Method for evaluating harbor and airline network vulnerability of complex network based on dynamic attack

Abstract

The invention provides a dynamic attack-based port and route network vulnerability assessment method for a complex network, and relates to the technical field of shipping management, and the method can construct a route network according to route data. And at least adopting each preset first type index to evaluate each port in the airline network, and determining the importance of each port. And meanwhile, evaluating the vulnerability of the airline network based on each second type index by adopting a dynamic attack mode, and determining a vulnerability evaluation result of the airline network. And determining a final evaluation result of the airline network according to the importance of each port and the vulnerability evaluation result, so as to accurately identify the key port and the influence of the key port on the airline network, and considering the dynamic change characteristics of the airline network, so that the vulnerability evaluation result is more accurate, the accuracy of the final evaluation result is improved, and the reliability of the airline network is improved. And an accurate and scientific decision basis is provided for a shipping company, so that the risk management capability is improved.

Description

Technical Field

[0001] This specification relates to the field of shipping management technology, and in particular to a method for evaluating the vulnerability of port and shipping line networks in complex networks based on dynamic attacks. Background Art

[0002] In a globalized economy, ports, as core nodes in international trade and logistics networks, are of undeniable importance. The operational efficiency and stability of ports directly impact the smoothness of the global supply chain, while the shipping routes connecting them are the critical link for cargo transportation. The vulnerability of shipping routes—that is, their susceptibility to natural disasters, technical failures, or human interference—is a pressing technical challenge in shipping management.

[0003] Currently, the importance of nodes and the stability of a route network are generally assessed based on the network's topology at a specific moment. Node importance is also assessed using metrics such as throughput or centrality. Furthermore, nodes or edges in the route network can be deleted in a pre-determined or random manner to simulate attacks on the network and assess its vulnerability.

[0004] However, neither the aforementioned assessments of node importance nor the vulnerability of shipping routes take into account the dynamic nature of shipping routes. Static analysis alone makes it difficult to assess node importance and shipping route vulnerability in dynamic scenarios. Furthermore, it ignores the potential for dynamic attacks in real-world scenarios, resulting in inaccurate assessment results. Therefore, assessing the vulnerability of complex port and shipping route networks under dynamic attacks is a crucial issue.

[0005] Based on this, this specification provides a method for evaluating the vulnerability of port and shipping line networks in complex networks based on dynamic attacks. Summary of the Invention

[0006] In order to solve the problem of low accuracy in the assessment results of the vulnerability of ports and shipping routes in complex networks, this specification provides a method for assessing the vulnerability of ports and shipping routes in complex networks based on dynamic attacks, so as to more accurately assess the importance of ports and the vulnerability of shipping routes in complex networks based on dynamic attacks.

[0007] This manual adopts the following technical solutions:

[0008] This document provides a method for assessing the vulnerability of port and shipping routes in complex networks based on dynamic attacks, including:

[0009] S1: Build route network: Build route network based on route data;

[0010] S2: Assessing the importance of ports: using at least the pre-set first type indicators, assess each port in the shipping route network to determine the importance of each port;

[0011] S3: Evaluate the vulnerability of the route network: using a dynamic attack method, based on each second type of indicator, evaluate the vulnerability of the route network and determine the vulnerability evaluation result of the route network;

[0012] S31: determining the degree of each port in the current route network based on the number of routes connected to the port, taking the port with the largest degree in the current route network as the target port, removing the target port and the routes connected to the target port from the current route network and regenerating the current route network, and calculating the index value of each second type index of the current route network;

[0013] S32: re-determining the degree corresponding to each port in the current shipping route network, and repeating step S31 until the end condition is met, and determining the vulnerability assessment result of the shipping route network based on the indicator value of each second type indicator determined during each dynamic attack;

[0014] S4: Generate final assessment results: Determine the final assessment results of the route network based on the importance of each port and the vulnerability assessment results.

[0015] Optionally, determining the vulnerability assessment result of the route network according to the indicator value of each second type indicator determined during each dynamic attack in S32 specifically includes:

[0016] When a preset static attack mode is used, determining the degree corresponding to each port in the route network;

[0017] According to the degrees, the ports are sorted in descending order to obtain a port sequence;

[0018] For each port in the port sequence, the port and the route connected to the port are removed from the route network in turn, and the index values ​​corresponding to the respective second-type indicators of the route network after the removal are determined. The next port of the port in the port sequence and the route connected to the next port are continuously removed from the route network after the removal, and the index values ​​corresponding to the respective second-type indicators are continuously determined until all the ports in the port sequence are removed. The vulnerability assessment result of the route network is determined according to the index values ​​of the respective second-type indicators determined during each static attack and the index values ​​of the respective second-type indicators determined during each dynamic attack.

[0019] Optionally, determining the vulnerability assessment result of the route network in S32 according to the index value of each second type index determined during each static attack and the index value of each second type index determined during each dynamic attack specifically includes:

[0020] When a preset random attack mode is adopted, a port is randomly selected from the ports included in the route network and used as a candidate port;

[0021] The candidate port and the route connected to the candidate port are removed from the route network, and the index values ​​corresponding to the respective second-type indicators of the route network after the removal are determined. A candidate port is reselected from the ports included in the route network after the removal, and the candidate port and the route connected to the candidate port are continuously removed from the route network after the removal, and the index values ​​corresponding to the respective second-type indicators are continuously determined until the end condition is reached. The vulnerability assessment result of the route network is determined according to the index values ​​of the respective second-type indicators determined during each static attack, the index values ​​of the respective second-type indicators determined during each random attack, and the index values ​​of the respective second-type indicators determined during each dynamic attack.

[0022] Optionally, determining the vulnerability assessment result of the route network in S32 according to the index value of each second type index determined during each static attack, the index value of each second type index determined during each random attack, and the index value of each second type index determined during each dynamic attack specifically includes:

[0023] Determining indicator values ​​corresponding to the respective second-type indicators of the route network and using them as initial values;

[0024] For each second-type indicator, a first change curve is constructed based on the indicator value corresponding to the second-type indicator during each static attack and the initial value corresponding to the second-type indicator, and a first AUC value is determined based on the first change curve; a second change curve is constructed based on the indicator value corresponding to the second-type indicator during each random attack and the initial value corresponding to the second-type indicator, and a second AUC value is determined based on the second change curve; a third change curve is constructed based on the indicator value corresponding to the second-type indicator during each dynamic attack and the initial value corresponding to the second-type indicator, and a third AUC value is determined based on the third change curve;

[0025] The entropy weight method is used to determine the indicator weights corresponding to each first AUC value, each second AUC value, and each third AUC value;

[0026] Using the weights of the indicators, weighting the first AUC values, the second AUC values, and the third AUC values ​​respectively;

[0027] Determine the sum of each weighted first AUC value, each weighted second AUC value, and each weighted third AUC value, and use it as a comprehensive vulnerability index;

[0028] A vulnerability assessment result of the route network is determined according to the comprehensive vulnerability index.

