A train timetable optimization method for urban rail line network considering transfer coordination

Abstract

This application discloses a train timetable optimization method for urban rail transit networks considering transfer coordination, belonging to the field of urban rail transit technology. The method includes: acquiring network topology, transfer station information, train operation parameters, and passenger flow data; constructing a timetable optimization model and generating an initial timetable, considering constraints such as departure intervals, station dwell times, travel times, and turnaround times, with the objective of minimizing the total travel time and operating costs of passengers on the line; identifying the set of transfer stations and direction mappings based on the network topology, and extracting train arrival and departure events from the timetable; optimizing the train time windows at each transfer connection point with the objective of minimizing the total waiting time for transfers across the entire network, forming a time window contract; adding this contract to the optimization model and resolving it to obtain a new timetable; and outputting the final timetable by judging whether the improvement in transfer waiting time has converged. This method effectively improves the overall service level and economic benefits of multi-line networks while reducing computational complexity.

Description

Technical Field

[0001] This application relates to the field of urban rail transit technology, and in particular to a method for optimizing train timetables for urban rail transit networks that considers transfer coordination. Background Technology

[0002] Urban rail transit network operation has become mainstream, with passenger journeys typically involving multiple transfers across lines. Transfer stations play a pivotal role in network passenger flow organization, and the quality of transfer connections directly impacts passengers' overall travel time, platform congestion, and operational service levels. To improve the overall transportation efficiency and passenger service level of urban rail transit networks, it is necessary to coordinate and optimize the arrival and departure times of cross-line trains at transfer stations, while ensuring the independent and stable operation of each line. This is crucial for reducing passenger waiting time, balancing line load, and enhancing network transport capacity.

[0003] Traditional timetable creation methods primarily rely on independent optimization of individual lines, with cross-line coordination depending on manual verification or experience-based adjustments. This makes it difficult to systematically minimize transfer waiting times and peak congestion at a network-wide scale, and their robustness to operational disturbances and passenger flow fluctuations is limited. While centralized network-wide mixed-integer linear programming is theoretically sound, it is computationally intensive and time-consuming under complex networks and peak window conditions. Heuristic local adjustments, lacking a network-wide perspective, are prone to getting trapped in local optima and struggle to ensure optimal coordination between lines. Summary of the Invention

[0004] To address the aforementioned shortcomings in existing technologies, this application provides a train timetable optimization method for urban rail transit networks that considers transfer coordination, solving the problems of long solution time and lack of a systematic, network-wide perspective in existing technologies.

[0005] To achieve the aforementioned objectives, the technical solution adopted in this application is as follows: This application provides a method for optimizing train timetables in urban rail transit networks that considers transfer coordination, including: S1: Obtain key datasets including network topology, transfer station information, train operation parameters, and passenger flow data; S2: Based on the key dataset, establish a timetable optimization model with the objective function of minimizing the total travel time and operating cost of passengers on this route, and with constraints of departure interval, stop time, running time and turnaround time, and generate an initial timetable; S3: Determine the set of all transfer stations and direction mappings for each line based on the network topology, and use the global coordinator to extract all train arrival and departure events involving transfer stations from the initial timetable. S4: Based on train arrival and departure events at transfer stations, with the goal of minimizing the total waiting time for transfers across the entire network, collaboratively optimize the train time windows at each transfer connection point and generate time window contracts; S5: Add the time window contract as a hard constraint to the timetable optimization model, solve it again and generate a new timetable; S6: Based on the new timetable, determine whether the improvement in the total waiting time for transfers meets the convergence condition. If not, return to S3; otherwise, obtain the final timetable for each line.

