A method for jointly adjusting a timetable and a running route for flexible marshalling

Abstract

The application is based on the dynamic travel demand of passengers, establishes a timetable and running route joint optimization adjustment model for flexible marshalling, and further obtains effective operation adjustment strategy based on model predictive control (MPC) algorithm. The coupling relationship between train departure and parking, route operation, train unmarshalling state and passenger volume is comprehensively considered, and a timetable adjustment and running route adjustment model for flexible marshalling is established. Based on the MPC algorithm, a joint adjustment model solving algorithm for the timetable and running route for flexible marshalling is designed, the optimization problem is converted into an optimal control problem, the optimization problem is solved in each control period to determine the optimal control strategy, the goal of minimizing the passenger retention is achieved, and an effective operation adjustment strategy is obtained. Compared with the traditional train operation method of route operation, the application effectively reduces the passenger retention at each station, and has wide research and application value.

Description

Technical Field

[0001] The present invention relates to the field of train operation adjustment, and in particular to a method for jointly adjusting a timetable and an operation route for flexible train formation. Background Art

[0002] With the rapid growth and expansion of urban scale in recent years, urban rail transit systems are gradually facing some new problems, one of which is how to better match the dynamic travel needs of passengers. Passenger flow demand is obviously unbalanced in spatial and temporal dimensions. During the morning rush hour, the passenger demand at some specific stations is always oversaturated, causing some passengers to be stranded at these stations, while the passenger demand at other stations is relatively low, which easily leads to a waste of transportation resources. In order to further improve the service quality of urban rail transit and reduce operating costs, dynamic operation adjustment strategies represented by mixed operation of large and small routes and flexible train formation have become a research hotspot in recent years.

[0003] With the support of flexible marshaling technology, operators can arrange trains with different marshaling patterns to implement large and small route operation service strategies based on the dynamic changes in passenger numbers on the line, thereby better matching passenger needs and improving service quality. Existing research has not yet explored joint optimization strategies for train formation patterns, large and small route operation strategies, and train timetables under flexible marshaling models. Summary of the Invention

[0004] The present invention proposes a method for the joint adjustment of timetables and running routes for flexible train formations. A joint adjustment model for timetables and running routes for flexible train formations is established to derive an effective operation adjustment strategy. First, by establishing a passenger dynamics equation to describe the relationship between train arrival and departure, route operation, train disassembly status, and passenger volume, the actual train operation and passenger demand constraints are strictly considered to achieve the establishment of a joint adjustment model for timetables and running routes for flexible train formations; further, the entire optimization problem is transformed into a control problem and decomposed into sub-problems of n steps to solve, thereby obtaining a real-time adjustment strategy for train operation. Through the comparison of different strategies, the results show that the proposed method is more effective in reducing passenger detention.

[0005] The adjustment method of the present invention comprises establishing a train schedule and operation route joint adjustment model oriented to flexible formation and designing a train schedule adjustment model solving algorithm.

[0006] The specific steps of establishing a joint adjustment model of train schedule and operation routes for flexible marshaling include:

[0007] Establish constraints related to train operation;

[0008] Establish a dynamic passenger flow model based on train timetable;

[0009] Establish constraints related to demarshalling and route switching operations;

[0010] Establish the objective function.

[0011] On the basis of the above scheme, the specific method of establishing the constraints related to train operation is: Establish formula (1):

[0012]

[0013] Among them, t i,k represents the departure time of train service k at station i, r i-1 represents the running time of the train service between station i-1 and station i, x i,k represents the stop time of train service k at station i; for the departure time of the train service at station a+1, the sum of the time for train service k2 to arrive at station a+1 and the time it stays at station a+1 is obtained as formula (2):

[0014]

[0015] Formula (3) represents the departure time of station B:

[0016]

[0017] Define the variable d i,k represents the time for train service k to arrive at station i, which is calculated by formula (4):

[0018]

[0019] The time for train service k to arrive at station i is obtained by adding its departure time at station i-1 and the inter-station running time from station i-1 to station i, where r i-1 Indicates that the running time from station i-1 to station i is a constant.

