Toughness-oriented emergency bus route optimization method considering structural redundancy

Abstract

The invention discloses a toughness-oriented emergency bus route optimization method considering structural redundancy, and belongs to the technical field of traffic emergency assessment, and the method comprises the steps: obtaining the stop time, operation time and geographic position information of subway stations, and constructing a spatial-temporal feature matrix between the stations; calculating the shortest travel time of the station pairs in the subway network before and after the accident, and the node connectivity ratio, the global redundancy level coefficient and the network toughness value when no connection bus is set after the accident; emergency bus types are classified, the influence of different connection modes on a network structure is analyzed, and the travel efficiency, connectivity and redundancy in the composite network are recalculated under multiple connection strategies; and finally, network toughness indexes corresponding to various types of emergency connection modes are obtained. According to the toughness guiding emergency bus route optimization method considering the structural redundancy, a decision basis is provided for scientifically formulating an emergency bus connection route, and the method is suitable for toughness evaluation and emergency scheduling optimization of an urban rail transit system.

Description

Technical Field

[0001] The present invention relates to the technical field of traffic emergency assessment, and in particular to a resilience-oriented emergency bus route optimization method considering structural redundancy. Background Art

[0002] With the acceleration of urbanization and the continuous increase in urban population density, the demand for urban transportation continues to grow. As an important component of urban public transportation, the rail transit system plays an increasingly important role in alleviating traffic congestion due to its significant advantages such as large carrying capacity, high operating speed, and high safety factor. However, due to the closed structure and poor flexibility of the rail transit system, once a line is interrupted due to an emergency, it often leads to a series of problems such as large passenger delays, sudden increase in transfer pressure, and insufficient supply of alternative transportation modes, seriously disrupting the normal operation of the urban transportation system. This exposes the obvious vulnerability of the rail transit network in the face of emergencies. Therefore, it is urgent to enhance its system resilience in responding to emergencies to ensure the continuity and reliability of urban transportation operations.

[0003] Resilience originally originated in physics, describing the ability of an object to resist deformation and return to its original shape under external forces. It has subsequently been introduced into fields such as psychology, ecology, social systems, and engineering systems. In transportation system research, resilience generally refers to the ability of a transportation network to maintain its core functions or to recover to an acceptable operating state within a short period of time when disturbed or damaged. In practical applications, a highly resilient transportation system should be able to ensure travel continuity in the event of an emergency through route reconstruction, mode switching, and temporary scheduling, thereby minimizing the negative impact of travel disruptions.

[0004] Current approaches to quantifying traffic resilience often focus on passive recovery at the single mode or node level, such as statically configuring shuttle buses to facilitate commuter transfers after a failure. However, such approaches often overlook the inherent redundancy and self-regulation capabilities of rail transit networks, failing to fully tap the network's potential to maintain partial connectivity and functionality despite localized damage. Furthermore, many optimization models remain static, struggling to dynamically reflect the evolution of network structure and traffic flow under disturbances and lacking the ability to capture complex real-world traffic environments. Summary of the Invention

[0005] The purpose of this invention is to propose a resilience-oriented emergency bus route optimization method that considers structural redundancy. The method is applicable to scenarios where a subway line is partially interrupted due to an emergency and an emergency bus is urgently needed to connect the route for rapid evacuation of passengers. The method can accurately evaluate the operational resilience of the rail transit-emergency bus composite network and thus find the optimal connection route.

[0006] To achieve the above objectives, the present invention proposes a resilience-oriented emergency bus route optimization method considering structural redundancy, which includes the following steps: Step S1: Obtain the stop time of each subway line at each station, the running time between adjacent stations, and the longitude and latitude coordinates of each subway station, and construct a spatiotemporal feature matrix between stations; Step S2: Calculate the shortest travel time between station pairs in the subway network before and after the accident, evaluate the node connectivity ratio and global redundancy level coefficient after the accident without connecting buses, and construct a network resilience value evaluation model to obtain the network resilience value; Step S3: classify emergency public transportation types and analyze the impact of different emergency public transportation types on the network structure; Step S4: Obtain the changes in network resilience values under different connecting routes and find the optimal emergency bus connecting route.

