A method for optimizing the coordinated operation of a bus and subway integrated network

Abstract

This invention discloses a collaborative operation optimization method for an integrated bus and metro network, comprising the following steps: S1, collecting and standardizing topology data, train timetable data, and passenger travel demand data; S2, constructing a multi-layer coupled spatiotemporal network; S3, performing K-shortest path search to generate a set of passenger reachable paths; S4, verifying the reachability of the passenger path selection set under train operation rules; S5, constructing a scheduling scheme based on the allocation probabilities output by the Logit model; S6, inputting the time-series operation data into an improved Mamba network to constrain and correct the number of train departure pairs and the first station departure time, forming an evaluation index for the optimization objective function. This invention achieves collaborative optimization of train operation sequence and passenger travel demand in an integrated bus and metro network, and is applicable to intelligent scheduling and dynamic passenger flow control scenarios in large-scale urban rail transit systems.

Description

Technical Field

[0001] This invention relates to the field of urban public transportation system optimization, and in particular to a collaborative operation optimization method for an integrated bus and subway network. Background Technology

[0002] In the current urban transportation system, subways and buses, as two major modes of public transportation, play a vital role in providing travel services in high-density commuting environments. However, due to the long-term independent operation of subways and buses in terms of planning, construction, operation management, and scheduling strategies, numerous problems of incoordination exist in terms of service capacity matching, transfer coordination, route connectivity, and operational efficiency. Specifically, during morning and evening rush hours, bus routes near subway stations are prone to uneven departure intervals, excessively long waiting times, or short-term congestion, making it difficult to effectively coordinate with the subway train schedule. This increases passengers' overall travel time and transfer costs, and reduces the network's operational efficiency.

[0003] Existing research on integrated bus-subway scheduling largely focuses on macro-level network planning or rule-based static scheduling optimization, lacking the ability to dynamically model differences in travel time, spatial routes, and passenger demand. Especially in scheduling coordination involving multiple routes, multiple train services, and multiple time periods, conventional methods struggle to simultaneously balance the feasibility of departure plans, passenger travel efficiency, and operational resource allocation. Furthermore, existing methods, in the joint optimization of multiple scheduling variables (such as the number of departure pairs and the first departure time), often overlook the complex coupling relationship between travel time and passenger demand, failing to effectively predict travel time and passenger flow response under cascading route changes, leading to deviations in actual operation after the scheduling plan is implemented.

[0004] To address the aforementioned issues, this paper proposes a collaborative optimization method for integrated public transport and metro systems based on multi-layer coupled spatiotemporal network modeling and an improved Mamba network prediction mechanism. By constructing a unified public transport-metro topology and operating network, it achieves joint optimization of scheduling variables under path reachability constraints. Furthermore, by combining state-space recursion and passenger flow distribution modeling, it enables high-precision prediction of running time and passenger flow status under the scheduling scheme. This method overcomes the limitations of traditional scheduling optimization, such as isolated variables, coarse constraints, and a single evaluation dimension, providing a new solution for improving the collaborative efficiency of integrated public transport and metro networks and enhancing passenger travel experience. Summary of the Invention

[0005] One objective of this invention is to propose a collaborative operation optimization method for integrated public transport and metro networks. This invention fully integrates multi-layer coupled spatiotemporal network modeling, K-shortest path search, Logit path allocation model, and an improved Mamba network prediction mechanism. It details the optimization modeling process for collaborative scheduling of urban rail transit and surface public transport systems, achieving dual optimization of departure plans and passenger travel efficiency. This method possesses advantages such as high scheduling accuracy, strong adaptability, and high operational efficiency, effectively improving the overall service level of urban multimodal transportation systems.

[0006] A method for optimizing the coordinated operation of an integrated public transport and subway network according to an embodiment of the present invention includes the following steps:

[0007] S1. Collect and standardize topology data, train timetable data, and passenger travel demand data;

[0008] S2. Construct a multi-layer coupled spatiotemporal network by using topological foundations, timetable constraint layers, and spatiotemporal constraint layers.

[0009] S3. Based on the multi-layer coupled spatiotemporal network, perform K-shortest path search to generate a set of passenger reachable paths;

[0010] S4. Set decision variables and optimize the objective function, and verify the accessibility of the passenger route selection set under the train operation rules;

[0011] S5. Based on the allocation probability output by the Logit model, calculate the average travel time of passengers and generate a scheduling scheme consisting of the number of departure pairs on the route and the departure time of the first station.

[0012] S6. Input the time-series operation data into the improved Mamba network. In the state space recursive unit, combine the operation time parameters and passenger flow distribution prediction results to perform constraint verification and correction on the number of train departure pairs and the first station departure time. Based on the feasible scheduling scheme, calculate the average travel time of passengers and the total number of kilometers traveled by trains to form the evaluation index of the optimization objective function.

[0013] Optionally, the standardization process refers to performing format unification, semantic alignment, structural regularization, and missing data repair operations on the collected topological data, train timetable data, and passenger travel demand data, specifically including:

[0014] Standardization of topological data: The station numbers, inter-station connections, and route direction information of each bus and subway line are modeled in a unified manner. A unified graph structure abstraction method is adopted to form a topological graph data structure consisting of a set of station nodes and a set of directed edges. The edge attributes of the bus-subway transfer connections are labeled.

[0015] Standardization of train timetable data: The time fields such as departure time, arrival time, and stop time in the original train timetable are uniformly converted into a standard timestamp format, the time offset problem across midnight is corrected, and the time information between different lines is comparable and continuous under a unified time coordinate system.

[0016] Standardized processing of passenger travel demand data: The original travel log data is cleaned into structured data entries containing departure station number, arrival station number, departure time and number of passengers. Null values, duplicates and abnormal data are removed. Passenger travel demand is coded and classified according to route direction and time period to form an input format that meets the needs of network modeling and scheduling optimization.

[0017] Unified data spatiotemporal benchmark: The spatial attributes of topological structure data and travel demand data are converted into a unified geographic coordinate system, and the time attributes of train timetable data are unified into minute-based integer time codes to ensure spatiotemporal consistency across different data sources.

[0018] Semantic field alignment and missing completion: To address the differences in field naming and inconsistent granularity in topological data, train timetable data, and passenger travel demand data, field mapping rules and unified semantic templates are established, and interpolation and structural completion operations are performed on missing time data and discontinuous station connection relationships.

[0019] Optionally, S2 specifically includes:

[0020] S21. Combining train timetable data, the integrated bus and subway network is abstracted into a directed graph, forming a set of stations, edges, and lines, which serves as the topological basis for a multi-layered coupled spatiotemporal network.

[0021] The abstraction process is as follows: all stations in the integrated bus and subway network are defined as nodes in a directed graph; bus sections, subway sections, and transfer relationships are defined as directed edges in the directed graph; and running time, transfer time, and train departure time attributes are added to the directed edges to obtain the directed graph.

[0022] The integrated bus-metro network is a comprehensive transportation network structure formed by merging bus and metro networks through topological integration. The integrated bus-metro network consists of three basic components: a station set, an edge set, and a route set. The station set includes all bus stops, metro stations, and transfer stations; the edge set includes bus section edges, metro section edges, and transfer edges, representing the operational relationships between adjacent bus stops, adjacent metro stations, and transfer relationships between buses and the metro, respectively; and the route set includes all bus routes and metro routes.

[0023] The process of generating the integrated bus-subway network is as follows:

[0024] Collect bus network topology data, including bus route directions, stop locations, and travel time between adjacent stops;

[0025] Collect subway network topology data, including the distribution of subway line stations, track information between sections, and train timetable data.

[0026] By integrating the aforementioned bus network data with the subway network data, a unified set of stations is constructed. Bus section edges, subway section edges, and transfer edges are then introduced into the station set to form a comprehensive set of lines that includes both bus and subway lines. This generates a bus-subway integrated network that can be used for subsequent modeling and optimization.

[0027] S22. Within a continuous time interval, for any node in the directed graph, record the departure time information of each train in the upward direction and the departure time information of each train in the downward direction to form a timetable constraint layer.

[0028] S23. For any directed edge in a directed graph, assign a time weight to form a spatiotemporal constraint layer:

[0029] If it belongs to the transfer side, the time weight is the corresponding transfer time;

[0030] If it is the edge of a bus route, the time weight is the bus route travel time;

[0031] If it is the edge of a subway section, the time weight is the subway section travel time;

[0032] S24. When passengers travel in the integrated bus and subway network, the passenger's starting point, destination, and departure time are set to consistent parameters, and a group of passengers with the same starting point, destination, and departure time is defined as a passenger group. Through the aforementioned topology foundation, timetable constraint layer, and spatiotemporal constraint layer, a multi-layer coupled spatiotemporal network is constructed.

