Bus dynamic allocation and path planning method in multi-mode emergency evacuation

Abstract

The invention relates to the technical field of bus distribution and path planning, and discloses a bus dynamic distribution and path planning method in multi-mode emergency evacuation, comprising the following steps: S1, according to an urban multi-mode traffic network, emergency traffic demands and shelter distribution, constructing a multi-mode super weighted directed graph considering buses and cars; s2, according to the multi-mode super-weighted directed graph, establishing a multi-mode emergency evacuation-oriented bus dynamic allocation and path planning optimization model; and S3, calculating and generating a multi-mode dynamic traffic emergency evacuation scheme considering bus dynamic allocation and path planning optimization. According to the invention, the method can achieve the dynamic distribution and path planning of buses in multi-mode emergency evacuation, can help to improve the efficiency of emergency evacuation, reduces the loss of life and property caused by emergencies, can effectively describe the dynamic characteristics and interaction influence of a multi-mode emergency evacuation system, and also can improve the efficiency of emergency evacuation. And bus location distribution and route planning can be dynamically optimized.

Description

Technical Field

[0001] The present invention relates to the technical field of bus allocation and path planning, and in particular to a method for dynamic bus allocation and path planning in multi-mode emergency evacuation. Background Art

[0002] The research on optimization of transportation network emergency evacuation modeling can help improve the efficiency of emergency evacuation and reduce the losses caused by emergency events, especially for predictable emergency events such as hurricanes. The research results can help identify the transportation capacity of the transportation network, the location of bottlenecks, the interaction of evacuation systems, and calculate the utilization rate of the evacuation system and the shortest time required for evacuation, which can be used to guide the planning and actual operation of transportation network emergency evacuation.

[0003] Most previous studies only considered the car as an evacuation mode, and relevant scholars conducted an in-depth literature review (see Murray-Tuite P., Wolshon B., Evacuation transportation modeling: An overview of research, development, and practice, Transportation Research Part C, 2013). Considering the development trend of urban comprehensive transportation and the advantages of public transportation such as large capacity and high evacuation efficiency, some scholars have gradually begun to pay attention to multi-mode emergency evacuation, but most of the current multi-mode emergency evacuation research is based on a static transportation network, that is, it does not consider the traffic congestion effect. For example: Abdelgawad et al. studied multimodal emergency evacuation in a static transportation network considering four different objective functions (see Abdegawad H., Abdulhai B., Wahba M., Multi objective optimization for multimodal evacuation, Transportation Research Record, 2010); Abdelgawad and Abdulhai modeled large-scale emergency evacuation based on subways and buses as a variant of a mature vehicle routing problem, but did not consider the congestion effect (see Abdelgawad H., Abdulhai B., Large-Scale Evacuation Using Subway and Bus Transit: Approach and Application in City of Toronto, ASCE Journal of Transportation Engineering, 2012).In addition, there are also a few related studies based on dynamic traffic networks. For example, Naghawi and Wolshon used TRANSIMS to simulate and analyze the multimodal emergency evacuation in the New Orleans metropolitan area (see Naghawi H., Wolshon B., Performance of Traffic Networks during Multimodal Evacuations: Simulation-Based Assessment, Natural Hazards Review, 2012); Jeroen et al. developed a general method for multimodal emergency evacuation, which combines an activity-based household travel choice behavior model and a macro / meso-multimodal dynamic network loading model (see Gun J., Pel A., Bart B, An Activity-Based Multimodal Model Structure to assess Trans portation Management Strategies for Urban Emergencies, The 3rd International Conference on Evacuation Modeling and Management, 2015); Yang et al. proposed an innovative macro-dynamic multi-modal evacuation model based on the background of vehicle networking and the optimal theory of dynamic systems, but for the convenience of operation and the familiarity of evacuees, it is assumed that buses run on regular routes and their peak schedules (see Yang X., Ban J., Mitchell J., Modeling multi-modal transportation network evacuation considering users' cooperative behavior, Transportation Research Part A, 2018).

[0004] Previous studies on multimodal emergency evacuation have different assumptions on whether evacuees choose to evacuate, departure time, evacuation method, evacuation shelter selection, and bus scheduling. However, with the rapid development of autonomous driving and connected technology, communication technology between vehicles, vehicles and infrastructure, and vehicles and people will become more mature, which will help to achieve real-time perception, dynamic management, and system optimization of emergency systems in urban multimodal emergency evacuation. Considering that buses are different from rail transit and their operating routes are not restricted by fixed tracks, it is necessary to further study a method based on previous research that takes dynamic system optimization as the goal, considers multimodal interaction, and dynamically optimizes bus allocation and path planning, so as to further improve multimodal coordination and emergency evacuation efficiency, thereby reducing the losses caused by emergency events and providing guidance for emergency evacuation planning of transportation networks.

[0005] To this end, we propose a method for dynamic bus allocation and path planning in multi-modal emergency evacuation. Summary of the invention

[0006] The present invention mainly solves the technical problems existing in the above-mentioned prior art and provides a method for dynamic allocation and path planning of buses in multi-mode emergency evacuation.

[0007] In order to achieve the above object, the present invention adopts the following technical solution, a method for dynamic allocation and path planning of buses in multi-mode emergency evacuation, comprising the following steps:

[0008] S1: Based on the urban multimodal transportation network, emergency transportation needs and shelter distribution, a multimodal super weighted directed graph considering buses and cars is constructed;

[0009] S2: establishing a bus dynamic allocation and path planning optimization model for multi-modal emergency evacuation according to the multi-modal super weighted directed graph;

[0010] S3: Based on the marginal travel time of road sections and the Method of Successive Average (MSA), a multi-modal dynamic traffic emergency evacuation plan is calculated and generated considering the dynamic allocation of public transportation and path planning optimization.

[0011] As a preferred technical solution of the present invention, S1 comprises the following steps:

[0012] S101: Set a virtual starting point for each starting point j∈O Use a virtual directed edge (i, j)∈L with a weight of 0 O Connect the virtual starting point i and starting point j, where L O Represents a set of directed edges between virtual starting points; sets up a virtual super shelter Use a virtual directed edge with weight 0 Connect each shelter i∈S to the virtual super shelter Where L S is the set of directed edges connecting the shelters to the virtual super shelters;

[0013] S102: First, a weighted directed graph of the bus operation network is established. The bus station set is Where B is the set of bus departure terminals; the set of directed edges (i.e., the set of directed road segments) where the bus runs is defined as L b , and based on the historical running time of bus k on the directed edge Set the weight of the directed edge. When all buses are the same, have Next, a weighted directed graph of the car operation network is established based on the road network. The directed edge set of the car operation is defined as L a , the weight of the directed edge is the time-varying running time of the car, where time is the discretized time unit r∈[0,T].

