Urban rail cross-line train operation scheduling simulation optimization method and system

Abstract

This invention provides a simulation optimization method and system for cross-line train operation scheduling in urban rail transit, belonging to the field of train operation scheduling technology. This invention incorporates processes such as passenger clearing at transfer stations, cross-line operation on connecting lines, and the execution of reinforcement services on interfering lines into a unified framework, meeting the actual shunting needs under the conditions of interconnected urban rail transit. By setting up reinforcement services and return-to-line services, it describes the entire process of reinforcement trains being dispatched from non-interfering lines, entering interfering lines for reinforcement, and returning to their original lines to continue operation after completing their tasks, thus improving completeness. While determining cross-line shunting decisions, it also considers the insertion of reinforcement services on interfering lines, the connection of return-to-line services on non-interfering lines, and related arrival and departure time adjustments, making the generated scheme more supported by the timetable and executable. By using the sum of the average travel time of passengers on all lines of the network and the operating cost of cross-line shunting together as optimization criteria, it can control shunting costs while improving passenger service levels.

Description

Technical Field

[0001] This invention relates to the field of train operation scheduling technology, specifically to a simulation optimization method and system for urban rail transit cross-line train operation scheduling. Background Technology

[0002] In recent years, with increasingly close transfer relationships between multiple lines, the operational organization methods within a single line have become insufficient to meet the needs of passenger flow organization, vehicle utilization, and scheduling coordination under network-based operation conditions. Against this backdrop, the interconnected operation model of urban rail transit has gradually gained attention.

[0003] Interoperable operation of urban rail transit refers to an operational model that enables cross-line train operation, resource sharing, and collaborative scheduling between different lines by unifying or ensuring compatibility of key systems such as rolling stock, signaling, power supply, communication, clearance, platform adaptation, and dispatching. Compared with traditional independent single-line operation, interoperable operation breaks through the relatively independent organizational boundaries between different lines, allowing trains to run across lines where technical conditions permit. This provides fundamental support for sharing capacity resources, flexible vehicle allocation, and multi-line collaborative organization within the network. Interoperable operation provides the infrastructure, vehicle technology, and dispatching organization conditions for cross-line train operation, and is an important prerequisite for realizing network-level capacity resource sharing and cross-line vehicle allocation. Based on the conditions of interoperable operation, researching cross-line train allocation and operation organization methods for specific operational scenarios has significant technical foundation and application value.

[0004] Urban rail transit capacity shortages typically manifest as the inability of line transport capacity to meet passenger demand during specific periods. The causes include demand-side shocks such as large-scale events, holiday travel, and peak passenger flow, as well as supply-side disturbances such as vehicle malfunctions, equipment abnormalities, and limited section capacity. Existing research addresses this issue primarily through demand-side management, supply-side adjustments, supply-demand coordination, and external transportation coordination. Demand-side management mainly includes methods such as passenger flow guidance, station entry restrictions, and diversion. For example, Tsuchiya et al. developed an early passenger flow guidance support system for sudden subway disruptions; Wang Yang et al. proposed a tiered and differentiated approach to issuing guidance information, considering the varying degrees of impact on different stations during emergencies; and Zhao Peng et al. constructed a multi-station collaborative flow restriction analysis framework at the line level during peak hours by introducing a passenger flow propagation coefficient. Supply-side adjustments mainly include methods such as adding trains, deploying spare trains, adjusting routes, reducing train intervals, and skipping stops. For instance, Yi Zhigang et al. established a train addition optimization model based on event-activity network theory, and Ye Mao et al. constructed a spare train deployment optimization model. Supply-demand coordination methods integrate passenger flow control and train operation adjustments into a unified framework. For example, Kang Chongren et al. proposed a coordinated optimization model for subway flow control and train timetables, while Jiang et al. proposed a coordinated optimization model for passenger flow management and train timetables based on Q-learning. External transportation coordination mainly relies on public transportation, taxis, and customized buses to share the burden of rail transit transportation. For instance, Kepaptsoglou et al. constructed an emergency bus vehicle dispatching model, and Li Xiaoyu studied the organization method of bus linkage response under sudden urban rail transit interruption events.

[0005] The above methods provide important support for alleviating the shortage of urban rail transit capacity. However, overall, the existing methods are mostly focused on passenger flow control within a single line, capacity adjustment within a single line, or external traffic diversion. They still pay relatively little attention to the cross-line coordinated allocation of train resources within the network under interconnection conditions.

[0006] Urban rail transit train operation adjustments are primarily used to reduce train delays and passenger travel losses under disturbances such as equipment failures, emergencies, and large passenger flow surges. These adjustments involve modifying train schedules, stopping plans, turnaround methods, train routes, and rolling stock utilization. Existing research initially focused on single-line operation adjustments, including delay recovery, interruption recovery, short-route turnarounds, skip-stop operations, adding trains, and rolling stock adjustments. For example, Xia Yiming et al. constructed an urban rail train operation adjustment model with the objective of simultaneously minimizing total delay time and delay recovery time; Wei et al. further considered the impact of passenger congestion during peak hours, minimizing delays by dynamically adjusting train turnaround time.

[0007] As network-based operations improve, related research has gradually expanded to multi-line coordinated adjustments, mainly including optimization of transfer station connections, optimization of last train connections, and coordination of network operation diagrams. For example, Wong et al. constructed a network operation diagram coordination optimization model with the goal of minimizing passenger transfer waiting time. Building upon this, Wu et al. introduced a fairness perspective and established a mixed-integer linear programming model that minimizes the maximum transfer waiting time. These methods can improve the time connection relationships between different lines and enhance network operation coordination, but most still rely on the existing line architecture and predetermined vehicle affiliations.

[0008] In the context of interconnected operation, cross-line train operation adjustments are gradually becoming a new research direction. For example, Yang et al. proposed a cross-line train operation adjustment method based on the coyote optimization algorithm; Zhang Xiran et al. proposed adjustment strategies such as short-route turnaround, suspension of operation, restoration of line access, cancellation of cross-line operations, and restoration of cross-line operations to address the scenario of reduced line capacity under fault interruption. Yang Xiaofeng systematically studied train operation adjustment strategies for different fault scenarios under the interconnected operation mode. Overall, existing research has gradually extended to the problem of train operation adjustment under cross-line operation conditions, but research on temporary cross-line shunting under local capacity shortage scenarios, as well as reinforcement services, return-to-line services, and coordinated adjustments of multi-line timetables is still insufficient.

[0009] In urban rail transit systems, passenger flow and train operation are mutually influential: changes in passenger flow affect train dwell time, carriage crowding, and passenger congestion, while train operation organization affects passenger waiting time, boarding opportunities, and total travel time. Therefore, the effectiveness evaluation of train operation adjustment plans needs to consider both the passenger travel process and the train operation process.

[0010] Existing passenger and vehicle flow coupling simulation methods mainly include mathematical analysis and network flow methods, discrete event simulation methods, and multi-agent methods. Mathematical analysis and network flow methods are easy to integrate with optimization models, but their characterization of actual operational processes is relatively abstract. Discrete event simulation methods use events such as passenger arrival, train arrival, boarding and alighting, passenger clearing, and departure to drive system state changes, effectively describing the interaction between passenger and vehicle flows. Multi-agent methods can characterize individual differences and local interactive behaviors, but their model complexity and computational cost are relatively high. For example, Zhang et al. constructed a passenger and vehicle flow coupling analysis model based on time-varying OD demand, train timetables, and network topology; Hassannayebi et al. combined discrete event simulation with genetic algorithms to construct a simulation optimization model of passenger flow affecting train operation; and Dong Hao et al. used a multi-agent architecture to characterize the mutual influence between train operation status and passenger flow aggregation.

