A method for jointly optimizing urban rail transit express and local train timetable and passenger distribution

Abstract

This invention discloses a joint optimization method for express and local train timetables and passenger allocation in urban rail transit, belonging to the field of transportation technology. The method includes: acquiring line station data, operational constraints, vehicle parameters, and dynamic passenger flow data; based on this, a mixed-integer linear programming model is constructed to simultaneously optimize train timetables and train formations, with the objective of minimizing the weighted sum of the total number of stranded passengers and the required total number of trains. The core constraints of the model include physical constraints on the timetable, station passenger flow allocation constraints considering different passenger choices for express and local trains, and train service and departure order mapping constraints to handle dynamic changes in train sequence caused by express trains overtaking local trains. A two-stage heuristic algorithm combined with a commercial solver is used to solve the model, outputting results including the precise arrival and departure times of each train, train formation schemes, and passenger flow allocation. This invention achieves efficient coordinated matching of capacity and passenger demand under a mixed express and local train operation mode.

Description

Technical Field

[0001] This invention relates to the field of transportation technology, and in particular to a method for jointly optimizing urban rail transit express and local train timetables and passenger allocation. Background Technology

[0002] Urban rail transit plays a crucial role in urban passenger transport. With the rapid growth of passenger demand, urban rail transit operators face increasingly severe challenges in increasing capacity to alleviate the pressure of massive passenger flow and reducing operating costs. Achieving a precise match between transport capacity and passenger demand is crucial for urban rail transit systems. In recent years, cost-oriented transport planning methods have received widespread attention, with their core focus on reducing operating costs such as labor costs, energy consumption, vehicle purchase and maintenance. Scholars have proposed many different co-optimization methods, such as the co-optimization of train timetables and routes, timetable development under skip-stop schemes, and the co-optimization of flexible train formation plans and train timetables. Among these, express and local train modes aim to reduce energy consumption and meet the travel needs of different passengers, but the occurrence of overtaking behavior also makes passenger allocation more complex. Flexible train formation schemes aim to significantly reduce vehicle depreciation costs. On the other hand, service-oriented transport planning focuses more on improving passenger service levels, such as maximizing the total demand attracted by trains, minimizing passenger waiting / travel time, and avoiding passenger congestion. Numerous studies have reached similar conclusions: compared to timetables with fixed departure intervals, single-stop patterns, and fixed train formations, timetables with mixed express and local train operations, flexible stop patterns, and flexible train formations can provide better service to passengers while saving more operating costs.

[0003] Therefore, how to construct complex scenarios for train operation under the mixed express and local train mode, consider the synergistic optimization of objectives such as passenger service level and operating cost, meet the diverse travel needs of passengers, and ensure the operational economic benefits of enterprises are technical problems that urgently need to be solved by those skilled in the art. Summary of the Invention

[0004] The purpose of this invention is to provide a method for jointly optimizing the timetables of urban rail transit express and local trains and passenger allocation, so as to systematically solve the various shortcomings existing in the background technology.

[0005] To achieve the above objectives, the present invention provides a method for joint optimization of urban rail transit express and local train timetables and passenger allocation, comprising: Acquire basic data for urban rail transit lines and for train timetable planning, including: station sets, line physical constraints (such as minimum / maximum running time between sections, minimum / maximum station dwell time, minimum safe headway), vehicle parameters (such as standard carriage capacity, maximum load factor, and set of train formation types), and dynamic passenger travel demand (OD) data obtained through the automatic fare collection (AFC) system. Discretize the continuous passenger flow data into average arrival rates over multiple time intervals.

[0006] Based on the mixed-integer linear programming optimization model for urban rail transit express and local train timetables that consider mixed vehicle configurations, the GUROBI commercial solver is used to solve the model and generate a flexible train timetable. The model generates optimization results that include the precise arrival and departure times of each train at each station and the train formation scheme specified for each train.

[0007] Record relevant data on train timetables, train formation schemes, and passenger flow allocation plans for the mixed vehicle configuration, and introduce key indicators such as average passenger waiting time and average train occupancy rate as evaluation indicators for the objective function.

[0008] Based on the aforementioned model and evaluation indicators, the performance of the proposed model and method is explored using different weighting coefficients, enabling decision-makers to make trade-offs between service quality and operating costs according to actual needs and select the solution that best meets their policy objectives.