[0029] Optionally, constructing the third change curve in S32 according to the indicator value corresponding to the second type indicator during each dynamic attack and the initial value corresponding to the second type indicator specifically includes:

[0030] For each dynamic attack, determining a ratio of the index value corresponding to the second type index during the dynamic attack to the initial value corresponding to the second type index, and using this ratio as the normalized index value; and determining a ratio of the number of removed ports after the dynamic attack to the initial number of ports in the route network, and using this ratio as the node ratio;

[0031] According to each normalized index value and each node ratio, a third variation curve is constructed, showing the normalized index value varying with the node ratio.

[0032] Optionally, in the route network, each port is regarded as a node, and each first-type indicator is an indicator that statically measures the importance of each node in the route network when the node is not removed. The first-type indicators include weighted degree centrality, betweenness centrality, closeness centrality and eigenvector centrality.

[0033] Optionally, in step S3, each second-type indicator is an indicator for dynamically measuring the vulnerability of the route network after removing the ports in the route network, and each second-type indicator includes the average clustering coefficient, the maximum proportion of strongly connected components, weighted efficiency and accessibility.

[0034] Optionally, in step S32, the termination condition is: all ports in the current route network are removed or a preset number of attacks is reached.

[0035] Optionally, the S2 specifically includes:

[0036] When using the pre-set first-type indicators for evaluation, for each port in the route network, a first indicator value corresponding to the weighted degree centrality of the port is determined based on the number of routes connected to the port and the weights on the routes; a second indicator value corresponding to the betweenness centrality of the port is determined based on the number of shortest paths between any two ports other than the port; a third indicator value corresponding to the closeness centrality of the port is determined based on the length of the shortest path from the port to other ports; and a fourth indicator value corresponding to the eigenvector centrality of the port is determined based on the adjacency matrix and the maximum eigenvalue of the port.

[0037] The importance of the port is determined according to the first index value, the second index value, the third index value, and the fourth index value.

[0038] Optionally, the S2 specifically includes:

[0039] For each port in the route network, determining the index values ​​corresponding to the respective preset first-type indicators of the port;

[0040] removing the port and the routes connected to the port from the route network, and determining the indicator values ​​corresponding to the respective second-type indicators based on the route network after the removal;

[0041] The importance of the port is determined according to the index values ​​corresponding to the first type indicators and the index values ​​corresponding to the second type indicators.

[0042] Optionally, determining the importance of the port according to the index values ​​corresponding to the first-type indicators and the index values ​​corresponding to the second-type indicators in S2 specifically includes:

[0043] Determining indicator values ​​corresponding to the respective second-type indicators of the route network and using them as initial values;

[0044] For each second-type indicator, determining a change rate corresponding to the second-type indicator according to the indicator value corresponding to the second-type indicator of the port and an initial value corresponding to the second-type indicator;

[0045] Adjusting and normalizing the change rate to obtain a change value corresponding to the second type indicator;

[0046] The importance of the port is determined according to the indicator values ​​corresponding to the first type indicators and the change values ​​corresponding to the second type indicators.

[0047] Optionally, determining the importance of the port according to the indicator values ​​corresponding to the first-type indicators and the change values ​​corresponding to the second-type indicators in S2 specifically includes:

[0048] Using the first type indicators and the second type indicators as evaluation indicators;

[0049] According to the index values ​​corresponding to the evaluation indicators corresponding to the ports, the importance weights corresponding to the evaluation indicators are determined by using the entropy weight method;

[0050] Determine the first score of the port by using the weighted average method based on the importance weights and the index values ​​of the evaluation indicators of the port; determine the second score of the port by using the ideal solution method based on the importance weights and the index values ​​of the evaluation indicators of the port; determine the third score of the port by using the rank sum ratio method based on the importance weights and the index values ​​of the evaluation indicators of the port;

[0051] Determine a sum of the first score, the second score, and the third score, and use the sum as a total score;

[0052] Based on the total score, the importance of the port is determined.

[0053] At least one of the above technical solutions adopted in this specification can achieve the following beneficial effects:

[0054] This specification provides a method for assessing the vulnerability of complex network ports and shipping routes based on dynamic attacks. This method begins by constructing a shipping route network based on shipping route data. Using at least pre-defined first-type indicators, each port in the shipping route network is evaluated to determine its importance. By assessing port importance using at least these first-type indicators, key ports can be accurately identified and their impact on the shipping route network.

[0055] At the same time, a dynamic attack approach is used to assess the vulnerability of the shipping route network based on each second-type indicator, and determine the vulnerability assessment result of the shipping route network. Specifically, the degree of each port in the current shipping route network is determined based on the number of routes connected to the port. The port with the highest degree in the current shipping route network is then selected as the target port. The target port and the routes connected to it are removed from the current shipping route network, and the current shipping route network is regenerated. The corresponding index values ​​of each second-type indicator in the current shipping route network are calculated. The corresponding degree of each port in the current shipping route network is re-determined, and this process is repeated until the termination condition is met. The vulnerability assessment result of the shipping route network is then determined based on the index values ​​of each second-type indicator determined during each dynamic attack. By dynamically determining the target port to be removed during each dynamic attack and calculating the index values ​​of each second-type indicator in the regenerated shipping route network to determine the vulnerability assessment result, the dynamic nature of the shipping route network is taken into account, resulting in a more accurate vulnerability assessment result. The final assessment results of the route network are then determined based on the importance and vulnerability assessment results of each port, which improves the accuracy of the final assessment results of the route network, provides shipping companies with more accurate and scientific decision-making basis, and thus enhances risk management capabilities.

[0056] When evaluating the importance of ports, in addition to using the first type of indicators to statically measure the importance of each node (i.e., port) in the route network, the present invention can also simulate port deletion and use the second type of indicators to evaluate the impact of deleting the port on the entire route network. That is, after removing the port from the route network, the second type of indicators are used to dynamically measure the performance of the route network. By adopting a multi-indicator fusion evaluation method to evaluate the port, the accuracy of the determined importance is higher. At the same time, when evaluating vulnerability, the present invention can also use a variety of attack methods to comprehensively and comprehensively evaluate the vulnerability of the route network, making the determined vulnerability evaluation results more accurate, thereby improving the accuracy of the final evaluation results of the route network. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The drawings described herein are used to provide a further understanding of this specification and constitute a part of this specification. The exemplary embodiments and descriptions of this specification are used to explain this specification and do not constitute an improper limitation of this specification. In the drawings:

[0058] Figure 1 This is a flowchart of a method for evaluating the vulnerability of port and shipping routes in complex networks based on dynamic attacks provided in this specification;

[0059] Figure 2 This is a schematic diagram of a process for determining the vulnerability assessment results of an air route network based on dynamic attacks provided in this specification. DETAILED DESCRIPTION

[0060] To make the objectives, technical solutions, and advantages of this specification more clear, the technical solutions of this specification will be clearly and completely described below in conjunction with the specific embodiments of this specification and the corresponding drawings. Obviously, the embodiments described are only part of the embodiments of this specification, not all of the embodiments. Based on the embodiments in this specification, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of this specification.

