of key node indicator weights

[0219] (1) Calculation of subjective weight

[0220] The FAHP method was used to determine the subjective weights of the indicators. Ten experts in related fields were invited to follow the “1-9 scaling method” to conduct pairwise comparative evaluations on the relative importance of each indicator in the same criterion layer. The judgment matrix of degree centrality, betweenness centrality and closeness centrality under the topological structure indicators was constructed as shown in Table 4.

[0221] Table 4 Structural index triangular fuzzy judgment matrix

[0222]

[0223] The calculated RI value is 0.525, and the CR is 0.017, which is less than 0.1. The judgment matrix has been tested for consistency. In the plateau mountain highway network, considering that the topological structure and traffic attributes have an equally important influence on the importance of key nodes, the criterion layer in the analysis hierarchy has the same weight of 0.5. The subjective weight results of each indicator are shown in Table 5.

[0224] Table 5 Subjective weights of key node evaluation indicators

[0225]

[0226] (2) Objective weight calculation

[0227] The key node evaluation indicators are all positive indicators, and it is only necessary to normalize the node data of the five indicators. According to the formula, the objective weight value of the indicator can be calculated, as shown in Table 6.

[0228] Table 6 Objective weights of key node evaluation indicators

[0229]

[0230] (3) Calculation of comprehensive weight

[0231] By bringing the obtained subjective weight and objective weight values ​​into the linear combination coefficient optimization objective function constructed based on game theory, the optimal linear combination coefficient and , and finally determine the comprehensive weight value of the evaluation index system of key nodes of the highway network in the mountainous area of ​​western Sichuan Plateau.

[0232] Table 7 Comprehensive weights of key node evaluation indicators

[0233]

[0234] 1.3.3 Key node identification results

[0235] Combining the values ​​and weights of key node indicators, the comprehensive importance of key nodes can be obtained according to the formula, and the comprehensive importance is introduced into the improved LeaderRank algorithm to obtain the importance ranking of key nodes. Table 8 lists the top 20 nodes of the key node ranking of the mountainous highway network in the western Sichuan Plateau obtained by the improved LeaderRank algorithm.

[0236] Table 8 Top 20 key nodes

[0237]

[0238] As can be seen from the table, the nodes such as Kangding, Ya'an, Mianning and Dujiangyan identified by the improved LeaderRank algorithm have higher criticality in the highway network than other nodes. From the perspective of network structure, these nodes themselves are connected to multiple paths and are connected to other nodes by multiple paths, which makes these nodes highly accessible in the highway network and they are in a central position in the network structure. In addition, most of the paths passing through these nodes are highways, and as high-grade highways, highways have higher traffic capacity and efficiency, which can shorten travel time. Therefore, whether these nodes are used as starting and ending points or waypoints, they can provide travelers with shorter travel time and facilitate travelers to achieve their travel goals.

[0239] 1.4 Analysis of key node identification effect

[0240] In order to compare and analyze the differences between the key node identification method of the present invention and other identification methods, the importance ranking results of different identification methods for highway network nodes in the four western plateau mountainous areas are compared, as shown in Table 9:

[0241] Table 9 Ranking statistics of key nodes identified by different methods

[0242]

[0243] In order to further analyze the impact of different key nodes on the highway network, the network nodes will be deliberately attacked one by one according to their importance, causing the node structure to be destroyed and the function to fail. The situation where the highway network node fails due to disasters and other factors is simulated to reflect the feasibility and accuracy of the identification method. The number of deleted key nodes is taken as the horizontal axis, and the network efficiency after deleting the nodes is taken as the vertical axis to obtain Figure 3 .

[0244] From the overall trend in the figure, in the early stage of removing key nodes, the network efficiency showed a significant downward trend, indicating that these methods can identify core nodes that have a significant impact on network efficiency. However, the identification results of different methods are different, resulting in significant differences in the degree of network efficiency reduction. The key nodes identified based on the improved LeaderRank algorithm have the greatest impact on network efficiency. When 40% of the key nodes are removed, the network efficiency drops rapidly and significantly, significantly exceeding the attack strategy based on the PageRank algorithm and degree centrality. As more key nodes fail, the network efficiency continues to decline but at a slower rate. Throughout the process, the network efficiency under the attack strategy based on the improved LeaderRank algorithm remains at a low level.

[0245] Figure 4 The changes in the connectivity rate of the highway network in the mountainous area of ​​the western Sichuan Plateau under the condition of node failure are shown.