[0006] Further, S2 includes: S201: Based on the key dataset, a comprehensive objective function is established, with the goal of minimizing the total travel time and operating cost of passengers on this route. The expression is as follows:

[0007]

[0008]

[0009] in, For the time period, the route Total passenger travel time For discrete time segments, and upper and lower bounds For the line The starting and ending station numbers on the map. For the line The total number of sites, For time segments At the station Boarding, destination is Will take the line The number of passengers For time segments At the station Average waiting time For the line From arrive The time spent traveling inside the vehicle, For time segments At the station Complete the transfer from other lines to this line, and then proceed on the line. Depend on Go to The number of passengers For those on the station The travel time for transfers, For the time period, the route Operating costs For time segments The number of trains operating. This is a comprehensive target considering the total travel time and operating costs for passengers on this route. and These are the weighting coefficients; S202: Establish interval operation consistency constraints and station stopping consistency constraints, the expression is:

[0010] in, For train number On the site The arrival time, For train number On the site The arrival time, For train number On the site The departure time For the site Stop time, For interval runtime For the first train during the study period, The last train during the study period; Establish the first departure interval constraint, expressed as:

[0011] in, , The upper and lower limits of the first train departure interval. For train number At the starting station The departure time For train number At the starting station Departure time; Establish a stop time constraint, expressed as follows:

[0012] in, , These are the upper and lower limits of the stop time. This refers to the stop time; Establish the interval running time constraint, the expression is:

[0013] in, , For interval The upper and lower bounds of the runtime; Establish a turnaround time constraint, expressed as follows:

[0014] in, For train number At the turnaround station The departure time For train number At the turnaround station The arrival time, Minimum turnaround time to the final destination; S203: Determine the initial value of the time-segment first train interval that satisfies the first train departure interval constraint based on the intensity of passenger flow demand, and obtain the number of trains to be operated based on the initial value of the time-segment first train interval. The expression is as follows:

[0015] in, This is the initial value for the first shift interval in different time slots. For the length of the film, For the line In time segment The number of trains operating on the platform; S204: Construct a timetable optimization model based on the objective function and constraints, solve the timetable optimization model, and extract the arrival and departure times of each train, the first departure interval of each time period, and the corresponding number of trains from the optimal or feasible solution to obtain the initial timetable.

[0016] Further, S4 includes: S401: Identify train arrival and departure events reported by all lines for transfer stations, group them by station-platform-direction, and construct a set of paired cross-line transfer pairs. The calculation formula is as follows:

[0017] in, For the set of cross-line transfer pairs, Indicates the train number of the sending line. Train numbers on the receiving line Connections at the same transfer station , For train number , The route in question The transfer station where the train incident occurred. For receiving train numbers At the arrival time at the transfer station, For the train number of the sending line At the departure time of the transfer station, For passengers from the departure line train number Get off at the receiving line. Transfer time required to board the train This is the upper limit of the maximum permissible transfer time window; S402: Based on the paired cross-line transfer pair set, an objective function is established to minimize the total transfer waiting time of the entire network. The calculation formula is as follows:

[0018] In the formula, To meet the demand for transfers, This refers to the actual waiting time. The actual waiting time satisfies the following constraints:

[0019] S403: Based on the objective function of minimizing the total transfer waiting time of the entire network and the waiting time satisfying the constraints, a line time window constraint is established, and the calculation formula is as follows:

[0020] in, For the train numbers corresponding to the initial timetable On the site The departure time For the train numbers corresponding to the initial timetable On the site The arrival time, and Adjust the time window range; S404: Based on the objective function of minimizing the total transfer waiting time across the entire network and the line time window constraint, the initial timetable is fine-tuned, and the fine-tuned timetable satisfies the following constraints:

[0021]

[0022] S405: The simulated annealing algorithm is used to solve the fine-tuned timetable, obtaining the time offset and updated arrival and departure times for each train on each line, thus obtaining the optimized timetable. The formula for calculating the time offset is:

[0023] in, This is the time offset. The updated departure times; S406: Based on the optimized timetable, a time window contract is generated for each time period of each route. The calculation formula is as follows:

[0024] in, For time window contracts, For containing time segments A collection of key train numbers for all trains involving transfer stations. For train number On the site The upper limit of the departure time window, For train number On the site The lower bound of the departure time window. For train number On the site The upper bound of the arrival time window, For train number On the site The lower bound of the arrival time window. This is the allowable cumulative duration range. This represents the cycle length of the time period corresponding to the initial running chart. To allow for a small degree of flexibility.