[0020] On the basis of the above scheme, a connection constraint is also added to indicate the train connection relationship between services k1, k2, and k3;

[0021] The train service for k2 comes from k1. The time for train service k2 to arrive at station a+1 is expressed as the departure time of train service k1 at station a plus the running time r between stations a and a+1. a , expressed as formula (5):

[0022]

[0023] For the train service from k1 in k3, the time when k3 arrives at station b is expressed as the departure time of the train service k1 it undertakes at station a plus the running time T between stations a and b. a,b , expressed as formula (6):

[0024]

[0025] For the train service of k3 from k2, it is expressed by formula (7):

[0026]

[0027] where r b-1 It represents the running time of the train between station b-1 and station b.

[0028] Based on the above scheme, the chasing interval between train services satisfies formula (8):

[0029]

[0030] in represents the minimum chasing interval, Indicates the maximum pursuit interval.

[0031] On the basis of the above scheme, the specific method of establishing a dynamic passenger flow model based on the train timetable is as follows:

[0032] The number of passengers arriving at station i between services k-1 and k is related to the time interval between the two adjacent services and the passenger arrival rate at the current station, which can be expressed as formula (9):

[0033]

[0034] Among them, μ i,k represents the passenger arrival rate at station i during the period between the departure of train service k-1 and the departure of train service k;

[0035] Define w i,k represents the number of passengers waiting for train service k at station i, which can be expressed as formula (10):

[0036]

[0037] The formula (10) consists of two parts. One part is the number of passengers a arriving at station i during the period between the departure of service k-1 and the arrival of service k. i,k The second part is that during peak hours, in addition to arriving passengers, waiting passengers also include stranded passengers who failed to successfully board the previous train due to no train service passing through the station or limited capacity, defined as s i,k ;

[0038] There are no waiting passengers at the terminal of the line, i.e. w I,k =w 2I,k =0;

[0039] The stranded passengers are expressed by formula (11):

[0040]

[0041] Among them, g i,k represents the number of passengers who successfully boarded the train serving k at station i;

[0042] Define p i,k It represents the number of passengers on train service k when train service k leaves station i. The dynamic change process of passengers in the train is defined by the behavior of getting on and off the train, which is expressed as formula (12):

[0043]

[0044] Based on the above scheme, the specific method for calculating the number of passengers who successfully boarded the train is as follows:

[0045]

[0046] Among them, ε k represents the number of fleets served by train k, C represents the maximum capacity of a single fleet, and the maximum capacity of the entire service is denoted as ε k C, and ε k Cp i-1,k +l i,k represents the remaining capacity of train serving k at station i;

[0047] There are no passengers boarding the bus at the terminal station of the line, i.e. I,k =g 2I,k =0;

[0048] Among them, a i,k is a binary variable indicating whether train service k passes through station i. Passing through station i indicates that it can provide service to station i. It is specifically expressed as formula (14):

[0049]

[0050] Among them, the variable l i,k represents the number of passengers who get off when train service k stops at station i, λ i,k represents the ratio of the number of passengers getting off the train to the number of passengers currently on the train service;

[0051] The calculation of passengers getting off the bus follows formula (15):

[0052]

[0053] Based on the above solution, the specific method of establishing the constraints related to decommissioning and route operation is as follows:

[0054] Define a binary logistic variable γ k , indicating whether train service k is disbanded, as shown in formula (16):

[0055]

[0056] When a train is separated at a switch, the number of train fleets forming the train service will change accordingly. The number of train fleets is 1 when the train is separated and 2 when the train is not separated. The number of train fleets is calculated according to formula (17):

[0057]

[0058] According to the defined regional variables of the station and the section of the train service operation, Equation (18) expresses the train stop situation at each station, that is, whether there is a train service passing through the station:

[0059]

[0060] Among them, for the stations from station 1 to station a, there are always train services passing through; for the stations from a+1 to b-1, the situation where a train passes through is a case of disassembly, at this time γ k =1; For stations from b to 2I, if the service is taken over by k1, then there must be a train service passing by. If the train service is taken over by K2, is the service consistent with K2?