[0033] Optionally, S3 specifically includes:

[0034] S31. In a multi-layer coupled spatiotemporal network, each station is designed with a path label data structure. The path label data structure records the path status, cumulative path time and cost, predecessor node information, path source, and current path arrival time information.

[0035] S32. Design a K-shortest path search algorithm for spatiotemporal networks: Initialize the departure station and departure time of passengers, initialize the path labels of all stations in the integrated bus and subway network to the default state; divide the directed edges in the directed graph into up-going edges, down-going edges and transfer edges according to the direction type, and store them respectively.

[0036] S33. During the K-shortest path search, determine whether each edge has a train that can be taken:

[0037] If available trains exist, record the earliest time the passenger can reach the next node;

[0038] For transfer edges, update the path time based on the transfer time.

[0039] In each iteration, the path with the shortest cumulative time is selected from all path labels that are still in a temporary state and expanded, and the path with the shortest time is updated to a permanent state.

[0040] S34. When all K paths leading to the destination are marked as permanent, the K-shortest path search algorithm terminates. Then, through backtracking, the algorithm extracts the maximum K reachable paths from the origin to the destination from the departure time from the path label data structure, forming the passenger path selection set.

[0041] Optionally, S4 specifically includes:

[0042] S41. Historical passenger travel demand includes the origin, destination, departure time and number of passengers for each passenger group; the transfer time for passengers in the same transfer direction is uniformly set to the same value.

[0043] S42. Set the number of train departure pairs on the line and the first departure time of each train as decision variables for scheduling optimization, where the number of train departure pairs represents the number of trains deployed during the study period, and the first departure time represents the specific departure time of each train.

[0044] S43. Set the optimization objective function as minimizing the weighted sum of passenger weighted average travel time and total train mileage; set an upper limit constraint on the number of train departures on the line to ensure that the number of departures does not exceed the maximum available capacity;

[0045] Define train operation rules: calculate the arrival and departure times of each train at each station, and require that the travel time match the section length; the section length is the physical operating section length of the line between two adjacent stations;

[0046] At transfer stations, the connection between trains is restricted to ensure that transfers are only possible between trains that have the necessary connection conditions.

[0047] The constraint on the connection relationship between trains specifically includes the following:

[0048] Arrival and departure time constraints: When a train arrives at a transfer station, the two trains are considered to be able to connect only if there is an interval of not less than the time required for the transfer between the arrival time of the train and the departure time of the other train.

[0049] Constraints on directional consistency: Passengers can only transfer from the arrival direction of one train to the departure direction of another, and this directional relationship must conform to the station's transfer organization structure. If the two trains' operating directions do not allow for transfer logic, a connection cannot be established.

[0050] Physical feasibility constraint: Transfer relationships must correspond to actual physical transfer pathways, such as transfer routes from buses to subways or transfer passages within subway stations. If there are no transfer facilities available for passengers to pass between stations, a connection relationship will not be established.

[0051] The conditions for connection are as follows: only train pairs that simultaneously meet the time, direction, and physical conditions can be considered to have a connection and be included in the path search process. If any condition is not met, the two trains cannot be transferred, and the transfer path is excluded from the set of accessible paths for passengers.

[0052] Accessibility verification is performed on each path in the passenger path selection set to ensure that each path meets the train connection conditions and timetable constraints;

[0053] The accessibility verification process involves checking each of the passenger route selection sets after they are generated to ensure that they are actually usable by passengers.

[0054] The specific content of reachability verification includes:

[0055] Timetable constraint verification: For each train segment in the route, check whether passengers can board the train at the scheduled departure time. If a passenger arrives at a station later than the train's departure time, that segment of the route is not feasible.

[0056] Connectivity verification: At nodes involving transfers in the route, check whether there is a valid connection between the two trains, that is, whether the time interval between the arrival of the previous train and the departure of the next train meets the time requirements for transfer.

[0057] Full-process feasibility verification: From the departure station to the destination station, all train operations and transfer links along the route are verified segment by segment. If any segment of the route does not meet the timetable constraints or connection conditions, the entire route is determined to be unreachable.

[0058] The results of reachability verification include: if a path passes all verification conditions, it is marked as a "reachable path"; if a path fails verification, it is removed from the passenger path selection set and does not participate in subsequent travel allocation and optimization.

[0059] Optionally, S5 specifically includes:

[0060] S51. For a path that meets the accessibility verification conditions, calculate the total travel time for passengers from the origin to the destination, including travel time, waiting time, and transfer time.

[0061] S52. Calculate the allocation probability of passengers in the passenger route selection set based on the Logit model. The allocation probability decreases as the total travel time of the route increases.

[0062] The probability of a passenger being assigned a route within the passenger route selection set is determined using a Logit model to probabilistically allocate passenger travel routes. Specifically, the Logit model is calculated based on the following principles:

[0063] The passenger route selection set corresponding to each passenger group is used as the candidate route set, and each candidate route has a corresponding total travel time. The total travel time includes the cumulative result of travel time, waiting time, and transfer time, and is used to reflect the complete time required for passengers to actually complete the journey along that route.

[0064] The total travel time of candidate routes is mapped to a route utility value. The shorter the total travel time, the higher the corresponding utility value; the longer the total travel time, the lower the corresponding utility value. This utility value is used to measure passengers' relative preference for different routes.

[0065] The Logit model normalizes the utility values ​​of each path, transforming them into a probability distribution. In this distribution, each path corresponds to an allocation probability, and the sum of the allocation probabilities of all paths is 1. Paths with shorter travel times have significantly higher allocation probabilities than paths with longer travel times, thus ensuring that passengers are more inclined to choose the less time-consuming path from the candidate path set.

[0066] Based on the allocation probabilities obtained from the Logit model, passenger groups can be assigned routes. That is, for all passengers in the same passenger group, their trips will be distributed in the candidate route set according to the allocation probabilities, so as to form a passenger route allocation result that conforms to the actual travel pattern.

[0067] S53. Calculate the travel time of passenger groups, combine the allocation probability with the total travel time of the route to obtain the expected travel time of each passenger group;

[0068] S54. Calculate the overall index, weight the expected travel time of all passenger groups by the number of people, and obtain the average travel time of passengers under the scheduling plan.

[0069] S55. Using average passenger travel time and total train mileage as evaluation indicators, output the final departure plan and scheduling results.

[0070] Optionally, S6 specifically includes:

[0071] S61. Based on the collected topology data of the bus network and subway network, train timetable data and historical passenger travel demand data, combined with the number of train departure pairs and the first departure time, generate time-series operation data of arrival time, departure time and passenger distribution of each train at different stations.

[0072] S62. Input the time-series running data into the improved Mamba network, combine the timetable constraint layer and passenger travel demand data, and use the graph-coupled state-space recursive unit for modeling. In the recursive calculation process: local recursive calculation is adopted, and the running time is recursively updated based on the physical interval length between adjacent stations. It is required that the running time of each train meets the running time and interval length matching condition, so as to obtain the running time sequence covering all physical segments.

[0073] The specific steps for generating the runtime time series include:

[0074] Interval length as constraint input: There is an interval length between adjacent stations on each line. This data comes from the topology of the multi-layer coupled spatiotemporal network and is used as an input condition together with the train timetable data in the timetable constraint layer.

[0075] Running time recursive update: When the state space recursive unit calculates the running time of each train in the interval, the calculation result must meet the rule of matching running time with interval length. The rule of matching running time with interval length means that in the multi-layer coupled spatiotemporal network, the physical interval length between two adjacent stations is proportional to the running time of the corresponding train, ensuring that the running time is not less than the physical minimum running time and does not exceed the maximum allowable running time of the interval.

[0076] Iterative correction mechanism: If the running time obtained by recursion deviates from the interval length constraint range, the recursion step size is automatically adjusted through the uncertainty perception gating mechanism, and the running time parameters are corrected within the allowed time window until the running time meets the interval length constraint.

[0077] After completing the above-mentioned constraint input, recursive update and iterative correction, the running time series covering all intervals and trains is obtained, which is part of the output of the improved Mamba network.