[0007] Preferably, in step S2, the shortest travel time between station pairs in the subway network before and after the accident is calculated, and the specific calculation formula is: ; in, For nodes The shortest path time, For nodes The shortest path time, To connect nodes and Path time.

[0008] Preferably, in step S2, the node connectivity ratio is evaluated after the accident occurs without setting a connecting bus. The specific calculation formula is: ; in, is the composite network connectivity ratio, is the point connectivity before destruction, is the point connectivity after destruction.

[0009] Preferably, in step S2, the global redundancy level coefficient is evaluated after the accident occurs without setting a connecting bus. The specific calculation formula is: ; in, For composite network redundancy, is the set of all node pairs, is the indicator function, is the effective redundant path coefficient threshold; is the effective redundant path coefficient between site i and site j; if =0, it means that the travel time of the second shortest redundant path after the damage is exactly the same as the travel time of the original shortest path, the efficiency of the second shortest redundant path is very high or the path is not damaged at all; if >0, it means that the travel time of the second shortest redundant path is longer than the shortest path; The larger the value, the lower the efficiency of the replacement path after the damage compared to the shortest path; in order to ensure that the penalty of the second shortest redundant path is not too large, Set a threshold , which represents the redundancy penalty level that the network can accept when the shortest path fails: when ,The redundancy between the sites is good; when ,The redundancy between the sites is poor; Preferably, in step S2, a network resilience value evaluation model is constructed to obtain the network resilience value, and the specific calculation formula is: ; in, It is a composite network resilience indicator.

[0010] Preferably, in step S3, a change index of the passenger travel time in the subway after connecting to different types of emergency buses is obtained. Each time the emergency bus connecting route changes, the passenger travel behavior is updated in the subway network. The shortest travel time of all passengers in the network under the latest connecting route, the composite network node connectivity ratio, and the global redundancy level coefficient are obtained. The network resilience value is obtained according to the network resilience value evaluation model. The specific steps are as follows: Step S31: Calculate the shortest travel time for each node pair in the subway-emergency bus composite network that the passenger passes through again after the accident occurs, under the conditions of different emergency bus types. Step S32: Calculate the node connectivity ratio of the subway-emergency bus composite network when different emergency bus types are connected after the accident occurs; Step S33: Calculate the global redundancy level coefficient of the subway-emergency bus composite network when different emergency bus types are connected after the accident occurs; Step S34: Calculate the resilience value of the subway-emergency bus composite network when different emergency bus types are connected after the accident occurs.

[0011] Therefore, the present invention proposes a resilience-oriented emergency bus route optimization method considering structural redundancy, which has the following beneficial effects: (1) The present invention uses the Dijkstra algorithm to update in real time the dynamic impact of changes in bus connection services on passengers' path choices and travel patterns, helping traffic managers predict changes in passenger behavior under different connection strategies and their impact on network performance.

[0012] (2) This invention takes into account the impact of network structure connectivity on the actual accessibility of redundant paths and introduces the "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 lowered. Redundancy is incorporated into the construction of network resilience indicators. By considering network redundancy, the adaptability and recovery capabilities of the network at the structural level during disturbances are comprehensively characterized. A quantitative index of the resilience of the subway-emergency bus composite network is proposed through a nonlinear weighted approach. With the help of this resilience quantitative index, the optimal emergency bus connection route is found, thereby quickly evacuating blocked passengers and restoring the network structure.

[0013] (3) The optimization method proposed in this invention can provide a scientific decision-making basis for urban traffic management departments, thereby improving emergency response capabilities, reducing the impact on traveling passengers and the impact on urban traffic networks, and alleviating the negative impact on social economy.