[0061] This specification provides a method for evaluating the vulnerability of port and shipping routes in complex networks based on dynamic attacks. The following describes in detail the technical solutions provided by the embodiments of this specification in conjunction with the accompanying drawings.

[0062] Figure 1 This is a flowchart of a method for evaluating the vulnerability of a complex network of ports and shipping routes based on dynamic attacks provided in this specification, which specifically includes the following steps:

[0063] S1: Build a route network: Build a route network based on route data.

[0064] In this specification, the device used for assessment can first construct a route network, that is, build a route network based on route data. This device can be a server or an electronic device such as a desktop or laptop computer. For ease of description, the following description uses the server as the execution entity to illustrate the method for assessing the vulnerability of complex port and route networks based on dynamic attacks, as provided in this specification.

[0065] The above-mentioned route data can be extracted from the Automatic Identification System (AIS) data. The AIS data refers to the dynamic navigation information sent in real time by the AIS equipment during ship operation, which is mainly used for information exchange between ships and information transmission between ships and shore-based. The AIS data may include data such as MMSI (Maritime Mobile Service Identity), ship name, ship type, latitude and longitude, speed, heading, draft, etc. The above-mentioned method of extracting route data from AIS data can be any existing extraction method, and this specification does not make specific restrictions. The route data may include at least MMSI, IMO number, target port and other data. When constructing the route network based on the route data, the data included in the route data can be matched with the data in the ship registration database through MMSI (Maritime Mobile Service Identity Code) and IMO (International Maritime Organization) number to determine a data set including several target data. Then, based on the data set, the route network is constructed. The ship registration database includes at least data such as MMSI, IMO number, starting port, departure time, arrival time, deadweight tonnage, and shipping company. The server can match the MMSI and IMO number in the route data with the MMSI and IMO number in the ship registration database, find several pieces of data from the ship registration database that match the MMSI and IMO number in the route data, and generate a data set based on the found pieces of data and the route data. The target data includes data in several fields, which can be represented as follows:

[0066] <IMO,source,target,start_time,end_time,DWT,cmpy>

[0067] Among them, IMO is the unique identification number of the ship, source is the starting port, target is the destination port, start_time and end_time are the departure time and arrival time respectively, DWT is the deadweight tonnage, and cmpy is the shipping company.

[0068] When constructing a route network based on the data set, a route network with ports as nodes and routes as edges can be constructed based on each data in the data set (i.e., the data corresponding to each route), and the weights on the edges (i.e., routes) of the route network can be the deadweight tonnage of the ship (i.e., DWT), or the cargo volume, or the voyage frequency. This specification does not limit the type and quantity of the weights on the edges, that is, the weights on the edges can include multiple types of weights, i.e., the weights can include multiple types of weights such as deadweight tonnage of the ship, cargo volume, and voyage frequency. In addition, in order to fully reflect the transportation characteristics of different types of goods, different construction methods can be used to construct route networks for transporting different types of goods. The route network for containers can be constructed using the P-space or L-space framework, while other route networks can be constructed using the L-space framework.

[0069] S2: Evaluate the importance of ports: use at least the preset first type indicators to evaluate each port in the route network to determine the importance of each port.

[0070] S3: Evaluate the vulnerability of the route network: adopt a dynamic attack method, based on each second type of indicator, evaluate the vulnerability of the route network, and determine the vulnerability evaluation result of the route network.

[0071] In this specification, the server may first assess port importance, i.e., using at least pre-set first-type indicators to evaluate each port in the route network and determine the importance of each port. Simultaneously, the server may assess the vulnerability of the route network, i.e., using at least pre-set dynamic attack methods to assess the vulnerability of the route network and determine the vulnerability assessment results of the route network.

[0072] Among them, the execution order of the above S2 and S3 is not particular, and they can also be executed simultaneously. The above-mentioned first-type indicators are selected in advance from the first indicator library, and can be selected randomly or according to specific needs. This specification does not make specific restrictions. The above-mentioned first indicator library is pre-constructed, and the first indicator library at least includes weighted degree centrality, betweenness centrality, closeness centrality and eigenvector centrality. Of course, it can also include throughput, degree centrality, etc. The above-mentioned first-type indicators may include weighted degree centrality, betweenness centrality, closeness centrality and eigenvector centrality. Of course, it can also include other indicators. This specification does not make specific restrictions, but the first-type indicators include at least two indicators in the first indicator library. In the route network, each port is regarded as a node, and each first-type indicator is an indicator that statically measures the importance of each node in the route network when the node is not removed. For the sake of convenience, the following explanation is based on the example that each first-type indicator includes weighted degree centrality, betweenness centrality, closeness centrality and eigenvector centrality. When using the pre-set first-type indicators for evaluation, the server can determine the index values ​​corresponding to the first-type indicators for each port in the shipping network, and then determine the importance of the port based on the index values ​​corresponding to the first-type indicators.

[0073] Specifically, when using the preset first type indicators for evaluation, for each port in the route network, the server may determine the first indicator value corresponding to the weighted degree centrality of the port based on the number of routes connected to the port and the weight of the routes. Specifically, the following formula may be used for calculation:

[0074] D w (P i )=∑ j w ij

[0075] Among them, D w (P i ) indicates port P i The first index value of port P i With Port P i All ports connected P j The sum of the weights on the routes between ij Indicates port P i and Port P j The weight of the routes between them (i.e. cargo volume or voyage frequency).

[0076] At the same time, the server can also determine the second index value corresponding to the betweenness centrality of the port based on the number of shortest paths between any two ports in the ports other than the port. The specific calculation can be performed using the following formula:

[0077]

[0078] Among them, B(P i ) indicates port P i The second index value, σ st Indicates the distance from node s to node t (i.e. port P s and Port P t ), σ st (P i ) represents σ st Through Port P i The number of shortest paths.

[0079] In addition, the server can also determine the third index value corresponding to the port's proximity centrality based on the shortest path length from the port to other ports. Specifically, the third index value can be calculated using the following formula:

[0080]

[0081] Among them, C(P i ) is port P i The third index value, d(P i ,P j ) is port P i To Port P j The shortest path length.