[0014] As a preferred technical solution of the present invention, S2 comprises the following steps:

[0015] S201: Define decision variables At the virtual starting point The number of users who choose cars and buses, is the time unit r at the virtual starting point The number of all bus users waiting, p ij (r) and v ij (r) are the directed edges (i, j)∈L in time unit r a The inflow and outflow of cars on is the number of users on bus k when it travels from station i to station j in time unit r, is the number of users of bus k at station i in time unit r, a 0-1 decision variable Describes whether bus k goes from station i to station j in time unit r. If so, otherwise

[0016] S202: Taking minimizing the weighted system evacuation time (Weighted System Evacuation Time, WSET) as the optimization goal, the total evacuation time includes the total running time and waiting time at the starting point of car users and the total running time and waiting time at the starting point of bus users, that is,

[0017]

[0018] Among them, α is the average passenger capacity of cars, Δ is the length of the time unit, and w z is the weight of the waiting time of the evacuation zone z∈Z. Evacuation areas with different urgency have different waiting time weights. is the set of virtual starting points within the evacuation zone z, is the downstream queue length of car r on the directed edge (i, j) in time unit, is the total running time of all car users, is the total waiting time of all car users at the virtual starting point, Γ is the total running time of all bus users, is the overall waiting time for all bus users at the virtual starting point.

[0019] As a preferred technical solution of the present invention, the steps for calculating the total running time Γ of all bus users in S202 are as follows:

[0020] S2021: Definition C k is the maximum passenger capacity of bus k; ξ is the average number of users getting on or off the bus in one time unit; is the number of travel time units of the bus on the directed edge (i, j) predicted based on historical data, The study assumes that all bus routes have the same travel time. have For bus k on the directed edge (i, j)∈L b The number of extended running time units on the directed edge (i, j), that is, the number of running time units of the bus on the directed edge (i, j), C k The sum of the number of time units of a user getting on the bus at station i and the number of time units of a user getting off the bus at station j, if And j∈ but like And j∈S then in It is C k The number of time units per user getting on or off the bus at a station is calculated as follows: The study also assumes that all buses are full and boarding and alighting times are the same. have

[0021] S2022: Calculate Γ:

[0022]

[0023] Γ is the total bus user travel time based on the extended travel time, minus the extra boarding time at the starting point when the bus is not full, minus the extra alighting time at the terminal shelter when the bus is not full;

[0024] S203: Determine the constraints of the optimization model, including: starting point user number conservation constraint, initialization condition constraint, car flow conservation constraint, directed edge car flow dynamic evolution constraint, starting point bus user number conservation constraint, bus on-board user number conservation constraint, directed edge bus flow conservation constraint, shelter capacity constraint, and car flow and bus flow interaction constraint.

[0025] As a preferred technical solution of the present invention, the constraint conditions for determining the optimization model in S203 include:

[0026] S203A: Starting point user number conservation constraint: Each virtual starting point The total number of users who need to be evacuated D i Number of car users Number of bus users The sum, so we have:

[0027]

[0028] S203B: Initialization condition constraints: including the initial car queues on the directed edges, the initial inflow and outflow of vehicles, the initial number of users in the bus queue at the virtual starting point, the initial state of the bus flow, and the initial number of users on the bus. Therefore, we have:

[0029]

[0030]

[0031] in, and are respectively the upstream queue length and downstream queue length of the car on the directed edge (i, j) in time unit r; p ij (r) and v ij (r) are the inflow and outflow of cars on the directed edge (i, j) in time unit r, respectively; is the time unit r at the virtual starting point The number of users waiting for the bus; 0-1 parameter Describes whether bus k departs from the bus departure terminal i∈B. If so, otherwise 0-1 decision variable Describes whether bus k goes from station i to station j in time unit r. Constraint (4) indicates that (i, j)∈L o The initial upstream and downstream queue lengths of cars on the virtual directed edge are the car demand at the virtual starting point; constraint (5) indicates that (i, j)∈L a \L o The initial upstream and downstream queue lengths of cars on the directed edge are 0; constraint (6) indicates that the initial inflow and outflow of cars on the directed edge are constrained to be 0; constraint (7) indicates that at the initial moment at the virtual starting point The number of bus waiting users is the bus user demand at the virtual starting point; constraint formula (8) and constraint formula (9) represent the initial operation state of the bus flow; constraint formula (10) indicates that the initial number of users on the bus is 0;

[0032] S203C: Car flow conservation constraint:

[0033]

[0034] Among them, constraint (11) indicates that in time unit r, a virtual directed edge (i, j)∈L S The inflow and outflow of cars on the network are equal; constraint (12) represents the regular nodes on the car operation network The inflow of cars is equal to the outflow;

[0035] S203D: Constraints on the dynamic evolution of directed edge car flow:

[0036]

[0037] in, and are the number of car shock wave running time units and free flow running time units on the directed edge (i, j), respectively, which are the car shock wave running time and free flow running time The calculation formula is: is the upper limit of the outflow of cars on the directed edge (i, j); Q ij is the upper limit of the length of the upstream queue of cars on the directed edge (i, j); Constraints (13) and (14) describe the changes of the upstream queue and the downstream queue in the double-queue model (Double-Queue-Model) that describes the dynamic evolution of car flow on the directed edge; Constraint (15) limits the length of the directed edge (i, j)∈L at the end of the evacuation a The inflow of cars on the road; constraint (16) describes the virtual directed edge (i, j)∈L o The car inflow is 0; constraint (17) describes the directed edge (i, j)∈L a The upper limit of the outflow of cars; constraint (18) describes the directed edge (i, j)∈L a The lower limit of the upstream and downstream car flow queues and the upper limit of the upstream car flow queues;

[0038] S203E: Conservation constraint on the number of bus users at the starting point:

[0039]

[0040] in, is the number of users who board bus k at bus stop i in time unit r. Constraint (19) describes the dynamic change of the number of users queuing at bus stop i. Constraint (20) describes the upper limit constraint of the number of users who board bus k at bus stop i in time unit r.

[0041] S203F: Conservation constraint on the number of users on a bus:

[0042]

[0043] in, is the number of users on bus k in time unit r. Constraint (21) describes the dynamic change of the number of users on the bus. Constraint (22) describes the upper limit constraint of the number of users on the bus. Constraint (23) indicates that all users get off the bus after it arrives at the shelter station, that is, the number of users on the bus departing from the shelter station is 0.

[0044] S203G: Directed edge bus flow conservation constraints:

[0045]

[0046] S203H: Shelter capacity constraints:

[0047]

[0048] Among them, H i is the upper limit of the number of users that shelter i can accommodate;

[0049] S203I: Interaction constraints between car and bus traffic:

[0050]

[0051] in, is the upper limit of the car inflow on the directed edge (i, j), β k is the standard car conversion factor (Passenger Car Equivalency, PCE) for bus k, Indicates whether the directed edge (i, j) is on the shortest path between site i′ and site j′.

[0052] As a preferred technical solution of the present invention, S3 comprises the following steps:

[0053] S301: Initialize the multi-modal traffic emergency evacuation network, including road section flow and operation time;

[0054] S302: According to the emergency evacuation sequence, gradually establish the evacuation sub-network and use CPLEX to optimize the sub-problems;

[0055] S303: Based on the MSA method, update the network status and determine whether it has converged.