[0061] Based on the above scheme, the objective function is formula (19):

[0062]

[0063] The joint adjustment model of timetable and operation route for flexible train formation is as follows:

[0064]

[0065] On the basis of the above scheme, the algorithm for solving the train schedule adjustment model is based on the MPC principle, and its steps are as follows:

[0066] In the t-th control cycle, the train timetable is planned within the optimization range [t, t+n];

[0067] Solve the real-time control strategy of the train within the control period, where the sample step size of the control period is n, which is consistent with the passenger flow prediction step size;

[0068] In the t+1th control cycle, the departure time and stop time of the updated train in the t+1th phase are used as the prediction input of the model;

[0069] Re-evaluate the train control strategy.

[0070] On the basis of the above scheme, based on the sample step size n, in each control cycle, the objective function of the train schedule optimization model is re-expressed as formula (22):

[0071] Beneficial effects of the present invention:

[0072] The present invention relates to the field of train operation adjustment and realizes a method for jointly adjusting timetables and running routes for flexible train formations. The benefit of the invention is mainly reflected in the establishment of a joint adjustment model for timetables and running routes for flexible train formations. Compared with traditional train operation adjustment methods based on fixed train formations, this method can arrange trains with different train formation modes to execute large and small route operation service strategies according to the dynamic changes in the number of passengers on the line, thereby better matching passenger needs and improving service quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] The present invention has the following accompanying drawings:

[0074] Figure 1 Urban rail transit line layout and train service maps;

[0075] Figure 2 Schematic diagram of the optimization model architecture;

[0076] Figure 3 Train operation adjustment model solution flow chart;

[0077] Figure 4 Adjustment strategy model - train schedule;

[0078] Figure 5 Adjustment strategy model - k2 passenger detention diagram;

[0079] Figure 6 Adjustment strategy model - k3 passenger detention diagram;

[0080] Figure 7 Adjustment Strategy Model 2 Train Schedule;

[0081] Figure 8 Adjustment Strategy Model 2 k1 passenger detention diagram;

[0082] Figure 9 Adjustment Strategy Model 2 k2 passenger detention diagram;

[0083] Figure 10Adjustment Strategy Model 2 k3 passenger detention diagram;

[0084] Figure 11 Adjustment Strategy Model Three Train Schedule;

[0085] Figure 12 Adjustment Strategy Model Three k1 passenger detention diagram;

[0086] Figure 13 Adjustment Strategy Model Three K2 Passenger Detention Diagram;

[0087] Figure 14 Adjustment strategy model three k3 passenger detention diagram. DETAILED DESCRIPTION

[0088] To make the purpose, advantages and features of the present invention more apparent, the following Figure 1-14 The present invention is further described in detail with reference to the following specific embodiments.

[0089] 1. Problem Description and Assumptions

[0090] This paper mainly analyzes the train operation adjustment model and studies the up and down sections of the urban rail transit system consisting of 2I stations. Figure 1 As shown in the figure, the train service set running on the section from station 1 to station a is defined as k1, the train service set running on the section from station a+1 to station b-1 is defined as k2, and finally the train service set running on the section from station b to station 2I is defined as k3. The area from station 1 to a and from station b to 2I is defined as the small cross-section area, and the area from station a+1 to station b-1 is defined as the large cross-section area. After passing station a, the train can choose two routes according to the passenger flow. One is the small cross-section, that is, all the trains will not be disassembled and will all run to station b. Figure 1 a) As shown; the second is that the train is disassembled, the first convoy of trains travels to station a+1, and the second convoy of trains travels to station b, as shown Figure 1 b). In actual operation, the train operation status is as follows: Figure 1 c). By default, train services arriving from the depot consist of two fleets. After demarshalling, these fleets become two separate fleets, identified as two train services. This study investigates the adjustment of train operations for flexible train formations and explores corresponding route solutions and timetable optimization. Ultimately, this approach matches passenger flow with train resources, improving passenger satisfaction while reducing unnecessary waste of train resources. The known parameters studied include the number of train services, the number of line stations, the maximum fleet capacity, passenger boarding and alighting rates at each station, the locations of route start and end areas, and the inter-station travel time.

