A flexible train formation diagram compilation method considering metro supply and demand matching

Abstract

The application discloses a kind of flexible train marshalling diagram compilation method considering subway supply-demand matching, belong to traffic transport technical field.It can be according to the passenger flow demand that changes with time, realize the hitching and unmarshalling of different train units at certain sites.In view of using a variety of train units, the hitching and unmarshalling of train unit must follow the specific re-marshalling rule of marshalling station.The mixed integer linear programming model in it aims at optimizing car bottom marshalling and train timetable, also incorporates passenger distribution constraints, to assess the number of passengers or the number of passengers stranded in the station in train service, reduce the number of stranded passengers, train marshalling quantity and operating cost.The application relaxes part of calculation and constraint condition by approximation method to improve calculation speed, and by two-stage heuristic method, the integrated optimization problem is decomposed into two sub-problems, and the two sub-problems are solved by heuristic search method, so that the passenger travel demand can be met as much as possible while reducing operating cost.

Description

Technical Field

[0001] This invention relates to the field of transportation technology, and in particular to a method for compiling flexible train formation timetables that takes into account the matching of subway supply and demand. Background Technology

[0002] Urban rail transit, an indispensable mode of transportation in many cities, is favored by commuters for its safe, reliable, and punctual service. Planning studies for urban rail transit can be broadly categorized into two types: cost-oriented and demand / service-oriented train operation planning. Over the past few decades, cost-oriented train operation planning has received initial attention, focusing on reducing operating costs such as labor costs, energy consumption, and vehicle acquisition and maintenance. In recent years, service-oriented planning has become increasingly popular, emphasizing improving passenger service levels, such as maximizing total demand attracted by trains, minimizing passenger waiting / travel times, and avoiding congestion. Numerous studies have reached similar conclusions: compared to timetables with fixed departure intervals, single-stop patterns, and fixed vehicle formations, flexible departure intervals, flexible stop patterns, and flexible vehicle formations provide better service to passengers while saving more operating costs. Summary of the Invention

[0003] The purpose of this invention is to provide a method for creating flexible train formation timetables that consider the matching of subway supply and demand, aiming to determine train timetables and vehicle dispatching plans that take into account flexible vehicle formation strategies. Unlike traditional fixed train formation modes, flexible vehicle formation strategies mean that train formations can be flexibly adjusted at selected stations according to different passenger demands along the rail transit line, thereby meeting passenger demands in different regions and time periods and further improving vehicle utilization.

[0004] To achieve the above objectives, this invention provides a method for compiling flexible train formation timetables that consider the matching of subway supply and demand, comprising the following steps:

[0005] S1. Obtain passenger flow information in urban rail transit and basic data for train timetable planning; the time-varying passenger flow data mentioned here refers to the uneven distribution and time correlation of passenger arrivals within a specific time period due to the random nature of passenger arrivals, including: daily automatic fare collection system data of urban rail transit, etc.; the basic data for train timetable compilation includes: train decoupling / coupling time, section running time, vehicle type, train stopping time, maximum / minimum train running interval time, maximum / minimum turnaround time;

[0006] S2. Based on the basic data of the train operation diagram, establish a train timetable optimization model under the flexible formation mode, solve it using the GUORBI commercial solver, and generate a flexible formation train timetable.

[0007] S3. Based on the aforementioned flexible train timetable, establish a collaborative optimization model for passenger flow allocation and train turnaround plan, solve it using the GUORBI commercial solver, and generate train turnaround plan and passenger flow allocation plan.

[0008] S4. Record relevant data of the flexible train timetable, rolling stock turnover plan and passenger flow allocation plan, and generate objective function evaluation indicators;

[0009] S5. Based on the evaluation index, through iterative optimization, select the iterative target optimization value that meets the termination condition and the result of flexible train timetable compilation.