[0056] As a preferred technical solution of the present invention, when performing S301, the following steps are included:

[0057] S3011: Determine the emergency evacuation order according to the urgency of the emergency evacuation at the starting point, and set the iteration index to Ite=1;

[0058] S3012: Initialize the traffic on each directed edge of the multi-mode super weighted directed graph. First, direct the edge (i, j)∈L a The time-varying initial inflow and initial outflow are both defined as 0, that is, when Ite=1, p Ite-1 (r) = v Ite-1 (r) = 0, where the boldfaced r represents the set of time units, and p(r) and v(r) represent the directed edges (i, j)∈L in each time unit. a The set of car inflows and outflows on L; secondly, the directed edge (i, j)∈L b The bus flow is defined as 0, that is, σ(r) = 0, where σ(r) represents A collection of;

[0059] S3013: Initialize the weights (i.e., running time) of each directed edge of the multi-mode super-weighted directed graph. First, the directed edge (i, j)∈L a The initial number of running time units on is the number of free flow running time units Initial marginal runtime units Also the number of free flow running time units Secondly, based on the bus on each directed edge (i, j)∈L b Based on the historical running time data on L, calculate the time of bus k on each directed edge (i, j)∈L b The number of extended runtime units

[0060] As a preferred technical solution of the present invention, when performing S302, the following steps are included:

[0061] S3021: Based on the bus k on each directed edge (i, j ∈ L b The number of extended runtime units Use Dijkstra algorithm to calculate the bus stops at each station The shortest extended runtime path between

[0062] S3022: For virtual starting point Based on the directed edge (i, j)∈L a The average marginal running time of each time unit is calculated using the Dijkstra algorithm at the virtual starting point. With the Virtual Super Shelter The shortest marginal running time path between (see Yang X., Ban J., Mitchell J., Modeling multi-modal transportation network evacuation considering users' cooperative behavior, Transportation Research Part A, 2018; Shen W., Nie Y., Zhang M., On path marginal cost analysis and its relationship to dynamic system optimal traffic signment, Transportation and Traffic Theory, 2007);

[0063] S3023: To improve the solution efficiency, assume that the bus always leaves with full load, so that the overall evacuation time of bus users is At this time, the original optimization objective formula (1) can be transformed from mixed-integer non-linear programming (MINLP) to mixed-integer linear programming (MILP), as shown in formula (27). Construct sub-networks, including buses in and The shortest extended running time path between and The shortest marginal running time path between ;

[0064]

[0065] S3024: According to the emergency evacuation sequence, Optimize each sub-network in sequence and record the car on each directed edge (i, j)∈L a The time-varying inflow p Ite (r) Time-varying outflow v Ite (r), and the overall evacuation time of bus users Tran Ite , and use the traffic solution of the optimized sub-network problem as the background traffic of the next sub-network problem.

[0066] As a preferred technical solution of the present invention, when performing S303, the following steps are included:

[0067] S3031: Settings If Ite>1, update the solution:

[0068]

[0069] According to SET Ite =Auto Ite +Tran Ite Calculate the system's overall evacuation time SET Ite , where Auto Ite is the overall evacuation time of car users, and the calculation formula is as follows:

[0070]

[0071] Previous studies have shown that formula (31) is equivalent to the first two terms in formula (1) (see Ma R., Ban X., Pang J. S., Continuous-time dynamic system optimal for single-destination traffic networks with queue spillbacks, Transportation Research Part B, 2014), that is:

[0072]

[0073] S3032: Check p Ite (r) Whether the following convergence conditions are met: If so, the calculation is stopped; otherwise, Ite=Ite+1 is updated and the process returns to S302 for iteration.

[0074]

[0075] The present invention provides a method for dynamic allocation and path planning of buses in multi-mode emergency evacuation. It has the following beneficial effects:

[0076] 1. The method for dynamic allocation and path planning of buses in multi-mode emergency evacuation can realize dynamic allocation and path planning of buses in multi-mode emergency evacuation, which can help improve the efficiency of emergency evacuation and thus reduce the loss of life and property caused by emergencies.

[0077] 2. The dynamic allocation and route planning method of buses in multimodal emergency evacuation can not only effectively describe the dynamic characteristics and interactive effects of the multimodal emergency evacuation system, but also dynamically optimize the allocation and route planning of buses, thereby shortening the overall evacuation time of the system and improving the efficiency of emergency evacuation, so it can guide actual emergency evacuation. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] The structures, proportions, sizes, etc. illustrated in this specification are only used to match the contents disclosed in the specification for people familiar with this technology to understand and read, and are not used to limit the conditions under which the present invention can be implemented, so they have no substantial technical significance.

[0079] Figure 1 It is a flow chart of the bus dynamic allocation and path planning method in multi-mode emergency evacuation of the present invention;

[0080] Figure 2 It is a schematic diagram of the bus route section expansion travel time of the present invention.

[0081] Figure 3 This is a schematic diagram of the Nguyen-Dupuis network topology for traffic emergency evacuation of the present invention.

[0082] Figure 4 It is a schematic diagram of a multi-mode super directed network for traffic emergency evacuation of the present invention;

[0083] Figure 5 is the change in the difference of the weighted system overall evacuation time obtained by the two evacuation schemes under different evacuation demands of the present invention;

[0084] Figure 6 It is a parameter table diagram of directed edges in the multi-modal transportation emergency evacuation network of the present invention;

[0085] Figure 7 It is a table of operation time and weighted system total evacuation time (WSET) before and after linearization of the present invention. DETAILED DESCRIPTION

[0086] In the embodiment of the present invention, the two modes of transportation, cars and buses, are mainly considered. All given running time parameters, including all directed edge running times based on the car and bus operation network, evacuation waiting time, bus station boarding and alighting time, etc., are integer multiples of the discrete time step. In addition, all car-based flow variables, including inflow rate, outflow rate, upstream queue length and downstream queue length, are converted into standard car numbers. The evacuees follow the Dynamic System Optimum (DSO) principle in the selection of evacuation mode, departure time, evacuation route and shelter to minimize the weighted system total evacuation time (WSET) composed of the total running time of all evacuees on the network and the total waiting time at the departure point. It should be noted that only buses will return to the starting point to continue to pick up and drop off evacuees, while cars will not return.

[0087] See also Figure 1 The method for dynamic allocation and path planning of buses in multi-mode emergency evacuation according to an embodiment of the present invention comprises the following steps:

[0088] S1: Based on the urban multimodal transportation network, emergency transportation needs and shelter distribution, a multimodal super weighted directed graph considering buses and cars is constructed;

[0089] S2: Based on the multi-modal super-weighted directed graph, a bus dynamic allocation and path planning optimization model for multi-modal emergency evacuation is established;

[0090] S3: Based on the marginal travel time of road sections and the successive averaging method, a multi-modal dynamic traffic emergency evacuation plan is calculated and generated considering the dynamic allocation of public transportation and path planning optimization.

[0091] Through the above steps, firstly, a multi-mode super-weighted directed graph based on the car and bus operation network is established; secondly, a bus dynamic allocation and path planning optimization model is constructed based on the super-weighted directed graph, and the modeling is simplified by assuming that the bus always departs with a full load, so that the objective function is transformed from nonlinear to linear, and the original mixed integer nonlinear problem is transformed into a mixed integer linear problem, which provides a good framework for the subsequent optimization algorithm based on marginal travel time and successive averaging method, and finally obtains a traffic emergency evacuation plan for bus dynamic allocation and path planning optimization that considers the interaction of multiple modes, thereby shortening the emergency evacuation time of the transportation system, reducing the losses caused by emergency events, and providing guidance for emergency evacuation planning of urban transportation networks.