[0014] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 This is a flowchart of the steps of a resilience-oriented emergency bus route optimization method considering structural redundancy of the present invention; Figure 2 The travel mode of passengers has changed; among them, Figure 2 (a) is the passenger’s mode of travel before the accident. Figure 2 (b) refers to the travel mode of passengers who did not use public transportation to connect after the accident; Figure 3 This is a schematic diagram of the subway-emergency bus composite network; Figure 4 This is a schematic diagram of the network resilience iteration broken line when only station-hopping connection is used after an accident occurs; Figure 5 This is a broken line diagram of network resilience iteration when a skip-station + station-to-station combination connection is used after an accident occurs. DETAILED DESCRIPTION

[0016] To make the technical solutions, advantages, and objectives of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below. The described embodiments are part of the embodiments of the present invention, not all of them. Based on the described embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0017] Unless otherwise defined, technical or scientific terms used in the present invention shall have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

[0018] Example 1 like Figure 1 As shown, the present invention provides a resilience-oriented emergency bus route optimization method considering structural redundancy, the steps are as follows: S1. Obtain the stop time of each subway line at each station, the travel time between adjacent stations, and the longitude and latitude coordinates of each subway station, and construct a spatiotemporal feature matrix between stations. The specific steps are as follows: S11. Arrange the data based on the stop time between two stations and the running time between two adjacent stations on the same subway line into a station sequence matrix for subsequent arrangement; S12. Obtain the longitude and latitude 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: ; ; ; in is an intermediate variable, representing the relative position relationship between two points on the sphere; is the latitude of any two stations, is the latitude difference, , in radians; is the longitude of any two stations, is the longitude difference, , in radians; is the central angle between the two points, in radians; R is the radius of the Earth, with an average value of 6371 kilometers; d is the calculated spherical distance, that is, the distance between the two stations, in kilometers; S13. According to the connection between subway stations, the connection is organized into an adjacency undirected graph matrix, as follows: For a subway network with n subway stations, Matrix A; The element in row i and column j of the matrix Indicates the connection between the subway station with station sequence i and the subway station with station sequence j. If the subway station with station sequence i is directly connected to the subway station with station sequence 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; stations between different station sequences at transfer stations are marked as 1; S14, organizing the distances between subway stations into a distance matrix; S15. Arrange the transfer time matrix based on the transfer time between subway stations. If there is no transfer between two stations, the matrix is 0. S16. Arrange the transfer time between subway stations into a travel time matrix. If there is no train running between two stations, the distance between the two stations is marked as 0. After obtaining the station's longitude and latitude, vehicle travel time between stations, and vehicle stop time at each station, each station was identified with a unique station number based on the station's line information. Based on the actual line connections and operational conditions, the data between stations was organized and a corresponding matrix model was constructed. Due to difficulties in obtaining data for some line stations, missing or incomplete data was appropriately deleted and cleaned. Ultimately, four 456×456 matrices were constructed to describe different types of station relationships and operational characteristics, providing basic data support for subsequent analysis, modeling, and optimization. The specific data are shown in Tables 1-4.

[0019] Table 1 Adjacency matrix between sites (partial) ;

[0020] Table 2 Matrix of vehicle travel time between stations (partial) ;

[0021] Table 3 Stop time matrix of each station (partial) ;

[0022] Table 4 Distance matrix between sites (partial) ;

[0023] S2, such as Figure 2-3 As shown in the figure, the shortest travel time between stations in the subway network before and after the accident is calculated, and the node connectivity ratio and global redundancy level coefficient are evaluated without setting up connecting buses after the accident. The network resilience value evaluation model is constructed to obtain the network resilience value. The steps are as follows: S21. Calculate the travel time of passengers in the subway network when no accidents occur. , travel time includes vehicle travel time and transfer time. For the travel time in the subway network, Dijkstra algorithm is used for calculation. The specific calculation formula is as follows: ; in, For nodes The shortest path time, For nodes The shortest path time, To connect nodes and The path time is min(·) which is the shortest travel time.

[0024] S22. After an accident, due to the existence of large and small intersections, the entire subway line will not be completely disabled, but there will be a partial "disabled section". At this time, passengers can be divided into three types, namely: ① Completely unaffected passengers: their travel routes will not change before or after the accident; ② When the starting point is within the ineffective zone, such passengers cannot complete their journey by relying solely on the subway and need to take emergency public transportation; ③ Passengers whose starting and ending points are not located in the invalid interval, but whose shortest path would pass through the invalid interval if it were not damaged. These passengers will choose to travel by subway or bus based on the shortest time; Calculate the travel time of passengers on the subway network path when no emergency bus connection is made after the accident.