[0009] Preferably, based on actual train timetable data and under the condition that the travel time and stop time within the service area are fixed, an optimization model for urban rail transit express and local train timetables considering mixed vehicle configurations was established, specifically including: The coupling and uncoupling of trains are assumed to take place at the depot or the originating and terminating stations; secondly, passenger transfers between different train services are not considered. If an arriving train stops at both the passenger's departure and destination stations and there is sufficient capacity on board, the passenger will board. The assumption that passengers tend to take the earliest departing train that will reach their destination significantly simplifies the calculation without unduly affecting the passenger allocation results, transforming complex, nonlinear passenger selection behavior into a deterministic, linearly expressible allocation process.

[0010] The variables in the timetable optimization section include variables related to train timetables and variables related to train formation. Among them, the variables related to train timetables include the specific arrival time and departure time of each train; the variables related to train formation include formation selection variables and vehicle quantity variables.

[0011] Such urban rail transit express and local train timetable optimization models that consider mixed vehicle configurations can simultaneously handle the physical constraints of timetable arrangement and the dynamic behavior of passenger flow, especially solving the problem of train sequence changes caused by express and local trains passing each other.

[0012] Preferably, the urban rail transit express and local train timetable optimization model considering mixed vehicle configuration is a mixed-integer linear programming model, and the specific modeling process is as follows: Establish the constraints required for each stage of the model, including: timetable-related constraints, passenger allocation constraints at each station, passenger allocation constraints for each train, and establishing a mapping relationship between train service and departure sequence; The objective function of the timetable optimization model is set to minimize the weighted sum of one or more operational indicators, specifically including: minimizing the total number of stranded passengers generated at all stations within the planning time domain to improve service quality; and minimizing the total number of trains required to execute the train schedule to reduce vehicle purchase and maintenance costs. Preferably, the urban rail transit express and local train timetable optimization technology considering mixed vehicle configuration proposes different calculation formulas for the number of waiting passengers and the number of stranded passengers for different passenger flow characteristics. At the same time, considering the computational complexity of the problem, the passenger allocation constraints of each station are linearized according to the mathematical properties of the constraints, transforming nonlinear constraints into linear constraints, which can effectively reduce the computational complexity of the problem.

[0013] Preferably, considering that express trains may overtake slow trains at certain stations, causing the relative order of trains at different stations to change dynamically, the urban rail transit express and slow train timetable optimization technology considering mixed vehicle configuration constructs a mapping constraint between train services and departure order, dynamically associates each independent train service identifier with its actual departure order at each station, determines the departure order of any two trains at each station, and calculates the specific departure order integer value of each train at that station, ensuring the logical consistency and accuracy of the model under dynamic changes in train order.

[0014] As can be seen, this invention proposes a mixed-integer linear programming (MILP) model to collaboratively optimize train formation and timetables based on actual passenger demand. The optimization objective is to minimize the number of stranded passengers and the required number of trains. The model includes two types of constraints: constraints related to timetable formation and constraints related to passenger allocation. Furthermore, timetable optimization is applicable to mixed traffic modes that include local trains (stop-at-every-station trains) and overtaking express trains. Express trains overtake local trains at specific stations; therefore, this study establishes mapping constraints to match each train service with the corresponding departure sequence at different stations to ensure the accuracy of passenger allocation. To effectively solve the comprehensive optimization problem, this study proposes 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. The optimization method proposed in this invention can effectively reduce the travel time of long-distance passengers, reduce operating costs (vehicle purchase investment), and flexibly respond to the changing passenger flow demand at different times (peak and off-peak), so as to effectively achieve the best match between transportation capacity and passenger demand and improve the operation and organization level of the rail transit system.

[0015] Therefore, the urban rail transit express and local train timetable and passenger allocation joint optimization method using the above structure of the present invention has the following beneficial effects: This invention is applicable to mixed service modes that include local trains that stop at every station and express trains that overtake, achieving coordinated optimization of train formation and timetables. This invention proposes a mixed-integer linear programming model that not only considers the mixed vehicle deployment strategy of using long formations during peak hours and short formations during off-peak hours, but also the complex scenario of express trains overtaking local trains, leading to dynamic changes in train departure order, and establishes mapping constraints to achieve precise matching of the actual departure order of all train services at each station, ensuring the accuracy of passenger flow allocation. The model aims to reduce the number of stranded passengers and the number of train formations. This invention can significantly improve passenger service levels, effectively reduce vehicle purchase and operating costs, and provide strong decision support for the refined and efficient operation of modern urban rail transit.