[0092] Embodiment 1:

[0093] In practical applications, based on the above steps, the bus dynamic allocation and path planning method in multi-mode emergency evacuation of the present invention can also be optimized according to the following steps:

[0094] S1: According to the urban multimodal transportation network, emergency transportation needs and shelter distribution, a multimodal super weighted directed graph considering buses and cars is constructed, including the following steps:

[0095] S101: Set a virtual starting point for each starting point j∈O Use a virtual directed edge (i, j)∈L with a weight of 0 O Connect the virtual starting point i and starting point j, where L O Represents a set of directed edges between virtual starting points; sets up a virtual super shelter Use a virtual directed edge with weight 0 Connect each shelter i∈S to the virtual super shelter Where L S It is the set of directed edges connecting the shelters to the virtual super shelters.

[0096] S102: First, a weighted directed graph of the bus operation network is established, and the bus station set is i∈ Where B is the set of bus departure terminals; the set of directed edges (i.e., the set of directed road segments) where the bus runs is defined as L b , and based on the historical running time of bus k on the directed edge Set the weight of the directed edge. When all buses are the same, have Next, a weighted directed graph of the car operation network is established based on the road network. The directed edge set of the car operation is defined as L a , the weight of the directed edge is the time-varying running time of the car, where time is the discretized time unit r∈[0,T].

[0097] S2: Based on the multi-modal super-weighted directed graph, a bus dynamic allocation and path planning optimization model for multi-modal emergency evacuation is established, including the following steps:

[0098] S201: Define decision variables At the virtual starting point The number of users who choose cars and buses, is the time unit r at the virtual starting point The number of all bus users waiting, p ij (r) and v ij (r) are the directed edges (i, j)∈L in time unit r a The inflow and outflow of cars on is the number of users on bus k when it travels from station i to station j in time unit r, is the number of users of bus k at station i in time unit r, a 0-1 decision variable Describes whether bus k goes from station i to station j in time unit r. If so, otherwise

[0099] S202: Taking minimizing the weighted system total evacuation time (WSET) as the optimization goal, including the total running time and waiting time at the starting point of car users and the total running time and waiting time at the starting point of bus users, that is,

[0100]

[0101] Among them, α is the average passenger capacity of a car, which can be estimated based on the type of car and the maximum number of people it can carry; Δ is the length of the time unit, which is generally 1 minute; w zis the weight of the waiting time of the evacuation area z∈Z. Evacuation areas with different urgency have different waiting time weights. The higher the urgency, the smaller the weight. The waiting time weight is generally set to 1-2. is the set of virtual starting points within the evacuation zone z, is the downstream queue length of car r on directed edge (i, j) in time unit r. is the total running time of all car users, is the total waiting time of all car users at the virtual starting point, Γ is the total running time of all bus users, is the overall waiting time for all bus users at the virtual starting point.

[0102] In order to calculate the total running time Γ of all bus users, the following steps are specifically included:

[0103] S2021: Definition C k is the maximum passenger capacity of bus k; ξ is the average number of users getting on or off the bus in one time unit; is the number of travel time units of the bus on the directed edge (i, j) predicted based on historical data, If all buses are the same, have For bus k on the directed edge (i, j)∈L b The number of extended running time units on the directed edge (i, j), that is, the number of running time units of the bus on the directed edge (i, j), C k The sum of the number of time units of a user getting on the bus at station i and the number of time units of a user getting off the bus at station j. and but like Figure 2 (a) as shown; if And j∈S then like Figure 2 (b). It is C k The number of time units per user getting on or off the bus at a station is calculated as follows: If all buses are the same, have

[0104] Maximum passenger capacity of bus C kIt can be estimated based on the formula "passenger seats (capacity) number = number of fixed passenger seats in the car + effective standing area in the car (square meters) × number of people allowed to stand per square meter". According to my country's standards, urban buses are approved to carry 0.125 square meters of passengers per person, that is, 8 people are allowed to stand per square meter. In general, the bus boarding and alighting speed can be set at 20 people per minute, and the average number of users getting on or off the bus in a time unit ξ can be converted according to the length of the time unit Δ. Unlike the time-varying running time of cars on directed edges that changes with traffic, the running time of buses on directed edges can be considered to be calculated according to a fixed schedule, that is, by assuming that the bus driver adjusts and maintains the original bus route running time by rushing on the path (i, j) and / or waiting at station j, which is expressed here as the number of bus travel time units. is a constant; it should be noted that this assumption may only apply to evacuations without severe congestion in foreseeable events such as hurricanes or floods; this assumption may not apply to unpredictable emergency evacuations such as earthquakes and terrorist attacks, and when severe congestion prevents buses from running on schedule.

[0105] S2022: Calculate Γ:

[0106]

[0107] Γ is the total bus user travel time based on the extended travel time, minus the extra boarding time at the starting point when the bus is not full, and minus the extra alighting time at the terminal shelter when the bus is not full.

[0108] S203: Determine the constraints of the optimization model, including: starting point user number conservation constraint, initialization condition constraint, car flow conservation constraint, directed edge car flow dynamic evolution constraint, starting point bus user number conservation constraint, bus on-board user number conservation constraint, directed edge bus flow conservation constraint, shelter capacity constraint, and car flow and bus flow interaction constraint.

[0109] Determining the constraints of the optimization model includes the following steps:

[0110] S203A: Starting point user number conservation constraint:

[0111]

[0112] Each virtual starting point The total number of users who need to be evacuated D i Number of car users Number of bus users When conducting numerical experiments, it is necessary to give the total number of users that need to be evacuated at each virtual starting point i, and at the same time set the number of car users and bus users at each virtual starting point i.

[0113] S203B: Initialization condition constraints: including the initial car queues on the directed edges, the initial inflow and outflow of vehicles, the initial number of users in the bus queue at the virtual starting point, the initial state of the bus flow, and the initial number of users on the bus. Therefore, we have:

[0114]

[0115] in, and are respectively the upstream queue length and downstream queue length of the car on the directed edge (i, j) in time unit r; p ij (r) and v ij (r) are the inflow and outflow of cars on the directed edge (i, j) in time unit r, respectively; is the time unit r at the virtual starting point The number of users waiting for the bus; 0-1 parameter Describes whether bus k departs from the bus departure terminal i∈B. If so, otherwise 0-1 decision variable Describes whether bus k goes from station i to station j in time unit r. Constraint (4) indicates that (i, j)∈L o The initial upstream and downstream queue lengths of cars on the virtual directed edge are the car demand at the virtual starting point; constraint (5) indicates that (i, j)∈L a \L o The initial upstream and downstream queue lengths of cars on the directed edge are 0; constraint (6) indicates that the initial inflow and outflow of cars on the directed edge are constrained to be 0; constraint (7) indicates that at the initial moment at the virtual starting point The number of bus waiting users is the bus user demand at the virtual starting point; Constraints (8) and (9) represent the initial operation state of the bus flow. Constraint (8) initializes the distribution of buses at the bus departure terminal, and constraint (9) ensures that after departing from the bus departure terminal, they will no longer return to the bus terminal; Constraint (10) indicates that the initial number of users on the bus is 0.