[0082] In addition, the server can also determine the fourth index value corresponding to the eigenvector centrality of the port based on the adjacency matrix and the maximum eigenvalue of the port, which can be calculated using the following formula:

[0083]

[0084] Among them, a ij For port P i The elements in the adjacency matrix represent the port P i and Port P j The weight of the route between, that is, if port P i and Port P j If there is a direct route between the two ports, the element is the weight of the route, which can be deadweight tonnage or voyage frequency. i and Port P j If there is no direct route between them, the element is 0. λ is the maximum eigenvalue of the adjacency matrix, that is, the eigenvalue with the largest absolute value among the eigenvalues ​​of the adjacency matrix (i.e., the spectral radius). E(P i ) indicates port P i The fourth indicator value.

[0085] Afterwards, the importance of the port is determined based on the first index value, the second index value, the third index value, and the fourth index value. Specifically, the server can directly use the sum of the first index value, the second index value, the third index value, and the fourth index value as the importance of the port. Of course, the server can also use the entropy weight method to determine the weighted weights corresponding to each first index based on each first index value (i.e., the first index value corresponding to each port), each second index value (i.e., the second index value corresponding to each port), each third index value (i.e., the third index value corresponding to each port), and each fourth index value (i.e., the fourth index value corresponding to each port), and then weight the first index value, the second index value, the third index value, and the fourth index value corresponding to the port according to each weighted weight, and then use the sum of the weighted first index value, the weighted second index value, the weighted third index value, and the weighted fourth index value as the importance of the port.

[0086] In the above-mentioned dynamic attack mode, based on each second type indicator, the vulnerability of the route network is evaluated. When determining the vulnerability evaluation result of the route network, the server may perform the following steps, specifically including the following steps:

[0087] S31: Determine the degree of each port in the current route network based on the number of routes connected to the port, take the port with the largest degree in the current route network as the target port, remove the target port and the routes connected to the target port in the current route network and regenerate the current route network, and calculate the indicator value of each second type indicator of the current route network.

[0088] S32: Re-determine the degree corresponding to each port in the current shipping route network, and repeat step S31 until the end condition is met, and determine the vulnerability assessment result of the shipping route network based on the indicator value of each second type indicator determined during each dynamic attack.

[0089] Specifically, the above steps S31 to S32 can be specifically as follows: Figure 2 As shown, Figure 2 The process shown is the specific implementation process of the above steps S31 to S32. Figure 2 This is a schematic diagram of a process for determining the vulnerability assessment results of an air route network based on dynamic attacks provided in this specification, which specifically includes the following steps:

[0090] S311: When a preset dynamic attack mode is adopted, the degree corresponding to each port in the current route network is determined based on the number of routes connected to the port.

[0091] S312: The port corresponding to the maximum degree in the current route network is used as the target port, the target port and the routes connected to the target port are removed from the current route network, and the current route network is regenerated.

[0092] S313: Calculate the index values ​​corresponding to the second type indicators of the current route network.

[0093] S321: Determine whether the end condition is met. If the end condition has not been met, redetermine the degree corresponding to each port in the current route network, and continue to remove the target port and the route connected to the target port in the current route network according to each degree, and regenerate the current route network, and redetermine the indicator value corresponding to each second type indicator of the current route network, that is, re-execute steps S311 to S313 until the end condition is met, and then execute step S322.

[0094] S322: Determine a vulnerability assessment result of the route network according to the indicator values ​​of each second type indicator determined during each dynamic attack.

[0095] The above steps S311 to S313 are the specific implementation process of the above step S31, and the above steps S321 to S322 are the specific implementation process of the above step S32. The degree of each port can be generated by the number of routes connected to the port, that is, the degree can be the number of routes connected to the port. The above second type of indicators are pre-selected from the second indicator library, and can be selected randomly or according to specific needs. This specification does not make specific restrictions. The above second indicator library is pre-constructed, and the second indicator library at least includes the average clustering coefficient, the maximum proportion of strongly connected components, the weighted efficiency and accessibility. Of course, it can also include other indicators. The above second type indicators are indicators that dynamically measure the performance of the route network after removing the ports in the route network. The above second type indicators can include the average clustering coefficient, the maximum proportion of strongly connected components, the weighted efficiency and accessibility. Of course, it can also include other indicators. This specification does not make specific restrictions, but the second type indicators at least include two indicators in the second indicator library. For ease of explanation, the following uses the second type indicators including the average clustering coefficient, the maximum strongly connected component ratio, the weighted efficiency, and the reachability as examples for explanation.

[0096] In the above step S31 of calculating the index values ​​of each second type index of the current route network, the server may determine the index value corresponding to the average clustering coefficient based on the number of ports in the current route network and the weights of the routes between the ports. Specifically, the following formula may be used for calculation:

[0097]

[0098] in, <c>represents the index value corresponding to the average clustering coefficient, N represents the number of ports in the current route network, is node i (i.e. port P i ), which can be calculated in the following way:

[0099]

[0100] Among them, w ij k represents the weight (i.e., ship tonnage DWT) of the edge (i.e., route) from node i to node j. i Represents the degree of node i, that is, the number of neighboring nodes directly connected to node i. j,h represents the sum of all neighbor pairs (j, h) of node i, that is, the sum of node pairs that may be formed between all direct neighbor nodes of node i, that is, the sum of node pairs between any two different neighbor nodes j and h of node i, where both nodes j and h are neighbor nodes directly connected to node i, w ih Represents the weight of the edge from node i to node h (i.e., ship tonnage DWT).

[0101] At the same time, the server can determine the maximum strongly connected component corresponding to the current route network, determine the ratio of the number of nodes (i.e., ports) in the maximum strongly connected component to the number of ports in the current route network, and use this as the indicator value corresponding to the maximum strongly connected component ratio. Specifically, the following formula can be used for calculation:

[0102]

[0103] Among them, the largest strongly connected component (LSCC) is the largest subgraph of the current route network, and there is a bidirectional path between any two nodes in this subgraph. LSCC It represents the ratio of the number of nodes in LSCC (i.e., subgraph) to the total number of nodes (i.e., the index value corresponding to the ratio of the largest strongly connected component), which is used to measure the overall connectivity of the network. LSCC The closer it is to 1, the more likely it is that most nodes in the network can reach each other through paths, and the connectivity is strong. s Indicates the number of nodes in the largest strongly connected component.

[0104] Furthermore, the server can use the inverse of the weight of the route in the current route network as the capacity weight of the route. It should be noted that this weight is DWT, and the capacity weight is the inverse of DWT. Based on the capacity weight of each route, the shortest path length based on the capacity weight between each port in the current route network is determined. Based on the determined shortest path length based on each capacity weight, the index value corresponding to the weighted efficiency is determined. Specifically, the following formula can be used for calculation:

[0105]

[0106] Among them, E c The index value corresponding to weighted efficiency is used to measure the efficiency of the network in utilizing high-capacity paths (i.e., ship tonnage DWT). By setting the inverse of the weight on the route as the capacity weight, high-capacity paths have a smaller capacity weight when calculating the shortest path, and are therefore preferred. c A larger value indicates that the network can more efficiently utilize high-capacity paths for connections and optimize transportation efficiency. Represents the shortest path length from node i to node j based on capacity weight. The shortest path length is the shortest path length among all possible paths from node i to node j. The path length is the sum of the capacity weights corresponding to all edges in the path. The capacity weight is DWT ij Indicates the tonnage of ships on route i→j.

