A method for optimizing resilience-oriented emergency bus route considering structural redundancy

Abstract

The application discloses a kind of structural redundancy considering toughness-oriented emergency bus route optimization method, belong to traffic emergency evaluation technical field, including obtaining the stop time of subway station, running time and geographic location information, construct the space-time characteristic matrix between station;Calculate the shortest travel time of station pair in subway network before and after accident, the node connectivity ratio when not setting up connecting bus after accident, global redundancy level coefficient and network toughness value;Classify emergency bus type, analyze the influence of different connecting mode on network structure, recalculate travel efficiency, connectivity and redundancy in composite network under multiple connecting strategies;Finally obtain the network toughness index corresponding to each type of emergency connecting mode.The application uses the above-mentioned structural redundancy considering toughness-oriented emergency bus route optimization method, provides decision basis for scientifically formulating emergency bus connecting path, is suitable for the toughness evaluation and emergency dispatch optimization of urban rail transit system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of traffic emergency evaluation, in particular to a resilience-oriented emergency bus path optimization method considering structural redundancy. BACKGROUND

[0002] With the acceleration of urbanization and the continuous rise of urban population density, the demand for urban travel continues to grow. As an important part of urban public transportation, the rail transit system plays an increasingly important role in relieving traffic congestion due to its large carrying capacity, fast running speed, and high safety factor. However, due to the characteristics of structural closure and poor flexibility of the rail transit system, once a line is disrupted due to a sudden event, it will often cause a large number of passengers to be stranded, increase the pressure of transfer, and lack of supply of alternative transportation modes, causing a chain of problems that seriously disrupt the normal operation of the urban transportation system. This exposes the obvious vulnerability of the rail transit network in the face of sudden events, and therefore, it is urgent to improve the system resilience to cope with sudden events to ensure the continuity and reliability of urban traffic operation.

[0003] Resilience originated from the field of physics, used to describe the ability of an object to resist deformation and return to its original state under external force, and was later introduced into the fields of psychology, ecology, social systems, and engineering systems. In the study of transportation systems, resilience generally refers to the ability of a transportation network to maintain core functions or recover to an acceptable operating state within a short period of time after being disturbed or damaged. In practical applications, a transportation system with high resilience should be able to ensure travel continuity and minimize the negative impact of travel disruption by means of path reconstruction, transportation mode conversion, and temporary scheduling when encountering sudden events.

[0004] Current methods for quantifying transportation resilience mainly focus on passive recovery at the single transportation mode or node level, such as using static configuration of connecting buses to complete commuter transfer after failure. However, such methods often ignore the redundant structure and self-regulating ability of the rail transit network itself, and fail to fully exploit the potential of the network to maintain partial connectivity and functionality under local damage. In addition, many optimization models still remain at the static level, making it difficult to dynamically reflect the evolution process of network structure and traffic flow state under disturbance, and lacking the ability to depict real complex traffic environments. SUMMARY

[0005] The purpose of the present application is to provide a resilience-oriented emergency bus path optimization method considering structural redundancy, which is suitable for the scenario where a subway line is locally disrupted under the influence of a sudden event and needs to be connected by an emergency bus for route connection to quickly evacuate passengers. The method can accurately evaluate the operating resilience of the rail transit-emergency bus composite network, and thus find the optimal connection route.

[0006] To achieve the above objectives, this invention proposes a resilience-oriented emergency bus route optimization method considering structural redundancy, the steps of which are as follows:

[0007] Step S1: Obtain the stopping time of each subway line at each station, the running time between adjacent stations, and the latitude and longitude coordinates of each subway station, and construct a spatiotemporal feature matrix between stations;

[0008] Step S2: Calculate the shortest travel time for station pairs in the subway network before and after the accident, and evaluate the node connectivity ratio and global redundancy level coefficient under the condition of no connecting bus after the accident, and construct a network resilience value evaluation model to obtain the network resilience value.

[0009] Step S3: Classify emergency bus types and analyze the impact of different emergency bus types on the network structure;

[0010] Step S4: Obtain the changes in network resilience values ​​under different connection routes and find the optimal emergency bus connection route.

[0011] Preferably, in step S2, the shortest travel time for station pairs in the subway network before and after the accident is calculated using the following formula:

[0012] ;

[0013] in, For nodes Shortest path time, For nodes Shortest path time, For connecting nodes and Path time.