[0025] Further, S5 includes: S501: The global coordinator transmits the generated time window contract to each line, and each line extracts key parameters from the time window contract. S502: Based on the extracted key parameters, the upper and lower bounds of the single-vehicle arrival and departure window specified in the time window contract are added as hard constraints to the time schedule optimization model on the decision variable boundary of the time schedule optimization model, narrowing the original flexible range to the time window specified in the contract. The calculation formula is as follows:

[0026] S503: Apply upper and lower bound constraints to the total running and stopping times of the time window contract train sets within each time period. The calculation formula is as follows:

[0027] S504: Based on departure interval constraints, stop time constraints, running time constraints, turnaround time constraints, contract hard constraints, and upper and lower bound constraints imposed by the total running and stop times of the time window contract train sets within each time period, the timetable optimization model is re-solved to generate a new timetable.

[0028] Further, S6 includes: S601: After each iteration, the latest timetables for each line are summarized, the total waiting time for transfers across the entire network is recalculated, and compared with the total waiting time for transfers in the previous round to obtain the improvement amount. The expression for the improvement amount is:

[0029] in, To improve the quantity, The total waiting time for transfers across the entire network is recalculated. This refers to the total waiting time for transfers across the entire network in the previous round; S602: Set the convergence threshold and the maximum number of iterations. If the improvement amount is lower than the threshold or the maximum number of iterations is reached, convergence is determined and the final timetable is output. Otherwise, update the total waiting time for transfers across the entire network, return to S3 to continue generating a new time window contract and re-optimize.

[0030] The beneficial effects of this application are: This application provides a train timetable optimization method for urban rail transit networks that considers transfer coordination. By establishing a hierarchical optimization framework and a time window contract mechanism, it achieves efficient synchronous scheduling of multi-line urban rail transit networks. Each line obtains its initial timetable by solving its optimization model and uploads train arrival and departure events involving transfer stations. The global coordinator identifies cross-line transfer pairings based on this aggregated information and fine-tunes train times within a small window, generating explicit time window contracts that each line adheres to during local re-optimization. This reduces passenger transfer waiting times across the entire network while maintaining the stability of each line's operating schedule. Compared to a one-time large-scale solution across the entire network, this method reduces computational complexity through strategy decomposition and information interaction, effectively improving the overall service level and economic benefits of the multi-line network. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other embodiments can be obtained based on these drawings.

[0032] Figure 1 This is a flowchart illustrating a method for optimizing train timetables in urban rail transit networks that considers transfer coordination, as provided in an embodiment of this application. Detailed Implementation

[0033] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art based on this application are within the scope of protection of this application.

[0034] Example 1: This application provides a method for optimizing train timetables in urban rail transit networks that considers transfer coordination, addressing the following technical problems: how to overcome the computational complexity and slow solution of traditional integrated optimization methods in large-scale urban rail transit networks, and achieve efficient timetable generation through hierarchical task decomposition; and how to ensure that cross-line transfer nodes coordinate while guaranteeing independent optimization of each line, thereby ensuring optimal overall network operating efficiency. This method can be found in [reference needed]. Figure 1 , Figure 1 The diagram shown is a flowchart illustrating a method for optimizing train timetables in urban rail transit networks that considers transfer coordination, as provided in an embodiment of this application. The method includes: S1: Obtain key datasets including network topology, transfer station information, train operation parameters, and passenger flow data.

[0035] S2: Based on the key dataset, establish a timetable optimization model with the objective function of minimizing the total travel time and operating cost of passengers on this route, and with constraints such as departure interval, stop time, running time and turnaround time, and generate an initial timetable.

[0036] The specific method of step S2 includes the following sub-steps: S201: Establish an objective function with the goal of minimizing the total travel time and operating cost of passengers on this route. Assume that the service mode adopts a stop-at-every-station, periodic operation, approximates demand according to time segments, and approximates the average waiting time of passengers at the platform with half departure intervals.