[0011] In cross-line shunting scenarios, the insertion of reinforcement trains into the interfering line will alter the capacity supply and passenger waiting conditions on the interfering line, while the withdrawal of trains from non-interfering lines may also affect the service level of the original line. Therefore, it is necessary to develop a passenger flow and train flow coupling simulation evaluation method for cross-line shunting scenarios to support the evaluation of the effectiveness of cross-line shunting schemes and optimization decisions.

[0012] Current methods for addressing capacity shortages in urban rail transit typically focus on adjustments within individual lines, such as limiting passenger flow at stations, adding extra trains, adjusting routes, and reducing headway to alleviate localized capacity strain. However, these methods are primarily limited to the affected lines and fail to fully utilize any surplus train resources that may exist on non-affected lines during specific time periods. When the affected line lacks sufficient spare vehicles, has limited room for timetable adjustments, or experiences a significant capacity shortfall, these line-specific measures are insufficient to replenish transport capacity in a timely and effective manner, leading to problems such as passenger congestion, extended waiting times, and a decline in line service levels.

[0013] Cross-line shunting not only requires determining whether to implement shunting, from which non-interfering line to dispatch which train, and in which direction to dispatch it onto the interfering line, but also needs to consider the insertion position of the reinforcement train in the timetable of the interfering line, its arrival and departure times, turnaround services, return-to-track services after the task is completed, and the restoration of the original timetable of the non-interfering line. Existing methods often only focus on single-level scheduling decisions or timetable adjustments, failing to incorporate cross-line dispatching decisions, reinforcement service generation, return-to-track service generation, and multi-line timetable adjustments into a unified framework for modeling. This results in cross-line shunting schemes lacking complete timetable support and having insufficient practical feasibility.

[0014] Cross-line shunting involves the entire process of a reinforcement train being moved from a non-interfering line to an interfering line to perform its reinforcement mission, and then returning to the original line to resume operation. Current technology lacks complete modeling of the "reinforcement service chain" and "return service chain" in cross-line shunting, and cannot effectively describe each stage of the process from the original line to the interfering line to perform its reinforcement mission and then back to the original line to resume operation. This results in existing solutions being unable to fully support the operation and coordination of the entire cross-line shunting process.

[0015] Existing methods typically evaluate the effectiveness of cross-line shunting schemes based on static indicators, making it difficult to comprehensively depict the overall impact after implementation. Cross-line shunting involves the allocation of capacity across multiple lines. The dispatching of reinforcement trains can not only improve the service level of the affected lines but may also affect the service capacity of non-affected lines, leading to changes in passenger waiting times. Therefore, a simulation evaluation method for cross-line shunting scenarios is needed, capable of comprehensively assessing the impact of shunting schemes on passenger service levels, train operation status, and the entire rail network.

[0016] Cross-line shunting involves multiple decision windows, multiple non-interfering lines, multiple candidate reinforcement trains, and multiple directions of shunting, resulting in a complex and high-dimensional decision space. Each candidate solution requires train timetable adjustments and simulation evaluation, leading to high costs for a single objective function evaluation. Existing techniques typically rely on exhaustive search or heuristic algorithms, but these methods are inefficient when faced with a large-scale solution space, making it difficult to find the optimal or near-optimal solution within a limited time, and resulting in excessive computational costs. Summary of the Invention

[0017] The purpose of this invention is to provide a simulation optimization method and system for urban rail transit cross-line train operation scheduling, so as to solve at least one of the technical problems existing in the background art.

[0018] To achieve the above objectives, the present invention adopts the following technical solution:

[0019] In a first aspect, the present invention provides a simulation optimization method for urban rail transit cross-line train operation scheduling, comprising:

[0020] Acquire basic network data, original train timetables, passenger flow demand data, transfer station connecting line information, train operation constraint parameters, and cross-line shunting operation cost parameters;

[0021] The period of sustained capacity shortage is divided into several decision windows, and within each decision window, it is determined whether to implement cross-line shunting, from which non-interfering line to allocate which train, and the initial running direction after being transferred to the interfering line.

[0022] Based on the cross-line shunting decision, reinforcement services and return-to-track services are generated and embedded into the train timetables of the interfering and non-interfering lines, respectively, so that the adjusted timetables meet the constraints of headway, stop time, section travel time, turnaround time and cross-line travel time.

[0023] A simulation and evaluation model for urban rail passenger and vehicle flow coupling for cross-line shunting is used to calculate the passenger service level under different schemes, and a comprehensive objective function value is formed by combining the cross-line shunting operation cost; among them, Bayesian optimization is used to iteratively search for cross-line shunting schemes.

[0024] Based on the evaluated schemes, a cross-line train operation scheduling optimization model considering shunting at transfer stations is constructed. The next set of candidate shunting schemes is selected, and the feasibility of the candidate schemes is solved. The scheme effects are calculated and the results are fed back to Bayesian optimization. After multiple iterations, the cross-line train scheduling scheme and the corresponding adjusted train timetable are output.

[0025] As a further limitation of the first aspect of the present invention, in the cross-line train operation scheduling optimization model considering shunting at transfer stations, an objective function is constructed based on the overall passenger service level of the network and the cross-line shunting operation cost as the comprehensive optimization basis, so that the cross-line shunting scheme can achieve a balance between improving the passenger service level and controlling the shunting cost. The sum of the average travel time of passengers on each line of the network is used as the passenger service level index. This index is obtained by calculating the average travel time of passengers on the interfering lines and each non-interfering line separately and summing the results of each line. The cross-line shunting operation cost is converted into an equivalent time cost using the passenger time value.

[0026] As a further limitation of the first aspect of this invention, the model solution constraints include three categories: constraints related to train cross-line dispatching decisions, constraints related to train timetable adjustments on interfering lines, and constraints related to train timetable adjustments on non-interfering lines. Specifically, the constraints related to train cross-line dispatching decisions are used to determine whether cross-line shunting should be implemented within each decision window, which non-interfering line should dispatch which reinforcement train, and the initial running direction of the reinforcement train after it enters the interfering line. The constraints related to train timetable adjustments on interfering lines are used to generate reinforcement service chains, determine the insertion position and arrival / departure times of reinforcement services, and ensure that the adjusted timetable for the interfering line meets the train operation requirements. The constraints related to train timetable adjustments on non-interfering lines are used to generate return-to-track service chains and determine the return-to-track services. The constraints for adjusting the train timetable for interfering lines include: when a reinforcement train is transferred to an interfering line, a corresponding reinforcement service chain needs to be inserted into the existing timetable of the interfering line; the reinforcement service chain is embedded into the interfering line timetable by adjusting the arrival and departure times of the relevant existing services, and the direction of the first reinforcement service is determined by the cross-line shunting decision, with subsequent reinforcement services connecting between the up and down directions according to the turnaround organization requirements; the constraints for adjusting the train timetable for non-interfering lines include: after completing the reinforcement task on the interfering line, the reinforcement train needs to return to the original non-interfering line via the transfer station connecting line, and a corresponding return-to-line service chain needs to be inserted into the existing timetable of the non-interfering line. The return-to-line service chain is embedded into the non-interfering line timetable by adjusting the arrival and departure times of the relevant existing services to ensure that the reinforcement train can return to the original line to continue its operational tasks.

[0027] As a further limitation of the first aspect of the present invention, Bayesian optimization is used to search for cross-line shunting schemes, including: taking the cross-line shunting decision vector as input, and through steps of constructing a candidate reinforcement train pool, fitting a surrogate model, selecting points for the data acquisition function, solving for timetable adjustments, and simulation evaluation feedback, the candidate schemes are gradually updated, and finally, a cross-line train dispatching scheme with better comprehensive objectives is output; wherein, the set of cross-line shunting decision variables is re-encoded, and the first... Each decision window, consisting of a decision vector of multiple binary variables, is compressed into a single integer component, and a complete shunting plan is redefined and encoded into a length of [length missing]. An integer vector.