[0116] S203C: Car flow conservation constraint:

[0117]

[0118] Among them, constraint (11) indicates that in time unit r, a virtual directed edge (i, j)∈L S The inflow and outflow of cars on the network are equal; constraint (12) represents the regular nodes on the car operation network The inflow of cars is equal to the outflow of cars.

[0119] S203D: Constraints on the dynamic evolution of directed edge car flow:

[0120]

[0121] in, and are the number of car shock wave running time units and free flow running time units on the directed edge (i, j), respectively, which are the car shock wave running time and free flow running time The calculation formula is: is the upper limit of the outflow of cars on the directed edge (i, j); Q ij is the upper limit of the length of the upstream queue of cars on the directed edge (i, j). Constraints (13) and (14) describe the changes in the upstream and downstream queues in the double-queue model (Double-Queue-Model) that describes the dynamic evolution of car flow on the directed edge, and can capture congestion effects such as queue overflow; Constraint (15) limits the length of the directed edge (i, j)∈L at the end of the evacuation. a The inflow of cars on the road; constraint (16) describes the virtual directed edge (i, j)∈L o The car inflow is 0; constraint (17) describes the directed edge (i, j)∈L a The upper limit of the outflow of cars; constraint (18) describes the directed edge (i, j)∈L a The lower limit of the upstream and downstream car flow queues and the upper limit of the upstream car flow queues.

[0122] The three variables involved in this constraint, namely, the car-based directed edge free flow running time, the directed edge shock wave running time, and the directed edge queuing capacity, need to be given according to the actual operation of cars in the traffic network when constructing the multi-modal super weighted directed graph.

[0123] S203E: Conservation constraint on the number of bus users at the starting point:

[0124]

[0125] in, is the number of users who board bus k at bus stop i in time unit r. Constraint (19) describes the dynamic change of the number of users queuing at bus stop i; constraint (20) describes the upper limit constraint of the number of users who board bus k at bus stop i in time unit r. hour, is a positive value, that is, only when bus k stays at the virtual origin i at the time interval r, can the evacuees board bus k at the virtual origin i at the time interval r.

[0126] S203F: Conservation constraint on the number of users on a bus:

[0127]

[0128]

[0129] in, is the number of users on bus k in time unit r. Constraint (21) describes the dynamic change of the number of users on the bus; Constraint (22) describes the upper limit constraint of the number of users on the bus; Constraint (23) indicates that all users get off the bus after it arrives at the shelter station, that is, the number of users on the bus departing from the shelter station is 0.

[0130] S203G: Directed edge bus flow conservation constraints:

[0131]

[0132] Formula (24) ensures that bus k can go to one and only one node j downstream if and only if bus k departs from a node i within the time interval r and at the same time In the example, bus k can only come from an upstream node i, thus ensuring the conservation of bus flow on the directed edge.

[0133] S203H: Shelter capacity constraints:

[0134]

[0135] Among them, H i is the upper limit of the number of users that shelter i can accommodate. In real life, the capacity of shelters is generally predetermined. Considering the capacity of shelters in the evacuation model helps to avoid underestimating the overall evacuation time of the weighted system.

[0136] S203I: Interaction constraints between car and bus traffic:

[0137]

[0138] in, is the upper limit of the car inflow on the directed edge (i, j). When constructing a multi-modal super-weighted directed graph, it is given according to the actual operation of cars in the traffic network; β k is the standard car conversion factor for bus k, which can be set according to actual conditions; Indicates whether the directed edge (i, j) is on the shortest path between station i′ and station j′. Formula (26) captures the interaction between car traffic and bus traffic through demand constraints, directed edge vehicle inflow capacity constraints, and shelter capacity constraints. In order to describe the congestion effect caused by buses, bus traffic is regarded as background traffic on shared roads, and the concept of standard car conversion coefficient is used to simulate the congestion effect caused by bus traffic. Therefore, subtracting bus traffic from the inflow capacity limits the car inflow of each connecting road.

[0139] S3: Based on the marginal travel time of the road section and the method of successive average (MSA), a multi-mode dynamic traffic emergency evacuation plan considering the dynamic allocation of public transportation and the optimization of path planning is calculated and generated, including the following steps:

[0140] S301: Initialize the multi-modal traffic emergency evacuation network, including road section flow and operation time.

[0141] When performing step S301, the flow and weight of each directed edge are initialized according to the actual situation of the city operation network. The detailed steps are as follows:

[0142] S3011: Determine the emergency evacuation order according to the urgency of the emergency evacuation at the starting point, and set the iteration index to Ite=1;

[0143] S3012: Initialize the traffic on each directed edge of the multi-mode super weighted directed graph. First, set the directed edge (i, j)∈L a The time-varying initial inflow and initial outflow are both defined as 0, that is, when Ite=1, p Ite-1 (r) = v Ite-1 (r) = 0, where the boldfaced r represents the set of time units, and p(r) and v(r) represent the directed edges (i, j)∈L in each time unit. a The set of car inflows and outflows on L. b The bus flow is defined as 0, that is, σ(r) = 0, where σ(r) represents A collection of .

[0144] S3013: Initialize the weights (i.e., running time) of each directed edge of the multi-mode super-weighted directed graph. First, the directed edge (i, j)∈L a The initial number of running time units on is the number of free flow running time units Initial marginal runtime units Also the number of free flow running time units Secondly, based on the bus on each directed edge (i, j)∈L bBased on the historical running time data on the L, the bus k is calculated according to the method described in S202A on each directed edge (i, j)∈L b The number of extended runtime units

[0145] S302: According to the emergency evacuation sequence, gradually establish the evacuation subnetwork and use CPLEX to optimize the subproblems.

[0146] When performing step S302, the shortest path is calculated according to the running time of the bus and the car on the directed edge of the corresponding network, the overall evacuation time of the bus users is calculated and a sub-network is constructed, and finally the sub-network is sequentially optimized according to the emergency evacuation sequence. The specific steps are as follows:

[0147] S3021: Based on the bus k on each directed edge (i, j ∈ L b The number of extended runtime units Use Dijkstra algorithm to calculate the bus stops at each station The shortest extended runtime path between .

[0148] S3022: For virtual starting point Based on the directed edge (i, j)∈L a The average marginal running time of each time unit is calculated using the Dijkstra algorithm at the virtual starting point. With the Virtual Super Shelter The shortest marginal runtime path between (see Yang X., Ban J., Mitchell J., Modeling multi-modal transportation network evacuation considering users' cooperative behavior, Transportation Research Part A, 2018; Shen W., Nie Y., Zhang M., On path marginal cost analysis and its relationship to dynamic system optimal traffic signment, Transportation and Traffic Theory, 2007).

[0149] S3023: To improve the solution efficiency, assume that the bus always leaves with full load. The total running time of all bus users is given by the first term in equation (2): It means that there is no need to deduct the extra boarding time at the starting point and the extra getting off time at the destination when the bus is not full. According to the total waiting time of all bus users at the virtual starting point represented by the fourth term in formula (1) and the total running time of all bus users in the case of full departure represented by the first term in formula (2), the total evacuation time of bus users is obtained as At this time, the original optimization objective formula (1) can be transformed from mixed-integer non-linear programming (MINLP) to mixed-integer linear programming (MILP), as shown in formula (27). Construct sub-networks, including buses in and The shortest extended running time path between and The shortest marginal running time path between .