[0078] Based on neighborhood coupling propagation using station sets and interval edge sets, the distribution of passenger travel origins, destinations, and departure times is mapped to a spatiotemporal network topology. During iterative propagation, a passenger flow distribution prediction sequence synchronized with the operational time series is generated. The spatiotemporal network topology refers to the spatial topology composed of station sets, interval edge sets, and line sets of the integrated bus-metro network. Based on this, passenger departure time distribution and train timetable constraints are introduced, coupling the spatial topology with the time index to form a multi-layered spatiotemporal graph structure covering the entire network. This structure is used to uniformly model the dynamic propagation relationship between operational time and passenger flow distribution.

[0079] The neighborhood coupling computation is adopted, and the passenger travel origin, travel destination and departure time distribution are mapped to the spatiotemporal network topology based on the neighborhood coupling propagation of the station set and the interval edge set. In the iterative propagation, a passenger flow distribution prediction sequence synchronized with the running time series is generated.

[0080] The specific steps for generating the passenger flow distribution prediction sequence include:

[0081] The origin, destination, and departure time distribution of passenger groups are used as input parameters and mapped onto the topology of a multi-layered coupled spatiotemporal network. The travel demand of each passenger group is projected onto the corresponding set of stations and interval edges, ensuring that the origin and destination are uniquely located in the network topology. The departure time serves as the time reference input for the timetable constraint layer.

[0082] In the state-space recursive unit of the improved Mamba network, the runtime prediction sequence and passenger travel demand are modeled simultaneously. Driven by graph-structured coupled propagation, the recursive unit expands the demand of each passenger group in the spatiotemporal dimensions, forming a set of candidate paths available for allocation. Based on this, combined with the previously verified path selection set, the allocation probability of each path is calculated using a Logit model. The allocation probability, as a weighting factor, is input into the recursive calculation along with the travel time of each path, enabling passenger demand to be dynamically allocated among different paths according to probability.

[0083] The recursive process iteratively allocates the demand for all passenger groups, mapping the allocation results to network nodes and interval edges at each time step. By normalizing the allocated number of passengers, the total number of passengers is kept constant, avoiding distortion caused by double counting or rounding errors. Passenger demand is reasonably unfolded on a continuous time series, and a passenger flow distribution matrix is ​​constructed using stations, intervals, and times as indices.

[0084] After iterative updates by the state-space recursive unit, the output passenger flow distribution matrix is ​​continuous in the time dimension and covers all station sets and interval edge sets in the spatial dimension, forming a passenger flow distribution prediction sequence. This prediction sequence not only depicts the path allocation and spatial distribution of each passenger group in different time periods, but can also be used together with the running time prediction sequence as input data for subsequent scheduling scheme optimization and evaluation.

[0085] S63. In the recursive computation process of the improved Mamba network, an uncertainty-aware selection gating mechanism is adopted: the ratio between local recursive computation and neighborhood coupled computation in the state space recursive unit is dynamically adjusted.

[0086] The specific steps of the dynamic adjustment include:

[0087] During the recursive calculation process, the interval running time parameters updated based on the interval length constraint are used as input conditions to form running time constraints for each train at the interval level. Passenger flow distribution information obtained by mapping the travel origin, travel destination, and departure time distribution of passenger groups is used as dynamic input to the timetable constraint layer to reflect the passenger carrying capacity of each interval and station at different times.

[0088] An uncertainty-aware gating mechanism is constructed to iteratively update the scaling factor between local recursive computation (relying solely on the evolution of the current interval's running time parameters) and neighborhood coupled computation (combining the joint propagation results of running time parameters from adjacent intervals and corresponding passenger flow distribution information). When differences arise between interval running time parameters and passenger flow distribution information between adjacent intervals, the scaling factor is adjusted towards neighborhood coupled computation to enhance dynamic propagation across intervals. When the differences between running time and passenger flow distribution between adjacent intervals are small and the uncertainty is low, the scaling factor converges towards local recursive computation to maintain computational stability and efficiency. Through this dynamic adjustment, the synchronous convergence of running time prediction and passenger flow distribution prediction in the spatiotemporal network topology is ensured, outputting adjusted running time series and passenger flow distribution prediction series.

[0089] Among them, the local recursive calculation is updated based on the interval running time parameters of each train, and the neighborhood coupling calculation is propagated based on the passenger flow distribution information of adjacent stations; the recursive output result adjusted by the uncertainty perception selection gating mechanism is matched with the number of train departures on the line and the departure time of the first station to obtain the adjusted running time parameter sequence and passenger flow distribution prediction sequence.

[0090] S64. In the generated scheduling scheme, the number of trains departing from the line and the departure time of the first station are constrained, checked and corrected in sequence.

[0091] Check the difference in the first departure time between two adjacent trains. If it is less than the preset minimum departure interval threshold, then adjust the first departure time of the subsequent trains in sequence until the minimum departure interval condition is met.

[0092] Check whether the departure time of the first station for all trains falls within the time window of the first and last trains. If it exceeds the boundary, correct the departure time of the first station to the boundary value of the first and last train time window.

[0093] Based on the total train capacity corresponding to the number of trains departing from each line, the passenger demand allocated to each section is compared with the capacity limit. If there is a situation where the capacity is exceeded, it is corrected by increasing the necessary number of trains or postponing the departure time of the first station, so that the carrying capacity of each line does not exceed the capacity limit.

[0094] After completing the constraint verification and correction of minimum departure interval, first and last train time window and capacity limit, the output number of trains departing from the line and the departure time of the first station constitute a feasible scheduling scheme that meets the constraints.

[0095] S65. Under the feasible scheduling scheme, combine the adjusted running time parameter sequence output by the improved Mamba network with the passenger flow distribution prediction sequence to calculate the average travel time of passengers and the total train mileage, which are used as evaluation indicators for the optimization objective function.

[0096] The specific steps are as follows:

[0097] Under the feasible scheduling scheme, based on the adjusted running time parameter sequence, the actual running time of each train in each section is determined, and a train timetable covering the entire line is obtained.

[0098] Based on this, the passenger flow distribution prediction sequence is projected onto the aforementioned train timetable. That is, according to the distribution of passenger groups' origins, destinations, and departure times, and combined with the path selection probability, the demand of each passenger group is matched with the specific train's operating time. For each feasible path, the calculated total travel time consists of three parts: waiting time, boarding time, and transfer time. The boarding time is provided by the operating time parameter sequence, while the waiting and transfer times are determined jointly by the passenger flow distribution prediction sequence and the train timetable.

[0099] The average travel time for each passenger can be obtained by taking a weighted average of the travel times of all passenger groups (the weight being the number of people in each passenger group).

[0100] Based on the correspondence between the running time and the length of each section in the running time parameter sequence, the total length of the sections covered by all trains during the entire study period is summarized to obtain the total number of kilometers traveled by the trains.

[0101] The average travel time of passengers and the total distance traveled by trains are used together as evaluation indicators of the optimization objective function to measure the service level and resource investment of the current scheduling scheme.

[0102] The beneficial effects of this invention are:

[0103] This invention constructs a multi-layered, coupled spatiotemporal network model of buses and subways, achieving unified modeling of the integrated bus-subway network structure, operational logic, and passenger travel behavior. Compared to traditional methods that only optimize scheduling for a single transportation system, this invention can more comprehensively depict the connection relationships and transition paths between multiple modes of travel, providing a more accurate structural foundation for route planning and scheduling decisions.

[0104] This invention, based on an improved Mamba network, introduces a graph-structured coupled state-space recursion mechanism, effectively combining interval running time parameters with passenger flow distribution information. During modeling, a combination of local recursion and neighborhood-coupled computation is employed, and an uncertainty-aware gating mechanism dynamically adjusts the weights of both. This ensures that the generated running time parameter sequences and passenger flow distribution prediction sequences more accurately reflect actual operational status and passenger demand fluctuations, improving the adaptability and accuracy of scheduling scheme predictions.

[0105] After generating the initial scheduling scheme, this invention sets multiple operational constraints, including minimum departure intervals, first and last train time windows, and capacity limits. Through constraint verification and correction processes, it reasonably adjusts the number of trains departing from each line and the departure time from the first station, thereby ensuring the generated scheduling scheme is both practically feasible and operationally safe. Finally, by combining the adjusted travel time parameter sequence with the passenger flow distribution prediction sequence, it jointly evaluates the average passenger travel time and the total train mileage, providing systematic and high-precision technical support for achieving coordinated and optimized operation of public transport and subway systems. Attached Figure Description

[0106] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0107] Figure 1 This is an overall flowchart of a collaborative operation optimization method for an integrated public transport and subway network proposed in this invention.