[0091] To facilitate the analysis of adjustment issues, a joint adjustment model of timetables and routes for flexible train formations was established. Based on the above scenario, the following assumptions were made for the existing research problem:

[0092] (1) Assumption 1: All trains do not overtake at stations;

[0093] (2) Assumption 2: The transport capacity of each fleet is the same and is not affected by the size of the route or the split-up situation;

[0094] (3) Assumption 3: The travel time between adjacent stations is constant and known;

[0095] (4) Assumption 4: Passengers do not transfer between different types of train services and always choose the train service that goes directly to their destination.

[0096] 2. Symbolic Representation

[0097] In response to the problem, the variables used in the subsequent modeling need to be explained. First, the basic variables of the scenario in the modeling process and their meanings are explained. See Table 1 for details.

[0098] Table 2 then explains the symbols and definitions used in the train schedule deduction. These primarily include time-related variables such as the departure time, operating time, and arrival time of train services, as well as variables indicating the connection relationship between train services. Connection variables can be used to determine whether a train service originates from k1 or k2 and to identify the order of train services.

[0099] Table 1 Scene related symbols

[0100]

[0101]

[0102] Table 2 Train timetable related symbols

[0103]

[0104] Based on the timetable, the passenger boarding and alighting situation at each station is derived through formula deduction. The symbols for the passenger section are shown in Table 3, which mainly include passenger-related arrival rate, number of arriving passengers, number of waiting passengers, and number of stranded passengers. The symbols related to the route and marshaling plan are explained in Table 4, mainly including variables such as the number of fleets, fleet capacity, and train separation. Finally, the decision variables of the model are shown in Table 5. In addition to train separation and train acceptance, these also include control actions for train stop time.

[0105] Table 3 Symbols for passengers getting on and off the bus

[0106]

[0107] Table 4 Intersection and marshaling related symbols

[0108]

[0109] Table 5 Decision variables

[0110] 3. Establishment of a joint adjustment model for train schedules and routes for flexible formations 1. First, establish constraints related to train operation.

[0111]

[0112] Among them, t i,k represents the departure time of train service k at station i, r i-1 represents the running time of the train service between station i-1 and station i, x i,k represents the time that train service k spends at station i. In particular, the departure time of train service k2 at station a+1 can be obtained by summing the time it takes for train service k2 to arrive at station a+1 and the time it spends at station a+1:

[0113]

[0114] Similarly, the departure time of station B can be expressed:

[0115]

[0116] Define the variable d i,k The time it takes for train service k to arrive at station i can be expressed as:

[0117]

[0118] The calculation is that the time for train service k to arrive at station i is obtained by adding its departure time at station i-1 and the inter-station running time from station i-1 to station i, where r i-1 It represents the running time from station i-1 to station i, which is a constant.

[0119] In particular, it is necessary to add some connection constraints between different services to indicate the train connection relationship between services k1, k2, and k3. Since the train services of k2 all come from k1, the time for train service k2 to arrive at station a+1 can be expressed as the departure time of train service k1 at station a plus the running time r between stations a and a+1. a , expressed as:

[0120]

[0121] For the train service from k1 in k3, the time when k3 arrives at station b can be expressed as the departure time of the train service k1 it undertakes at station a plus the running time T between stations a and b. a,b , because there is no platform between station a and station b, in order to better serve passengers, the running time of this section is also set to a constant. This process is expressed as:

[0122]

[0123] For the train service of k3 from k2, the formula can be used:

[0124]

[0125] To express, where r b-1 It represents the running time of the train between station b-1 and station b.