[0025] S23. After an accident occurs, the global redundancy level (GRL) of the network is calculated. This is a global indicator that measures whether the subway network has good alternative paths after damage. The closer the GRL value is to 1, the higher the efficiency of the network's alternative paths after damage, the better the redundancy, and the better the network can adapt to the failure of certain stations or lines. A lower GRL value means that the network's alternative paths are less efficient after damage and the overall redundancy is poor. The specific calculation formula is: ; in For composite network redundancy, is the set of all node pairs; is an indicator function, the value is 1 when the condition is met, otherwise it is 0; is the effective redundant path coefficient threshold; is the effective redundant path coefficient between site i and site j; if =0, it means that the travel time of the second shortest redundant path after the damage is exactly the same as the travel time of the original shortest path, the efficiency of the second shortest redundant path is very high or the path is not damaged at all; if >0, it means that the travel time of the second shortest redundant path is longer than the shortest path; The larger the value, the lower the efficiency of the replacement path after the damage compared to the shortest path; in order to ensure that the penalty of the second shortest redundant path is not too large, Set a threshold , which represents the redundancy penalty level that the network can accept when the shortest path fails: when ,The redundancy between the sites is good; when , the redundancy between the sites is poor.

[0026] S24. After the accident occurs, calculate the network connectivity ratio. The specific calculation formula is as follows: ; in, is the composite network connectivity ratio, is the point connectivity before destruction, is the point connectivity after destruction; S25. After the accident occurs, calculate the network resilience quantitative index. The calculation formula is: ; in, It is a composite network resilience indicator.

[0027] In this example, it is assumed that the section numbered 167-171 is an inoperative section. In this case, the station number is located in the city center. Trains cannot pass through this inoperative section. After the accident, the passenger travel time, connectivity ratio, and global redundancy level coefficient are obtained without bus connection. The impact of the accident on passenger travel is obtained. The specific data is shown in Table 5.

[0028] In this embodiment, Take 0.3, the bus speed is 10km / h, and there are 3 bus connecting routes; Table 5 Post-accident trip matrix of non-connecting bus network stations in a certain city (partial) ;

[0029] When no recovery measures are taken, the node connectivity ratio is 0.995614, the global redundancy level coefficient is 0.989670, and the network resilience is 0.989714.

[0030] S3. Classify emergency public transportation types and analyze the impact of different emergency public transportation types on the network structure. The specific steps are as follows; S31. Public transportation types are divided into two categories: one is stop-at-every-station operation, which means that it stops at every station within the outage interval. This provides wide coverage and ensures local accessibility, but has lower operating efficiency. The other is stop-at-every-station operation with skipping stops, which includes skipping stops within the outage interval or skipping stops across intervals. This focuses on connecting core nodes or crossing outage intervals to normal intervals, improving travel efficiency and enhancing network connectivity and redundancy. S32. Use genetic algorithms to optimize the results: Each iteration will cause changes in the network structure, and the network resilience will change according to the changes in emergency bus connections. Each connection will recalculate the network resilience, and the optimal solution will be obtained through multiple iterations.

[0031] S4. Obtain the changes in network resilience values under different connecting routes and find the optimal emergency bus connecting route. The steps are as follows: S41, such as Figure 4 As shown in Table 6, the optimal emergency bus connection route is calculated based on the maximum network resilience using only skip-stop connections. The calculation results are as follows: When only hop connection is used, 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)]; Table 6 Trip matrix of a city's composite network stations using skip-stop bus connections after an accident (partial) ;

[0032] According to the above calculation results, it can be found that the optimization algorithm converges well, reaching the optimal solution around the 35th generation, and the optimal fitness of each generation remains stable, indicating that the algorithm has strong search ability and convergence stability. Throughout the optimization process, the fitness value shows a rapid upward trend, with obvious improvement in the early stage and stabilization in the later stage. This shows that the algorithm can effectively explore the solution space in the early stage and quickly approach the global optimal area. In the later stage, it achieves fine adjustment through the local search mechanism. The final result stabilizes at a fitness of 0.996904, further verifying that the optimization strategy has good global search ability and robustness for this problem. S42, such as Figure 5 As shown in Table 7, the optimal emergency bus connection route is calculated based on the maximum network resilience using skipping stations and station-to-station connection. The calculation results are as follows: When using hop-station + 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)]; Table 7 Trip matrix of a city's composite network using skip-stop and stop-to-stop bus connections after an accident (partial) ;

[0033] Based on the above calculation results, it can be found that after adding skip-stop connections, the overall network resilience is not greatly improved, and the travel time between nodes does not change much. This is because, without considering the number of vehicles, departure frequency, full load rate, etc., skip-stop connections alone can meet the needs of most passenger travel in the event of city center damage and restore the damaged network structure.