[0150]

[0151] S3024: According to the emergency evacuation sequence, Optimize each sub-network in sequence and record the car on each directed edge (i, j)∈L a The time-varying inflow p Ite (r) Time-varying outflow v Ite (r), and the overall evacuation time of bus users Tran Ite , and use the traffic solution of the optimized sub-network problem as the background traffic of the next sub-network problem.

[0152] S303: Based on the MSA method, update the network status and determine whether it has converged.

[0153] When performing step S303, the solution result is updated according to the recorded time-varying inflow and outflow of cars on each directed edge, the overall evacuation time of the system is calculated, and it is determined whether the updated time-varying inflow of cars meets the convergence condition. The specific steps are as follows:

[0154] S3031: Settings If Ite>1, update the solution:

[0155]

[0156] According to SET Ite =Auto Ite +Tran Ite Calculate the system's overall evacuation time SET Ite, where Auto Ite is the overall evacuation time of car users, and the calculation formula is as follows:

[0157]

[0158] Previous studies have shown that formula (31) is equivalent to the first two terms in formula (1) (see Ma R., Ban X., Pang J. S., Continuous-time dynamic system optimal for single-destination traffic networks with queue spillbacks, Transportation Research Part B, 2014), that is:

[0159]

[0160] S3032: Check p Ite (r) Whether the following convergence conditions are met: If so, the calculation is stopped; otherwise, Ite=Ite+1 is updated and the process returns to S302 for iteration.

[0161]

[0162] In the above optimization steps, based on the marginal travel time of the road segment and the successive averaging method, each iteration will generate a new car on each directed edge (i, j)∈L a The time-varying inflow p Ite (r) and the time-varying outflow v Ite (r), according to the time-varying inflow The overall evacuation time of car users is calculated to obtain the overall evacuation time of the system. Through continuous iteration, the time-varying outflow before and after the iteration is Keep approaching until its change reaches the algorithm termination condition. The calculated weighted system overall evacuation time SET Ite The smallest solution is the optimal multi-modal dynamic traffic emergency evacuation plan under given set conditions.

[0163] The method of Example 1 is specifically analyzed with actual data below:

[0164] Embodiment 2:

[0165] The method for dynamic allocation and path planning of buses in multi-mode emergency evacuation according to an embodiment of the present invention comprises the following steps:

[0166] S1: Based on the city’s multimodal transportation network, emergency transportation needs, and shelter distribution (e.g. Figure 3 As shown in Figure 2), we construct weighted directed graphs for bus and car operation networks respectively. Figure 4 Specifically, in this embodiment, the multimodal evacuation network considered includes 1 bus departure terminal (node ​​15), 2 evacuation starting points (node ​​1 and node 2), and 2 shelters (node ​​11 and node 13). Set a virtual starting point for each starting point (node ​​16 and node 17), and use a virtual directed edge (i, j) ∈ {(16, 1), (17, 2)} with a weight of 0 to connect the virtual starting point i and the starting point j; set a virtual super shelter (node ​​14), and use a virtual directed edge with a weight of 0 Connect each shelter i∈{11,13}=S to the virtual super shelter Based on the historical running time of bus k on the directed edge Set the weight of the bus running directed edge; based on the free flow running time of cars Set the weight of the directed edge of the car operation. Specifically in this embodiment, the parameters required by the evacuation system include the free flow running time, shock wave running time, directed edge inflow capacity, directed edge queuing capacity based on the car, and the directed edge running time based on the bus, such as Figure 6 shown.

[0167] exist Figure 4 In the figure, all blue solid lines and green solid lines are car-based road links; all orange dashed lines are bus-based links, representing the shortest path between two connected nodes. Bus routes can be either bus-only routes or roads shared with cars. For example, the bus driving directed edge (16, 13) represents the shortest path of the bus between nodes 1 and 13, which is composed of directed edges (16, 1), (1, 8), (8, 12), and (12, 13). The green links represent sharing with cars. In order to consider the interaction or congestion effect between them, the bus vehicle flow on the link (16, 13) is regarded as the car background flow on directed edges (16, 1), (1, 8), (8, 12), and (12, 13), as shown in formula (26).

[0168] S2: Based on the above multi-mode super weighted directed graph, define the bus dynamic allocation and path planning optimization decision variables, objective functions and constraints, and build a bus dynamic allocation and path planning optimization model for multi-mode emergency evacuation. Specifically in this embodiment, it is assumed that the capacity of the buses is the same, so the waiting time and extended operation time of each bus are the same.

[0169] This example assumes that the maximum passenger capacity of the bus is C k =40, time unit Δ = 1, the average number of users getting on or off the bus in one time unit is ξ = 20, C kThe number of time units for a user to get on or off a bus at a station is When not specified in the experiment, the number of available buses for evacuation is |K|=10, and the above parameters can be set according to actual conditions.

[0170] The congestion effect between car traffic and bus traffic is demonstrated through experimental design. The demand D2 of evacuation point 2 is set to 0, and the waiting time weight w1 is set to 1.5. The changes in the weighted system overall evacuation time calculated under the two evacuation schemes are analyzed when the demand D1 of evacuation point 1 changes from 1000 to 6000. The two evacuation schemes include: (1) all buses are on the dedicated road, and (2) the bus routes between nodes 16 and 11 and between nodes 16 and 13 (there are only these two routes because the demand at evacuation point 2 is 0) are shared by cars and buses, that is, the bus traffic on the directed edges (1, 4)-(4, 5)-(5, 6)-(6, 7)-(7, 11) and the directed edges (1, 8)-(8, 12)-(12, 13) will be used as background traffic.

[0171] Substituting all the relevant parameter values ​​determined above into the objective function formula (1) and constraint formulas (3) to (26) in Example 1 can determine the bus dynamic allocation and path planning optimization model corresponding to this embodiment.

[0172] S3: Based on the above generated model and the marginal travel time of the road section and the successive average method design algorithm, a multi-mode dynamic traffic emergency evacuation plan considering the dynamic allocation of public transportation and the optimization of path planning is calculated and generated. The calculation steps are as follows:

[0173] S301: Determine the emergency evacuation order according to the urgency of the emergency evacuation at the starting point, and initialize the flow and weight of each directed edge based on the actual situation of the operation network. a The time-varying initial inflow and initial outflow are both defined as 0, and the initial running time unit is the free flow running time unit. Initial marginal runtime units Also the number of free flow running time units On the bus operation network, there is a directed edge (i, j)∈L b The traffic is defined as 0, and the weight is the number of extended running time units.

[0174] S302: Using Dijkstra algorithm, based on bus k on each directed edge (i, j)∈L b The number of extended runtime units Calculate the number of buses at each stop The shortest extended runtime path between the two, based on the car on the directed edge (i, j)∈La The average marginal running time of each time unit is calculated by With the Virtual Super Shelter The shortest marginal running time path between . Assuming the bus is fully loaded, the conversion optimization goal is Construct an evacuation subnetwork and use CPLEX to optimize the subproblems step by step according to the emergency evacuation sequence, recording the cars on each directed edge (i, j)∈L a The time-varying inflow p Ite (r) Time-varying outflow v Ite (r), and the overall evacuation time of bus users Tran Ite , and use the traffic solution of the optimized sub-network problem as the background traffic of the next sub-network problem.