[0028] As a further limitation of the first aspect of the present invention, the construction of the candidate pool for reinforcement trains includes: scanning each decision window for trains that meet the cross-line dispatching conditions based on the train operation diagram information of each non-interfering line, and constructing a candidate pool for reinforcement trains; wherein, for each candidate reinforcement train, its line, dispatching direction, transfer station, and the time window in which it can be used to depart from the interfering line after clearing passengers at the transfer station are recorded; the candidate pool for reinforcement trains remains unchanged throughout the optimization process and serves as a lookup table for decoding and decoding; for decision windows that do not contain any valid trains, their corresponding decision components are fixed at 0 and do not participate in the Bayesian optimization search process, thereby effectively compressing the search space and improving optimization efficiency.

[0029] As a further limitation of the first aspect of the present invention, in order to avoid the initial samples being overly concentrated in local areas, three initial sampling strategies are set up, and initial solutions are generated for different shunting quantities, including:

[0030] Strategy 1: Diversified Sampling: According to the "route" Upward → Line Downstream → Line Upward → Line The order of "downward →..." is rotated, and shunting options are selected sequentially from the available decision windows corresponding to each line and direction, so that the initial sample has a relatively balanced coverage in terms of line and direction dimensions.

[0031] Strategy 2: Random sampling. Randomly select several windows from all decision windows containing valid candidate trains, and randomly assign a legal shunting option to each selected window to increase sample diversity.

[0032] Strategy 3, continuous window sampling, is suitable for Timing: Prioritize combinations of decision windows that are consecutive in time to simulate concentrated reinforcement scenarios in actual operations, including: identifying a length no less than the target shunting quantity. From a continuous valid window segment, randomly select a segment and extract a length of [length missing]. A continuous subsequence is then randomly assigned shunting options.

[0033] Secondly, the present invention provides a simulation and optimization system for urban rail transit cross-line train operation scheduling, comprising:

[0034] The acquisition module is used to acquire basic network data, original train timetables, passenger flow demand data, transfer station connecting line information, train operation constraint parameters, and cross-line shunting operation cost parameters.

[0035] The cross-line shunting decision module is used to divide the period of continuous capacity shortage into several decision windows, and within each decision window, it determines whether to implement cross-line shunting, from which non-interfering line to dispatch which train, and the initial running direction after being dispatched to the interfering line.

[0036] The timetable adjustment module is used to generate reinforcement services and return-to-track services based on cross-line shunting decisions, and embed them into the train timetables of interfering and non-interfering lines respectively, so that the adjusted timetable meets the constraints of headway, station dwell time, section travel time, turnaround time and cross-line travel time.

[0037] The simulation optimization module is used to call the urban rail passenger and train flow coupling simulation evaluation model for cross-line shunting, calculate the passenger service level under different schemes, and form a comprehensive objective function value by combining the cross-line shunting operation cost. Among them, Bayesian optimization is used to iteratively search for cross-line shunting schemes. Based on the evaluated schemes, a cross-line train operation scheduling optimization model considering shunting at transfer stations is constructed, and the next set of candidate shunting schemes is selected. The feasibility of the candidate schemes is solved, the scheme effect is calculated, and the results are fed back to Bayesian optimization. After multiple rounds of iteration, the cross-line train scheduling scheme and the corresponding adjusted train timetable are output.

[0038] Thirdly, the present invention provides a non-transitory computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the urban rail transit cross-line train operation scheduling simulation optimization method as described in the first aspect.

[0039] Fourthly, the present invention provides a computer device including a memory and a processor, wherein the processor and the memory communicate with each other, the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the urban rail transit cross-line train operation scheduling simulation optimization method as described in the first aspect.

[0040] Fifthly, the present invention provides an electronic device, comprising: a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing the urban rail transit cross-line train operation scheduling simulation optimization method as described in the first aspect.

[0041] Terminology Explanation: Cross-line shunting in urban rail transit: This refers to a method of train dispatching where, when a line in the urban rail transit network experiences a short-term capacity shortage, the operating organization temporarily dispatches some trains from other lines to the line with the capacity shortage via transfer station connecting lines to perform reinforcement tasks. After completing the task, the trains are returned to their original lines to restore normal operation. Capacity shortage: This refers to a situation where, within a specific time period and spatial range, the line's transport capacity is insufficient to meet passenger travel demand, leading to passenger backlogs, extended waiting times, or train congestion. Disrupting line: This refers to a line experiencing a significant capacity shortage during a specific time period due to rapid passenger flow accumulation, vehicle malfunctions, equipment abnormalities, or other operational disturbances, requiring capacity supplementation. Non-disrupting line: This refers to a line that has transfer connections or connecting lines with the disrupting line, and where passenger flow pressure is relatively low during the disruption period, allowing for some train dispatching space. Transfer station connecting line: This refers to a track connection facility located between different lines that enables cross-line train transfers and is a fundamental condition for implementing cross-line shunting. Reinforcement Train: Refers to a train selected from a non-interfering line and transferred to the interfering line via a connecting line at a transfer station to perform a temporary capacity supplementation task. Reinforcement Service: Refers to the temporary operational service performed within the interfering line after a reinforcement train has been transferred across lines. Reinforcement Service Chain: Refers to several reinforcement services performed sequentially within the interfering line by the same reinforcement train after it has been transferred across lines. Return-to-Line Service: Refers to the operational service performed by a reinforcement train after completing its reinforcement task within the interfering line, returning to its original non-interfering line via a connecting line at a transfer station, and continuing to operate on the original line. Return-to-Line Service Chain: Refers to several return-to-line services performed sequentially on the original line by the same reinforcement train after it has returned to its original non-interfering line. Cross-Line Shunting Simulation Evaluation: Refers to a method for evaluating the effectiveness of cross-line shunting schemes, based on the concept of passenger flow and train flow coupling simulation, dynamically depicting the passenger travel process, train operation process, and the interaction between the two, and quantitatively analyzing the implementation effect of the scheme, in order to meet the needs of cross-line shunting scheme effectiveness evaluation. Bayesian optimization is a sequential optimization method applicable to black-box functions and high-cost evaluation problems. It searches for a better solution within a finite number of evaluations using a surrogate model and a collection function.

[0042] The beneficial effects of this invention are as follows: By using the connecting line of the transfer station as the cross-line transfer channel, the process of clearing passengers at the transfer station, cross-line operation of the connecting line, and the transfer of trains to interfering lines to perform reinforcement services are incorporated into a unified framework, which better meets the actual shunting needs under the conditions of urban rail transit interconnection; by setting up reinforcement services and return-to-line services, the entire process of reinforcement trains being transferred from non-interfering lines, entering interfering lines to provide reinforcement, and returning to the original line to continue operation after completing their tasks is described, improving the completeness of the scheme; while determining the cross-line shunting decision, the insertion of reinforcement services on interfering lines, the connection of return-to-line services on non-interfering lines, and the adjustment of related arrival and departure times are considered in a coordinated manner, so that the generated scheme has better timetable support and executability; by using the sum of the average travel time of passengers on all lines of the network and the cross-line shunting operation cost as the optimization basis, the scheme can control shunting costs while improving passenger service levels.

[0043] The advantages of additional aspects of the invention will be set forth more clearly in the following description or will be learned by practice of the invention. Attached Figure Description

[0044] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 This is a flowchart illustrating the simulation optimization method for cross-line train scheduling in urban rail transit under the scenario of capacity shortage, as described in an embodiment of the present invention.