[0014] Preferably, in step S2, the node connectivity ratio is evaluated after the accident without the provision of connecting public transportation. The specific calculation formula is as follows:

[0015] ;

[0016] in, This represents the connectivity ratio of a composite network. The connectivity of the points before the disruption. The connectivity of the points after the disruption.

[0017] Preferably, in step S2, the global redundancy level coefficient is evaluated under the condition that no connecting bus service is provided after the accident. The specific calculation formula is as follows:

[0018] ;

[0019] in, For the redundancy of composite networks, is the set of all node pairs, is the indicator function, is the effective redundancy path coefficient threshold value; is the effective redundancy path coefficient between node i and node j; if = 0, it means that the travel time of the second shortest redundant path after the destruction is completely equal to the original shortest path, the efficiency of the second shortest redundant path is very high or the path is completely not destroyed; if > 0, it means that the travel time of the second shortest redundant path is longer than the shortest path; The larger the value is, the lower the efficiency of the replacement path after the destruction is compared with the shortest path; in order to ensure that the penalty of the second shortest redundant path is not too large, the effective redundancy path coefficient is set to be a threshold value , which represents the acceptable redundancy penalty level of the network when the shortest path is invalid:

[0020] When , the redundancy between the nodes is good;

[0021] When , the redundancy between the nodes is poor;

[0022] Preferably, in step S2, the network resilience value is obtained by constructing a network resilience value evaluation model, and the specific calculation formula is:

[0023] ;

[0024] Wherein, is the composite network resilience index.

[0025] Preferably, in step S3, the change index of the travel time of passengers in the subway after different types of emergency bus transfer is obtained, the passenger travel behavior is updated in the subway network every time the emergency bus transfer route changes, the shortest travel time of passengers in the whole network, the composite network node connectivity ratio and the global redundancy level coefficient under the latest transfer route are obtained, and the network resilience value is obtained according to the network resilience value evaluation model. The specific steps are as follows:

[0026] Step S31, calculating the shortest travel time of the node pair in the subway-emergency bus composite network through which the passengers pass again under different emergency bus types after the accident occurs;

[0027] Step S32, calculating the node connectivity ratio of the subway-emergency bus composite network under different emergency bus types after the accident occurs;

[0028] Step S33, calculating the global redundancy level coefficient of the subway-emergency bus composite network under different emergency bus types after the accident occurs;

[0029] Step S34: Calculate the resilience value of the metro-emergency bus composite network when different types of emergency buses connect after an accident.

[0030] Therefore, this invention proposes a resilience-oriented emergency bus route optimization method that considers structural redundancy, with the following beneficial effects:

[0031] (1) This invention uses the Dijkstra algorithm to update the dynamic impact of changes in public transport connection services on passengers’ route selection and travel patterns in real time, helping traffic managers to predict changes in passenger behavior under different connection strategies and their impact on network performance.

[0032] (2) This invention takes into account the impact of network connectivity on the actual reachability of redundant paths and introduces "connectivity ratio" as a correction factor. When the network maintains good connectivity, the redundancy performance evaluation will be enhanced; otherwise, the redundancy level will be reasonably reduced. Redundancy is incorporated into the construction of network resilience indicators. By considering network redundancy, the adaptability and recovery capability of the network at the structural level under disturbances are comprehensively characterized. A quantitative index of the resilience of the subway-emergency bus composite network is proposed through nonlinear weighting. With the help of this quantitative index of resilience, the optimal emergency bus connection route is found, thereby quickly evacuating obstructed passengers and restoring the network structure.

[0033] (3) The optimization method proposed in this invention can provide scientific decision-making basis for urban traffic management departments, thereby improving emergency response capabilities, reducing the impact on passengers and the impact on urban traffic networks, and mitigating the negative impact on the social economy.

[0034] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0035] Figure 1 The present invention provides a flowchart of the steps of a resilience-oriented emergency bus route optimization method that considers structural redundancy.

[0036] Figure 2 This is due to changes in passengers' travel patterns; among them, Figure 2 (a) in the text represents the passenger's mode of transportation before the accident. Figure 2 (b) in the text represents the mode of transportation for passengers who did not receive public transportation after the accident;

[0037] Figure 3 This is a schematic diagram of a combined subway and emergency bus network.

[0038] Figure 4 This is a schematic diagram of the network resilience iteration when only station skipping is used after an accident.