[0108] Figure 2 This is a schematic diagram of an improved Mamba network structure for a collaborative operation optimization method for an integrated public transport and subway network proposed in this invention.

[0109] Figure 3 This is a schematic diagram of the multi-layered coupled spatiotemporal network structure of the collaborative operation optimization method for an integrated public transport and subway network proposed in this invention. Detailed Implementation

[0110] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0111] refer to Figure 1-3 A collaborative operation optimization method for an integrated public transport and subway network includes the following steps:

[0112] S1. Collect and standardize topology data, train timetable data, and passenger travel demand data;

[0113] S2. Construct a multi-layer coupled spatiotemporal network by using topological foundations, timetable constraint layers, and spatiotemporal constraint layers.

[0114] S3. Based on the multi-layer coupled spatiotemporal network, perform K-shortest path search to generate a set of passenger reachable paths;

[0115] S4. Set decision variables and optimize the objective function, and verify the accessibility of the passenger route selection set under the train operation rules;

[0116] S5. Based on the allocation probability output by the Logit model, calculate the average travel time of passengers and generate a scheduling scheme consisting of the number of departure pairs on the route and the departure time of the first station.

[0117] S6. Input the time-series operation data into the improved Mamba network. In the state space recursive unit, combine the operation time parameters and passenger flow distribution prediction results to perform constraint verification and correction on the number of train departure pairs and the first station departure time. Based on the feasible scheduling scheme, calculate the average travel time of passengers and the total number of kilometers traveled by trains to form the evaluation index of the optimization objective function.

[0118] This invention proposes an integrated bus-metro scheduling optimization method based on a multi-layer coupled spatiotemporal network and an improved Mamba network. By collecting and standardizing topology data, train timetable data, and passenger travel demand data, a multi-layer coupled spatiotemporal network is constructed, encompassing the topology foundation, timetable constraint layer, and spatiotemporal constraint layer. A set of reachable paths for passengers is generated based on K-shortest path search. Under the conditions of setting decision variables and optimization objective function, the reachability of the passenger path selection set is verified, and the average passenger travel time is calculated using the allocation probability output by the Logit model, forming a preliminary scheduling scheme. Furthermore, the improved Mamba network is used to model the running time parameters and passenger flow distribution prediction results in the state-space recursive unit, realizing the constraint verification and correction of the number of train departure pairs and the first station departure time. Finally, an optimized scheduling scheme that considers both the average passenger travel time and the total train travel distance is output. This invention not only improves the adaptability of the scheduling scheme to passenger demand but also significantly enhances the overall efficiency and feasibility of integrated bus-metro collaborative operation.

[0119] In this embodiment, the standardization processing refers to performing format unification, semantic alignment, structural regularization, and missing data repair operations on the collected topological structure data, train timetable data, and passenger travel demand data, specifically including:

[0120] Standardization of topological data:

[0121] The station numbers, inter-station connections, and route direction information of each bus and subway line are modeled in a unified manner. A unified graph structure abstraction method is adopted to form a topological graph data structure consisting of a set of station nodes and a set of directed edges. The edge attributes of the bus-subway transfer connection relationship are labeled.

[0122] Standardization of train timetable data:

[0123] The departure time, arrival time, and stop time in the original train timetable are uniformly converted into a standard timestamp format to correct the time offset problem across midnight and ensure that the time information between different lines is comparable and continuous under a unified time coordinate system.

[0124] Standardized processing of passenger travel demand data:

[0125] The original travel log data was cleaned into structured data entries containing departure station number, arrival station number, departure time and number of passengers. Null values, duplicates and data with abnormal format were removed. Passenger travel needs were coded and classified according to route direction and time period to form an input format that meets the needs of network modeling and scheduling optimization.

[0126] Unified data spatiotemporal benchmark:

[0127] The spatial attributes of topological data and travel demand data are converted into a unified geographic coordinate system (such as WGS-84), and the time attributes of train timetable data are unified into minute-based integer time codes to ensure spatiotemporal consistency across different data sources.

[0128] Semantic field alignment and missing field completion:

[0129] To address the differences in field naming and inconsistent granularity in topological data, train timetable data, and passenger travel demand data, field mapping rules and a unified semantic template are established. Interpolation and structural completion operations are performed on missing time data and discontinuous station connection relationships.

[0130] In this embodiment, S2 specifically includes:

[0131] S21. Combining train timetable data, the integrated bus and subway network is abstracted into a directed graph, forming a set of stations, edges, and lines, which serves as the topological basis for a multi-layered coupled spatiotemporal network.

[0132] The abstraction process is as follows: all stations in the integrated bus and subway network are defined as nodes in a directed graph; bus sections, subway sections, and transfer relationships are defined as directed edges in the directed graph; and running time, transfer time, and train departure time attributes are added to the directed edges to obtain the directed graph.

[0133] The integrated bus-metro network is a comprehensive transportation network structure formed by merging bus and metro networks through topological integration. The integrated bus-metro network consists of three basic components: a station set, an edge set, and a route set. The station set includes all bus stops, metro stations, and transfer stations; the edge set includes bus section edges, metro section edges, and transfer edges, representing the operational relationships between adjacent bus stops, adjacent metro stations, and transfer relationships between buses and the metro, respectively; and the route set includes all bus routes and metro routes.

[0134] The process of generating the integrated bus-subway network is as follows:

[0135] Collect bus network topology data, including bus route directions, stop locations, and travel time between adjacent stops;

[0136] Collect subway network topology data, including the distribution of subway line stations, track information between sections, and train timetable data.

[0137] By integrating the aforementioned bus network data with the subway network data, a unified set of stations is constructed. Bus section edges, subway section edges, and transfer edges are then introduced into the station set to form a comprehensive set of lines that includes both bus and subway lines. This generates a bus-subway integrated network that can be used for subsequent modeling and optimization.

[0138] S22. Within a continuous time interval, for any node in the directed graph, record the departure time information of each train in the upward direction and the departure time information of each train in the downward direction to form a timetable constraint layer.

[0139] S23. For any directed edge in a directed graph, assign a time weight to form a spatiotemporal constraint layer:

[0140] If it belongs to the transfer side, the time weight is the corresponding transfer time;

[0141] If it is the edge of a bus route, the time weight is the bus route travel time;

[0142] If it is the edge of a subway section, the time weight is the subway section travel time;

[0143] S24. When passengers travel in the integrated bus and subway network, the passenger's starting point, destination, and departure time are set to consistent parameters, and a group of passengers with the same starting point, destination, and departure time is defined as a passenger group. Through the aforementioned topology foundation, timetable constraint layer, and spatiotemporal constraint layer, a multi-layer coupled spatiotemporal network is constructed.

[0144] This invention proposes a method for modeling an integrated bus-metro network. First, by combining train timetable data, the integrated bus-metro network is abstracted into a directed graph, forming a unified set of stations, edges, and routes, clarifying the operational and transfer relationships between sections. Based on this, bus network data and metro network data are fused to construct a comprehensive route set including bus section edges, metro section edges, and transfer edges, generating an integrated bus-metro network with a unified topology. Further, the departure times of trains in both directions at each node are recorded within continuous time intervals, forming a timetable constraint layer. Time weights, such as travel time and transfer time, are assigned to directed edges, constructing a spatiotemporal constraint layer. Finally, the passenger's origin, destination, and departure time are modeled as consistent parameters to form passenger groups, and the passenger travel path is modeled and represented in a multi-layered coupled spatiotemporal network. This invention, through the unified construction of the topological foundation, timetable constraint layer, and spatiotemporal constraint layer, enables the integrated description of bus and metro networks under the same model, ensuring a complete expression of operational patterns and transfer characteristics, and providing a high-precision modeling foundation for subsequent passenger travel path analysis and scheduling optimization.

[0145] In this embodiment, S3 specifically includes:

[0146] S31. In a multi-layer coupled spatiotemporal network, each station is designed with a path label data structure. The path label data structure records the path status, cumulative path time and cost, predecessor node information, path source, and current path arrival time information.

[0147] S32. Design a K-shortest path search algorithm for spatiotemporal networks: Initialize the departure station and departure time of passengers, initialize the path labels of all stations in the integrated bus and subway network to the default state; divide the directed edges in the directed graph into up-going edges, down-going edges and transfer edges according to the direction type, and store them respectively.