[0010] Preferably, based on actual train schedule data and under the condition that the travel time and stop time within the train service area are fixed, a timetable optimization model under the flexible formation mode is established, specifically including:

[0011] During train service, vehicle formations may be coupled and detached during operation, and the vehicle formation upon arrival at the terminal station may differ from the formation upon departure from the origin station. To facilitate calculation, this invention decomposes a complete train service into multiple train journeys based on the selected number of marshalling yards and establishes a series of constraints to complete the conversion between train services and train journeys, so as to subsequently calculate the capacity of the train service in each section.

[0012] The variables in the timetable optimization section are the train intervals and rerouting times between services. The algorithm starts by finding the optimal departure head, gradually reducing the maximum allowable head to avoid passenger congestion on the platform. The initial maximum departure head is set based on actual maximum head patterns (usually provided by the metro company's operating guidelines to ensure minimum service frequency for passengers). Typically, the maximum departure time is shorter during peak hours and on busy directions than during off-peak hours and on less busy directions.

[0013] This type of flexible train formation optimization method can optimize train arrival / departure times and car formations, better meeting the time-dependent and unbalanced passenger demands.

[0014] Preferably, the timetable optimization model under the flexible grouping mode is a mixed integer programming model, and the specific modeling process is as follows:

[0015] Establish the constraints required for each stage of the model, including: train service interval constraints, train service arrival and departure time constraints, train service reorganization time constraints at marshalling yards, and train service turnaround time constraints; and establish a mapping between train departure time and departure period.

[0016] The objective function of the timetable optimization model is defined, specifically including: maximizing the running interval between adjacent train services.

[0017] Preferably, the flexible train formation technology considers that trains can be coupled / decoupled not only at the starting and ending stations (connected to the depot) of urban rail transit lines, but also at intermediate stations with multiple tracks. This greatly increases the flexibility of train formation, enabling the generated train timetable to better meet the time-dependent and unbalanced passenger demands, while effectively reducing train operating costs.

[0018] Preferably, the collaborative optimization model for passenger flow allocation and rolling stock turnover plan established based on the optimization results of flexible train timetables is specifically modeled as follows:

[0019] Establish the constraints required for each stage of the model, including: rolling stock turnover constraints, marshalling yard capacity constraints, train service adaptation constraints, train service marshalling constraints, mapping constraints between train services and each train journey, and passenger flow allocation constraints.

[0020] Based on the mathematical properties of the constraints, the nonlinear constraints are transformed into linear constraints;

[0021] The objective functions of the timetable optimization model are defined, specifically: minimizing the number of stranded passengers, minimizing the purchase cost of train units, and minimizing the operating cost of trains. The priorities for these three objective functions are determined as follows: the first priority is meeting passenger travel demand, the second priority is reducing the purchase cost of train units, and the third priority is reducing the operating cost of trains.

[0022] Therefore, the flexible train formation timetable compilation method of the present invention, which adopts the above structure and considers the matching of subway supply and demand, has the following beneficial effects:

[0023] This invention generates train service formation plans and timetables that match the unevenly distributed passenger flow in time and space by establishing and solving a MILP model, thereby reducing the number of stranded passengers, train units, and operating costs. To effectively solve the comprehensive optimization problem, this study proposes an approximation method and a two-stage heuristic algorithm, combined with a hybrid solution using the GUROBI commercial solver. The approximation method approximately relaxes some computational and constraint conditions to improve computational speed. The two-stage heuristic method divides the comprehensive optimization problem into two sub-problems and uses a heuristic search method to solve these two sub-problems. Furthermore, the modeling fully considers the equipment and facilities at each station along the line, combined with passenger flow distribution characteristics, ensuring the feasibility of the train turnaround plan while quickly generating flexible formation operation diagrams that conform to the existing facilities and equipment of the line and match passenger flow. This meets the requirements of operating companies for flexible formation operation diagrams that accurately allocate capacity, reduce operating costs, and improve service quality, providing significant theoretical guidance for the application of flexible formation in practical scenarios.