[0107] In addition, the server can determine the first port pair in the current route network that has a path, and determine all second port pairs in the current route network. Based on the first port pair and the second port pair, the server can determine the index value corresponding to the reachability. Specifically, the following formula can be used for calculation:

[0108]

[0109] Among them, A represents the index value corresponding to reachability, which is used to measure the proportion of node pairs in the network that can still reach each other, reflecting the connectivity of the network after some nodes fail. In a directed route network, reachability focuses on whether there is a directed path from the starting point to the end point. The closer A is to 1, the stronger the network connectivity is. pairs It indicates the number of node pairs (i, j) in the network where there is a path from node i to node j, that is, the number of first port pairs. pairs Indicates all possible node pairs in the current route network, i.e., second port pairs. In a directed network, the number of second port pairs is N(N-1), and in an undirected network, the number of second port pairs is

[0110] The above-mentioned termination condition can be reaching a preset number of attacks or all ports in the current route network are removed, which is not specifically limited in this specification. For ease of explanation, the following termination conditions are all described using the removal of all ports in the current route network as an example.

[0111] In step S32, when determining the vulnerability assessment result of the route network based on the index values ​​of each second-type indicator determined during each dynamic attack, the index values ​​corresponding to each second-type indicator of the route network are determined and used as initial values. For each second-type indicator, a third variation curve is constructed based on the index value corresponding to the second-type indicator during each dynamic attack and the initial value corresponding to the second-type indicator. Based on the third variation curve, a third Area Under Curve (AUC) value is determined. Based on each third AUC value, a weight corresponding to each third AUC value is determined. The third AUC values ​​are then weighted based on the determined weights. The sum of the weighted third AUC values ​​is determined and used as a comprehensive vulnerability index. Based on the comprehensive vulnerability index, the vulnerability assessment result of the route network is determined. The weight corresponding to each third AUC value can be the ratio of the third AUC value to the sum of the third AUC values. The vulnerability assessment result can be directly converted into a comprehensive vulnerability index. AUC stands for Area Under Curve, and the third AUC value is the area under the third variation curve.

[0112] When constructing the third change curve in S32 based on the indicator value corresponding to the second type indicator during each dynamic attack and the initial value corresponding to the second type indicator, the server may determine, for each dynamic attack, a ratio of the indicator value corresponding to the second type indicator during the dynamic attack to the initial value corresponding to the second type indicator, and use the ratio as the normalized indicator value. Specifically, the ratio may be calculated using the following formula:

[0113]

[0114] in, Represents the normalized index value, M k represents the value of the second type indicator during the dynamic attack, M0 represents the initial value of the second type indicator, and k represents the number of ports removed after the dynamic attack.

[0115] At the same time, the server can determine the ratio of the number of removed ports after the dynamic attack to the initial number of ports in the route network and use it as the node ratio, which can be expressed as follows:

[0116]

[0117] Where f represents the node ratio and K represents the number of ports in the route network when no nodes are removed.

[0118] Afterwards, a third variation curve of the normalized index value as the node ratio changes is constructed according to each normalized index value and each node ratio.

[0119] When calculating the third AUC value, the following formula can be used for calculation:

[0120]

[0121] Among them, AUC M It represents the third AUC value. The smaller the AUC value, the faster the route network performance degrades and the more fragile the route network is.

[0122] S4: Generate final assessment results: Determine the final assessment results of the route network based on the importance of each port and the vulnerability assessment results.

[0123] In this specification, the server may determine a final assessment result for the route network based on the importance and vulnerability assessment results of each port. This final assessment result may include the importance and vulnerability assessment results of each port. After obtaining the final assessment result, the server may display it to an operator, allowing the operator to manage the ports and routes in the route network based on the final assessment result.

[0124] In some embodiments of the present specification, in addition to using a dynamic attack approach to assess the vulnerability of a route network, the server may also use a static attack approach. Specifically, in step S32, when determining the vulnerability assessment result of the route network based on the values ​​of each second-type indicator determined during each dynamic attack, the server may determine the degree corresponding to each port in the route network when using a preset static attack approach. Based on these degrees, the ports are sorted from largest to smallest to obtain a port sequence. For each port in the port sequence, the port and the routes connected to it are sequentially removed from the route network. The values ​​corresponding to each second-type indicator of the route network after removal are determined. The port next to the port in the sequence and the routes connected to it are then removed from the route network. The values ​​corresponding to each second-type indicator are then determined again. This continues until all ports in the port sequence have been removed. The vulnerability assessment result of the route network is then determined based on the values ​​of each second-type indicator determined during each static attack and the values ​​of each second-type indicator determined during each dynamic attack.

[0125] In each static attack, ports are removed in the order of their sequence. The process of determining the index values ​​corresponding to the respective second-type indicators of the route network after removal is consistent with the process of calculating the index values ​​of the respective second-type indicators of the current route network in S32, and will not be repeated here.

[0126] In S32, when determining the vulnerability assessment result of the route network based on the indicator values ​​of each second-type indicator determined during each static attack and the indicator values ​​of each second-type indicator determined during each dynamic attack, the server may determine the indicator values ​​corresponding to each second-type indicator of the route network and use them as initial values. For each second-type indicator, a third variation curve is constructed based on the indicator value corresponding to the second-type indicator during each dynamic attack and the initial value corresponding to the second-type indicator, and a third Area Under Condition (AUC) value is determined based on the third variation curve. Simultaneously, a first variation curve is constructed based on the indicator value corresponding to the second-type indicator during each static attack and the initial value corresponding to the second-type indicator, and a first AUC value is determined based on the first variation curve. Subsequently, an entropy weighting method is used to determine the indicator weights corresponding to each third AUC value and each first AUC value. Each third AUC value and each first AUC value are then weighted using the indicator weights. The sum of each weighted third AUC value and each weighted first AUC value is determined and used as the comprehensive vulnerability index. The comprehensive vulnerability index is used to determine the vulnerability assessment result of the route network.

[0127] The process of constructing the first change curve based on the indicator value corresponding to the second type indicator during each static attack and the initial value corresponding to the second type indicator is similar to the process of constructing the third change curve based on the indicator value corresponding to the second type indicator during each dynamic attack and the initial value corresponding to the second type indicator, and will not be repeated here. The first AUC value is the area under the first change curve. Each of the first AUC values ​​and each of the third AUC values ​​has a corresponding indicator weight. When weighting each of the first AUC values ​​and each of the third AUC values, the indicator weight corresponding to each AUC value is used for weighting.