[0046] Figure 2 This is a flowchart of the cross-line train scheduling algorithm based on Bayesian optimization as described in an embodiment of the present invention. Detailed Implementation

[0047] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0048] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0049] It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as here.

[0050] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, and / or groups thereof.

[0051] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0052] To facilitate understanding of the present invention, the present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. However, the specific embodiments do not constitute a limitation on the embodiments of the present invention.

[0053] Those skilled in the art should understand that the accompanying drawings are merely schematic diagrams of embodiments, and the components in the drawings are not necessarily essential for implementing the present invention.

[0054] This invention proposes a simulation optimization method for cross-line train dispatching in urban rail transit systems facing capacity shortages. This method enables cross-line train dispatching based on transfer station connecting lines: Addressing the problem that existing technologies mainly rely on terminal stations or vehicle parking locations for cross-line dispatching, making them unsuitable for transfer station shunting scenarios, this invention uses transfer station connecting lines as cross-line transfer channels. This allows trains on non-interfering lines to be transferred to interfering lines to perform reinforcement tasks after passenger clearing at the transfer station, thereby improving the flexibility and applicability of cross-line shunting organization. This method also improves the collaborative efficiency of cross-line shunting scheme search and simulation evaluation: Addressing the issues of a large number of cross-line shunting schemes and high costs per simulation evaluation, this invention introduces Bayesian optimization based on simulation evaluation. A surrogate model guides the search for candidate schemes, reducing the number of invalid scheme evaluations, thus finding a better cross-line train dispatching scheme within a limited number of computations. This method achieves coordination between cross-line reinforcement services and multi-line timetable adjustments: Addressing the issue that cross-line shunting simultaneously affects the operational organization of both interfering and non-interfering lines, this invention, while determining cross-line shunting decisions, considers the embedding of reinforcement services in the timetable of interfering lines and the connection of return-to-track services in the timetable of non-interfering lines, ensuring that cross-line shunting schemes are consistent with the timetable adjustments of relevant lines. This method comprehensively describes the process of reinforcement train arrival, reinforcement, and return-to-track restoration: Addressing the insufficient characterization of the entire cross-line shunting service organization in existing technologies, this invention, through the setting of reinforcement and return-to-track services, describes the entire process of reinforcement trains being dispatched from non-interfering lines, entering interfering lines via transfer station connecting lines to perform capacity replenishment tasks, and returning to their original lines to continue operation after completing their tasks, thereby improving the completeness of cross-line shunting schemes. This method takes into account both passenger service quality and cross-line shunting operation costs: In response to the problem that existing technologies mainly focus on passenger time indicators and do not adequately consider shunting operation costs, this invention uses the sum of the average travel time of passengers on each line of the network and the cross-line shunting operation costs as optimization criteria, and converts the operation costs into equivalent time costs through passenger time value, so that the solution can achieve a balance between service improvement and cost control.

[0055] Example 1

[0056] In this embodiment 1, a simulation optimization system for urban rail transit cross-line train operation scheduling is first provided, including: an acquisition module, used to acquire basic network data, original train timetables, passenger flow demand data, transfer station connecting line information, train operation constraint parameters, and cross-line shunting operation cost parameters; a cross-line shunting decision module, used to divide the period of continuous capacity shortage into several decision windows, and within each decision window determine whether to implement cross-line shunting, from which non-interference line to dispatch which train, and the initial running direction after dispatching into the interference line; and a timetable adjustment module, used to generate reinforcement services and return-to-track services based on the cross-line shunting decisions, and embed them into the train timetables of the interference line and the non-interference line respectively, so that the adjusted timetables can be optimized. The train schedule satisfies constraints on headway, stop time, interval travel time, turnaround time, and cross-line travel time. The simulation optimization module calls the urban rail passenger flow and train flow coupling simulation evaluation model for cross-line shunting to calculate the passenger service level under different schemes and form a comprehensive objective function value by combining the cross-line shunting operating cost. Among them, Bayesian optimization is used to iteratively search for cross-line shunting schemes. Based on the evaluated schemes, a cross-line train operation scheduling optimization model considering shunting at transfer stations is constructed, and the next set of candidate shunting schemes is selected. The feasibility of the candidate schemes is solved, the scheme effect is calculated, and the results are fed back to Bayesian optimization. After multiple rounds of iteration, the cross-line train scheduling scheme and the corresponding adjusted train schedule are output.

[0057] In this embodiment, the above-mentioned system is used to implement a simulation optimization method for urban rail transit cross-line train operation scheduling, including: acquiring basic network data, original train timetables, passenger flow demand data, transfer station connecting line information, train operation constraint parameters, and cross-line shunting operation cost parameters; dividing the period of continuous capacity shortage into several decision windows, and determining whether to implement cross-line shunting, from which non-interfering line to dispatch which train, and the initial running direction after being dispatched to the interfering line within each decision window; generating reinforcement services and return-to-track services based on the cross-line shunting decisions, and embedding them into the train timetables of the interfering and non-interfering lines respectively, so that the adjusted timetable meets the headway requirements. Constraints on station dwell time, interval travel time, turnaround time, and cross-line travel time are implemented. A simulation evaluation model of urban rail passenger and vehicle flow coupling for cross-line shunting is used to calculate passenger service levels under different schemes, and a comprehensive objective function value is formed by combining the cross-line shunting operating cost. Bayesian optimization is used to iteratively search for cross-line shunting schemes. Based on the evaluated schemes, a cross-line train operation scheduling optimization model considering shunting at transfer stations is constructed, and the next set of candidate shunting schemes is selected. The feasibility of the candidate schemes is solved, the scheme effects are calculated, and the results are fed back to Bayesian optimization. After multiple iterations, the cross-line train scheduling scheme and the corresponding adjusted train timetable are output.

[0058] In this embodiment, the urban rail transit cross-line train operation scheduling simulation optimization method is a simulation optimization method for urban rail transit cross-line train scheduling in scenarios of capacity shortage. The overall framework is as follows: Figure 1 As shown in the figure, this method addresses the problem of localized line capacity shortages under interconnected urban rail transit operation conditions. It takes network infrastructure data, original train timetables, passenger demand data, transfer station connection information, train operation constraints, and cross-line shunting operation cost parameters as inputs. Through a technical process of "cross-line shunting decision generation - train timetable adjustment - simulation evaluation - Bayesian optimization iterative search," it outputs cross-line shunting schemes and corresponding adjusted train timetables. This method mainly includes three interconnected modules: a cross-line shunting decision module, a timetable adjustment module, and a simulation optimization module. The cross-line shunting decision module divides the period of capacity shortage into several decision windows, and within each decision window determines whether to implement cross-line shunting, from which non-interfering line to dispatch which train, and the initial running direction after shunting into the interfering line. The timetable adjustment module generates reinforcement services and return-to-line services based on the cross-line shunting decisions, and embeds them into the train timetables of the interfering and non-interfering lines, respectively, so that the adjusted timetable meets constraints such as headway, station dwell time, section running time, turnaround time, and cross-line running time. The simulation optimization module is used to call the urban rail passenger flow and train flow coupling simulation evaluation method for cross-line shunting, calculate the passenger service level under different schemes, and form a comprehensive objective function value by combining the cross-line shunting operation cost.

[0059] In the solution process, this method employs Bayesian optimization to iteratively search for cross-line shunting schemes. The Bayesian optimization module constructs a surrogate model based on the evaluated schemes and selects the next set of candidate shunting schemes; the timetable adjustment module performs feasibility analysis on the candidate schemes; and the simulation evaluation module calculates the scheme's effectiveness and feeds the results back to the Bayesian optimization module. After multiple iterations, the final cross-line train scheduling scheme with the best overall objective is output.