[0024] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0025] Figure 1 A flowchart of a method for creating flexible train formation operation diagrams for urban rail transit lines that takes into account supply and demand matching, provided by the present invention.

[0026] Figure 2 This is a diagram illustrating the relationship between train services and train journeys to which this invention applies.

[0027] Figure 3 This is a schematic diagram illustrating the train service coupling and uncoupling process to which this invention applies. Detailed Implementation

[0028] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0029] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0030] Example

[0031] like Figure 1-3 As shown, this invention provides a method for creating flexible train formation timetables that considers the matching of subway supply and demand, as detailed below:

[0032] S1: Initialization, including initializing the number of iterations u=0 and the maximum train interval. Number of stranded people Adjacent train journeys at marshalling yards Objective function weights J1 *(0) =J2 *(0) =J3 *(0) =0,L (0) =0, etc., and input the relevant train operation data.

[0033] S2: Establish a two-stage heuristic algorithm.

[0034] S3: Update iteration count u = u + 1, update train relocation time, and update maximum train running interval.

[0035] S4: Establish train timetable optimization model M2, the specific model is as follows:

[0036] To facilitate the calculation of train service reorganization and arrival / departure status at each station, each complete train service i is divided into different train journeys g according to the number of marshalling yards.

[0037] Among them, to maximize the adjacent trains (d) g,χ and The departure time interval is the objective function, and its expression is as follows:

[0038]

[0039] The constraints are as follows:

[0040]

[0041]

[0042] Where, m g,χ The train journey from station χ before train journey g, where g and g′ are indices of the train journey, T pair It is the set of pairs connecting train journeys, (g,g′) is a set of pairs connecting train journeys, (g,g′)∈T pair s g-g′ This refers to the connection between train journeys g and g′ at marshalling yard s. g-g′ ∈T pair χ is the index of the destination station, S f Let K be the set of destination stations, and K be the set of stations, where K = {1, 2, ..., |K|}. k is the index of a station, where k ∈ K. s,v Let V be the set of train journeys originating from station S in the direction of v. The collection of train journeys ending at the final destination χ. The set of train journeys originating from station χ and ending at station χ. D is the set of directions, D = {down, up}, and v is the index of the direction, v ∈ D. g,s The arrival time of train journey g at station s (a g,s′ a g,χ Similarly), d g,s The departure time of train journey g at station s, t0,t f t represents the start and end times of the service. g-g' The adjusted time between train journey g and train journey g′. Let r be the minimum and maximum train intervals for station s. g The specified travel time for a section of train journey g is dw g,χ The time the train spends at station χ during its journey g (dw) g,s Similarly), m g,s For the train journey g to the station s before the previous train, M is a very large positive number; η g,g′,χ For binary variables, if train journey g and train journey g′ are connected at station χ (g precedes g′), then η g,g′,χ =1. Let χ be the minimum and maximum turnaround time for train service at the station, and H be the set of time intervals. As an auxiliary variable, it equals (d i,k -d i-1,k )·α i,k,h α i,k,h This is a binary variable representing whether the time when train service i leaves station k is within [t]. h-1 ,th Within the specified time period. i,k Let f(k,S) be the departure time of train service i at station k. Let o be the index of station k in the marshalling yard set S, if f(k,S)=1 exists. i,o The train journey corresponding to train service i when it leaves station o. For the train service's operating time within the section between station k and k+1, dw k The stop time of the train at station k. v t is the collection of train services in direction v, where i is the index of the train service. h Indicates t h time.