[0148] S33. During the K-shortest path search, determine whether each edge has a train that can be taken:

[0149] If available trains exist, record the earliest time the passenger can reach the next node;

[0150] For transfer edges, update the path time based on the transfer time.

[0151] In each iteration, the path with the shortest cumulative time is selected from all path labels that are still in a temporary state and expanded, and the path with the shortest time is updated to a permanent state.

[0152] S34. When all K paths leading to the destination are marked as permanent, the K-shortest path search algorithm terminates. Then, through backtracking, the algorithm extracts the maximum K reachable paths from the origin to the destination from the departure time from the path label data structure, forming the passenger path selection set.

[0153] This invention proposes a passenger route search modeling method for multi-layered coupled spatiotemporal networks. First, a route label data structure is designed for each station in the network to record key information such as route status, cumulative time cost, predecessor nodes, and route origin, thereby achieving full-process tracking of route status. Based on this, a K-shortest path search algorithm suitable for integrated bus-metro networks is constructed. By initializing the passenger's departure station and departure time, and dividing directed edges into upbound, downbound, and transfer edges, the path search can distinguish different types of operation and transfer relationships. During the search process, the route time is dynamically updated based on the availability of available trains and transfer times, and the path with the shortest cumulative time is iteratively selected for expansion, gradually generating a set of feasible paths. Once the first K paths to the destination station are all marked as permanent, reachable paths are extracted through backtracking, ultimately constructing a passenger route selection set. This invention, by combining the route label data structure with K-shortest path search, achieves efficient multi-path search under complex spatiotemporal constraints, providing accurate data support for passenger travel route modeling and scheduling optimization.

[0154] In this embodiment, S4 specifically includes:

[0155] S41. Historical passenger travel demand includes the origin, destination, departure time and number of passengers for each passenger group; the transfer time for passengers in the same transfer direction is uniformly set to the same value.

[0156] S42. Set the number of train departure pairs on the line and the first departure time of each train as decision variables for scheduling optimization, where the number of train departure pairs represents the number of trains deployed during the study period, and the first departure time represents the specific departure time of each train.

[0157] S43. Set the optimization objective function as minimizing the weighted sum of passenger weighted average travel time and total train mileage; set an upper limit constraint on the number of train departures on the line to ensure that the number of departures does not exceed the maximum available capacity;

[0158] Define train operation rules: calculate the arrival and departure times of each train at each station, and require that the travel time match the section length; the section length is the physical operating section length of the line between two adjacent stations;

[0159] At transfer stations, the connection between trains is restricted to ensure that transfers are only possible between trains that have the necessary connection conditions.

[0160] The constraint on the connection relationship between trains specifically includes the following:

[0161] Arrival and departure time constraints: When a train arrives at a transfer station, the two trains are considered to be able to connect only if there is an interval of not less than the time required for the transfer between the arrival time of the train and the departure time of the other train.

[0162] Constraints on directional consistency: Passengers can only transfer from the arrival direction of one train to the departure direction of another, and this directional relationship must conform to the station's transfer organization structure. If the two trains' operating directions do not allow for transfer logic, a connection cannot be established.

[0163] Physical feasibility constraint: Transfer relationships must correspond to actual physical transfer pathways, such as transfer routes from buses to subways or transfer passages within subway stations. If there are no transfer facilities available for passengers to pass between stations, a connection relationship will not be established.

[0164] The conditions for connection are as follows: only train pairs that simultaneously meet the time, direction, and physical conditions can be considered to have a connection and be included in the path search process. If any condition is not met, the two trains cannot be transferred, and the transfer path is excluded from the set of accessible paths for passengers.

[0165] Accessibility verification is performed on each path in the passenger path selection set to ensure that each path meets the train connection conditions and timetable constraints;

[0166] The accessibility verification process involves checking each of the passenger route selection sets after they are generated to ensure that they are actually usable by passengers.

[0167] The specific content of reachability verification includes:

[0168] Timetable constraint verification: For each train segment in the route, check whether passengers can board the train at the scheduled departure time. If a passenger arrives at a station later than the train's departure time, that segment of the route is not feasible.

[0169] Connectivity verification: At nodes involving transfers in the route, check whether there is a valid connection between the two trains, that is, whether the time interval between the arrival of the previous train and the departure of the next train meets the time requirements for transfer.

[0170] Full-process feasibility verification: From the departure station to the destination station, all train operations and transfer links along the route are verified segment by segment. If any segment of the route does not meet the timetable constraints or connection conditions, the entire route is determined to be unreachable.

[0171] The results of reachability verification include: if a path passes all verification conditions, it is marked as a "reachable path"; if a path fails verification, it is removed from the passenger path selection set and does not participate in subsequent travel allocation and optimization.

[0172] This invention proposes a scheduling optimization and accessibility verification method for integrated bus-metro networks. First, passenger group data is constructed based on historical passenger travel demand, and transfer time parameters are set under a unified transfer direction. Second, the number of train departure pairs and the departure time of each train's first station are used as decision variables for scheduling optimization. Under the objective function of minimizing the weighted average travel time of passengers and the weighted sum of the total train travel distance, combined with section length constraints and train operation rules, the scheduling scheme is ensured to meet actual operating conditions. Furthermore, three types of continuity constraints—time, direction, and physical conditions—are introduced at transfer stations to rigorously screen the continuity relationships between trains, thereby ensuring the rationality and feasibility of transfer paths. Finally, timetable constraint verification, continuity condition verification, and full-process feasibility verification are performed on each passenger path selection set, eliminating unreachable paths and retaining only reachable paths that truly meet travel conditions. This invention, through the combination of scheduling optimization and accessibility verification, not only improves the reliability and rationality of passenger path selection but also effectively balances operational efficiency and travel experience while ensuring capacity constraints.

[0173] In this embodiment, S5 specifically includes:

[0174] S51. For a path that meets the accessibility verification conditions, calculate the total travel time for passengers from the origin to the destination, including travel time, waiting time, and transfer time.

[0175] S52. Calculate the allocation probability of passengers in the passenger route selection set based on the Logit model. The allocation probability decreases as the total travel time of the route increases.

[0176] The probability of a passenger being assigned a route within the passenger route selection set is determined using a Logit model to probabilistically allocate passenger travel routes. Specifically, the Logit model is calculated based on the following principles:

[0177] The passenger route selection set corresponding to each passenger group is used as the candidate route set, and each candidate route has a corresponding total travel time. The total travel time includes the cumulative result of travel time, waiting time, and transfer time, and is used to reflect the complete time required for passengers to actually complete the journey along that route.

[0178] The total travel time of candidate routes is mapped to a route utility value. The shorter the total travel time, the higher the corresponding utility value; the longer the total travel time, the lower the corresponding utility value. This utility value is used to measure passengers' relative preference for different routes.

[0179] The Logit model normalizes the utility values ​​of each path, transforming them into a probability distribution. In this distribution, each path corresponds to an allocation probability, and the sum of the allocation probabilities of all paths is 1. Paths with shorter travel times have significantly higher allocation probabilities than paths with longer travel times, thus ensuring that passengers are more inclined to choose the less time-consuming path from the candidate path set.

[0180] Based on the allocation probabilities obtained from the Logit model, passenger groups can be assigned routes. That is, for all passengers in the same passenger group, their trips will be distributed in the candidate route set according to the allocation probabilities, so as to form a passenger route allocation result that conforms to the actual travel pattern.

[0181] S53. Calculate the travel time of passenger groups, combine the allocation probability with the total travel time of the route to obtain the expected travel time of each passenger group;

[0182] S54. Calculate the overall index, weight the expected travel time of all passenger groups by the number of people, and obtain the average travel time of passengers under the scheduling plan.

[0183] S55. Using average passenger travel time and total train mileage as evaluation indicators, output the final departure plan and scheduling results.