[0060] Through the above framework, this method enables trains on non-interference lines to be transferred to interference lines via connecting lines at transfer stations to perform reinforcement tasks in scenarios of capacity shortage, and to return to the original line to continue operation after the task is completed, thus forming a complete cross-line shunting scheme that includes shunting decision-making, reinforcement services, return-to-line services, adjusted timetable and scheme evaluation results.

[0061] The method described in this embodiment considers an optimization model for cross-line train operation scheduling involving shunting at transfer stations. After the implementation of the cross-line shunting scheme, the operational status of both interfering and non-interfering lines will be affected simultaneously. On the one hand, the insertion of reinforcement trains into the interfering line can increase the capacity supply, shorten passenger waiting times, and improve the service level of the interfering line. On the other hand, the removal of trains from non-interfering lines will correspondingly reduce their existing service capacity, potentially leading to increased waiting times for passengers on non-interfering lines. Furthermore, cross-line shunting also incurs additional operating costs such as empty train operation, passenger clearing organization, and scheduling coordination. Therefore, this invention uses the overall passenger service level of the network and the operating cost of cross-line shunting as the comprehensive optimization basis to construct an objective function, enabling the cross-line shunting scheme to achieve a balance between improving passenger service levels and controlling shunting costs.

[0062] To evaluate the impact of cross-line shunting schemes on the overall service level of the network, the sum of the average travel times of passengers on all lines of the network is used. As a passenger service level indicator, this indicator is calculated by separately calculating the average passenger travel time on the interfering line and each non-interfering line, and then summing the results for each line. This indicator reflects two types of impacts simultaneously: first, the service improvement effect brought about by the insertion of reinforcement trains into the interfering line; and second, the potential service loss caused by the removal of trains from non-interfering lines. Therefore, this indicator can be used to comprehensively measure the overall passenger travel time changes across the network under a given cross-line shunting scheme.

[0063] Cross-line shunting operating costs include energy consumption from empty train operation, passenger clearing organization costs, dispatching and coordination costs, and vehicle operation adjustment costs. Since average passenger travel time is measured in time, while cross-line shunting operating costs are measured in currency, the two cannot be directly added together. To achieve unified optimization, this embodiment uses Passenger Time Value (VOT) to convert cross-line shunting operating costs into equivalent time costs.

[0064] Assuming the operating cost of a single cross-line shunting is (Yuan), passenger time value is VOT (Yuan / (person·hour)), then the equivalent total time cost corresponding to the single cross-line shunting operation cost is:

[0065] ;

[0066] in, This represents the equivalent total time cost for a single cross-line shunting operation, expressed in person-seconds; the coefficient 3600 is used to convert hours to seconds. This formula indicates that the operating cost of executing a single cross-line shunting operation can be equivalent to the total time cost shared by passengers across the network.

[0067] Furthermore, let the total number of passengers on the network during the interference period be... The average equivalent time increment per person for a single cross-line shunting operation is:

[0068] ;

[0069] set up This represents the set of cross-line shunting decisions during the entire period of interference. In the decision set The sum of the average travel times of passengers on each line of the network obtained from simulation evaluation; assuming For cross-line shunting decision variables, when the first Non-interference lines within each decision window Candidate trains Reassigned to interference lines The value is 1 if the direction is in play, and 0 otherwise.

[0070] The average equivalent time cost per person for all cross-line shunting operations is:

[0071] ;

[0072] In summary, the overall objective function is as follows:

[0073] ;

[0074] The constraints are divided into three categories: constraints related to train cross-line dispatching decisions, constraints related to train timetable adjustments on interfering lines, and constraints related to train timetable adjustments on non-interfering lines.

[0075] Among them, the constraints related to train cross-line dispatching decisions are used to determine whether cross-line shunting should be implemented within each decision window, which non-interference line should dispatch which reinforcement train, and the initial running direction of the reinforcement train after it enters the interference line; the constraints related to the adjustment of the train timetable of the interference line are used to generate the reinforcement service chain, determine the insertion position and arrival and departure time of the reinforcement service, and ensure that the adjusted timetable of the interference line meets the train operation requirements; the constraints related to the adjustment of the train timetable of the non-interference line are used to generate the return service chain, determine the insertion position and arrival and departure time of the return service, and ensure that the reinforcement train can continue to perform its operation tasks after returning to the original line.

[0076] The constraints related to train cross-line dispatching decisions include:

[0077] Domain constraints of decision variables: decision variables For 0-1 integer variables: when At, it indicates the time. Within each decision window, non-interference lines On the train As reinforcement trains, they were reassigned to the jammed lines. Provide reinforcement services in the direction; when When the time is specified, it indicates that the train will maintain its original operating plan and will not be subject to cross-line shunting. The decision variables within each decision window constitute the decision vector for that window, and the decision vectors of all decision windows together constitute a complete cross-line shunting plan.

[0078] ;

[0079] ;

[0080] .

[0081] The number of trains that can be dispatched within each decision window is limited: taking into account the capacity of the connecting lines at transfer stations and the complexity of cross-line shunting operations, it is stipulated that at most one train can be dispatched to the interfering line within each decision window, so as to avoid multiple trains crossing the line at the same time and causing operational conflicts.

[0082] ;

[0083] Uniqueness constraint of train dispatch direction: For any candidate reinforcement train, it can only be dispatched to a specific direction of the interfering line within the same decision window, so as to avoid the same train being dispatched repeatedly or undertaking reinforcement tasks in multiple directions at the same time.

[0084] ;

[0085] Total number of vehicles to be deployed: For each non-interference line The total number of trains that are dispatched during the entire period of interference shall not exceed the maximum number of trains allowed to be dispatched on that line. .

[0086] .

[0087] Constraints related to train timetable adjustments on interfering lines include: When a reinforcement train is shunted to the interfering line, a corresponding reinforcement service chain needs to be inserted into the existing timetable of the interfering line. The reinforcement service chain is embedded into the interfering line timetable by adjusting the arrival and departure times of relevant existing services. The direction of the first reinforcement service is determined by the cross-line shunting decision, and subsequent reinforcement services operate in a coordinated manner between the up and down directions according to turnaround requirements. This type of constraint mainly includes the following:

[0088] Connective variable domain constraint: To establish the logical connection between cross-line allocation decisions and reinforcement service chain generation, connective variables are introduced. Insert position variables for reinforcement services Connect variables This is a 0-1 integer variable used to identify reinforcement trains that are dispatched across lines. Has the corresponding backup service chain been successfully inserted into the interference line operation diagram? When, it indicates that a corresponding reinforcement service chain has been generated; when When the value is 0, it indicates that the function has not been generated.

[0089] ;

[0090] Insert position variable Both are 0-1 integer variables used to determine the reinforcement trains. The specific insertion position of each reinforcement service in the corresponding reinforcement service chain within the existing interference line operation diagram: when At that time, it indicated that reinforcement services were being provided. Inserted into existing services Then; otherwise, take 0:

[0091] ;

[0092] The cross-line dispatch decision and the generation of the reinforcement service chain correspond to the following constraints: A necessary and sufficient condition relationship must be satisfied between the cross-line dispatch decision and the generation of the reinforcement service chain, i.e., reinforcement trains... When performing cross-line deployment, a corresponding reinforcement service chain is generated if and only if such a chain is created:

[0093] .

[0094] Reinforcement service chain length constraint: If reinforcement trains A reinforcement service chain was generated ( If the chain contains at least one reinforcement service and no more than [a certain number of services], then the total number of reinforcement services in the chain is no less than [a certain number] and no more than [a certain number of services]. Article; among which, This is a preset upper limit for the length of the reinforcement service chain, used to control the maximum number of times a single reinforcement train can continuously perform reinforcement services within the interfered line. If no chain is generated ( If the number of reinforcement service entries is zero, then the number of service entries will be zero.