[0039] Figure 5 This is a schematic diagram of the network resilience iteration when using a combination of skip-station and station-to-station connection after an accident. Detailed Implementation

[0040] To make the technical solutions, advantages, and objectives of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below. The described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the protection scope of the present invention.

[0041] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0042] Example 1

[0043] like Figure 1 As shown, this invention provides a resilience-oriented emergency bus route optimization method considering structural redundancy, the steps of which are as follows:

[0044] S1. Obtain the stopping time of each subway line at each station, the travel time between adjacent stations, and the latitude and longitude coordinates of each subway station to construct a spatiotemporal feature matrix between stations. The specific steps are as follows:

[0045] S11. Based on the stopping time between two stations and the running time between two adjacent stations on the same subway line, organize the data into a station sequence matrix for subsequent processing.

[0046] S12. Obtain the latitude and longitude data between each subway station, and use the Haversine formula to calculate the distance between any two stations. The specific calculation formula is as follows:

[0047] ;

[0048] ;

[0049] ;

[0050] in As an intermediate variable, it represents the relative positional relationship between two points on the sphere; Let the latitudes of any two stations be denoted as . Due to latitude difference, The unit is radians; Let the longitudes of any two stations be denoted as . Due to longitude difference, The unit is radians; R is the central angle between the two points, in radians; R is the Earth's radius, averaging 6371 kilometers; d is the calculated spherical distance, i.e., the distance between the two stations, in kilometers.

[0051] S13. Based on the connections between subway stations, organize the data into an adjacency undirected graph matrix, as follows:

[0052] For a subway network with n subway stations, it is... Matrix A;

[0053] The element in the i-th row and j-th column of the matrix This indicates the connection between subway station i and subway station j. If there is a direct connection between subway station i and subway station j, then... Otherwise, it is 0. For transfer stations, stations on the same line are marked as 1, and stations on different lines are marked as 0; different station sequences at transfer stations are marked as 1.

[0054] S14. Based on the distances between subway stations, organize the data into a distance matrix;

[0055] S15. Based on the transfer times between subway stations, organize them into a transfer time matrix. If there is no transfer between two stations, the value is 0.

[0056] S16. Based on the transfer time at subway stations, organize the time into a travel time matrix. If there is no train service between two stations, mark the distance between the two stations as 0.

[0057] After obtaining the latitude and longitude of the stations, the travel time between each subway station, and the stopping time of each station, each subway station was identified with a unique station number based on the subway line information. According to the actual line connections and operational status, the data between stations was organized to construct a corresponding matrix model. Due to difficulties in obtaining data for some lines and stations, missing or incomplete data underwent reasonable deletion and cleaning. Finally, a 456×456 matrix with four dimensions was constructed to describe different types of station relationships and operational characteristics, providing basic data support for subsequent analysis, modeling, and optimization. Specific data are shown in Tables 1-4.

[0058] Table 1. Adjacency matrix between sites (local)

[0059] ;

[0060] Table 2. Matrix of vehicle travel time between stations (partial)

[0061] ;

[0062] Table 3 Station stop time matrix (local)

[0063] ;

[0064] Table 4 Distance matrix between stations (local)

[0065] ;

[0066] S2, as Figures 2-3 shown, the shortest travel time of the station pair in the subway network before and after the accident is calculated, and the node connectivity ratio, global redundancy level coefficient under the condition of not setting the connecting bus after the accident is evaluated, the network resilience value evaluation model is constructed to obtain the network resilience value, the steps are as follows:

[0067] S21, calculate the travel time of passengers in the subway network when no accident occurs , the travel time includes vehicle travel time and transfer time, and for the travel time in the subway network, Dijkstra algorithm is used for calculation, the specific calculation formula is as follows:

[0068] ;

[0069] Wherein, is the shortest path time of node , is the shortest path time of node , is the path time of connecting node and , min(·) is the shortest travel time.

[0070] S22, after the accident, due to the existence of large and small routes, the whole subway line will not be completely disabled, but there will be a "disabled interval", at this time the passengers can be divided into three types, which are:

[0071] ①Completely unaffected passengers, this type of passenger will not change their travel path before and after the accident;

[0072] ②When the starting point is located in the disabled interval, this type of passenger cannot complete the trip completely by relying on the subway, and needs to take emergency buses for travel;

[0073] ③The starting and ending points are not located in the disabled interval, but the shortest path will pass through the disabled interval when not damaged, this part of passengers will choose to travel in the subway or bus according to the shortest time;

[0074] Calculate the travel time of passengers in the subway network path after the accident without connecting emergency buses.