[0126] In addition, in order to satisfy passengers and ensure the safety of train operation, the train frequency should meet the maximum and minimum chasing intervals during actual operation. represents the minimum chasing interval, Indicates the maximum chasing interval. The chasing interval between train services should meet the following requirements:

[0127]

[0128] Afterwards, a dynamic passenger flow model is established based on the train schedule. The number of passengers arriving at station i between services k-1 and k is related to the time interval between the two adjacent services and the passenger arrival rate of the current station, which can be expressed as:

[0129]

[0130] Among them, μ i,k Denotes the passenger arrival rate at station i during the period between the departure of train service k-1 and the departure of train service k. Define w i,k represents the number of passengers waiting for train service k at station i. This variable can be expressed as:

[0131]

[0132] It consists of two parts: one is the number of passengers a arriving at station i after service k-1 leaves and before service k arrives. i,k The second part is that during peak hours, in addition to arriving passengers, waiting passengers also include stranded passengers who failed to successfully board the previous train due to no train service passing through the station or limited capacity, defined as s i,k ,In particular, there are no waiting passengers at the terminal of the line, i.e., w I,k =w 2I,k= 0. Stranded passengers are represented by the following formula:

[0133]

[0134] Among them, g i,k Denotes the number of passengers who successfully boarded the train serving k at station i. Define p i,k It represents the number of passengers on train service k when train service k leaves station i. The dynamic change process of passengers in the train can be expressed as follows:

[0135]

[0136] To calculate the number of passengers who have successfully boarded the train, we first need to consider whether the train service k passes through station i. If the service is provided through station i, we need to compare the number of arriving passengers with the train capacity to determine whether the waiting passengers can board the train. This process can be expressed as:

[0137]

[0138] Among them, ε k represents the number of fleets served by train k, C represents the maximum capacity of a single fleet, and the maximum capacity of the entire service is denoted as ε k C, then we can get ε k Cp i-1,k +l i,k Indicates the remaining capacity of train service k at station i. In particular, if there are no passengers boarding the train at the terminal station, g I,k =g 2I,k =0. Among them, α i,k is a binary variable indicating whether train service k passes through station i. If it passes through station i, it means that it can provide service to station i. It can be expressed as:

[0139]

[0140] Among them, the variable l i,k Denote the number of passengers who get off the train service k when it stops at station i, and assuming that this number is proportional to the number of passengers on the current train service, use λ i,k To express this ratio. As for passengers who board the bus, the prerequisite for getting off the bus is that there is a train service, so passengers who get off the bus also need to add the variable α i,k Considering the above, the calculation of passengers getting off the bus follows the following formula:

[0141]

[0142] After that, the constraints related to decompilation and route operation are established. Define the binary logic variable γ k , used to indicate whether train service k is disassembled, there is

[0143]

[0144] When a train is split at a switch, the number of fleets forming the train service will change accordingly. The number of fleets forming the split is 1, and the number of fleets forming the split is 2. The number of fleets forming the split is calculated according to the following formula:

[0145]

[0146] Train service k1 provides service until the station before the switch, so it is not affected by whether the train is disbanded or not, and the number of train teams is 2; for train service k2, it is related to whether the train is disbanded or not. In the case of disbanding, the number of train teams passing through the large route section is 1, and in the case of not disbanding, the number of train teams passing through the large route section is 0; for train service k3, if the train service is inherited from k2, the number of train teams is consistent with that of k2. If it is inherited from k1, it is necessary to pass the variable Determine which train service K1 is being taken over, and then analyze whether the train service is being disbanded to determine the corresponding fleet number. If the train is disbanded, the fleet number is 1; if it is not disbanded, the fleet number is 2.

[0147] Based on the defined station area variables and the sections where the train services are running, the train stop status at each station can be indicated, that is, whether there is a train service passing through the station:

[0148]

[0149] Among them, for the stations from station 1 to station a, there are always train services passing through; for the stations from a+1 to b-1, the situation where a train passes through is a case of disassembly, at this time γ k =1; For stations from b to 2I, if the service is taken over by k1, then there must be a train service passing by. If the train service is taken over by K2, is the service situation consistent with K2?