[0043] The objective function (Formula (1)) is to maximize the number of adjacent trains (d) g,χ and The departure intervals of trains must be within the limits set by the station, and their departure intervals cannot exceed the maximum departure interval stipulated by the station. (As constrained by constraint (2)). Due to actual operating conditions, the departure interval between adjacent train services must be kept within a certain range. As shown in constraint (3), formula (4) ensures that the travel time between adjacent stations for each train journey meets the specified travel time r. g Formulas (5) and (7) ensure that each train journey requires a fixed stop time at each station. To allow passengers to board and alight normally, formula (5) indicates that additional stopping time at marshalling yards needs to be considered for train refitting. g-g' ,like Figure 3 As shown. Formula (6) is to ensure that the departure time of each train service must be within the experimental time period. Formulas (8)-(10) ensure the turnaround time a of the train service. g',χ -d g,χ -t g-g' (where t) g-g' (Adjusting train schedules) within a reasonable range Formulas (11)-(12) are (d i,k -d i-1,k )·α i,k.h The linearization formula is used. The departure time of each train service at each station can be calculated using constraint (13). Formulas (14)-(17) are used to determine which time period the departure time of train services in both directions at their respective departure stations belongs to, so as to calculate the passenger flow in different time periods.

[0044] In this model, we assume that the train service’s running time and stop time in each section are constant. Therefore, the variables in this part only include the train running interval and the adaptation time between each train journey.

[0045] S5: Use the GUROBI commercial solver to solve the timetable optimization model in S4, and obtain the train turnaround parameters. and parameters related to passenger flow distribution and And output the parameters;

[0046] S6: Input the train turnaround-related parameters and passenger flow allocation-related parameters obtained from S5 into the passenger flow allocation and rolling stock turnover plan collaborative optimization model M3.

[0047] S7: Establish a collaborative optimization model M3 for passenger flow allocation and vehicle turnover planning. The specific model is as follows:

[0048] The objective functions are: minimizing the number of stranded passengers J1, minimizing the fixed cost of the vehicle chassis J2 (i.e., the cost of purchasing the chassis), and minimizing the operating cost of the chassis (by reducing the number of times the chassis is used through flexible grouping) J3.

[0049] min J1,J2,J3(18);

[0050] Each train journey g can only have one type of train formation p (Formula (19)):

[0051]

[0052] Furthermore, the length of its train formation cannot exceed the length of the station platform (Formula (20)):

[0053]

[0054] Formula (21) calculates the number of train units in the current train journey:

[0055]

[0056] Formulas (22) and (23) ensure that the carriage refit between adjacent train journeys meets the refitting rules of the station:

[0057]

[0058]

[0059] Formula (24) calculates the number of train unit deviations between adjacent train journeys:

[0060]

[0061] η g,g',χ The variable is a binary variable, indicating whether the train journey g connects to the return train journey g' after turning back at station χ. Formulas (25)-(26) ensure that each outgoing train journey can connect to at most one return train journey after turning back.

[0062]

[0063] Formula (27) indicates that if train journey g arrives at station χ and there is no subsequent train journey connecting to it, then the train car comes from the depot and returns to the depot δ. g',χ :

[0064]

[0065] Formula (28) If, after a train journey g arrives at station χ, there is no subsequent train journey connecting it, then the train car needs to return to the depot τ. g,χ :

[0066]

[0067] Formulas (29)-(30) ensure that the adaptation of adjacent train journeys after turning back at the turnaround station complies with the station's formation rules:

[0068]

[0069] The deviation in the number of train units between adjacent turnaround connections at the terminal station can be calculated using formula (33), where formulas (31)-(32) represent β. g,p,g',p',χ ·η g,g',χ Linearization constraints:

[0070]

[0071] Regarding the capacity of train sets at stations, the first priority is to ensure that the number of train units used on the line does not exceed the maximum number of available train units N. u (e.g., constraint (34)):

[0072]

[0073] In addition, the initial number of train units at each station in each direction, as well as the number of train units remaining at the station after each train journey departs, must not exceed the maximum number of train units specified for each direction. (As per constraints (35)-(36)), formula (37) calculates the train journey g at ordinary marshalling yards respectively. The number of train units in stock at the station after departure is shown below:

[0074]