[0095] .

[0096] Constraints on the adjustment range of arrival and departure times for existing services on interfering lines: The arrival and departure times of existing services on interfering lines are allowed to be adjusted within a certain range at each station, but the adjustment range shall not exceed the preset maximum deviation, so as to ensure that the reinforcement service is embedded in the timetable while minimizing disruption to the original operation order.

[0097] ;

[0098] ;

[0099] Insertion position constraints for reinforcement services: Reinforcement trains In the corresponding reinforcement service chain, each reinforcement service has one and only one insertion point, namely the reinforcement service. It is inserted precisely between a pair of adjacent existing services: .

[0100] Spatiotemporal Coordination Constraints of the Reinforcement Service Chain: The operational direction of the first reinforcement service in the reinforcement service chain is directly determined by the cross-line dispatch decision, and its originating station is the reinforcement train. Non-interference line Transfer stations between interfering lines Its departure time at the originating station must be coordinated with the train's cross-line transfer process after the passenger clearing operation is completed on the original non-interference line, that is, it should fall within the feasible time window jointly determined by the passenger clearing completion time and the cross-line running time of the connecting line:

[0101] ;

[0102] .

[0103] In a reinforcement service chain, the operating directions of two adjacent reinforcement services are strictly opposite, and the turnaround time requirements between adjacent services must be met:

[0104] .

[0105] Train dwell time constraints on interfering lines: The dwell time of both existing and reinforcement services on interfering lines at each station must meet the minimum and maximum dwell time limits.

[0106] ;

[0107] .

[0108] Train travel time constraints on interfering lines: The travel time of both existing and supplementary services on interfering lines between adjacent stations must meet minimum and maximum travel time limits.

[0109] ;

[0110] .

[0111] Minimum safe headway constraint for trains on interfering lines: The departure times of any two adjacent trains serving the same station on interfering lines must meet the minimum safe headway requirement to ensure safe and reliable train operation. This is handled in the following two scenarios:

[0112] Scenario 1: Between two adjacent existing services:

[0113] ;

[0114] Scenario 2: Between existing services and adjacent reinforcement services:

[0115] ;

[0116] .

[0117] The trainset utilization plan on the interfering line must remain constrained: During the adjustment of arrival and departure times at existing stations along the interfering line, the original trainset utilization plan must remain feasible. Specifically, for existing services in the original timetable that use the same trainset for consecutive operation, the plan must be maintained. and Even after the adjustment, the turnaround time requirements must still be met at the turnaround station:

[0118] ;

[0119] Constraints related to train timetable adjustments on non-interference lines include: After completing their support mission on the interference line, reinforcement trains need to return to the original non-interference line via the connecting line at the transfer station, and a corresponding return-line service chain needs to be inserted into the existing timetable of the non-interference line. The return-line service chain is embedded into the non-interference line timetable by adjusting the arrival and departure times of relevant existing services to ensure that the reinforcement trains can return to their original line to continue their operational tasks. This type of constraint is similar in structure to the constraints for adjusting timetables on interference lines, but adds a restriction on the maximum departure interval on the non-interference line, as detailed below.

[0120] Connectivity variable domain constraint: To establish the logical connection between cross-line dispatching decisions and backhaul service chain generation, connectivity variables are introduced. Insert position variable for loop service Connect variables This is a 0-1 integer variable used to identify reinforcement trains that are dispatched across lines. Has the corresponding return service chain been successfully inserted into the original non-interference line operation diagram? When, it indicates that the corresponding loopback service chain has been generated; when When the value is 0, it indicates that the function has not been generated.

[0121] ;

[0122] Insert position variable Both are 0-1 integer variables used to determine the reinforcement trains. The specific insertion position of each loop service in the corresponding loop service chain within the existing non-interference line operation diagram: when When, it indicates a return-to-line service. Inserted into existing services Then; otherwise, take 0:

[0123] .

[0124] Cross-line dispatching decision and backhaul service chain generation correspondence constraints: There is a correspondence between cross-line dispatching decisions and backhaul service chain generation, i.e., reinforcement trains... After completing the cross-line reinforcement mission, a corresponding return service chain is generated in the original non-interference line operation diagram only if and only if:

[0125] .

[0126] Constraints on the adjustment range of arrival and departure times for existing services on non-interference lines: Adjustments to the arrival and departure times of existing services at each station must adhere to time boundary constraints. To minimize disruption to the existing operational order, the adjustment range must not exceed the maximum deviation. :

[0127] ;

[0128] .

[0129] Insertion position constraints for loop service: reinforcement train In the corresponding backhaul service chain, each backhaul service has one and only one insertion position, that is, each backhaul service It is inserted precisely between a pair of adjacent existing services:

[0130] .

[0131] Spatiotemporal connectivity constraints of the reinforcement service chain: The operating direction of the first return line service in the return line service chain is determined by the reinforcement train. The operational status of the interfering line was determined after the completion of its final reinforcement service; its originating station was the original non-interfering line. Transfer stations between interfering lines Its departure time at the originating station must be coordinated with the passenger clearing operation and the return process on the connecting line after the reinforcement train has completed its reinforcement mission. That is, it should fall within the feasible time window jointly determined by the end time of the last reinforcement service and the cross-line running time of the connecting line.

[0132] ;

[0133] .

[0134] In a loop service chain, the operating directions of two subsequent adjacent loop services are strictly opposite, and the turnaround time requirements between adjacent services must be met at the turnaround station:

[0135] .

[0136] Train dwell time constraints on non-interference lines: The dwell time of all trains serving any station on non-interference lines must meet the maximum and minimum dwell time limits.

[0137] ;

[0138] .

[0139] Train travel time constraints on non-interference lines: The travel time of all train services between adjacent stations on non-interference lines must meet minimum and maximum travel time limits.

[0140] ;

[0141] .

[0142] Minimum safe headway constraint for trains on non-interfering lines: The departure times of any two adjacent trains serving the same station on a non-interfering line must meet the minimum safe headway requirement, which is handled in the following two cases:

[0143] Scenario 1: Between two adjacent existing services:

[0144] ;

[0145] Scenario 2: Between existing services and adjacent loop services:

[0146] ;

[0147] .

[0148] Maximum train interval constraint on non-interference lines: If reinforcement trains on non-interference lines At a certain decision-making window If a train is transferred from the same line, its original rolling stock will be temporarily withdrawn from operation on that line, potentially leading to a lack of subsequent connecting trains and thus increasing the actual headway on that line. To avoid a significant decline in the service level of non-interfering lines due to the continuous withdrawal of trains from the same line and direction, regulations stipulate that the headway between any two adjacent trains in any direction on non-interfering lines at each station must not exceed the maximum headway.

[0149] .

[0150] The use of rolling stock on non-interference lines must remain constrained: When adjusting the arrival and departure times of existing stations on non-interference lines, it must be ensured that the original rolling stock usage plan remains feasible. Specifically, for existing services in the original timetable that use the same rolling stock for connecting operations, this constraint must be maintained. and Even after the adjustment, the turnaround time requirements must still be met at the turnaround station to avoid disrupting the original car body turnover relationship due to the time adjustment: .

[0151] In this embodiment, Bayesian optimization is used to search for cross-line shunting schemes. The algorithm takes the cross-line shunting decision vector as input and updates the candidate schemes step by step through steps such as constructing a candidate reinforcement train pool, fitting a surrogate model, selecting data acquisition function points, solving for timetable adjustments, and simulation evaluation feedback. Finally, it outputs a cross-line train dispatching scheme with the best overall objective. The algorithm flow is as follows: Figure 2 As shown.