[0016] 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

[0017] Figure 1 A flowchart of a method for jointly optimizing urban rail transit express and local train timetables and passenger allocation provided by the present invention; Figure 2 This is a graph showing the discrete time period and arrival rate to which this invention applies; Figure 3This is a schematic diagram of passenger flow distribution at various stations to which this invention applies; Figure 4 This is a mapping diagram showing the train departure and departure sequences to which this invention applies. Detailed Implementation

[0018] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0019] 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.

[0020] Example Based on actual operational data from existing urban rail transit timetables and the actual spatiotemporal distribution of passenger flow, this study focuses on an urban rail transit line with multiple stations, aiming to optimize the train timetable in one direction. Unlike most urban subway lines with a single train speed, this corridor features two different types of train operations: express trains and local trains. Express trains stop only at stations with multiple tracks, while local trains stop at every station, allowing express trains to overtake local trains at stations with sufficient overtaking conditions. A mixed-integer linear programming model is proposed to optimize train formation and timetables. Furthermore, the model includes timetable-related constraints, station passenger allocation constraints, and train passenger allocation constraints, and also establishes a mapping constraint between train service and departure order. This model aims to reduce the number of stranded passengers and lower operating costs.

[0021] To effectively solve comprehensive optimization problems, this invention proposes a hybrid solution method combining a two-stage heuristic algorithm with the GUROBI commercial solver to improve computational speed. The urban rail transit express and local train timetables generated by the proposed method, considering mixed vehicle configurations, can significantly improve the matching degree between capacity supply and passenger flow, thereby enhancing the service level of urban rail transit systems while reducing enterprise costs. This has significant theoretical guiding significance for the operation and organization of urban rail transit under a mixed vehicle formation strategy.

[0022] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0023] like Figure 1 As shown, the present invention provides a joint optimization method for urban rail transit express and local train timetables and passenger allocation, comprising: S1: Initialization, including objective function weights. and And input relevant route and station data: number of stations Meet at the station And the specific set of stations where express trains are allowed to overtake slow trains; passenger demand data: the planning cycle for train timetable optimization problems. Within, the number of passengers for each OD pair and the arrival times of passengers at the departure station; Train and operational parameters: including the set of train services. The maximum number of carriages in the train formation scheme and minimum number of carriages, and minimum headway Minimum stop time , interval running time Operating parameters, etc.

[0024] S2: Establish an optimization model for urban rail transit express and local train timetables that considers mixed vehicle configurations. The specific model is as follows: Objective function: (1); in, This represents the objective function of the optimization problem; Indicates train The number of carriages; Represents the set of stations and its index. , ; Indicates the collection of slow trains. ; Indicates at the station Waiting to board the first The number of passengers who departed on a train and were unable to take an express train; Indicates at the station Reaching the top The number of passengers on the departing train; and These are weighting coefficients, reflecting policymakers' preference for the two optimization indicators: the number of stranded passengers and the number of vehicles in use. The value of the weighting coefficient can be flexibly adjusted according to the needs of the operational scenario (such as focusing on reducing congestion during peak hours and controlling vehicle deployment during off-peak hours) to reflect the optimization priorities under different decision-making orientations.

[0025] Discretize continuous time into several time intervals of equal duration (e.g.) Figure 2 The discrete time period and arrival rate are shown in the diagram. The set of discrete time points is denoted as , where... Represents the duration of a single time interval, and satisfies (Right now , (This represents the total number of discrete time intervals). Based on this, parameters are introduced to characterize OD pairs. In time interval The passenger travel rate within the area is calculated using the following formula: , (2); , (3); in, Indicates in During the time period, the OD (Original Direction) of the vehicle is Passenger rate, ; Indicates the start time of the experiment; Represents a set of time periods and its index. ; indicates in During the time period, the OD (Original Direction) for train travel is The number of passengers arriving at the station during that time period accounted for a significant portion of the total number of passengers arriving at the station. The proportion of total passengers ; This indicates that the research period was long.