[0037] ① Establish the target total travel time for passengers based on the formula:

[0038] in, For the time period, the route Total passenger travel time For discrete time segments, and upper and lower bounds For the line The starting and ending station numbers on the map. For the line The total number of sites, For time segments At the station Boarding, destination is Will take the line The number of passengers For time segments At the station Average waiting time For the line From arrive The time spent traveling inside the vehicle, For time segments At the station Complete the transfer from other lines to this line, and then proceed on the line. Depend on Go to The number of passengers For those on the station The travel time for transfers.

[0039] ② Establish operating cost targets based on the formula:

[0040] in, For the time period, the route Operating costs For time segments The number of trains operating.

[0041] ③ Based on the formula, establish an objective function with the overall goal of minimizing total passenger travel time and operating costs:

[0042] in, This is a comprehensive target considering the total travel time and operating costs for passengers on this route. , These are the weighting coefficients.

[0043] S202: Establish constraints, including: Establish interval operation consistency constraints and station stop consistency constraints based on the formula:

[0044] in, For the site, For train number, For train number On the site The arrival time, For train number On the site The arrival time, For train number On the site The departure time For the site Stop time, For interval runtime For the first train during the study period, This refers to the last train during the study period.

[0045] Establish the first shift departure interval constraint based on the formula:

[0046] in, , The upper and lower limits of the first train departure interval. For train number At the starting station The departure time For train number At the starting station The departure time.

[0047] Establish stop time constraints based on the formula:

[0048] in, , These are the upper and lower limits of the stop time. This refers to the stop time.

[0049] Establish interval running time constraints based on the formula:

[0050] in, , For interval The upper and lower bounds of the runtime.

[0051] Establish turnaround time constraints based on the formula:

[0052] in, For train number At the turnaround station The departure time For train number At the turnaround station The arrival time, This is the minimum turnaround time at the final destination.

[0053] S203: Based on passenger demand intensity, provide initial values ​​for time-segmented first-shift intervals that satisfy the first-shift departure interval constraint. According to the formula based on film length Rounding to estimate time segment Number of trains operating:

[0054] in, For the line In time segment The number of trains operating on the platform.

[0055] S204: Solve the established timetable optimization model using the Gurobi solver. After the solution is completed, extract the arrival and departure times of each train from the optimal or feasible solution. , First bus departure intervals in different time slots and the corresponding column count Export the initial timetable and record the departure and arrival times of each train at each station in vector form to form the route. The complete running graph and objective function values.

[0056] S3: The global coordinator extracts train schedule information for all trains involving transfer stations along the line.

[0057] The specific method for step S3 is as follows: In the analysis window Inside (of which, To analyze the start time of the window, To analyze the end time of the window, the set of all transfer stations and direction mappings for each line are first determined based on the network topology. The global coordinator then filters the arrival and departure events of these stations from the generated timetable, including the line, station, train number, direction, arrival and departure times.

[0058] S4: Based on train arrival and departure events at transfer stations, the upper-level global coordinator aims to minimize the total waiting time for transfers across the entire network, collaboratively optimizes the train time windows at each transfer connection point, and generates time window contracts.

[0059] The specific method of step S4 includes the following sub-steps: S401: Identify all reported transfer station arrival and departure events based on the formula, group them by station-platform-direction, and construct a set of pairable cross-line transfer pairs. :

[0060] Among them, each pair Indicates the train number of the sending line. Train numbers on the receiving line Connections at the same transfer station satisfy both time window and walking time constraints. , , For train number , The route in question The transfer station where the train incident occurred. For receiving train numbers At the arrival time at the transfer station, For the train number of the sending line At the departure time of the transfer station, For passengers from the departure line train number Get off at the receiving line. Transfer time required to board the train This is the upper limit of the maximum permissible transfer time window.

[0061] S402: Based on the set of paired cross-line transfer pairs, an objective function is established to minimize the total transfer waiting time of the entire network, according to the formula:

[0062] in, To meet the demand for transfers, This represents the actual waiting time.

[0063] S403: Establish actual waiting time constraints based on the formula:

[0064] S404: Establish time window constraints for the line based on the formula:

[0065] in, For the train numbers corresponding to the initial timetable On the site The departure time For the train numbers corresponding to the initial timetable On the site The arrival time, and To adjust the time window range, the arrival and departure times of each route's initial timetable are only allowed within the window. Internal fine-tuning to ensure that the original first shift interval and operation schedule structure are not disrupted. , It can be set by time period or train number.