[0184] This invention proposes a passenger route allocation and scheduling result evaluation method based on the Logit model. First, it calculates the total travel time for passengers on routes that meet accessibility verification conditions, comprehensively considering factors such as boarding time, waiting time, and transfer time to ensure the accuracy of travel time. Second, it uses the Logit model to perform utility modeling on candidate routes, mapping the total travel time of a route to a path utility value and converting it into allocation probabilities. This makes the distribution of passengers in the route selection set more closely resemble actual travel patterns, ensuring the rationality and authenticity of route allocation. Furthermore, by combining allocation probabilities and total travel time, it calculates the expected travel time for each passenger group, and then weights the data by number of passengers to obtain the average travel time under the scheduling scheme, thus comprehensively measuring the impact of different scheduling strategies on overall travel efficiency. Finally, it uses the average passenger travel time and the total train mileage as comprehensive evaluation indicators to output the final departure scheme and scheduling results. This invention, by introducing probabilistic route allocation and weighted travel time calculation, effectively improves the ability of scheduling results to depict real travel patterns, achieving a dynamic balance between passenger travel experience and train operation efficiency.

[0185] In this embodiment, S6 specifically includes:

[0186] S61. Based on the collected topology data of the bus network and subway network, train timetable data and historical passenger travel demand data, combined with the number of train departure pairs and the first departure time, generate time-series operation data of arrival time, departure time and passenger distribution of each train at different stations.

[0187] S62. Input the time-series running data into the improved Mamba network, combine the timetable constraint layer and passenger travel demand data, and use the graph-coupled state-space recursive unit for modeling. In the recursive calculation process: local recursive calculation is adopted, and the running time is recursively updated based on the physical interval length between adjacent stations. It is required that the running time of each train meets the running time and interval length matching condition, so as to obtain the running time sequence covering all physical segments.

[0188] The specific steps for generating the runtime time series include:

[0189] Interval length as constraint input: There is an interval length between adjacent stations on each line. This data comes from the topology of the multi-layer coupled spatiotemporal network and is used as an input condition together with the train timetable data in the timetable constraint layer.

[0190] Running time recursive update: When the state space recursive unit calculates the running time of each train in the interval, the calculation result must meet the rule of matching running time with interval length. The rule of matching running time with interval length means that in the multi-layer coupled spatiotemporal network, the physical interval length between two adjacent stations is proportional to the running time of the corresponding train, ensuring that the running time is not less than the physical minimum running time and does not exceed the maximum allowable running time of the interval.

[0191] Iterative correction mechanism: If the running time obtained by recursion deviates from the interval length constraint range, the recursion step size is automatically adjusted through the uncertainty perception gating mechanism, and the running time parameters are corrected within the allowed time window until the running time meets the interval length constraint.

[0192] After completing the above-mentioned constraint input, recursive update and iterative correction, the running time series covering all intervals and trains is obtained, which is part of the output of the improved Mamba network.

[0193] Based on neighborhood coupling propagation using station sets and interval edge sets, the distribution of passenger travel origins, destinations, and departure times is mapped to a spatiotemporal network topology. During iterative propagation, a passenger flow distribution prediction sequence synchronized with the operational time series is generated. The spatiotemporal network topology refers to the spatial topology composed of station sets, interval edge sets, and line sets of the integrated bus-metro network. Based on this, passenger departure time distribution and train timetable constraints are introduced, coupling the spatial topology with the time index to form a multi-layered spatiotemporal graph structure covering the entire network. This structure is used to uniformly model the dynamic propagation relationship between operational time and passenger flow distribution.

[0194] The neighborhood coupling computation is adopted, and the passenger travel origin, travel destination and departure time distribution are mapped to the spatiotemporal network topology based on the neighborhood coupling propagation of the station set and the interval edge set. In the iterative propagation, a passenger flow distribution prediction sequence synchronized with the running time series is generated.

[0195] The specific steps for generating the passenger flow distribution prediction sequence include:

[0196] The origin, destination, and departure time distribution of passenger groups are used as input parameters and mapped onto the topology of a multi-layered coupled spatiotemporal network. The travel demand of each passenger group is projected onto the corresponding set of stations and interval edges, ensuring that the origin and destination are uniquely located in the network topology. The departure time serves as the time reference input for the timetable constraint layer.

[0197] In the state-space recursive unit of the improved Mamba network, the runtime prediction sequence and passenger travel demand are modeled simultaneously. Driven by graph-structured coupled propagation, the recursive unit expands the demand of each passenger group in the spatiotemporal dimensions, forming a set of candidate paths available for allocation. Based on this, combined with the previously verified path selection set, the allocation probability of each path is calculated using a Logit model. The allocation probability, as a weighting factor, is input into the recursive calculation along with the travel time of each path, enabling passenger demand to be dynamically allocated among different paths according to probability.

[0198] The recursive process iteratively allocates the demand for all passenger groups, mapping the allocation results to network nodes and interval edges at each time step. By normalizing the allocated number of passengers, the total number of passengers is kept constant, avoiding distortion caused by double counting or rounding errors. Passenger demand is reasonably unfolded on a continuous time series, and a passenger flow distribution matrix is ​​constructed using stations, intervals, and times as indices.

[0199] After iterative updates by the state-space recursive unit, the output passenger flow distribution matrix is ​​continuous in the time dimension and covers all station sets and interval edge sets in the spatial dimension, forming a passenger flow distribution prediction sequence. This prediction sequence not only depicts the path allocation and spatial distribution of each passenger group in different time periods, but can also be used together with the running time prediction sequence as input data for subsequent scheduling scheme optimization and evaluation.

[0200] S63. In the recursive computation process of the improved Mamba network, an uncertainty-aware selection gating mechanism is adopted: the ratio between local recursive computation and neighborhood coupled computation in the state space recursive unit is dynamically adjusted.

[0201] The specific steps of the dynamic adjustment include:

[0202] During the recursive calculation process, the interval running time parameters updated based on the interval length constraint are used as input conditions to form running time constraints for each train at the interval level. Passenger flow distribution information obtained by mapping the travel origin, travel destination, and departure time distribution of passenger groups is used as dynamic input to the timetable constraint layer to reflect the passenger carrying capacity of each interval and station at different times.

[0203] An uncertainty-aware gating mechanism is constructed to iteratively update the scaling factor between local recursive computation (relying solely on the evolution of the current interval's running time parameters) and neighborhood coupled computation (combining the joint propagation results of running time parameters from adjacent intervals and corresponding passenger flow distribution information). When differences arise between interval running time parameters and passenger flow distribution information between adjacent intervals, the scaling factor is adjusted towards neighborhood coupled computation to enhance dynamic propagation across intervals. When the differences between running time and passenger flow distribution between adjacent intervals are small and the uncertainty is low, the scaling factor converges towards local recursive computation to maintain computational stability and efficiency. Through this dynamic adjustment, the synchronous convergence of running time prediction and passenger flow distribution prediction in the spatiotemporal network topology is ensured, outputting adjusted running time series and passenger flow distribution prediction series.

[0204] Among them, the local recursive calculation is updated based on the interval running time parameters of each train, and the neighborhood coupling calculation is propagated based on the passenger flow distribution information of adjacent stations; the recursive output result adjusted by the uncertainty perception selection gating mechanism is matched with the number of train departures on the line and the departure time of the first station to obtain the adjusted running time parameter sequence and passenger flow distribution prediction sequence.

[0205] S64. In the generated scheduling scheme, the number of trains departing from the line and the departure time of the first station are constrained, checked and corrected in sequence.

[0206] Check the difference in the first departure time between two adjacent trains. If it is less than the preset minimum departure interval threshold, then adjust the first departure time of the subsequent trains in sequence until the minimum departure interval condition is met.

[0207] Check whether the departure time of the first station for all trains falls within the time window of the first and last trains. If it exceeds the boundary, correct the departure time of the first station to the boundary value of the first and last train time window.

[0208] Based on the total train capacity corresponding to the number of trains departing from each line, the passenger demand allocated to each section is compared with the capacity limit. If there is a situation where the capacity is exceeded, it is corrected by increasing the necessary number of trains or postponing the departure time of the first station, so that the carrying capacity of each line does not exceed the capacity limit.

[0209] After completing the constraint verification and correction of minimum departure interval, first and last train time window and capacity limit, the output number of trains departing from the line and the departure time of the first station constitute a feasible scheduling scheme that meets the constraints.

[0210] S65. Under the feasible scheduling scheme, combine the adjusted running time parameter sequence output by the improved Mamba network with the passenger flow distribution prediction sequence to calculate the average travel time of passengers and the total train mileage, which are used as evaluation indicators for the optimization objective function.

[0211] The specific steps are as follows:

[0212] Under the feasible scheduling scheme, based on the adjusted running time parameter sequence, the actual running time of each train in each section is determined, and a train timetable covering the entire line is obtained.