[0075] Formula (38) means that for a terminal station in one direction (v = up, if x = s) f ;v = down, if χ = s0), only when the train journey chooses to return to the depot at this station. This will affect the changes in the station's vehicle inventory, as shown in the following expression:

[0076]

[0077] Formulas (39)-(40) are for N g,u ·τ g,χ The linearization process:

[0078]

[0079]

[0080] Similarly, for a starting point in one direction (v = down, if χ = s) f ;v=up,ifχ=s0), when the train journey g originates from the garage Or adapted from a return trip and this station (Z) g,u All of these factors will affect changes in the station's vehicle inventory:

[0081]

[0082] (42)-(43) are the nonlinear components N related to train service departure. g,u ·δ g,χ The linearization process:

[0083]

[0084] In reality, the time spent on train services during coupling and decoupling is different. Therefore, it is necessary to determine the reorganization status of train services at this station based on the deviation in the number of train formations between two adjacent train journeys, and calculate the reorganization time separately, as shown in formulas (44)-(51). The specific expressions are as follows:

[0085]

[0086]

[0087] In the constraints related to passenger flow allocation, formula (52) is based on the arrival rate of each pair of OD(k,k') passengers at each time point:

[0088]

[0089] The cumulative number of OD passengers arriving during the period from the departure time of the last train service to the departure time of the current train service is counted. Constraints (53)-(54) are linearization constraints:

[0090]

[0091] Formula (55) represents the total number of arriving passengers at the station:

[0092]

[0093] The number of waiting passengers includes both newly arriving passengers and stranded passengers who were unable to leave on the previous train service (Formula (56)):

[0094]

[0095] The number of passengers boarding cannot exceed the total number of waiting passengers (constraint (57)):

[0096]

[0097] To ensure that the remaining capacity of arriving trains is not exceeded (constraint (58)):

[0098]

[0099] The difference between waiting passengers and boarding passengers is the number of stranded passengers.

[0100]

[0101] The proportion of different origin-destination (OD) points is calculated based on historical passenger flow data. Passengers from different OD points board the bus proportionally, and the number of passengers alighting can also be calculated proportionally.

[0102]

[0103] The number of passengers served by each train depends only on the passengers' actions of getting on and off the train:

[0104]

[0105] Formula (62) is a calculation of the remaining capacity of train service, which is only related to the number of passengers on board and the number of passengers getting off:

[0106]

[0107] Finally, since train services may undergo refitting operations at marshalling yards, which will affect the capacity of train services, it is necessary to determine the capacity of train services in different sections using formula (63), as shown below:

[0108]

[0109] S8: Use the GUROBI commercial solver to solve for the undercarriage turnover plan and passenger flow allocation plan, and output the objective function value J1. *(u) J2 *(u) J3 *(u)Number of stranded passengers Linkage or delinking time

[0110] S9: Based on the output results of steps S5 and S8, calculate the optimization objective value L for this iteration. (u) =J1 *(u) +J2 *(u) +J3 *(u) .

[0111] S10: Determine the loop termination condition based on the solution generation and the number of iterations. The determination condition is as follows: |L (u) -L (u -1) |≤ε, that is, to determine the objective function value L at the current iteration number. (u) The objective function value L obtained from the previous iteration (u -1) Is the absolute value of the difference less than a minimum value ε?