[0128] In some embodiments of this specification, in addition to using dynamic and static attack methods to assess the vulnerability of the route network, the server may also use a random attack method to assess the vulnerability of the route network. Specifically, in step S32, when determining the vulnerability assessment result of the route network based on the indicator values ​​of each second-type indicator determined during each static attack and the indicator values ​​of each second-type indicator determined during each dynamic attack, the server may randomly select a port from the ports included in the route network as a candidate port when using a pre-set random attack method. The candidate port and the routes connected to the candidate port are removed from the route network, and the index values ​​corresponding to the respective second-type indicators of the route network after the removal are determined. A new candidate port is continuously selected from the ports included in the route network after the removal, and the candidate port and the routes connected to the candidate port are continuously removed from the route network after the removal, and the index values ​​corresponding to the respective second-type indicators are continuously determined until the termination condition is reached. The vulnerability assessment result of the route network is determined based on the index values ​​of the respective second-type indicators determined during each static attack, the index values ​​of the respective second-type indicators determined during each random attack, and the index values ​​of the respective second-type indicators determined during each dynamic attack.

[0129] In step S32, when determining the vulnerability assessment result of the route network based on the index values ​​of each second-type indicator determined during each static attack, the index values ​​of each second-type indicator determined during each random attack, and the index values ​​of each second-type indicator determined during each dynamic attack, the server may determine the index values ​​corresponding to each second-type indicator of the route network and use them as initial values. For each second-type indicator, a first variation curve is constructed based on the index value corresponding to the second-type indicator during each static attack and the initial value corresponding to the second-type indicator, and a first Area Under Corresponding Unit (AUC) value is determined based on the first variation curve. Simultaneously, a second variation curve is constructed based on the index value corresponding to the second-type indicator during each random attack and the initial value corresponding to the second-type indicator, and a second AUC value is determined based on the second variation curve. Furthermore, a third variation curve is constructed based on the index value corresponding to the second-type indicator during each dynamic attack and the initial value corresponding to the second-type indicator, and a third AUC value is determined based on the third variation curve. Subsequently, an entropy weighting method is used to determine the indicator weights corresponding to each first AUC value, each second AUC value, and each third AUC value. Using the weights of each indicator, each first AUC value, each second AUC value, and each third AUC value are weighted. The sum of each weighted first AUC value, each weighted second AUC value, and each weighted third AUC value is determined and used as a comprehensive vulnerability index. Based on this comprehensive vulnerability index, a vulnerability assessment result for the route network is determined.

[0130] Among them, the above-mentioned first ACU values ​​are the ACU values ​​of the first change curves corresponding to the second type indicators under static attacks, the above-mentioned second ACU values ​​are the ACU values ​​of the second change curves corresponding to the second type indicators under random attacks, and the above-mentioned third ACU values ​​are the ACU values ​​of the third change curves corresponding to the second type indicators under dynamic attacks.

[0131] Each first AUC value under the above static attack can be AUC <c> ，s < / c> , AUC A，s , the second AUC value under the above random attack can be AUC <c> ，r < / c> , AUC A，r , the third AUC value under the above dynamic attack can be AUC <c> ，d < / c> , AUC A，d The above-mentioned calculation of the comprehensive vulnerability index can be performed using the following formula:

[0132]

[0133] Among them, I v represents the comprehensive vulnerability index, w j Indicates the indicator weight corresponding to the j-th AUC value, AUC j represents the jth AUC value, I v The smaller it is, the higher the overall vulnerability of the route network is, because the smaller the AUC value corresponding to a certain indicator is, the weaker the route network's ability to resist attacks in this indicator is.

[0134] The process of constructing the second variation curve based on the indicator value corresponding to the second type indicator during each random attack and the initial value corresponding to the second type indicator is similar to the process of constructing the third variation curve based on the indicator value corresponding to the second type indicator during each dynamic attack and the initial value corresponding to the second type indicator, and will not be repeated here. Each first AUC value, each second AUC value, and each third AUC value has a corresponding indicator weight. When weighting each first AUC value, each second AUC value, and each third AUC value, the indicator weight corresponding to each AUC value is used for weighting.

[0135] In some embodiments of the present specification, when evaluating the vulnerability of the route network, at least a dynamic attack method is used for evaluation. Of course, a static attack method or a random attack method can also be used for evaluation. That is, the vulnerability of the route network can be evaluated by only a dynamic attack method, or by a combination of a dynamic attack method and a static attack method. The vulnerability of the route network can also be evaluated by a combination of a dynamic attack method and a random attack method. The vulnerability of the route network can also be evaluated by a combination of a dynamic attack method, a static attack method and a random attack method. As for which single or combined attack method is used to evaluate the vulnerability of the route network, this specification does not make a specific limitation. The above only uses the use of a combination of a dynamic attack method, a static attack method and a random attack method to evaluate the vulnerability of the route network as an example.

[0136] In some embodiments of this specification, when determining the importance of each port, in addition to using the first-type indicators for evaluation, the server may also simulate node deletion and, after deletion, evaluate the entire route network using the second-type indicators. Specifically, in step S2, the server may determine, for each port in the route network, the corresponding index values ​​for each pre-set first-type indicator. The port and the routes connected to it are removed from the route network, and based on the removed route network, the corresponding index values ​​for each second-type indicator are determined. The importance of the port is determined based on the index values ​​corresponding to the first-type indicators and the index values ​​corresponding to the second-type indicators.

[0137] In S2, when determining the importance of the port based on the index values ​​corresponding to each first-type indicator and the index values ​​corresponding to each second-type indicator, the server may determine the index values ​​corresponding to each second-type indicator of the route network and use them as initial values. For each second-type indicator, the server may determine the rate of change corresponding to the second-type indicator based on the index value corresponding to the second-type indicator for the port and the initial value corresponding to the second-type indicator. The rate of change is adjusted and normalized to obtain the change value corresponding to the second-type indicator. The importance of the port is determined based on the index values ​​corresponding to each first-type indicator and the change values ​​corresponding to each second-type indicator.

[0138] The above-mentioned change value can be calculated using the following formula:

[0139]

[0140] Wherein, M represents the initial value corresponding to the second type indicator in the original route network G (i.e., the route network when the port is not removed), M' represents the indicator value corresponding to the second type indicator in the modified network G' (i.e., the route network after removing the port and the routes connected to the port), and ΔM represents the rate of change corresponding to the second type indicator.

[0141] When adjusting and normalizing the change rate, the server first multiplies the change rate by -1 to adjust the change rate. Specifically, the following formula can be used for calculation:

[0142] ΔM adj =-ΔM

[0143] Among them, ΔM adj represents the adjusted rate of change, the ΔM adj The larger the value is, the more serious the performance degradation of the route network will be after the port is removed, and the more important the port is.