[0213] Based on this, the passenger flow distribution prediction sequence is projected onto the aforementioned train timetable. That is, according to the distribution of passenger groups' origins, destinations, and departure times, and combined with the path selection probability, the demand of each passenger group is matched with the specific train's operating time. For each feasible path, the calculated total travel time consists of three parts: waiting time, boarding time, and transfer time. The boarding time is provided by the operating time parameter sequence, while the waiting and transfer times are determined jointly by the passenger flow distribution prediction sequence and the train timetable.

[0214] The average travel time for each passenger can be obtained by taking a weighted average of the travel times of all passenger groups (the weight being the number of people in each passenger group).

[0215] Based on the correspondence between the running time and the length of each section in the running time parameter sequence, the total length of the sections covered by all trains during the entire study period is summarized to obtain the total number of kilometers traveled by the trains.

[0216] The average travel time of passengers and the total distance traveled by trains are used together as evaluation indicators of the optimization objective function to measure the service level and resource investment of the current scheduling scheme.

[0217] This invention proposes a joint optimization method for train scheduling parameter constraint verification and passenger travel prediction based on an improved Mamba network. First, it collects topology data of bus and subway networks, train timetables, and historical passenger travel demand data to generate time-series operational data reflecting the operational status and passenger distribution of each train. Then, this data is input into the improved Mamba network. Relying on a state-space recursion mechanism and an uncertainty-aware gating mechanism, and combining physical interval length and passenger flow intensity, and based on the matching condition of the operating time interval, it jointly models the operating time prediction sequence and the passenger flow distribution prediction sequence, realizing the dynamic propagation and synchronous evolution of cross-interval information in a multi-layered coupled spatiotemporal network. Furthermore, a constraint verification module systematically corrects the number of train departure pairs and the first station departure time by applying minimum departure intervals, first and last train time windows, and capacity limits, ensuring the feasibility and constraint consistency of the scheduling parameters. Finally, under the adjusted scheduling scheme, the average passenger travel time and total train mileage are calculated based on the prediction results, serving as evaluation indicators for the optimization objective function, reflecting the service level and operational efficiency of the scheduling scheme. This invention introduces state recursion, neighborhood coupling, and dynamic adjustment mechanisms to achieve high-precision linkage modeling of running time and passenger flow distribution, thereby enhancing the intelligence and practicality of scheduling scheme generation and evaluation.

[0218] In this embodiment, the improved Mamba network includes the following specific structure and steps:

[0219] The input data preparation module receives topology data of a multi-layered coupled spatiotemporal network, train timetable data, and historical passenger travel demand data. Combining this with the number of train departure pairs and the first departure time from the first station, it generates arrival time, departure time, and passenger distribution information for each train at the station level, forming a structured time-series operational data input tensor. In this input tensor, each dimension corresponds to the station number, time index, train number, and number of passengers, respectively.

[0220] The state-space recursive unit consists of a local recursive calculation module and a neighborhood coupled calculation module. The state-space recursive unit receives time-series operational data, combines it with timetable constraint layers and passenger travel demand data, and performs recursive modeling based on graph structure coupling. In the local recursive calculation module, an interval length constraint vector is constructed based on the physical interval length. The interval operation time parameters for each train are input, and a recursive update operation of the operation time is performed to generate an operational time series that satisfies the minimum and maximum allowable operation time constraints.

[0221] The neighborhood coupling computation module is based on a spatial adjacency matrix composed of a set of stations and a set of interval edges. It receives passenger travel origin, destination, and departure time distribution data, and maps passenger demand to graph structure nodes and edges through a neighborhood propagation mechanism, generating a temporally continuous and spatially comprehensive passenger flow distribution prediction sequence. At each time step, the neighborhood coupling computation module iteratively propagates the path allocation results, combines the path allocation probabilities, expands passenger group demand in the network, and constructs a passenger flow distribution matrix.

[0222] An uncertainty-aware gating mechanism controls the scaling factor between the local recursive calculation module and the neighborhood coupled calculation module. Within each recursive cycle, the scaling factor is adjusted based on the difference between the running time parameters of adjacent intervals and the passenger flow distribution of the corresponding intervals. When there is a significant difference between adjacent intervals, the weight of the neighborhood coupled calculation is increased; when the difference is small, the weight of the local recursive calculation is increased, outputting a synchronously converged sequence of running time parameters and a passenger flow distribution prediction sequence.

[0223] The scheduling parameter verification module performs joint constraint verification on the running time parameter sequence and the passenger flow distribution prediction sequence. Based on the generated departure pairs and the first departure time, it compares the minimum departure interval threshold, the first and last train time windows, and the capacity limit constraints, and performs time delay, boundary correction, and capacity adjustment operations respectively to form an adjusted scheduling scheme that meets the constraints.

[0224] The optimization index calculation module generates a train schedule and route allocation mapping table based on the adjusted travel time parameter sequence and passenger flow distribution prediction sequence. It then performs a weighted average calculation on the travel time of all passenger groups, outputting the average passenger travel time; and based on the relationship between travel time and interval length, it accumulates the train's travel interval length, outputting the total train travel kilometers, which are used to construct the evaluation index results.

[0225] Example 1:

[0226] To verify the feasibility of this invention in practical applications, it was applied to a comprehensive transportation corridor area. This area comprises a multi-layered coupled network structure of rail transit and surface public transport, with a daily passenger flow of approximately 420,000 to 470,000 passengers. The area experiences significant congestion during morning and evening rush hours. Traditional scheduling methods often rely solely on empirical rules to create timetables, failing to adequately address the differentiated needs of long-distance commuters and short-distance transfer passengers. This results in some lines being overloaded while others have idle capacity, leading to high average waiting times and transfer delays, and a poor overall travel experience for passengers.

[0227] In actual deployment, data on the topology of the rail lines, historical timetables for each line, and multi-day passenger demand data were first collected through a data acquisition interface and then standardized. Subsequently, a multi-layered coupled spatiotemporal network was constructed based on the topology, timetable constraints, and spatiotemporal constraints. Through this network, without relying on a single shortest path algorithm, this invention performed a K-shortest path search, generating a candidate set of up to 10 reachable paths, enabling different passenger groups to find travel options that meet their needs. Next, a Logit model was used to assign probabilities to each path, and a path utility value was constructed by combining travel time, waiting time, and transfer time, mapping the overall travel choice to a probability distribution. This mechanism allows for a more realistic portrayal of the travel preferences of different passenger groups. Specific experimental data are shown in Table 1 below:

[0228] Table 1 Comparison of Scheduling Optimization Effects

[0229] Indicator Name Historical scheduling schemes The generation scheme of this invention Average train interval on rail lines (minutes) 7.4 6.1 Average departure interval (minutes) for public transport transfer routes 11.0 9.2 Average passenger wait time (minutes) 6.3 4.2 Passenger transfer waiting time (minutes) 5.7 3.4 Passenger route reachability (%) 93.2 98.6 Average travel time for long-distance passengers (minutes) 53.0 45.0 Average travel time (minutes) for short-distance passengers 28.0 23.0 Total distance traveled by the train (km) 96320 92240 Transportation resource saving rate (%) - 4.2 Average convergence time of the model (seconds) - 20

[0230] This invention optimizes the reachability of candidate routes and constrains scheduling variables using an optimization model to generate a preliminary departure plan, which is then input into an improved Mamba network. This network simultaneously incorporates runtime time series and passenger flow prediction sequences into its state-space recursive unit for fusion modeling, dynamically verifying the number of departure pairs and the first departure time. An uncertainty-aware gating unit adjusts the ratio of local path propagation to neighborhood state propagation, ultimately yielding a revised scheduling plan. In practical operation, this invention optimizes scheduling for both the morning peak (7:00-9:00) and evening peak (17:00-19:00).

[0231] Table 1 shows that, after five consecutive days of verification data statistics, the average departure interval of rail lines decreased from 7.4 minutes to 6.1 minutes, the average departure interval of bus lines shortened from 11.0 minutes to 9.2 minutes, the average passenger waiting time decreased from 6.3 minutes to 4.2 minutes, the transfer waiting time decreased from 5.7 minutes to 3.4 minutes, and the overall passenger route accessibility increased to 98.6%. The average travel time for long-distance commuters decreased from 53 minutes to 45 minutes, and the average travel time for short-distance passengers decreased from 28 minutes to 23 minutes. More importantly, under the premise of reasonable allocation of transport capacity, the total mileage of trains decreased from 96,320 kilometers to 92,240 kilometers, with a transportation resource saving rate of 4.2%. The system's computational efficiency ensured that the single scheduling model converged within 20 seconds, meeting the needs of large-scale real-time scheduling.