[0026] In the timetable-related constraints, formulas (4) and (5) ensure that the train's stopping time at each station and the running time between sections are within a reasonable range, as follows: , (4); , (5); in, Indicates that the train is at the station. The minimum and maximum stopping times, ; Represents any train At the station departure time, ; Represents any train At the station To the station The minimum and maximum interval running time, ; Indicates a set of express trains; Indicates train The collection of stop stations, ; Represents any train At the station The arrival time, .

[0027] Formula (6) ensures a safe departure interval between adjacent trains and is a nonlinear constraint, as detailed below: , (6); in, Indicates adjacent trains at the station Action occurs To action The interval length, ; Represents any train At the station Execute action Time, ; Indicates train index, .

[0028] Therefore, integer variables are introduced. and binary variables Perform linearization: when When, it means; conversely Based on this, the linearization transformation process of constraint (5) can be expressed as formulas (7)-(11), as follows: , (7); , (8); , (9); , (10); , (11); in, This represents the set of actions a train takes at a station and its index. , This indicates that the train has arrived at the station. This indicates that the train has left the station. This indicates that the train passes through the station without stopping. Indicates adjacent trains With the train At the station Departure intervals, ; The variable is 0-1, if it exists If , then = 1; otherwise = 0, and ; It is a very large positive number; In the constraints related to passenger flow allocation at each station, formula (12) stipulates that the first... The departure time for each train is unique, as detailed below: , (12); in, The variable is 0-1. If at the station The day of departure The departure time of this train is within the time period If it is inside, then =1; otherwise =0; Indicates at the station The set of trains stopping at each station and their departure order index. , .

[0029] Constraint (13) is used to determine the first The specific time period to which the train's departure time belongs; constraint (14) is based on the first... The actual departure time of this train has been determined. The value of is represented by formula (15) for the variable. The type; Formula (16) is the constraint for calculating the number of arriving passengers; Formula (17) represents the number of passengers arriving from any station. Before the first train departed. ( The number of new arriving passengers at the station within minutes (given in advance); Formulas (8)-(20) are the results of linearizing Formula (16); Formula (21) represents the number of new arriving passengers at any station. , No. trip and the first The number of new passengers during the departure period of a train; Formulas (22) and (23) respectively represent the number of passengers who can ride both express and local trains. (i.e., regardless of the number) Whether the train is an express or local train, it will stop at its destination station, as well as passengers who cannot take the express train. (That is, express trains will not stop at their destination); at any station The Before the train departs, the composition of passengers waiting on the platform is as follows: Figure 3As shown in the passenger allocation diagram, the number of waiting passengers who cannot take the express train is represented by formula (24), while the number of waiting passengers who can take both express and local trains is represented by formula (25); formula (26) represents the number of passengers on the platform willing to take the first train. The total number of passengers on a train is linearized using two constraint equations (27) and (28) since the formula is nonlinear; equations (29) and (30) represent the total number of passengers on any train. You can take the train at the station. The number of passengers leaving the train; Formulas (31) and (32) represent the number of stranded passengers who cannot take the express train and the number of stranded passengers who can take both express and local trains, respectively. These two formulas are also nonlinear formulas. Formulas (33)-(42) are used to linearize the two formulas respectively. The specific expressions are as follows: , (13); in, It represents a very small positive number.

[0030] , (14); , (15); in, Indicates from the station The day of departure The train has a departure time.

[0031] , (16); , (17); , (18); , (19); , (20); in, Indicates the first trip and the first The departing trains arrive at the station between their departure times. And the destination is the station. The number of passengers; As an auxiliary variable, it equals .

[0032] , (twenty one); , (twenty two); in, Indicates the first trip and the first The train arrives at the station between departure times. The number of passengers, Indicates the first trip and the first The departing trains arrive at the station between their departure times. And the number of passengers who are unable to take the express train. The variable is 0-1; if the express train is not at the station... or station If the car stops, the value is 1; otherwise, it is 0.

[0033] , (twenty three); in, Indicates the first trip and the first The departing trains arrive at the station between their departure times. And the number of passengers who can ride on both express and local trains.