[0112] Where K is the set of stations, K = {1, 2, ..., |K|}. k, k′, k″ are the indices of the stations, k, k′, k″ ∈ K. s, s′ are the indices of the stations, s, s′ ∈ S. s0,s f Let Γ be the starting and ending stations of the line. U is the set of train types, where u is the index of a train type, u∈U. P is a set of possible train formations, where p is the index of a train formation, p∈P; ε is a set of adaptation rules, ε={O,X,abO,aXb}, where e is the index of an adaptation rule, e∈ε. e Let P be a train formation pair (p, p′) (p, p′ ∈ P) such that the train formation changes from p to p′ after being adapted according to the adaptation rule e ∈ ε. D is the set of directions, D = {down, up}, and v is the index of the direction, v ∈ D. v Let i be the set of train services in direction v, and i be the index of the train service, i∈I. v T v It is the collection of train journeys in the direction v. g, g′ are the indices of the train journeys, g, g′∈T v T pair It is the set of pairs connecting train journeys. (g,g′) is a set of pairs connecting train journeys, (g,g′)∈T. pair . s g-g′ To connect train journeys g and g′ at marshalling yard s, s g-g′ ∈T pair e s The routing rules used on site S. f It is the collection of the final destination, S f ={s0,s f}. χ is the index of the terminal station, χ∈S f n p,u M represents the number of u-type train units in train formation p. g,s,v This represents the set of train journeys that start from station s and are planned to depart in the direction of v before train journey g. This represents a set of train journeys to the destination station χ that are planned to arrive before the train journey g (inclusive). N represents the set of train journeys departing from stations that are scheduled to arrive at the final destination χ before train journey g (inclusive). u This represents the total number of available U-shaped train units. c ,t uc This indicates the time for train service coupling and uncoupling. The minimum and maximum turnaround time at the station for train service is χ. k,k',h For in [t h-1 ,t h [Time period] The arrival rate of passengers traveling from station k to station k'. μ k”,k Let ζ represent the percentage of passengers at station k whose destination is also station k. ζ is a positive time interval. p Let be the standard passenger capacity of train formation p. f(k,S) is a function to determine if station k is a marshalling yard. ξ is the maximum permissible load factor for the train. dw k The stop time of the train at station k. The operating time of the train service within the section between station k and k+1. u The cost of purchasing train unit u. π g,p The cost of using train sets p for a train journey g. It is a binary variable. If a train unit is decoupled when the train journey g is transitioned to g', otherwise It is a binary variable. If a train unit is coupled when the train journey changes from g to g', otherwise

[0113] x g,p N is a binary variable indicating whether combination p is used for train journey g; g,u `l` is an integer variable representing the number of U-shaped train units used in the train journey `g`. p L is the length of group g; g β is the length of the shortest platform corresponding to the train journey g; g,p,g′,p′ This is a binary variable indicating whether train journey g is a train set p, and whether train journey g′ is a train set p′. Z g,u Let Z be an integer variable, representing the coupling before the train journey g.g,u >0) or decompile (Z) g,u The number of u-type train units with values ​​<0. η g,g′,χ For binary variables, if train journey g and train journey g′ are connected at station χ (g precedes g′), then η g,g′,χ =1. δ g,χ For binary variables, if the train journey g departs from station χ, then δ g,χ =1. τ g,χ Let τ be a binary variable. If the train journey g enters the depot at station χ, then τ g,χ =1. As an auxiliary variable, it is equal to β. g,p,g′,p′ ·η g,g′,χ . This represents the number of U-shaped train units stored at station s in the direction of train journey g after the train departs. This represents the initial number of U-shaped train units stored at station s in the v direction. As an auxiliary variable, it equals N. g,u ·τ g,χ . As an auxiliary variable, it equals N. g,u ·δ g,χ . Let α be the number of passengers who arrive at station k and travel to k' during the time interval between train service time i-1 and departure time i. i,k,h This is a binary variable representing whether the time when train service i leaves station k is within [t]. h-1 ,t h Within the time period. As an auxiliary variable, it equals (d i,k -d i-1,k )·α i,k,h . This represents the number of passengers who arrive at station k during the time interval between train service i-1 and departure time i. This represents the number of people waiting at station k for train service i. This represents the number of passengers who boarded train service i at station k and left the station. This represents the number of remaining passengers on train i when it arrives at station k and all disembarking passengers have disembarked. This represents the number of passengers on the train after train service i departs from station k. The number of passengers disembarking at station k for train service i. This represents the number of passengers remaining in station k after train service i departs. This represents the maximum passenger capacity of train service i after it leaves station k. i,k This indicates the departure time of train service i at station k.