[0075] S23, after the accident, the global redundancy level coefficient (hereinafter referred to as GRL) of the network is calculated, which is a global index for measuring whether the subway network has good alternative path after the destruction. The closer the GRL value is to 1, the higher the efficiency of the alternative path of the network after the destruction, and the better the redundancy. The whole network can better adapt to the failure of some stations or lines. A lower GRL value means that the efficiency of the alternative path of the network after the destruction is low, and the overall redundancy is poor. The specific calculation formula is:

[0076] ;

[0077] wherein is the redundancy of the composite network, is the set of all node pairs; is an indicator function, which is 1 when the condition is met, otherwise 0; is the effective redundancy path coefficient threshold value;

[0078] is the effective redundancy path coefficient between station i and station j; if =0, it means that the travel time of the second shortest redundant path after the destruction is completely equal to the original shortest path. The efficiency of the second shortest redundant path is very high or the path is completely destroyed; if >0, it means that the travel time of the second shortest redundant path is longer than the shortest path. The larger the value is, the lower the efficiency of the alternative path after the destruction is compared with the shortest path; in order to ensure that the penalty of the second shortest redundant path is not too large, the threshold value is set, which represents the acceptable redundancy penalty level of the network when the shortest path is invalid: When

[0079] , the redundancy between the stations is good; When

[0080] , the redundancy between the stations is poor.

[0081] S24, after the accident, the connectivity ratio of the network is calculated, and the specific calculation formula is as follows:

[0082] ;

[0083] wherein, is the connectivity ratio of the composite network, is the point connectivity before the destruction, is the point connectivity after the destruction;

[0084] S25, after the accident, the resilience quantitative index of the network is calculated, and the calculation formula is: ​

[0085] ;

[0086] wherein, is the composite network resilience index.

[0087] In this embodiment, it is assumed that the intervals numbered 167-171 are failure intervals, and the station numbers are located in the central area of the city. In the failure intervals, the train cannot pass through. After obtaining the travel time of passengers in the subway after the accident without public transport transfer, the connectivity ratio, the global redundancy level coefficient, and the influence of the accident on passenger travel are obtained. The specific data are shown in Table 5.

[0088] In this embodiment, 0.3 is taken, the bus speed is taken as 10 km / h, and there are 3 public transport transfer lines.

[0089] Table 5. Post-accident non-transfer public transport station travel matrix (local) of a city

[0090] ;

[0091] When no measures are taken for recovery, the node connectivity ratio is 0.995614, the global redundancy level coefficient is 0.989670, and the network resilience is 0.989714.

[0092] S3, classify the emergency public transport types, analyze the influence of different emergency public transport types on the network structure, and the specific steps are as follows:

[0093] S31, divide the public transport types into two categories. One category is station-to-station stopping, that is, stopping at each station inside the failure interval, covering a wide range and ensuring local accessibility, but the running efficiency is low. The other category is station-to-station plus skip-station, including skip-station operation inside the failure interval or cross-interval skip-station operation, which focuses on connecting core nodes or crossing the failure interval to the normal interval, improving the travel efficiency and enhancing the network connectivity and redundancy.

[0094] S32, optimize the results by using genetic algorithm: each iteration will cause changes in the network structure, and the network resilience will change according to the changes in emergency public transport transfer. Each transfer will re-calculate the network resilience. In multiple iterations, the optimal solution is obtained.

[0095] S4, obtain the change of network resilience value under different transfer lines, and find the optimal emergency public transport transfer route, and the steps are as follows:

[0096] S41, as shown in Table 6, calculate the optimal emergency public transport transfer route obtained according to the maximum network resilience under the condition of only skip-station transfer, and the calculation results are as follows: Figure 4

[0097] ​With only hop-to-hop connections, the node connectivity ratio is 1, the global redundancy level coefficient is 0.996904, the network resilience is 0.996904, and the connection path is [(167, 169), (103, 169), (170, 171)].

[0098] Table 6. Partial travel matrix of a city's composite network of shuttle buses using skip-stop connections after an accident.

[0099] ;

[0100] Based on the above calculation results, it can be found that the optimization algorithm has good convergence performance, reaching the optimal solution around the 35th generation. The optimal fitness remains stable in subsequent generations, indicating that the algorithm has strong search ability and convergence stability. Throughout the optimization process, the fitness value shows a rapid upward trend, with a significant increase in the early stage and a tendency to stabilize in the later stage. This indicates that the algorithm can effectively explore the solution space in the early stage and quickly approach the global optimal region. In the later stage, it achieves fine adjustment through a local search mechanism. The final result is stable at a fitness of around 0.996904, which further verifies that the optimization strategy has good global search ability and robustness in this problem.