[0066] S405: Fine-tune the initial timetable according to the formula:

[0067] The slightly adjusted timetable continues to meet the consistency requirements of arrival / departure and interval, as well as the upper and lower limits of the first shift interval at the originating station, ensuring that the operation plan is physically feasible and that the service level is not degraded.

[0068] S406: Apply constraints to all transfer pairs according to the formula:

[0069] Among these, for all transfer pairs, the arrival time of the mandatory pick-up is no earlier than the departure time plus walking time. The absence of circular dependencies ensures that the arrival and departure times of each train have a legal order after the time window is fine-tuned, avoiding the situation where three constraints cannot be satisfied at the same transfer station, which would lead to an infeasible solution to the optimization problem.

[0070] S407: Considering the scale and complexity of this mixed-integer programming problem, simulated annealing is used to accelerate convergence and reduce computational resource consumption. After processes such as initialization, neighborhood generation, constraint checking and objective calculation, cooling, and iteration, the optimal solution encountered throughout the process is extracted, corresponding to the time offset of each train on each line. With the updated arrival and departure times , Record metadata such as the final target value, percentage of improvement, number of iterations, and solution time to evaluate the suitability of algorithm parameters and solution quality.

[0071] S408: According to the formula, for each line Each time period Generate time window contract structure :

[0072] in, This is a set of key train services, which includes time periods. All train services involving transfer stations within the area, , These are the upper and lower limits of the arrival and departure window for a single train. During subsequent optimization of each route, the arrival and departure times of that train at that station must fall within this window to ensure the feasibility of transfers and connections with other routes. For train number On the site The upper limit of the departure time window, For train number On the site The lower bound of the departure time window. For train number On the site The upper bound of the arrival time window, For train number On the site The lower bound of the arrival time window. This is the allowable cumulative duration range. This represents the cycle length of the time period corresponding to the initial running chart. To allow for slight flexibility, this constraint applies to the window. All contracted train services The sum of total running time and stop time is subject to upper and lower limits to ensure that contracted train services do not significantly change the stability of the operating cycle and vehicle turnover efficiency while meeting transfer coordination requirements.

[0073] S5: After receiving the contract, each lower-level line adds it as a hard constraint to the timetable optimization model, solves it again, and generates a new timetable.

[0074] The specific method of step S5 includes the following sub-steps: S501: The global coordinator will generate the contract structure. The data is passed to each line, and each line extracts key parameters such as the sub-index set and the upper and lower bounds of the arrival and departure times of each train at each station from the contract structure.

[0075] S502: Based on the formula, the upper and lower bounds of the single-vehicle arrival and departure window specified in the contract are added as hard constraints to the timetable optimization model on the decision variable boundary of the S2 optimization model. This narrows the original flexible range to the time window specified in the contract, ensuring that the solver automatically meets the global coordination requirements when searching within the feasible region.

[0076] S503: Time period based on formula Upper and lower bound constraints are applied to the total running and stopping times of the inner contract train set:

[0077] S504: Re-solve the timetable optimization model according to the formula, and re-optimize each route using the solver:

[0078] The objective function maintains the weighted minimization of travel time and operating costs, with added hard contract constraints; the solution is obtained from the initial solution of S2 to obtain a new optimal solution that satisfies the contract, and the objective function value is recorded.

[0079] S6: Determine whether the improvement in the total waiting time for transfers meets the convergence condition. If not, return to S3; otherwise, obtain the final timetable for each line.

[0080] The specific method for step S6 is as follows: S601: After each iteration, summarize the latest timetables for each line and recalculate the total waiting time for transfers across the entire network. And compared with the total waiting time for the previous transfer. The improvement amount was obtained by comparison. .

[0081] S602: Set convergence threshold and maximum number of iterations If the improvement amount is below the threshold or the maximum number of iterations is reached, convergence is determined, and the final timetable is output; otherwise, the timetable is updated. Then, return to the upper layer to continue generating new time window contracts and re-optimize.