[0150] Finally, regarding the objective function, to improve passenger satisfaction, the number of waiting passengers at each station should be minimized. When overall passenger flow on a line is high, train service can be increased by reducing departure intervals. For stations in large route areas, trains can be routed along large or small routes, or even split based on passenger flow, to balance passenger flow and reduce the number of waiting passengers at stations. Dynamic adjustments to departure intervals and train service types can effectively balance stranded passengers at stations with vehicle utilization.

[0151] Therefore, the objective function is:

[0152]

[0153] In summary, the joint adjustment model of timetable and operation routes for flexible train formation is as follows:

[0154]

[0155] Finally, the architecture of the entire optimization model is shown in Figure 2 shown.

[0156] 4. Design of solution algorithm

[0157] Design an algorithm to solve a joint optimization model for train formations, routes, and train schedules. First, collect information from the current time period t to predict the system's behavior over a specified period of time. Then, use an optimization algorithm to generate an optimal control strategy to achieve the control objectives and constraints defined by the prediction model. The control strategy consists of the optimal control input for the current state and the optimal control input sequence for the prediction period, and is implemented at each sampling time step.

[0158] Based on the MPC control method, the original joint optimization problem is converted into an optimal control problem. Furthermore, the entire train schedule optimization problem is converted into a series of sub-problems with a step size of n. In each control cycle, the optimization sub-problems within the given prediction range are solved online to provide a real-time optimization control strategy. For example, in the t-th control cycle, the train schedule is planned within the optimization range [t, t+n], and the real-time control strategy of the train in the control cycle is solved based on mixed integer programming to adjust the train status and reduce passenger delays. Similarly, in the t+1-th control cycle, the MPC method uses the updated measured departure time and stop time of the train in the t+1 phase as the prediction input of the model, and then re-estimates the control strategy of the train. In the entire process, only the first control output of the calculated optimal control sequence is applied to the system, and the subsequent control cycles are analogous. The train operation adjustment algorithm process is as follows: Figure 3 shown.

[0159] In each control cycle, the mixed integer programming method is used to solve the following sub-problems. Based on the sample step size n, the objective function of the train schedule optimization model in each control cycle can be reformulated as:

[0160]

[0161] Through this sliding window optimization, real-time adjustment of timetables and operating routes for flexible formations is achieved based on real-time passenger flow conditions, ensuring real-time control effects in the entire joint optimization model solution process.

[0162] 5. Results Analysis

[0163] Different train operation adjustment schemes were designed and evaluated using comparative experiments. The different operation adjustment model experiments were based on actual passenger flow on the Yizhuang Line during the morning rush hour on the same day. Model 1, the method proposed in this study, is based on dynamic passenger flow, fully considers passenger demand, and flexibly determines large and small routes and train formations. To emphasize the importance of dynamic passenger flow, Model 2 does not make real-time adjustments, but instead draws on historical passenger flow data, similarly determining large and small route operation and train formations. Model 3, based on dynamic passenger flow data, only performs large and small route loops and does not consider dynamic train formations. The key factors of the three train operation adjustment models are shown in Table 6.

[0164] Table 6 Different train operation adjustment models

[0165]

[0166] Based on model 1, the train schedule is as follows: Figure 4 As shown, the dotted part represents the train services separated after de-assembly, and the same color represents the connection relationship between train services.

[0167] The stranded passengers of each train service are recorded, and the passenger stranded situation of train services k2 and k3 at each station is as follows Figure 5 and Figure 6 As shown, train service k1 has no passengers stranded at any station.

[0168] Model 2 adjusts the train operation based on static passenger flow, and the resulting timetable is as follows: Figure 7 As shown in Figure 2, based on the operational adjustments of Model 2, there are passengers stranded on all three services. The number of stranded passengers is as follows: Figure 8 、 Figure 9 and Figure 10 shown.