[0034] , (twenty four); in, Indicates at the station Waiting to board the first The number of passengers who departed on a train and were unable to take an express train.

[0035] , (25); in, Indicates at the station Waiting to board the first The number of passengers on a departing train that can be used on both express and local trains.

[0036] , (26); in, Indicates at the station Waiting to board the first The number of passengers on the departing train.

[0037] , (27); , (28); , (29); , (30); , (31); , (32); , (33); , (34); , (35); in, Indicates failure to board from the station The day of departure The number of passengers on a train that can be used for both express and local services. Indicates failure to board from the station The day of departure The number of passengers on the train who are unable to take the express train. The variable is 0-1. If from the station The day of departure If the train is an express train, then =1; otherwise =0.

[0038] , (36); , (37); , (38); , (39); , (40); , (41); , (42); in, As an auxiliary variable, its value is 0-1. =0, then =1; if = - If , then = 0; As an auxiliary variable, its value is 0-1. =0, then =1; if = - If , then = 0. As an auxiliary variable, it equals max{ - ,0}. As an auxiliary variable, it equals max{ - ,0}.

[0039] In the train-related passenger flow allocation constraints, formula (43) represents any train service The corresponding number of passengers inside the train (i.e., the train's passenger capacity); Formula (44) represents the number of passengers at the station. Previous station boarding train service And the destination is The number of passengers, and introduce auxiliary variables that satisfy constraints (45) and formula (46). The nonlinear part in the substitution ( The constraints are rewritten as (47); formula (48) represents arbitrary train service. Arriving at the station The remaining capacity after; Formula (49) represents any train service The number of carriages is limited; Formula (50) represents any train service The number of passengers carried cannot exceed the train's maximum passenger capacity requirement. The specific expression for the above formula is as follows: , (43); in, Indicates train Leaving the station The number of passengers inside the vehicle at that time; Indicates at the station board the train The number of passengers; Indicates train At the station The number of passengers who alighted.

[0040] , (44); in, The variables are 0-1, if the train At the station The departure time in the time period If it is inside, then =1; otherwise =0.

[0041] , (45); in, As an auxiliary variable, it equals .

[0042] , (46); , (47); , (48); in, Indicates train Arriving at the station The remaining capacity inside the car.

[0043] , (49); in, Indicates the minimum and maximum number of carriages in a train; Indicates train The number of carriages.

[0044] , (50); in, This indicates the maximum occupancy rate of a train carriage. This indicates the standard passenger capacity of a train carriage.

[0045] In the mapping constraint between train departure and arrival sequences, in actual operation scenarios, express trains will complete overtaking operations of regular trains at specific stations (such as...). Figure 4 As shown), based on this, formula (51) indicates that if Then at the station Train service exists On train service Then leave; conversely, . Indicates at the station Compared to train service The number of trains that depart first, the integer variable in formula (52) Indicates train service At the station The order of departure is expressed as 0-1 integer variables in formula (53); formulas (54)-(56) introduce two binary variables and Used to indicate at the station The day of departure Whether a train corresponds to a train service; Formulas (57)-(59) represent the process of converting the interaction variables associated with the departure order at the station into variables related to the train service; Formulas (60)-(61) construct the following mapping relationship from the train service order to the train departure order, and the specific expressions of the above formulas are shown below: , (51); in, The variables are 0-1, if the train On the train Then leave the station =1; otherwise =0.

[0046] , (52); , (53); in, Indicates train At the station The order of departure.

[0047] , (54); , (55); , (56); , (57); , (58); , (59); , (60); , (61); in, The variable is 0-1. If from the station The day of departure A train is a train If the value is 1, then =1; otherwise =0. The variable is 0-1. If from the station The train that departed was the train. If the result is positive, then the value is 1; otherwise, it is 0.

[0048] In this model, we assume that: train refitting is only completed at the depot or the starting and ending stations of the line; shunting operations within each depot are not within the scope of this study, and the model assumes them as known input conditions; we do not consider passenger transfer behavior between different train services, and passengers will only choose to board the train if it stops at both the passenger's departure and destination stations at the same time and there is remaining capacity in the carriage; we also assume that passengers prioritize the "earliest departing train that can take them to their destination".