[0144] Afterwards, the adjusted change rate is normalized to obtain the change value corresponding to the second type indicator, which can be calculated specifically using the following formula:

[0145]

[0146] Among them, min(ΔM adj ) represents the smallest adjusted change rate among the adjusted change rates corresponding to the second type of indicators of all ports, max(ΔM adj ) represents the largest adjusted change rate among the adjusted change rates corresponding to the second type of indicators of all ports, ΔM norm Indicates the change value corresponding to the second type indicator.

[0147] In S2 above, when determining the importance of the port based on the indicator values ​​corresponding to each first-type indicator and the change values ​​corresponding to each second-type indicator, the server may use each first-type indicator and each second-type indicator as evaluation indicators. Based on the indicator values ​​corresponding to each evaluation indicator for each port, the entropy weight method is used to determine the importance weights corresponding to each evaluation indicator. Based on the importance weights and the indicator values ​​of each evaluation indicator for the port, the distance weighted averaging (DWA) method is used to determine the first score for the port. Based on the importance weights and the indicator values ​​of each evaluation indicator for the port, the technique for order preference by similarity to ideal solution (TOPSIS) method is used to determine the second score for the port. Based on the importance weights and the indicator values ​​of each evaluation indicator for the port, the rank sum ratio (RSR) method is used to determine the third score for the port. The server may then determine the sum of the first, second, and third scores as the total score. The importance of the port is determined based on the total score.

[0148] The first score can be expressed as S DWA，i , the second score can be expressed as S TOPSIS，i , the third score can be expressed as S RSR，i , the following formula can be used to calculate the total score:

[0149] S Total，i =S DWA，i +S TOPSIS，i +S RSR，i

[0150] Among them, S Total，i Indicates the total score. The higher the total score, the more critical the port is.

[0151] When determining the importance of the port based on the total score, the server can directly use the total score as the importance of the port. Of course, the server can also sort the ports in descending order of total score to obtain an importance sequence. The importance of the port is determined based on the importance sequence.

[0152] In some embodiments of the present specification, each time a port and routes connected to the port are removed, the above-mentioned regenerated route network, the current route network, or the route network after removal needs to be regenerated based on the structure of the remaining route network, that is, the server can redetermine the connection paths between the remaining nodes based on the structure of the remaining route network after removing the port and routes connected to the port, and generate the current route network or the route network after removal based on the connection paths between the remaining nodes and the remaining nodes.

[0153] When re-determining the connection paths between the remaining nodes based on the structure of the remaining route network after removing the ports and the routes connected to them, the server may first determine the paths in the route network before removal that pass through the removed ports and the routes connected to them, and define these determined paths as first paths. Then, based on the structure of the remaining route network after removing the ports and the routes connected to them, the server may determine alternative paths corresponding to the first paths in the remaining route network, and determine the connection paths between the remaining nodes based on the first and alternative paths. The first paths are the paths that originally served the transportation tasks that relied on the vessel traffic associated with the removed nodes or edges. The determination of alternative paths may be based on the principle of "shortest path reallocation," with the alternative paths being the ones with the shortest distance or lowest cost. These alternative paths are the paths that are used to complete the transportation tasks that originally relied on the vessel traffic associated with the removed nodes and edges (i.e., routes). Furthermore, when multiple alternative paths exist, a probabilistic allocation method based on path costs (e.g., a softmax function) is used to proportionally distribute the vessel traffic among the multiple alternative paths. Specifically, alternative paths corresponding to the first paths with different vessel traffic are determined proportionally from the multiple alternative paths.

[0154] When determining the connection paths between the remaining nodes based on the first path and the alternative path, the server may update the first path in the remaining route network to the alternative path to obtain the connection paths between the remaining nodes.

[0155] In the embodiment that takes into account the transport capacity of the route, only alternative routes with sufficient capacity will take over the transferred ship traffic, otherwise some ship traffic may be abandoned or forced to rely on other ports for transshipment between ports. Removing a port is equivalent to deleting a node and its associated edges in the route network, and removing a route is deleting an edge. This will lead to a decrease in the connectivity and average path efficiency of the route network, especially when key nodes or key edges are removed, which may cause structural breaks in the entire route network. Some subgraphs may be separated from the main graph to form isolated components, causing originally reachable ports to become unreachable. After the ship traffic is redistributed, some secondary routes may become important because they have undertaken alternative transportation tasks, and their weights will increase significantly, thereby triggering dynamic changes in the weight of the route network.

[0156] The foregoing is merely an example of the present invention and is not intended to limit the present invention. Various modifications and variations are possible for those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be included within the scope of the claims of the present invention.< / c>

Claims

1. A method for evaluating the vulnerability of port and shipping line networks in complex networks based on dynamic attacks, characterized in that: include: S1: Build route network: Build route network based on route data; S2: Assessing the importance of ports: using at least the pre-set first type indicators, assess each port in the shipping route network to determine the importance of each port; S3: Evaluate the vulnerability of the route network: using a dynamic attack method, based on each second type of indicator, evaluate the vulnerability of the route network and determine the vulnerability evaluation result of the route network; S31: determining the degree of each port in the current route network based on the number of routes connected to the port, taking the port with the largest degree in the current route network as the target port, removing the target port and the routes connected to the target port from the current route network and regenerating the current route network, and calculating the index value of each second type index of the current route network; S32: re-determining the degree corresponding to each port in the current shipping route network, and repeating step S31 until the end condition is met, and determining the vulnerability assessment result of the shipping route network based on the indicator value of each second type indicator determined during each dynamic attack; S4: Generate final assessment results: Determine the final assessment results of the route network based on the importance of each port and the vulnerability assessment results.

2. The method for evaluating the vulnerability of a port and shipping line network of a complex network based on dynamic attack according to claim 1, characterized in that: Determining the vulnerability assessment result of the route network according to the indicator values ​​of each second type indicator determined during each dynamic attack in S32 specifically includes: When a preset static attack mode is used, determining the degree corresponding to each port in the route network; According to the degrees, the ports are sorted in descending order to obtain a port sequence; For each port in the port sequence, the port and the route connected to the port are removed from the route network in turn, and the index values ​​corresponding to the respective second-type indicators of the route network after the removal are determined. The next port of the port in the port sequence and the route connected to the next port are continuously removed from the route network after the removal, and the index values ​​corresponding to the respective second-type indicators are continuously determined until all the ports in the port sequence are removed. The vulnerability assessment result of the route network is determined according to the index values ​​of the respective second-type indicators determined during each static attack and the index values ​​of the respective second-type indicators determined during each dynamic attack.