[0152] To improve the algorithm's search efficiency, this embodiment re-encodes the set of cross-line shunting decision variables. Since there is at most one valid dispatch decision within each decision window, the first... Each decision window consists of multiple binary variables. The constructed decision vector Compressed into a single integer component And a complete shunting plan is redefined and encoded into a length of integer vectors :

[0153] ;

[0154] in, Let be the total number of decision windows, and be the in the vector. Each component The meanings of the values ​​are as follows:

[0155] ;

[0156] This encoding method maps the combined decisions of multiple lines, multiple directions, and multiple windows into low-dimensional integer vectors, simplifying the representation and operation of the search space, and maintaining a direct mapping relationship with the original cross-line shunting decision variables.

[0157] The feasibility of the solution is verified by two types of constraints: First, the total number of reinforcement trains dispatched to each non-interference line during the entire interference period does not exceed the preset upper limit of the corresponding line. : Second, the selection within each decision window must correspond to an actual available train in the candidate pool of reinforcement trains. Solutions that do not meet the above conditions are deemed infeasible and are penalized in the objective function evaluation.

[0158] .

[0159] During the algorithm initialization phase, based on the train timetable information of each non-interfering line, trains that meet the cross-line dispatch conditions within each decision window are scanned one by one to construct a candidate pool of reinforcement trains. For each candidate reinforcement train Record its associated route Allocation direction transfer station And the time window available after passengers have been cleared from the transfer station to initiate interference with the line. .

[0160] The candidate pool of reinforcement trains remains unchanged throughout the optimization process, serving as a lookup table for encoding and decoding. For decision windows that do not contain any valid trains, their corresponding decision components are fixed at 0 and do not participate in the Bayesian optimization search process, thereby effectively compressing the search space and improving optimization efficiency.

[0161] Since cross-line shunting schemes are encoded as discrete integer vectors composed of integer components of each decision window, traditional continuous kernel functions based on Euclidean distance (such as the RBF kernel and Matérn kernel) are insufficient to accurately reflect the structural differences between two shunting schemes. Therefore, this embodiment employs an exponential kernel function based on Hamming distance to measure the similarity of the solution space:

[0162] ;

[0163] The Hamming distance is defined as follows:

[0164] ;

[0165] That is, the number of positions where the two shunting plans take different values ​​within the corresponding decision window. As a length-scale hyperparameter, controlling the similarity decay rate, this embodiment takes... The intuitive meaning of this kernel function is: the more decision windows two shunting schemes make the same choice, the closer the kernel function value is to 1, and the more similar their objective function values ​​are considered by the surrogate model; conversely, if the two schemes make different decisions in a large number of windows, the kernel function value tends to 0, indicating that the correlation between their objective function values ​​is weak. This similarity measurement method is highly consistent with the combinatorial structure of the cross-line shunting problem.

[0166] In the posterior prediction process, the objective function values ​​of historical feasible solutions are standardized to improve numerical stability and accelerate the kernel matrix inversion calculation. Let the set of feasible solutions be... Then the standardized observation values ​​are:

[0167] .

[0168] To address the condition number issue of the kernel matrix, a small number of noise terms are added to the diagonal: .

[0169] When the number of feasible solutions At this point, the surrogate model degenerates into a uniform random search until a sufficient number of feasible observations are accumulated.

[0170] In this embodiment, Expected Improvement (EI) is used as the acquisition function. Let the current historical optimal feasible objective function value be as follows:

[0171] ;

[0172] At candidate point At this point, EI is defined as the objective function value being lower than... The expected improvement is:

[0173] ;

[0174] Based on the analyticity of the posterior distribution of Gaussian processes, EI has a closed-form solution as follows:

[0175] ;

[0176] in and These are the cumulative distribution function (CDF) and probability density function (PDF) of the standard normal distribution, respectively. To explore and utilize the trade-off parameters. When When (i.e., the point has been fully observed), define .

[0177] In the optimization process of the acquisition function, it is first randomly generated within the search space. For each candidate solution, calculate its EI value and sort them in descending order; then, select the top-ranked solutions. A local neighborhood search is performed on each candidate solution—each valid decision window is tried to be replaced with other valid options, and the solution with the highest EI value is retained as the next evaluation point. This two-stage strategy of "random sampling + local refinement" is used to balance search efficiency and candidate solution quality.

[0178] To avoid excessive concentration of initial samples in local areas, this embodiment sets three initial sampling strategies, and targets different shunting numbers ( Initial solutions are generated for each vehicle.

[0179] Strategy 1 (Diversified Sampling): According to the "line" Upward → Line Downstream → Line Upward → Line The order of "downward →..." is rotated, and shunting options are selected sequentially from the available decision windows corresponding to each line and direction, so that the initial sample has a relatively balanced coverage in terms of line and direction dimensions.

[0180] Strategy 2 (Random Sampling): Randomly select several windows from all decision windows containing valid candidate trains, and randomly assign a legal shunting option to each selected window to increase sample diversity.

[0181] Strategy 3 (continuous window sampling, applicable to) hour):

[0182] Prioritize selecting decision window combinations that are consecutive in time to simulate concentrated reinforcement scenarios in actual operations. Specifically, identify windows with a length not less than the target shunting quantity. From a continuous valid window segment, randomly select a segment and extract a length of [length missing]. A continuous subsequence is then randomly assigned shunting options.

[0183] After generating initial samples using the three strategies described above, the objective function evaluation module is called for each initial sample to obtain observation values, and an initial observation dataset is constructed. .

[0184] In this embodiment, "number of consecutive periods without improvement" and "maximum number of iterations" are used as termination criteria: if consecutive... If no new solution better than the current optimal solution is found in any of the iterations, the optimization is terminated early. The termination condition is... ,in This is a counter for the current number of consecutive iterations without improvement. It is reset to 0 whenever a better solution is found, and incremented by 1 otherwise. Additionally, a maximum number of iterations is set. This serves as a supplementary termination condition to prevent the algorithm from running indefinitely in extreme cases.

[0185] In this embodiment, for a given shunting decision vector The evaluation process for the objective function is as follows:

[0186] First, based on the candidate reinforcement train pool Decode the data to extract the dispatched train information (route, direction, transfer station, time window) corresponding to each non-zero component. Then, perform the following operations sequentially on each reinforcement train:

[0187] 1) Transfer the reinforcement train from the corresponding non-interference line Remove it from the running graph and check whether the line satisfies the following maximum departure interval constraint after removal. If the constraint is violated, it is determined to be an infeasible solution.

[0188]

[0189] 2) Input the modified timetable into the Gurobi solver to accurately solve the train timetable adjustment problem for the interfering and non-interfering lines, determine the arrival and departure times of each reinforcement service in the reinforcement service chain at each station on the interfering line, and determine the arrival and departure times of each return service in the return service chain at each station on the non-interfering line.

[0190] 3) Calculate the objective function. After adjusting the train schedule, the adjusted multi-line train schedule, passenger flow OD data, network topology data, and cross-line shunting schemes are used as inputs to conduct a simulation evaluation of urban rail passenger flow coupling for cross-line shunting. During the simulation, simulation entities such as passengers, trains, and station-line are constructed. The system state changes are driven by events, sequentially handling events such as passenger arrival, train arrival, passenger disembarkation, passenger clearing, passenger boarding, and train departure. The simulation covers passenger waiting, boarding, delays, clearing and re-waiting after passenger clearing, as well as train stopping, departure, turnaround, cross-line operation, and return-to-line operation under different cross-line shunting schemes. After the simulation, the average travel time for passengers on each line is calculated, and the sum of the average travel times for passengers on all lines of the network is calculated. Then, the comprehensive objective function value is calculated in conjunction with the cross-line shunting operating cost. For Bayesian optimization outer search, the negative of the comprehensive objective function can be taken, transforming the minimization problem into a maximization problem for processing.