[0082] This application provides a train timetable optimization method for urban rail transit networks that considers transfer coordination. By establishing a hierarchical optimization framework and a time window contract mechanism, it achieves efficient synchronous scheduling of multi-line urban rail transit networks. Each line obtains its initial timetable by solving its optimization model and uploads train arrival and departure events involving transfer stations. The global coordinator identifies cross-line transfer pairings based on this aggregated information and fine-tunes train times within a small window, generating explicit time window contracts for each line to adhere to during local re-optimization. This reduces passenger transfer waiting times across the entire network while maintaining the stability of each line's operating schedule. Compared to a one-time large-scale solution across the entire network, this method reduces computational complexity through decomposition strategies and information interaction, effectively improving the overall service level and economic benefits of the multi-line network.

[0083] It should be noted that those skilled in the art will recognize that the embodiments described herein are for the purpose of helping readers understand the principles of this application, and should be understood as not limiting the scope of protection of this application to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this application without departing from the essence of this application, and these modifications and combinations are still within the scope of protection of this application.

Claims

1. A method for optimizing train timetables in urban rail transit networks considering transfer coordination, characterized in that, include: S1: Obtain key datasets including network topology, transfer station information, train operation parameters, and passenger flow data; S2: Based on the key dataset, establish a timetable optimization model with the objective function of minimizing the total travel time and operating cost of passengers on this route, and with constraints of departure interval, stop time, running time and turnaround time, and generate an initial timetable; S3: Determine the set of all transfer stations and direction mappings for each line based on the network topology, and use the global coordinator to extract all train arrival and departure events involving transfer stations from the initial timetable. S4: Based on train arrival and departure events at transfer stations, with the goal of minimizing the total waiting time for transfers across the entire network, collaboratively optimize the train time windows at each transfer connection point and generate time window contracts; S5: Add the time window contract as a hard constraint to the timetable optimization model, solve it again and generate a new timetable; S6: Determine whether the improvement in the total waiting time for transfers meets the convergence condition based on the new timetable. If not, return to S3. Otherwise, obtain the final timetable for each route.

2. The method for optimizing train timetables for urban rail transit networks considering transfer coordination according to claim 1, characterized in that, S2 includes: S201: Based on the key dataset, a comprehensive objective function is established, with the goal of minimizing the total travel time and operating cost of passengers on this route. The expression is as follows: in, For the time period, the route Total passenger travel time For discrete time segments, and upper and lower bounds For the line The starting and ending station numbers on the map. For the line The total number of sites, For time segments At the station Boarding, destination is Will take the line The number of passengers For time segments At the station Average waiting time For the line From arrive The time spent traveling inside the vehicle, For time segments At the station Complete the transfer from other lines to this line, and then proceed on the line. Depend on Go to The number of passengers For those on the station The travel time for transfers, For the time period, the route Operating costs For time segments The number of trains operating. This is a comprehensive target considering the total travel time and operating costs for passengers on this route. and These are the weighting coefficients; S202: Establish interval operation consistency constraints and station stopping consistency constraints, the expression is: in, For train number On the site The arrival time, For train number On the site The arrival time, For train number On the site The departure time For the site Stop time, For interval runtime For the first train during the study period, The last train during the study period; Establish the first departure interval constraint, expressed as: in, , The upper and lower limits of the first train departure interval. For train number At the starting station The departure time For train number At the starting station Departure time; Establish a stop time constraint, expressed as follows: in, , These are the upper and lower limits of the stop time. This refers to the stop time; Establish the interval running time constraint, the expression is: in, , For interval The upper and lower bounds of the runtime; Establish a turnaround time constraint, expressed as follows: in, For train number At the turnaround station The departure time For train number At the turnaround station The arrival time, Minimum turnaround time to the final destination; S203: Determine the initial value of the time-segment first train interval that satisfies the first train departure interval constraint based on the intensity of passenger flow demand, and obtain the number of trains to be operated based on the initial value of the time-segment first train interval. The expression is as follows: in, This is the initial value for the first shift interval in different time slots. For the length of the film, For the line In time segment The number of trains operating on the platform; S204: Construct a timetable optimization model based on the objective function and constraints, solve the timetable optimization model, and extract the arrival and departure times of each train, the first departure interval of each time period, and the corresponding number of trains from the optimal or feasible solution to obtain the initial timetable.