3. The method for evaluating the vulnerability of a port and shipping line network of a complex network based on dynamic attack according to claim 2, characterized in that: Determining the vulnerability assessment result of the route network in S32 according to the index value of each second type index determined during each static attack and the index value of each second type index determined during each dynamic attack specifically includes: When a preset random attack mode is adopted, a port is randomly selected from the ports included in the route network and used as a candidate port; The candidate port and the route connected to the candidate port are removed from the route network, and the index values ​​corresponding to the respective second-type indicators of the route network after the removal are determined. A candidate port is reselected from the ports included in the route network after the removal, and the candidate port and the route connected to the candidate port are continuously removed from the route network after the removal, and the index values ​​corresponding to the respective second-type indicators are continuously determined until the end condition is reached. The vulnerability assessment result of the route network is determined according to the index values ​​of the respective second-type indicators determined during each static attack, the index values ​​of the respective second-type indicators determined during each random attack, and the index values ​​of the respective second-type indicators determined during each dynamic attack.

4. The method for evaluating the vulnerability of a port and shipping line network of a complex network based on dynamic attack according to claim 3, characterized in that: Determining the vulnerability assessment result of the route network in S32 according to the index value of each second type index determined during each static attack, the index value of each second type index determined during each random attack, and the index value of each second type index determined during each dynamic attack specifically includes: Determining indicator values ​​corresponding to the respective second-type indicators of the route network and using them as initial values; For each second-type indicator, a first change curve is constructed based on the indicator value corresponding to the second-type indicator during each static attack and the initial value corresponding to the second-type indicator, and a first AUC value is determined based on the first change curve; a second change curve is constructed based on the indicator value corresponding to the second-type indicator during each random attack and the initial value corresponding to the second-type indicator, and a second AUC value is determined based on the second change curve; a third change curve is constructed based on the indicator value corresponding to the second-type indicator during each dynamic attack and the initial value corresponding to the second-type indicator, and a third AUC value is determined based on the third change curve; The entropy weight method is used to determine the indicator weights corresponding to each first AUC value, each second AUC value, and each third AUC value; Using the weights of the indicators, weighting the first AUC values, the second AUC values, and the third AUC values ​​respectively; Determine the sum of each weighted first AUC value, each weighted second AUC value, and each weighted third AUC value, and use it as a comprehensive vulnerability index; A vulnerability assessment result of the route network is determined according to the comprehensive vulnerability index.

5. The method for evaluating the vulnerability of a port and shipping line network of a complex network based on dynamic attack according to claim 4, characterized in that: The step S32 of constructing the third change curve according to the indicator value corresponding to the second type indicator during each dynamic attack and the initial value corresponding to the second type indicator specifically includes: For each dynamic attack, determining a ratio of the index value corresponding to the second type index during the dynamic attack to the initial value corresponding to the second type index, and using this ratio as the normalized index value; and determining a ratio of the number of removed ports after the dynamic attack to the initial number of ports in the route network, and using this ratio as the node ratio; According to each normalized index value and each node ratio, a third variation curve is constructed, showing the normalized index value varying with the node ratio.

6. The method for evaluating the vulnerability of a port and shipping line network of a complex network based on dynamic attack according to claim 1, characterized in that: In the route network, each port is regarded as a node, and each first-type indicator is an indicator that statically measures the importance of each node in the route network when the node is not removed. The first-type indicators include weighted degree centrality, betweenness centrality, closeness centrality and eigenvector centrality.

7. The method for evaluating the vulnerability of a port and shipping line network of a complex network based on dynamic attack according to claim 1, characterized in that: In step S3, the second-type indicators are indicators for dynamically measuring the performance of the route network after removing the ports in the route network. The second-type indicators include average clustering coefficient, maximum strongly connected component ratio, weighted efficiency and accessibility.

8. The method for evaluating the vulnerability of a port and shipping line network of a complex network based on dynamic attack according to claim 1, characterized in that: In step S32, the termination condition is: all ports in the current route network are removed or the preset attack times are reached.

9. The method for evaluating the vulnerability of a port and shipping line network of a complex network based on dynamic attack according to claim 6, characterized in that: The S2 specifically includes: When using the pre-set first-type indicators for evaluation, for each port in the route network, a first indicator value corresponding to the weighted degree centrality of the port is determined based on the number of routes connected to the port and the weights on the routes; a second indicator value corresponding to the betweenness centrality of the port is determined based on the number of shortest paths between any two ports other than the port; a third indicator value corresponding to the closeness centrality of the port is determined based on the length of the shortest path from the port to other ports; and a fourth indicator value corresponding to the eigenvector centrality of the port is determined based on the adjacency matrix and the maximum eigenvalue of the port. The importance of the port is determined according to the first index value, the second index value, the third index value, and the fourth index value.

10. The method for evaluating the vulnerability of a port and shipping line network of a complex network based on dynamic attack according to claim 1, characterized in that: The S2 specifically includes: For each port in the route network, determining the index values ​​corresponding to the respective preset first-type indicators of the port; removing the port and the routes connected to the port from the route network, and determining the indicator values ​​corresponding to the respective second-type indicators based on the route network after the removal; The importance of the port is determined according to the index values ​​corresponding to the first type indicators and the index values ​​corresponding to the second type indicators.

11. The method for evaluating the vulnerability of a port and shipping line network of a complex network based on dynamic attack according to claim 10, characterized in that: The step S2 of determining the importance of the port according to the index values ​​corresponding to the first type indicators and the index values ​​corresponding to the second type indicators specifically includes: Determining indicator values ​​corresponding to the respective second-type indicators of the route network and using them as initial values; For each second-type indicator, determining a change rate corresponding to the second-type indicator according to the indicator value corresponding to the second-type indicator of the port and an initial value corresponding to the second-type indicator; Adjusting and normalizing the change rate to obtain a change value corresponding to the second type indicator; The importance of the port is determined according to the indicator values ​​corresponding to the first type indicators and the change values ​​corresponding to the second type indicators.

12. A method for evaluating the vulnerability of a port and shipping line network of a complex network based on dynamic attacks as claimed in claim 11, characterized in that: The step S2 of determining the importance of the port according to the indicator values ​​corresponding to the first type indicators and the change values ​​corresponding to the second type indicators specifically includes: Using the first type indicators and the second type indicators as evaluation indicators; According to the index values ​​corresponding to the evaluation indicators corresponding to the ports, the importance weights corresponding to the evaluation indicators are determined by using the entropy weight method; Determine the first score of the port by using the weighted average method based on the importance weights and the index values ​​of the evaluation indicators of the port; determine the second score of the port by using the ideal solution method based on the importance weights and the index values ​​of the evaluation indicators of the port; determine the third score of the port by using the rank sum ratio method based on the importance weights and the index values ​​of the evaluation indicators of the port; Determine a sum of the first score, the second score, and the third score, and use the sum as a total score; Based on the total score, the importance of the port is determined.

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