[0049] S3: Input the model into the Gurobi Business Optimization Solver for solving. The solver uses advanced heuristic algorithms to find the optimal decision variable values ​​that minimize the objective function. The final solution includes: the objective function value, the precise arrival and departure times of each train (express or local) at each station, the specific number of train cars per train, and the predicted passenger boarding, alighting, and congestion information for each station and time period.

[0050] S4: Calculate the average passenger waiting time using the output from step S3. With average train load factor The specific quantitative calculation method is shown in formulas (62)-(63), as follows: (62); (63); To intuitively reflect the impact of the operation plan on passengers' travel time costs, and to intuitively represent the utilization efficiency of transportation resources—too high a load factor means that transportation capacity is tight and may affect passengers' comfort; too low a load factor indicates that transportation capacity is idle and resources are wasted, so as to scientifically evaluate the effectiveness of the optimization plan.

[0051] 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 method for joint optimization of urban rail transit express and local train timetables and passenger allocation, characterized in that, Includes the following steps: S1. Obtain basic data of urban rail transit lines and basic data for train timetable planning. The basic data includes: station set, line physical constraints, vehicle parameters, and passenger travel demand data that changes dynamically over time through the automatic fare collection system. The continuous passenger flow data is discretized into the average arrival rate over multiple time intervals. S2. Establish a mixed-integer linear programming model for the joint optimization of urban rail transit express and local train timetables and passenger allocation, considering mixed vehicle configurations. The model includes timetable-related constraints, passenger allocation constraints at each station, passenger allocation constraints for each train, and constraints for establishing the mapping relationship between train service and departure sequence. The objective function of the above model is also set. S3. Input the model established in step S2 into the solver to solve it, and generate optimization results including the precise arrival and departure times of each train at each station and the train formation scheme of each train. S4. Record relevant data on train timetables, train formation schemes, and passenger flow allocation plans for mixed vehicle configurations, and calculate key indicators.

2. The method according to claim 1, characterized in that, In step S1, the physical constraints of the line include the minimum / maximum running time of the section, the minimum / maximum stopping time of the station, and the minimum safe headway; the vehicle parameters include the standard capacity of the carriages, the maximum load factor, and the set of train formation types.

3. The method according to claim 1, characterized in that, In step S2, the objective function of the model is set to minimize the weighted sum of one or more operational indicators, including: minimizing the total number of stranded passengers generated at all stations within the planning time domain, and minimizing the total number of trains required to execute the train timetable; the weighting coefficients are adjusted to balance passenger service levels and operating costs.

4. The method according to claim 1, characterized in that, In step S2, a mapping relationship constraint between train service and departure order is established. This constraint determines the departure order of any two trains at each station by introducing a first set of binary variables, and calculates the integer value of the specific departure order of each train at that station accordingly. At the same time, a second set of auxiliary variables is introduced to mathematically associate the timetable variable based on the train service identifier with the passenger allocation variable based on the departure order.

5. The method according to claim 1, characterized in that, In step S2, the passenger allocation constraints for each station include: calculating the number of waiting passengers and the number of stranded passengers of different types according to the different passenger flow characteristics. The different types include passengers who cannot take express trains and passengers who can take both express and local trains; and linearizing the nonlinear passenger allocation constraints for each station according to the mathematical properties of the constraints, transforming the nonlinear constraints into linear constraints.

6. The method according to claim 1, characterized in that, In step S3, a combination of heuristic algorithms and commercial solvers is used to solve the mixed-integer linear programming model. The heuristic algorithm is a two-stage heuristic algorithm that divides the comprehensive optimization problem into two subproblems and solves them using a heuristic search method to improve the computation speed.

7. The method according to claim 1, characterized in that, In step S2, the timetable-related constraints include the train's stopping time at each station, the interval running time constraint, and the safe departure interval constraint between adjacent trains; among them, the safe departure interval constraint is a nonlinear constraint, which is linearized by introducing integer variables and binary variables.

8. The method according to claim 1, characterized in that, In step S4, key indicators include average passenger waiting time and average train occupancy rate. The optimization results are used to calculate the average passenger waiting time and average train occupancy rate to intuitively reflect the impact of the operation plan on passenger travel time costs and the utilization efficiency of transportation resources.

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