3. The method for optimizing train timetables for urban rail transit networks considering transfer coordination according to claim 2, characterized in that, S4 includes: S401: Identify train arrival and departure events reported by all lines for transfer stations, group them by station-platform-direction, and construct a set of paired cross-line transfer pairs. The calculation formula is as follows: in, For the set of cross-line transfer pairs, Indicates the train number of the sending line. Train numbers on the receiving line Connections at the same transfer station , For train number , The route in question The transfer station where the train incident occurred. For receiving train numbers At the arrival time at the transfer station, For the train number of the sending line At the departure time of the transfer station, For passengers from the departure line train number Get off at the receiving line. Transfer time required to board the train This is the upper limit of the maximum permissible transfer time window; S402: Based on the paired cross-line transfer pair set, an objective function is established to minimize the total transfer waiting time of the entire network. The calculation formula is as follows: In the formula, To meet the demand for transfers, This refers to the actual waiting time. The actual waiting time satisfies the following constraints: S403: Based on the objective function of minimizing the total transfer waiting time of the entire network and the waiting time satisfying the constraints, a line time window constraint is established, and the calculation formula is as follows: in, For the train numbers corresponding to the initial timetable On the site The departure time For the train numbers corresponding to the initial timetable On the site The arrival time, and Adjust the time window range; S404: Based on the objective function of minimizing the total transfer waiting time across the entire network and the line time window constraint, the initial timetable is fine-tuned, and the fine-tuned timetable satisfies the following constraints: S405: The simulated annealing algorithm is used to solve the fine-tuned timetable, obtaining the time offset and updated arrival and departure times for each train on each line, thus obtaining the optimized timetable. The formula for calculating the time offset is: in, This is the time offset. The updated departure times; S406: Based on the optimized timetable, a time window contract is generated for each time period of each route. The calculation formula is as follows: in, For time window contracts, For containing time segments A collection of key train numbers for all trains involving transfer stations. For train number On the site The upper limit of the departure time window, For train number On the site The lower bound of the departure time window. For train number On the site The upper bound of the arrival time window, For train number On the site The lower bound of the arrival time window. This is the allowable cumulative duration range. This represents the cycle length of the time period corresponding to the initial running chart. To allow for a small degree of flexibility.

4. The method for optimizing train timetables for urban rail transit networks considering transfer coordination according to claim 3, characterized in that, S5 includes: S501: The global coordinator transmits the generated time window contract to each line, and each line extracts key parameters from the time window contract. S502: Based on the extracted key parameters, the upper and lower bounds of the single-vehicle arrival and departure window specified in the time window contract are added as hard constraints to the time schedule optimization model on the decision variable boundary of the time schedule optimization model, narrowing the original flexible range to the time window specified in the contract. The calculation formula is as follows: S503: Apply upper and lower bound constraints to the total running and stopping times of the time window contract train sets within each time period. The calculation formula is as follows: S504: Based on departure interval constraints, stop time constraints, running time constraints, turnaround time constraints, contract hard constraints, and upper and lower bound constraints imposed by the total running and stop times of the time window contract train sets within each time period, the timetable optimization model is re-solved to generate a new timetable.

5. The method for optimizing train timetables for urban rail transit networks considering transfer coordination according to claim 4, characterized in that, S6 includes: S601: After each iteration, the latest timetables for each line are summarized, the total waiting time for transfers across the entire network is recalculated, and compared with the total waiting time for transfers in the previous round to obtain the improvement amount. The expression for the improvement amount is: in, To improve the quantity, The total waiting time for transfers across the entire network is recalculated. This refers to the total waiting time for transfers across the entire network in the previous round; S602: Set the convergence threshold and the maximum number of iterations. If the improvement amount is lower than the threshold or the maximum number of iterations is reached, convergence is determined and the final timetable is output. Otherwise, update the total waiting time for transfers across the entire network, return to S3 to continue generating a new time window contract and re-optimize.

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