[0175] S303: The iteration sequence based on the marginal travel time of the road section and the successive averaging method is continuously optimized, and the network state is updated according to the recorded time-varying inflow and time-varying outflow of cars on each directed edge, until the time-varying inflow of cars meets the convergence condition and the optimal solution is found.

[0176] The weighted system total evacuation time calculated under the two evacuation schemes is defined as WSET 专用 、WSET 共享 According to the above steps, the calculation results are as follows Figure 5 The results show that the proposed model can capture the congestion effect caused by bus flow to a certain extent, and the WSET-weighted system evacuation time value generated when buses and cars share the road is always higher than the WSET-weighted system evacuation time value generated when the bus station operates on a bus-only network.

[0177] The following is a specific analysis of the calculation time before and after the optimization objective linearization and the weighted system total evacuation time (WSET) for the multi-mode super weighted directed graph constructed in Implementation Case 2:

[0178] Embodiment 3:

[0179] against Figure 4 Experimental design was conducted. In the following numerical analysis, the waiting time weights of the two evacuation zones were set as w1 = 1.1 and w2 = 1, respectively, and the upper limits of the number of users that the two shelters can accommodate were H 11 =6000, H 13 = 2000, the total number of users D1, D2 and the total number of buses |K| that need to be evacuated at the virtual starting point are changed in the test. The comparative analysis results are shown in Figure 7 shown.

[0180] from Figure 7It can be seen that: (1) When using the proposed MINLP model, by comparing test 1, test 2 and test 3, it can be seen that the operation time of the model increases sharply with the increase of demand; by comparing test 4, 5, 6 and test 1, 2, 3 respectively, it can be seen that the operation time of the model increases sharply with the increase of the number of available buses |K| (resulting in an increase in binary variables). (2) When using the MILP model after the optimization objective is linearized, it can be seen from the saved operation time of the six tests that the linearization technique helps to greatly reduce the calculation time. (3) The difference in the weighted system total evacuation time (WSET) calculated using the MINLP model and the MILP model is negligible, especially when the demand is large. When the demand is small and evacuation using cars is more efficient, the WSET may be overestimated.

[0181] In summary, the computational time of the studied evacuation problem depends largely on the number of variables in the established model. An increase in the network size, demand, evacuation time, or number of buses will lead to an increase in the number of variables, which in turn leads to a sharp increase in computational time. Therefore, reasonable linearization techniques can greatly reduce the computational difficulty while maintaining highly reliable performance.

[0182] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited by the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements all fall within the scope of the present invention to be protected.

Claims

1. A method for dynamic bus allocation and path planning in multi-mode emergency evacuation, characterized in that: The following steps are involved: S1: Based on the urban multimodal transportation network, emergency transportation needs and shelter distribution, a multimodal super weighted directed graph considering buses and cars is constructed; S2: establishing a bus dynamic allocation and path planning optimization model for multi-modal emergency evacuation according to the multi-modal super weighted directed graph; S3: Based on the marginal travel time of road sections and the successive averaging method, a multi-modal dynamic traffic emergency evacuation plan is calculated and generated considering the dynamic allocation of public transportation and path planning optimization.

2. The method for dynamic bus allocation and path planning in multi-mode emergency evacuation according to claim 1, characterized in that: The S1 comprises the following steps: S101: Set a virtual starting point for each starting point j∈O Use a virtual directed edge (i, j)∈L with a weight of 0 O Connect the virtual starting point i and starting point j, where L O Represents a set of directed edges between virtual starting points and starting points; sets up a virtual super shelter Use a virtual directed edge with weight 0 Connect each shelter i∈S to the virtual super shelter Where L S is the set of directed edges connecting the shelters to the virtual super shelters; S102: First, a weighted directed graph of the bus operation network is established. The bus station set is Where B is the set of bus departure terminals; the set of directed edges (i.e., the set of directed road segments) where the bus runs is defined as L b , and based on the historical running time of bus k on the directed edge Set the weight of the directed edge. When all buses are the same, have Next, a weighted directed graph of the car operation network is established based on the road network. The directed edge set of the car operation is defined as L a , the weight of the directed edge is the time-varying running time of the car, where time is the discretized time unit r∈[0,T].

3. The method for dynamic bus allocation and path planning in multi-mode emergency evacuation according to claim 1, characterized in that: The S2 comprises the following steps: S201: Define decision variables At the virtual starting point The number of users who choose cars and buses, is the time unit r at the virtual starting point The number of all bus users waiting, p ij (r and v ij (r) are the directed edges (i,j∈L in time unit r a The inflow and outflow of cars on is the number of users on bus k when it travels from station i to station j in time unit r, is the number of users of bus k at station i in time unit r, a 0-1 decision variable Describes whether bus k goes from station i to station j in time unit r. If so, otherwise S202: Taking minimizing the weighted system overall evacuation time as the optimization goal, the overall evacuation time includes the overall running time and waiting time at the starting point of car users and the overall running time and waiting time at the starting point of bus users, that is, Among them, α is the average passenger capacity of cars, Δ is the length of the time unit, and w z is the weight of the waiting time of the evacuation zone z∈Z. Evacuation areas with different urgency have different waiting time weights. is the set of virtual starting points within the evacuation zone z, is the downstream queue length of car r on the directed edge (i,j) in time unit, is the total running time of all car users, is the total waiting time of all car users at the virtual starting point, Γ is the total running time of all bus users, is the overall waiting time for all bus users at the virtual starting point.

4. The method for dynamic bus allocation and path planning in multi-mode emergency evacuation according to claim 3, characterized in that: The steps for calculating the total running time Γ of all bus users in S202 are as follows: S2021: Definition C k is the maximum passenger capacity of bus k; ξ is the average number of users getting on or off the bus in one time unit; is the number of travel time units of the bus on the directed edge (i, j) predicted based on historical data, The study assumes that all bus routes have the same travel time. have For bus k on the directed edge (i,j)∈L b The number of extended running time units on the directed edge (i, j), that is, the number of running time units of the bus on the directed edge (i, j), C k is the sum of the time units of the user getting on the bus at station i and the time units of the user getting off the bus at station j. And j∈ but like And j∈S then in It is C k The number of time units per user getting on or off the bus at a station is calculated as follows: The study also assumes that all buses are full and boarding and alighting times are the same. have S2022: Calculate Γ: Γ is the total bus user travel time based on the extended travel time, minus the extra boarding time at the starting point when the bus is not full, minus the extra alighting time at the terminal shelter when the bus is not full; S203: Determine the constraints of the optimization model, including: starting point user number conservation constraint, initialization condition constraint, car flow conservation constraint, directed edge car flow dynamic evolution constraint, starting point bus user number conservation constraint, bus on-board user number conservation constraint, directed edge bus flow conservation constraint, shelter capacity constraint, and car flow and bus flow interaction constraint.