[0034] It is worth noting that the contents not elaborated in detail in the present invention are all prior art and are well known to those skilled in the art.

[0035] Therefore, the present invention provides a resilience-oriented emergency bus route optimization method that takes structural redundancy into consideration, which effectively promotes the rapid recovery of the transportation network structure and system resilience, and realizes the efficient evacuation of affected passengers; at the same time, by combining the characteristics of different regions and rationally matching different types of emergency bus services, it helps to improve response efficiency and reduce resource consumption, thereby providing more scientific and reliable decision-making support for emergency assessment and response of urban rail transit systems under disturbance conditions.

[0036] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A resilience-oriented emergency bus route optimization method considering structural redundancy, characterized in that: The following steps are involved: Step S1: Obtain the stop time of each subway line at each station, the running time between adjacent stations, and the longitude and latitude coordinates of each subway station, and construct a spatiotemporal feature matrix between stations; Step S2: Calculate the shortest travel time between station pairs in the subway network before and after the accident, evaluate the node connectivity ratio and global redundancy level coefficient after the accident without connecting buses, and construct a network resilience value evaluation model to obtain the network resilience value; Step S3: classify emergency public transportation types and analyze the impact of different emergency public transportation types on the network structure; Step S4: Obtain the changes in network resilience values under different connecting routes and find the optimal emergency bus connecting route.

2. The resilience-oriented emergency bus route optimization method considering structural redundancy according to claim 1 is characterized in that: In step S2, the shortest travel time between station pairs in the subway network before and after the accident is calculated. The specific calculation formula is: ； in, For nodes The shortest path time, For nodes The shortest path time, To connect nodes and Path time.

3. The resilience-oriented emergency bus route optimization method considering structural redundancy according to claim 1 is characterized in that: In step S2, the node connectivity ratio is evaluated after the accident occurs without setting up a connecting bus. The specific calculation formula is: ； in, is the composite network connectivity ratio, is the point connectivity before destruction, is the point connectivity after destruction.

4. The resilience-oriented emergency bus route optimization method considering structural redundancy according to claim 1 is characterized in that: In step S2, the global redundancy level coefficient is evaluated after the accident occurs without setting up a connecting bus. The specific calculation formula is: ； in, For composite network redundancy, is the set of all node pairs, is the indicator function, is the effective redundant path coefficient between site i and site j, is the effective redundant path coefficient threshold.

5. The resilience-oriented emergency bus route optimization method considering structural redundancy according to claim 1 is characterized in that: In step S2, a network resilience value evaluation model is constructed to obtain the network resilience value. The specific calculation formula is: ； in, It is a composite network resilience indicator.

6. The resilience-oriented emergency bus route optimization method considering structural redundancy according to claim 1 is characterized in that: In step S3, the change indicators of passengers' travel time in the subway after different types of emergency bus connections are obtained. Every time the emergency bus connection route changes, the passenger travel behavior is updated in the subway network. The shortest travel time of passengers in the entire network under the latest connection route, the composite network node connectivity ratio, and the global redundancy level coefficient are obtained. The network resilience value is obtained according to the network resilience value evaluation model. The specific steps are as follows: Step S31: Calculate the shortest travel time for each node pair in the subway-emergency bus composite network that the passenger passes through again after the accident occurs, under the conditions of different emergency bus types. Step S32: Calculate the node connectivity ratio of the subway-emergency bus composite network when different emergency bus types are connected after the accident occurs; Step S33: Calculate the global redundancy level coefficient of the subway-emergency bus composite network when different emergency bus types are connected after the accident occurs; Step S34: Calculate the resilience value of the subway-emergency bus composite network when different emergency bus types are connected after the accident occurs.

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