[0101] S42, such as Figure 5 As shown in Table 7, the optimal emergency bus connection route obtained based on the maximum network resilience under the method of skipping stops and connecting every stop is calculated, and the calculation results are as follows;

[0102] With the adoption of hop-to-hop + station-to-station connection, the node connectivity ratio is 1, the global redundancy level coefficient is 0.997201, the network resilience is 0.997201, and the connection path is [(80,170), (169,167), (103,169)];

[0103] Table 7. Partial travel matrix of a city's composite bus network using skip-stop and all-stop shuttle bus services after the accident.

[0104] ;

[0105] Based on the above calculation results, it can be found that adding skip-stop connections does not significantly improve the overall network resilience, nor does it change the travel time between nodes. This is because, without considering factors such as the number of vehicles, departure frequency, and load factor, skip-stop connections alone can meet the travel needs of most passengers in the city center under the damage, thus restoring the damaged network structure.

[0106] It is worth noting that all contents not described in detail in this invention are existing technologies and are well known to those skilled in the art.

[0107] Therefore, the application provides a resilience-oriented emergency bus route optimization method considering structural redundancy, effectively promotes the rapid recovery of the traffic network structure and system resilience, and realizes the efficient evacuation of affected passengers; at the same time, by combining different regional characteristics and reasonably matching different types of emergency bus services, the response efficiency is improved and the resource consumption is reduced, thereby providing more scientific and reliable decision support for the emergency evaluation and response of the urban rail transit system under the disturbance condition.

[0108] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application, but not to limit them, although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that: it can still modify or equivalently replace the technical solutions of the present application, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present application.

Claims

1. A resilience-oriented emergency bus route optimization method considering structural redundancy, characterized in that, Includes the following steps: Step S1: Obtain the stopping time of each subway line at each station, the running time between adjacent stations, and the latitude and longitude coordinates of each subway station, and construct a spatiotemporal feature matrix between stations; Step S2: Calculate the shortest travel time for station pairs in the subway network before and after the accident, and evaluate the node connectivity ratio and global redundancy level coefficient under the condition of no connecting bus after the accident, and construct a network resilience value assessment model to obtain the network resilience value. Step S3: Classify emergency bus types and analyze the impact of different emergency bus types on the network structure; Step S4: Obtain the changes in network resilience values ​​under different connection routes and find the optimal emergency bus connection route; In step S2, the shortest travel time for station pairs in the subway network before and after the accident is calculated. The specific calculation formula is as follows: ； in, For nodes Shortest path time, For nodes Shortest path time, For connecting nodes and Path time; The specific formula for calculating the node connectivity ratio after an accident, without the provision of connecting public transportation, is as follows: ； in, This represents the connectivity ratio of a composite network. The connectivity of the points before the disruption. The connectivity of the points after the disruption; The global redundancy level coefficient is assessed after an accident without the provision of connecting public transportation. The specific calculation formula is as follows: ； in, For the redundancy of composite networks, For the set of all node pairs, For indicator functions, The effective redundancy path coefficient between station i and station j The threshold for effective redundant path coefficients; A network resilience value assessment model is constructed to obtain the network resilience value. The specific calculation formula is as follows: ； in, As an indicator of the resilience of composite networks; In step S3, the changes in passenger travel time in the subway after different types of emergency bus connections are obtained. Each time the emergency bus connection route changes, passenger travel behavior is updated in the subway network. The shortest travel time for all passengers under the latest connection route, the connectivity ratio of composite network nodes, and the global redundancy level coefficient are obtained. The network resilience value is obtained based on the network resilience evaluation model. The specific steps are as follows: Step S31: Calculate the shortest travel time for the node pairs in the metro-emergency bus composite network that passengers re-pass through after the accident, under different emergency bus connection types. Step S32: Calculate the node connectivity ratio of the metro-emergency bus composite network when different types of emergency buses connect after an accident. Step S33: Calculate the global redundancy level coefficient of the metro-emergency bus composite network when different emergency bus types connect after an accident. Step S34: Calculate the resilience value of the metro-emergency bus composite network when different types of emergency buses connect after an accident.

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