[0169] Model 3 does not consider the operation adjustment of train disassembly. The train operation diagram based on Model 3 is as follows: Figure 11 As shown in the timetable, it can also be seen that there is only a large-scale loop running situation, and no splitting situation occurs. The train operation diagram and passenger detention situation of model 3 are shown in Figure 12 、 Figure 13 and Figure 14 shown.

[0170] Comparing the numerical experimental results of Model 1 and Model 2 clearly shows that adjusting train operations based on actual passenger flow is more effective in reducing passenger detention at stations than relying solely on historical static passenger flow data. Furthermore, a comparison of the results of Model 1 and Model 3 shows that incorporating flexible routes and train formations can further reduce passenger detention compared to methods that focus solely on the operation of large and small routes.

[0171] The above embodiments are only used to illustrate the present invention, and are not intended to limit the present invention. Ordinary technicians in the relevant technical field may make various changes and modifications without departing from the essence and scope of the present invention. Therefore, all equivalent technical solutions also fall within the scope of the present invention. The scope of patent protection of the present invention should be defined by the claims.

[0172] The contents not described in detail in this specification belong to the prior art known to those skilled in the art.

Claims

1. A method for adjusting timetable and operation routes for flexible train formation, characterized in that: This includes establishing a joint adjustment model for train schedules and routes for flexible train formations and designing a solution algorithm for the joint adjustment model; The specific steps of establishing a joint adjustment model of train schedule and operation routes for flexible marshaling include: Establish constraints related to train operation; Establish a dynamic passenger flow model based on train timetable; Establish constraints related to demarshalling and route switching operations; Establish the objective function; The specific method of establishing the constraints related to decommissioning and route operation is as follows: Define binary logical variables , indicating train service Whether to decompress, as shown in formula (16): ; When a train is separated at a switch, the number of train fleets forming the train service will change accordingly. The number of train fleets is 1 when the train is separated and 2 when the train is not separated. The number of train fleets is calculated according to formula (17): ; According to the defined regional variables of the station and the section of the train service operation, Equation (18) expresses the train stop situation at each station, that is, whether there is a train service passing through the station: ; Among them, for site 1 to site There is always a train service for stations in the area; arrive At the station of the section, if a train passes by, it is a case of disassembly. ;for arrive Stations in the sector, if the train service is undertaken by Then there must be a train service passing by. If the train service is undertaken by , then provide services and Stay consistent, that is: ; in, Indicates station 1 to station Index of train services in the direction, Indicates the station To the station Direction and station To the station Index of train services in direction, Indicates the station To the station Index of train services in the direction, Indicates station 1 to station Train service collection in direction Indicates the station To the station Direction and station To the station Direction train service collection Indicates the station To the station Train service collection in direction Indicates the station index, Represents the set of all stations Integer variable, used to represent Number of fleets under service, represents a binary variable, indicating the train service Perform decompression operation, equal to 1 means no decompression, Represents a binary variable, used to indicate the train service operation status, equal to 1 means service Undertaken by service ; Otherwise, it is equal to 0, indicating that it is not inherited from Represents a binary variable, used to indicate the train service operation status, equal to 1 means service Undertaken by service ; Otherwise, it is equal to 0, indicating that it is not inherited from Represents a binary variable, equal to 1 means train service for The station provides services, that is, when it is running, Station, equal to 0 means no service, that is, train service Not passing through stand, include or or .

2. A method for adjusting a timetable and a running route for flexible train formation according to claim 1, characterized in that: The specific method of establishing the constraints related to train operation is to establish formula (1): ; in, Indicates train service exist The departure time of the station, Indicates that the train service is Station and Run time between stations, Indicates train service exist The stop time at the station; Train services at the station Departure times by train service arrive Station times and train services exist The sum of the time spent at the station is obtained as formula (2): ; Formula (3) indicates Departure time of the station: ; Defining variables Indicates train service arrive The time of the station is calculated by formula (4): ; Train services arrive The time of standing is determined by The departure time of the station and Stand The inter-station running time of the stations is added together, where express Stand The running time of the station is a constant; in, Indicates train service exist The departure time at the station, Indicates train service arrive Standing time, Indicates train service exist The control action of the residence time of the station.