[0114] 1) The objective function value L at the current iteration number (u) The objective function value L obtained from the previous iteration (u-1) If the absolute value of the difference is less than ε, then proceed to step S3;

[0115] 2) If none of the above termination conditions are met, then exit the loop and output all current solutions.

[0116] Therefore, the present invention adopts the above-mentioned flexible train formation operation diagram compilation method that considers the matching of subway supply and demand. It can be applied to scenarios where the spatial and temporal distribution of passenger flow is uneven and the transportation capacity does not match the demand. It adopts the method of flexibly changing the train formation length at specific stations to match the passenger flow demand in different regions and time periods, while improving vehicle utilization and ensuring the feasibility of the rolling stock turnover plan. It provides a reference for operating companies to apply flexible formation technology in practice.

[0117] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A flexible train formation diagram compilation method considering metro supply and demand matching, characterized in that: Includes the following steps: S1. Obtain passenger flow information in urban rail transit and basic data for train timetable planning; S2. Based on the basic data of the train operation diagram, establish an optimization model of the train timetable under the flexible formation mode, use the GUORBI commercial solver to solve it, and generate a flexible formation train timetable. S3. Based on the flexible train timetable, establish a collaborative optimization model for passenger flow allocation and train turnaround plan, use the GUORBI commercial solver to solve the model, and generate train turnaround plan and passenger flow allocation plan. S4. Record relevant data on flexible train timetables, rolling stock turnover plans, and passenger flow allocation plans, and generate objective function evaluation indicators; S5. Based on the evaluation indicators, through iterative optimization, the iterative target optimization value that meets the termination condition and the result of flexible train timetable compilation are selected. In step S2, the timetable optimization model under the flexible grouping mode is established as follows: Depending on the number of marshalling yards selected, a complete train service is broken down into multiple train journeys. Establish a series of constraints to complete the mapping between train services and train journeys, and calculate the capacity of train services in each section; The variables in the timetable optimization section are the running intervals and rescheduling times between train services; Starting from the initial departure locomotive, the search for the optimal departure locomotive is initiated, and the maximum allowable value of the locomotive is gradually reduced. The initial value of the maximum departure locomotive is set according to the actual maximum locomotive pattern. In step S3, the timetable optimization model under the flexible grouping mode is a mixed integer programming model, and the specific modeling process is as follows: Establish the constraints required for each stage of the model, including: train service interval constraints, train service arrival and departure time constraints, train service reorganization time constraints at marshalling yards, and train service turnaround time constraints; and establish the mapping between train departure time and departure period. Define the objective function of the timetable optimization model, which includes maximizing the running interval between adjacent train services. 2.The method of claim 1, wherein the method further comprises: determining a train formation based on the demand and supply of the metro line. In step S1, the passenger flow information in urban rail transit includes: daily automatic fare collection system data for urban rail transit; the basic data for train timetable compilation includes: train decoupling / coupling time, interval travel time, vehicle type, train stop time, maximum / minimum train interval time, and maximum / minimum turnaround time. 3.The method of claim 1, wherein the method further comprises: determining a train formation based on the demand and supply of the metro line. In step S4, the collaborative optimization model for passenger flow allocation and train turnaround plan, established based on the optimization results of the flexible train timetable, is modeled as follows: Establish the constraints required for each stage of the model, including: rolling stock turnover constraints, marshalling yard capacity constraints, train service adaptation constraints, train service marshalling constraints, mapping constraints between train services and each train journey, and passenger flow allocation constraints. Based on the mathematical properties of the constraints, nonlinear constraints are transformed into linear constraints; The objective function of the timetable optimization model is defined, specifically including: minimizing the number of stranded passengers, minimizing the purchase cost of train units, and minimizing the operating cost of trains.

Images