[0232] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for collaborative operation optimization of an integrated public transport and subway network, characterized in that, Includes the following steps: S1. Collect and standardize topology data, train timetable data, and passenger travel demand data; S2. Construct a multi-layer coupled spatiotemporal network by using topological foundations, timetable constraint layers, and spatiotemporal constraint layers. S3. Based on the multi-layer coupled spatiotemporal network, perform K-shortest path search to generate a set of passenger reachable paths; S4. Set decision variables and optimize the objective function, and verify the accessibility of the passenger route selection set under the train operation rules; S5. Based on the allocation probability output by the Logit model, calculate the average travel time of passengers and generate a scheduling scheme consisting of the number of departure pairs on the route and the departure time of the first station. S6. Input the time-series operation data into the improved Mamba network. In the state space recursive unit, combine the operation time parameters and passenger flow distribution prediction results to perform constraint verification and correction on the number of train departure pairs and the first station departure time. Based on the feasible scheduling scheme, calculate the average travel time of passengers and the total number of kilometers traveled by trains to form the evaluation index of the optimization objective function. S6 specifically includes: S61. Based on the collected topology data of the bus network and subway network, train timetable data and historical passenger travel demand data, combined with the number of train departure pairs and the first departure time, generate time-series operation data of arrival time, departure time and passenger distribution of each train at different stations. S62. Input the time-series running data into the improved Mamba network, combine the timetable constraint layer and passenger travel demand data, and use the graph-coupled state-space recursive unit for modeling. In the recursive calculation process: local recursive calculation is adopted, and the running time is recursively updated based on the physical interval length between adjacent stations. It is required that the running time of each train meets the running time and interval length matching condition, so as to obtain the running time sequence covering all physical segments. The neighborhood coupling computation is adopted, and the passenger travel origin, travel destination and departure time distribution are mapped to the spatiotemporal network topology based on the neighborhood coupling propagation of the station set and the interval edge set. In the iterative propagation, a passenger flow distribution prediction sequence synchronized with the running time series is generated. S63. In the recursive computation process of the improved Mamba network, an uncertainty-aware selection gating mechanism is adopted: the ratio between local recursive computation and neighborhood coupled computation in the state space recursive unit is dynamically adjusted. Among them, the local recursive calculation is updated based on the running time parameters of each train, and the neighborhood coupling calculation is propagated based on the passenger flow distribution information of adjacent stations. The recursive output result adjusted by the uncertainty perception selection gating mechanism is matched with the number of train departures on the line and the departure time of the first station to obtain the adjusted running time parameter sequence and passenger flow distribution prediction sequence. S64. In the generated scheduling scheme, the number of trains departing from the line and the departure time of the first station are constrained, checked and corrected in sequence. Check the difference in the first departure time between two adjacent trains. If it is less than the preset minimum departure interval threshold, then adjust the first departure time of the subsequent trains in sequence until the minimum departure interval condition is met. Check whether the departure time of the first station for all trains falls within the time window of the first and last trains. If it exceeds the boundary, correct the departure time of the first station to the boundary value of the first and last train time window. Based on the total train capacity corresponding to the number of trains departing from each line, the passenger demand allocated to each section is compared with the capacity limit. If there is a situation where the capacity is exceeded, it is corrected by increasing the necessary number of trains or postponing the departure time of the first station, so that the carrying capacity of each line does not exceed the capacity limit. After completing the constraint verification and correction of minimum departure interval, first and last train time window and capacity limit, the output number of trains departing from the line and the departure time of the first station constitute a feasible scheduling scheme that meets the constraints. S65. Under the feasible scheduling scheme, the average travel time of passengers and the total number of kilometers traveled by trains are calculated by combining the adjusted running time parameter sequence output by the improved Mamba network and the passenger flow distribution prediction sequence, and used as the evaluation index of the optimization objective function.

2. The method for collaborative operation optimization of an integrated public transport and subway network according to claim 1, characterized in that, The standardization process refers to performing operations such as format unification, semantic alignment, structural regularization, and missing data repair on the collected topological data, train timetable data, and passenger travel demand data.

3. The method for collaborative operation optimization of an integrated public transport and subway network according to claim 1, characterized in that, S2 specifically includes: S21. Combining train timetable data, the integrated bus and subway network is abstracted into a directed graph, forming a set of stations, edges, and lines, which serves as the topological basis for a multi-layered coupled spatiotemporal network. S22. Within a continuous time interval, for any node in the directed graph, record the departure time information of each train in the upward direction and the departure time information of each train in the downward direction to form a timetable constraint layer. S23. For any directed edge in a directed graph, a time weight is assigned to form a spatiotemporal constraint layer: if it is a transfer edge, the time weight is the corresponding transfer time. If it is the edge of a bus route, the time weight is the bus route travel time; If it is the edge of a subway section, the time weight is the subway section travel time; S24. When passengers travel in the integrated bus and subway network, the passenger's starting point, destination, and departure time are set to consistent parameters, and a group of passengers with the same starting point, destination, and departure time is defined as a passenger group. Through the aforementioned topology foundation, timetable constraint layer, and spatiotemporal constraint layer, a multi-layer coupled spatiotemporal network is constructed.

4. The method for collaborative operation optimization of an integrated public transport and subway network according to claim 1, characterized in that, S3 specifically includes: S31. In a multi-layer coupled spatiotemporal network, each station is designed with a path label data structure. The path label data structure records the path status, cumulative path time and cost, predecessor node information, path source, and current path arrival time information. S32. Design a K-shortest path search algorithm for spatiotemporal networks: Initialize the departure station and departure time of passengers, initialize the path labels of all stations in the integrated bus and subway network to the default state; divide the directed edges in the directed graph into up-going edges, down-going edges and transfer edges according to the direction type, and store them respectively. S33. During the K-shortest path search, determine whether there is a train available for each edge: if there is a train available, record the earliest time that the passenger can reach the next node. For transfer edges, update the path time based on the transfer time; In each iteration, the path with the shortest cumulative time is selected from all path labels that are still in a temporary state and expanded, and the path with the shortest time is updated to a permanent state. S34. When the first K paths to the destination are all marked as permanent, the K shortest path search algorithm terminates. Then, through backtracking, the maximum K reachable paths from the origin to the destination for passengers are extracted from the path label data structure from the departure time, forming the passenger path selection set.

5. The method for collaborative operation optimization of an integrated public transport and subway network according to claim 1, characterized in that, S4 specifically includes: S41. Historical passenger travel demand includes the origin, destination, departure time and number of passengers for each passenger group; the transfer time for passengers in the same transfer direction is uniformly set to the same value. S42. Set the number of train departure pairs on the line and the first departure time of each train as decision variables for scheduling optimization, where the number of train departure pairs represents the number of trains deployed during the study period, and the first departure time represents the specific departure time of each train. S43. Set the optimization objective function as minimizing the weighted sum of the passenger weighted average travel time and the total train mileage; set an upper limit constraint on the number of trains departing on the line to ensure that the number of departures does not exceed the capacity limit; Define train operation rules: calculate the arrival and departure times of each train at each station, and require that the travel time match the section length; the section length is the physical operating section length of the line between two adjacent stations; At transfer stations, the connection between trains is restricted to ensure that transfers are only possible between trains that have the necessary connection conditions. Accessibility verification is performed on each path in the passenger path selection set to ensure that each path meets the train connection conditions and timetable constraints.

6. The method for collaborative operation optimization of an integrated public transport and subway network according to claim 1, characterized in that, S5 specifically includes: S51. For a path that meets the accessibility verification conditions, calculate the total travel time for passengers from the origin to the destination, including travel time, waiting time and transfer time. S52. Calculate the allocation probability of passengers in the passenger route selection set based on the Logit model. The allocation probability decreases as the total travel time of the route increases. S53. Combine the allocation probability with the total travel time of the route to obtain the expected travel time for each passenger group; S54. Weight the expected travel times of all passenger groups by the number of passengers to obtain the average travel time of passengers under the scheduling plan. S55. Using the average passenger travel time and total train mileage as the evaluation indicators of the optimization objective function, the final scheduling scheme is output, which consists of the number of train departure pairs on the line and the departure time of the first station.

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