3. The method for adjusting the timetable and operation routes for flexible train formation according to claim 2, characterized in that: It also includes adding connection constraints to indicate that the service The train connection relationship between them; for The train services are from , for train services arrive Station times are expressed as train services exist The departure time of the station plus the train at Station and Running time between stations , expressed as formula (5): ; for From Train services, arrive The time of a station indicates the train service it undertakes exist The departure time of the station plus the train at Station and Running time between stations , expressed as formula (6): ; for From The train service is expressed by formula (7): ; in Indicates that the train is at the station To the station The running time between.

4. The method for adjusting the timetable and route of a flexible train formation according to claim 3, characterized in that: The chasing interval between train services satisfies formula (8): ; in represents the minimum chasing interval, Indicates the maximum pursuit interval.

5. The method for adjusting the timetable and operation routes for flexible train formation according to claim 4, characterized in that: The specific method of establishing the dynamic passenger flow model based on the train timetable is as follows: exist and Arrival between services The number of passengers at a station is related to the time interval between two adjacent services and the passenger arrival rate of the current station, which can be expressed as formula (9): ; in, Indicates train service Departures and train services During departure, passenger arrival rate at the station; definition Indicates Station waiting for train service The number of passengers is expressed as formula (10): ; The formula (10) consists of two parts, one of which is After the service leaves Arrived during this time before the service arrives Passengers at the station ,The second part is that during peak hours, in addition to arriving passengers, waiting passengers also include stranded passengers who failed to successfully board the previous train due to no train service passing through the station or limited capacity, defined as ; There are no waiting passengers at the line's terminus, i.e. ; The stranded passengers are expressed by formula (11): ; in, Indicates Station successfully boarded the train service the number of passengers; definition Indicates train service leave Station time, train service The number of passengers on the bus is defined by the behavior of getting on and off the bus, and the dynamic change process of the passengers in the bus is expressed as formula (12): ； in, Indicates train service leave Station and train services arrive The number of passengers arriving during the station, Indicates Station from train service The number of passengers who got off the bus.

6. The method for adjusting the timetable and operation routes for flexible train formation according to claim 5, characterized in that: The specific method for calculating the number of passengers who successfully boarded the train is as follows: ; in, express The number of train fleets serving the train, represents the maximum capacity of a single fleet, and the maximum capacity of the entire service is expressed as , we can conclude Indicates Station-time train service The remaining capacity of There are no passengers boarding the bus at the terminal station of the line, i.e. ; in, is a binary variable representing the train service Passed Station, through Station means it can The station provides services; specifically expressed as formula (14): ; Among them, the variable Indicates train service Stay The number of passengers getting off at the stop, represents the ratio of the number of passengers getting off the train to the number of passengers currently on the train service; The calculation of passengers getting off the bus follows formula (15): 。 7. The method for adjusting the timetable and operation routes for flexible train formation according to claim 6, characterized in that: The objective function is formula (19): ; The joint adjustment model of timetable and operation route for flexible train formation is as follows: ; 。 8. The method for adjusting the timetable and operation routes for flexible train formation according to claim 7, characterized in that: The joint adjustment model solving algorithm is designed based on the MPC principle, and the joint optimization model solving algorithm of the design grouping mode, running route and train schedule is designed. The steps are: In the control cycles, within the optimization range Internal planned train timetable; Solve the real-time control strategy of the train within the control period, where the sample step size of the control period is , which is consistent with the passenger flow prediction step length; In the control cycle, the updated The measured departure and stop times of trains in each stage are used as the prediction input of the model; Re-evaluate the train control strategy.

9. The method for adjusting the timetable and operation routes for flexible train formation according to claim 8, characterized in that: Sample-based step size , in each control cycle, the objective function of the train schedule optimization model is re-expressed as Equation (22): 。

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