[0246] It can be observed from the figure that the remaining connectivity rate of the highway network in the mountainous area of ​​western Sichuan Plateau shows significant differences when the key nodes fail. The attack strategy based on the improved LeaderRank algorithm leads to the lowest remaining connectivity rate of the network, which is only 21.03% of the initial network. This shows that the network structure is most severely damaged under this attack strategy, resulting in a significant decrease in network connectivity. In contrast, under the attack strategies based on the PageRank algorithm and degree centrality, although the network connectivity is affected, the connectivity rate is relatively high, which is 37.44% and 33.73% of the initial network respectively. This shows that the improved LeaderRank algorithm has high effectiveness and accuracy in identifying key nodes in the highway network in the plateau and mountainous areas, and the effect is better than the other two methods.

[0247] Starting from the complex network theory, the present invention establishes an evaluation index system for key nodes of the plateau mountainous road network, calculates the comprehensive weight of the nodes on this basis, and proposes to identify key nodes with the improved LeaderRank algorithm. Finally, the road network in western Sichuan is taken as the analysis object, and the importance ranking of each node in the road network structure of the western Sichuan plateau mountainous area in different key node identification algorithms is calculated and analyzed. The research results show that the improved LeaderRank algorithm combined with the comprehensive importance of nodes achieves good results in identifying key nodes of the plateau mountainous road network, and the evaluation results produced by other general key node evaluation methods are more accurate and effective. At the same time, it provides a scientific theoretical reference for the structural layout, planning, design and operation management of the plateau mountainous road network.

[0248] Example 4

[0249] This embodiment provides a system device for implementing a method for identifying key nodes in a plateau mountainous area highway network. The system device includes the following modules:

[0250] 1. Network topology building blocks

[0251] This module is used to receive and process the basic data of the plateau mountain road network and abstract it into an undirected weighted network model. The network topology construction module can obtain road nodes, edge information and related traffic data from external databases or sensors and generate the corresponding network topology structure.

[0252] 2. Index calculation module

[0253] The index calculation module is used to calculate the importance evaluation index of key nodes, including degree centrality, betweenness centrality, closeness centrality, travel time weight and adjacent node travel time degree. This module executes relevant algorithms, calculates and stores the index value of each node, and provides basic data for the subsequent node identification process.

[0254] 3. Weight calculation module

[0255] This module is responsible for calculating the subjective weight and objective weight using the fuzzy analytic hierarchy process (FAHP) and the CRITIC method improved by entropy weight, and determining the comprehensive weight in combination with the game theory comprehensive weighting method. The module can dynamically adjust the weight calculation parameters to adapt to different application scenarios and network complexity.

[0256] 4. Key node identification module

[0257] The key node identification module improves the LeaderRank algorithm based on comprehensive weights and network topology to identify key nodes in the plateau mountain highway network. The improvements in this module include adding background nodes to the original network and establishing unidirectional connections with all other nodes, performing initialization and iterative calculation of LR values, and iteratively calculating the LR values ​​of nodes until convergence; finally outputting the ranking results of key nodes.

[0258] 5. Simulation test module

[0259] The simulation test module is used to simulate changes in network connectivity and stability when key nodes fail. This module simulates node attacks on the network, evaluates the impact of identified key nodes on overall network performance, and provides optimization suggestions for decision-making.

[0260] 6. User interface module

[0261] This module provides a graphical user interface (GUI) for users to operate and view network topology, key node indicators and identification results. The user interface module supports the visualization of results, including node importance ranking, network topology diagram and simulation test results.

[0262] Example 5

[0263] This embodiment provides a device for implementing the functional modules of the above system. The device includes:

[0264] 1. Processor

[0265] The processor is used to execute the program code of each of the above functional modules, process data and execute algorithms. Specifically, it is used to execute program instructions stored in the memory, and the program instructions include: constructing an undirected and weighted network model of the plateau mountain highway network, calculating the importance evaluation index of each node, determining the subjective weight and the objective weight, improving the LeaderRank algorithm to identify key nodes, and simulating the changes in network connectivity and stability when key nodes fail. The processor can be a general-purpose central processing unit (CPU), a graphics processing unit (GPU) or an application-specific integrated circuit (ASIC).

[0266] 2. Memory

[0267] The memory is used to store network topology data, node indicators, weight calculation parameters, and simulation test results. The memory can be a combination of volatile memory (such as RAM) and non-volatile memory (such as ROM, hard disk, or solid state drive).

[0268] 3. Communication interface

[0269] The communication interface is used to connect to external data sources and receive real-time traffic data and geographic information. The data is used for network model construction and indicator calculation, and the calculation results are transmitted to external systems or user terminals.

[0270] 4. Display

[0271] The display screen is used to display the user interface and provide an interactive interface between the user and the system. Through the display screen, the user can view the network topology, indicator calculation results, key node identification and simulation test reports.

[0272] 5. Input devices

[0273] The input device is used to receive user input commands and parameter configurations to perform the key node identification process and adjust system settings. Users can configure algorithm parameters, start calculation processes, and view results through the input device.