5. The method for dynamic bus allocation and path planning in multi-mode emergency evacuation according to claim 4, characterized in that: The constraint conditions for determining the optimization model in S203 include: S203A: Starting point user number conservation constraint: Each virtual starting point The total number of users who need to be evacuated D i Number of car users Number of bus users The sum, so we have: S203B: Initialization condition constraints: including the initial car queues on the directed edges, the initial inflow and outflow of vehicles, the initial number of users in the bus queue at the virtual starting point, the initial state of the bus flow, and the initial number of users on the bus. Therefore, we have: in, and are the upstream queue length and downstream queue length of cars on the directed edge (i, j) in time unit r, respectively; p ij (r) and v ij (r) are the inflow and outflow of cars on the directed edge (i, j) at time unit r, respectively; is the time unit r at the virtual starting point The number of users waiting for the bus; 0-1 parameter Describes whether bus k departs from the bus departure terminal i∈B. If so, otherwise 0-1 decision variable Describes whether bus k goes from station i to station j in time unit r. Constraint (4) indicates that (i, j)∈L o The initial upstream and downstream queue lengths of cars on the virtual directed edge are the car demand at the virtual starting point; constraint (5) indicates that (i, j)∈L a \L o The initial upstream and downstream queue lengths of cars on the directed edge are 0; constraint (6) indicates that the initial inflow and outflow of cars on the directed edge are constrained to be 0; constraint (7) indicates that at the initial moment at the virtual starting point The number of bus waiting users is the bus user demand at the virtual starting point; constraint formula (8) and constraint formula (9) represent the initial operation state of the bus flow; constraint formula (10) indicates that the initial number of users on the bus is 0; S203C: Car flow conservation constraint: Among them, constraint (11) indicates that in time unit r, a virtual directed edge (i, j)∈L S The inflow and outflow of cars on the network are equal; constraint (12) represents the regular nodes on the car operation network The inflow of cars is equal to the outflow; S203D: Constraints on the dynamic evolution of directed edge car flow: in, and are the number of car shock wave running time units and free flow running time units on the directed edge (i, j), respectively, which are the car shock wave running time and free flow running time The calculation formula is: is the upper limit of the outflow of cars on the directed edge (i, j); Q ij is the upper limit of the length of the upstream queue of cars on the directed edge (i, j); Constraints (13) and (14) describe the changes of the upstream queue and the downstream queue in the double-queue model (Double-Queue-Model) that describes the dynamic evolution of car flow on the directed edge; Constraint (15) limits the length of the directed edge (i, j)∈L at the end of the evacuation a The inflow of cars on the road; constraint (16) describes the virtual directed edge i, j)∈L o The car inflow is 0; constraint (17) describes the directed edge (i, j)∈L a The upper limit of the outflow of cars; constraint (18) describes the directed edge (i, j)∈L a The lower limit of the upstream and downstream car flow queues and the upper limit of the upstream car flow queues; S203E: Conservation constraint on the number of bus users at the starting point: in, is the number of users who board bus k at bus stop i in time unit r. Constraint (19) describes the dynamic change of the number of users queuing at bus stop i. Constraint (20) describes the upper limit constraint of the number of users who board bus k at bus stop i in time unit r. S203F: Conservation constraint on the number of users on a bus: in, is the number of users on bus k in time unit r. Constraint (21) describes the dynamic change of the number of users on the bus. Constraint (22) describes the upper limit constraint of the number of users on the bus. Constraint (23) indicates that all users get off the bus after it arrives at the shelter station, that is, the number of users on the bus departing from the shelter station is 0. S203G: Directed edge bus flow conservation constraints: S203H: Shelter capacity constraints: Among them, H i is the upper limit of the number of users that shelter i can accommodate; S203I: Interaction constraints between car and bus traffic: in, is the upper limit of the car inflow on the directed edge (i, j), β k is the standard car conversion factor for bus k, Indicates whether the directed edge (i, j) is on the shortest path between site i' and site j'.

6. The method for dynamic bus allocation and path planning in multi-mode emergency evacuation according to claim 1, characterized in that: The S3 comprises the following steps: S301: Initialize the multi-modal traffic emergency evacuation network, including road section flow and operation time; S302: According to the emergency evacuation sequence, gradually establish the evacuation sub-network and use CPLEX to optimize the sub-problems; S303: Based on the MSA method, update the network status and determine whether it has converged.

7. The method for dynamic bus allocation and path planning in multi-mode emergency evacuation according to claim 6, characterized in that: When performing S301, the following steps are included: S3011: Determine the emergency evacuation order according to the urgency of the emergency evacuation at the starting point, and set the iteration index to Ite=1; S3012: Initialize the traffic on each directed edge of the multi-mode super weighted directed graph. First, set the directed edge (i, j)∈L a The time-varying initial inflow and initial outflow are both defined as 0, that is, when Ite=1, p Ite-1 (r) = v Ite-1 (r) = 0, where the boldface r represents the set of time units, and p(r) and v(r) represent the directed edges (i, j)∈L in each time unit. a The set of car inflows and outflows on L; secondly, the directed edge (i, j)∈L b The bus flow is defined as 0, that is, σ(r) = 0, where σ(r) represents A collection of; S3013: Initialize the weights (i.e., running time) of each directed edge of the multi-mode super-weighted directed graph. First, the directed edge (i, j)∈L a The initial number of running time units on is the number of free flow running time units Initial marginal runtime units Also the number of free flow running time units Secondly, based on the bus on each directed edge (i,j)∈L b The historical running time data on the bus is used to calculate the time of bus k on each directed edge (i, j)∈L b The number of extended runtime units 8. The method for dynamic bus allocation and path planning in multi-mode emergency evacuation according to claim 7, characterized in that: When performing S302, the following steps are included: S3021: Based on bus k on each directed edge (i, j ∈ L b The number of extended runtime units Use Dijkstra algorithm to calculate the bus stops at each station The shortest extended runtime path between S3022: For virtual starting point Based on the directed edge (i,j)∈L a The average marginal running time of each time unit is calculated using the Dijkstra algorithm at the virtual starting point. With the Virtual Super Shelter The shortest marginal running time path between ; S3023: To improve the solution efficiency, assume that the bus always leaves with full load, so the overall evacuation time of bus users is At this time, the original optimization objective formula (1) can be transformed from mixed integer nonlinear programming to mixed integer linear programming, as shown in formula (27). Construct sub-networks, including buses in and The shortest extended runtime path between and The shortest marginal running time path between ; S3024: According to the emergency evacuation sequence, Optimize each sub-network in sequence and record the car on each directed edge (i, j)∈L a The time-varying inflow p Ite (r) Time-varying outflow v Ite (r), and the overall evacuation time of bus users Tran Ite , and use the traffic solution of the optimized sub-network problem as the background traffic of the next sub-network problem.

9. The method for dynamic bus allocation and path planning in multi-mode emergency evacuation according to claim 1, characterized in that: When performing S303, the following steps are included: S3031: Settings If Ite>1, update the solution: According to SET Ite =Auto Ite +Tran Ite Calculate the system's overall evacuation time SET Ite , where Auto Ite is the overall evacuation time of car users, and the calculation formula is as follows: Previous studies have shown that formula (31) is equivalent to the first two terms in formula (1), namely: S3032: Check p Ite (r) Whether the following convergence conditions are met, if so, stop the calculation, otherwise update Ite=Ite+1 and return to S302 for iteration,

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