[0274] The device described in this embodiment integrates the above modules to realize the identification and evaluation of key nodes of the highway network in plateau mountainous areas, and can provide effective support for traffic planning and management.

[0275] Those skilled in the art will appreciate that the embodiments of the present invention may be provided as methods, systems or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware.

[0276] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0277] The above-mentioned embodiments only express several implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A method for identifying key nodes of a highway network in a plateau mountainous area, characterized in that: The following steps are involved: S1. Construct a topological structure model of the plateau mountain highway network and abstract the nodes and edges in the network; S2. Establish an importance evaluation index system for key nodes, including degree centrality, betweenness centrality, closeness centrality, travel time weight, and adjacent node travel time degree; The travel time weight The expression is , , n is the total number of nodes, is the weight of the edge between node i and node j; The adjacent node passability The expression is , is the travel time weight between node i and node j; S3, combining subjective weight and objective weight, calculate the comprehensive weight of each node in the network; S4. Identify and sort the key nodes in the network based on the comprehensive weight and the improved LeaderRank algorithm, specifically including: S41, adding a background node in the network and establishing a bidirectional connection with all other nodes; S42, initializing the value of the node according to the comprehensive weight of the node, and obtaining the node LR value through iterative calculation; S43, identifying and sorting the nodes according to the LR values ​​to obtain key nodes; The iteration formula of the LeaderRank algorithm in step S4 is: ,in, is the LR value of node i at time t; is the out-degree of node i; Indicates the connection status between node i and node j in the network. When node i has an edge pointing to node i, is 1, otherwise it is 0; ,in, For node i The LR value that reaches the convergence state at the moment iteration; For background node g The LR value at the moment; the iterative calculation is performed until the LR value of the node reaches a convergence state; S5. Perform simulation test on the identified key nodes.

2. The method for identifying key nodes of a plateau mountainous highway network according to claim 1 is characterized in that: The network in step S1 is an undirected weighted network model, denoted as ,in Represents a collection of nodes, represents the set of edges, m is the total number of edges, and the adjacency matrix Represents the weight distribution of a weighted network.

3. The method for identifying key nodes of a plateau mountainous highway network according to claim 1 is characterized in that: The expression of degree centrality in step S2 is: ,in, Represents the number of other nodes directly connected to node i in the network.

4. The method for identifying key nodes of a plateau mountainous highway network according to claim 1 is characterized in that: The expression of betweenness centrality in step S2 is: , where s and t are two nodes in the network, and ; is the number of shortest paths from node s to node t; is the number of paths passing through node i in the shortest path from node s to node t.

5. The method for identifying key nodes of a plateau mountainous highway network according to claim 2 is characterized in that: The expression of the closeness centrality in step S2 is: ,in, is the shortest path length between node i and node j.

6. The method for identifying key nodes of a plateau mountainous highway network according to claim 1, characterized in that: The subjective weight in step S3 is determined by the fuzzy hierarchical analysis method, which specifically includes: constructing a decision hierarchy, establishing a fuzzy judgment matrix and performing a consistency test, and finally calculating the subjective weight of each indicator through fuzzy comprehensive evaluation; the objective weight is calculated by the CRITIC method improved by entropy weight, including data dimensionless, volatility analysis, conflict analysis, entropy value calculation and determination of objective weight, and finally combining the subjective weight and objective weight to determine the comprehensive weight of each node in the network through the game theory comprehensive weighting method.

7. A system device for identifying key nodes of a plateau mountain highway network, characterized in that: The system device is used to implement a method for identifying key nodes in a plateau mountainous area highway network as claimed in any one of claims 1 to 6, and the system device comprises: A network topology construction module is used to receive basic data of the plateau mountain highway network and construct it into an undirected weighted network model, wherein the network model includes a node set, an edge set and a weight matrix; An index calculation module, used to calculate the importance evaluation index of each node based on the network model, wherein the index includes degree centrality, betweenness centrality, closeness centrality, travel time weight and adjacent node travel time degree; The weight calculation module is used to determine the subjective weight using the fuzzy analytic hierarchy process, and calculate the objective weight using the CRITIC method improved by entropy weight, and finally determine the comprehensive weight of each node in combination with the game theory comprehensive weighting method; A key node identification module is used to improve the LeaderRank algorithm based on the comprehensive weight to identify the key nodes in the plateau mountain road network. The improvement includes adding background nodes to the original network and establishing unidirectional connections with all other nodes, and iteratively calculating the LR value of the node until convergence; The simulation test module is used to simulate the changes in network connectivity and stability when key nodes fail, so as to verify the impact of the identified key nodes on the overall performance of the highway network.

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