[0191] If any intermediate step fails (e.g., violation of non-interference line departure interval constraints, Gurobi solver returns infeasibility), the solution is deemed infeasible and a penalty value is assigned. .in, This is a preset large penalty value used to exclude infeasible solutions during subsequent search processes.

[0192] In summary, in this embodiment, the complete process of the Bayesian optimization-based cross-line train scheduling algorithm is divided into three stages, as follows: Figure 2 As shown.

[0193] Phase 1: Initialization.

[0194] Step 1: Read in the original timetables (Schedules) and passenger data (Passengers) for each route, and set the algorithm parameters ( wait).

[0195] Step 2: Run a simulation evaluation under the condition of no cross-line shunting, and calculate the baseline objective function value. Simultaneously calculate the equivalent time increment of the single shunting operation cost. .

[0196] Step 3: Based on the timetables of each non-interference line, scan each train in each decision window that meets the dispatch conditions to build a pool of candidate reinforcement trains. Determine the set of valid options for each window.

[0197] Step 4: Initialize the historical observation dataset Current optimal solution , No improvement counter .

[0198] Step 5: Check the number of shunting cars Diverse sampling, random sampling, and continuous window sampling were used respectively. (At time) Generate initial solutions; for each initial solution, call the objective function evaluation module to obtain observations. ,Will join in and update and .

[0199] Phase Two: Sequential Optimization.

[0200] Step 6: When Repeat the following steps.

[0201] Step 6.1: From Selecting feasible solution sets ;like Then, the objective value of the feasible solution is standardized, and a Gaussian process posterior model is fitted based on the Hamming distance exponential kernel to calculate the posterior mean function. and posterior standard deviation function Otherwise, proceed to Step 6.3 to perform a random search.

[0202] Step 6.2: Randomly generate Given 10 candidate solutions, calculate the expected improvement value for each candidate solution. Take the largest EI value. The candidate solutions are refined locally in their neighborhoods, and the solution with the largest EI value is finally selected. This will be the next evaluation point.

[0203] Step 6.3: Call the objective function evaluation module to evaluate the objective function. Evaluation was conducted as follows: (a) Candidate schemes were decoded, and trains were removed from each non-interfering line in sequence, while verifying the maximum departure interval constraint; (b) The Gurobi solver was used to accurately solve the train timetable adjustment problem for interfering and non-interfering lines; (c) The simulation module was used to evaluate the sum of the average travel times of passengers on each line of the network and to calculate the objective function value for the modified multi-line timetable. If any step fails, a penalty value is assigned. .

[0204] Step 6.4: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require join in ;like Then update , , ;otherwise .

[0205] Phase 3: Output Results.

[0206] Step 7: If Then, based on the optimal decision vector set Generate optimized train timetables for each line and calculate the improvement rate of the objective function. Output the optimal cross-line shunting plan and the optimized train timetable; otherwise, determine that the shunting revenue is insufficient to cover operating costs and maintain the original operation plan unchanged.

[0207] Step 8: Output the optimization convergence curve and various statistical information, and return the optimal solution. .

[0208] Example 2

[0209] This embodiment 2 provides a non-transitory computer-readable storage medium for storing computer instructions. When the computer instructions are executed by the processor, the simulation optimization method for urban rail transit cross-line train operation scheduling described above is implemented.

[0210] Example 3

[0211] This embodiment 3 provides a computer device, including a memory and a processor. The processor and the memory communicate with each other. The memory stores program instructions that can be executed by the processor. The processor calls the program instructions to execute the urban rail transit cross-line train operation scheduling simulation optimization method as described above.

[0212] Example 4

[0213] This embodiment 4 provides an electronic device, including: a processor, a memory, and a computer program; wherein, the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes instructions to implement the urban rail cross-line train operation scheduling simulation optimization method as described above.

[0214] In summary, the urban rail transit cross-line train operation scheduling simulation optimization method described in this embodiment of the invention uses a cross-line shunting decision-making mechanism based on transfer station connecting lines. It uses the transfer station connecting lines as cross-line transfer channels, divides the period of sustained capacity shortage into several decision windows, and determines within each window whether to implement cross-line shunting, which non-interfering line and which train to allocate, and the initial running direction after being transferred into the interfering line. This achieves cross-line vehicle resource allocation based on transfer stations. The reinforcement service chain and return service chain collaborative generation mechanism describe the temporary operational services continuously executed by the reinforcement train after it is transferred into the interfering line, and the return service chain describes the operational services that the reinforcement train continues to execute after completing its task and returning to the original non-interfering line. This comprehensively depicts the entire process of "transfer-cross-line-reinforcement-return-restoration of operation". A coordinated constraint system for cross-line shunting decisions and multi-line timetable adjustments: Cross-line shunting decisions, reinforcement service insertion, and return-to-line service restoration are uniformly incorporated into timetable adjustment constraints. This system comprehensively considers constraints such as service insertion location, spatial and temporal connections, turnaround time, station dwell time, interval travel time, headway, rolling stock continuity, and maximum departure interval on non-interfering lines to ensure the practical feasibility of shunting plans. A comprehensive objective function for uniformly measuring passenger service level and cross-line shunting operating costs: Passenger service level is represented by the sum of average passenger travel times across all lines in the network. Passenger time value is used to convert cross-line shunting operating costs into equivalent time costs per passenger, constructing a comprehensive objective function that balances service improvement on interfering lines, service loss on non-interfering lines, and shunting operating costs. A Bayesian optimization-timetable adjustment-simulation evaluation coupled scheme search framework: Cross-line shunting schemes are encoded as integer vectors, and Bayesian optimization search is performed using a Gaussian process surrogate model based on Hamming distance and an expected improvement acquisition function; after each candidate scheme is evaluated by timetable adjustment and passenger and train flow coupled simulation, the objective function value is fed back to the optimization module, thereby obtaining a better cross-line train scheduling scheme within a limited number of evaluations.

[0215] This invention uses the connecting lines at transfer stations as cross-line transfer channels, incorporating processes such as passenger clearing at transfer stations, cross-line operation on connecting lines, and the insertion of trains into interfering lines to provide reinforcement services into a unified framework, which better meets the actual shunting needs under the conditions of urban rail transit interconnection. By setting up reinforcement services and return-to-line services, it describes the entire process of reinforcement trains being transferred from non-interfering lines, entering interfering lines for reinforcement, and returning to the original line to continue operation after completing their tasks, thus improving the completeness of the scheme. While determining cross-line shunting decisions, it also considers the insertion of reinforcement services on interfering lines, the connection of return-to-line services on non-interfering lines, and related arrival and departure time adjustments, giving the generated scheme better operational support and executability. The sum of the average travel time of passengers on all lines in the network and the cross-line shunting operating costs are used together as optimization criteria, enabling the scheme to control shunting costs while improving passenger service levels. This invention introduces a Bayesian optimization method based on simulation evaluation, guiding the search of candidate schemes through a surrogate model, reducing the repeated evaluation of inefficient schemes, and improving the search efficiency of cross-line shunting schemes.

[0216] In practical applications, this invention preferably uses the connecting line of the transfer station as the cross-line shunting channel. When conditions allow for train cross-line transfer, depot, parking lot access lines, turnaround lines, or other connecting line nodes can also be used as access points to facilitate the dispatch of trains from non-interfering lines to interfering lines. This invention describes the entire cross-line shunting process through reinforcement services and return-to-track services. In practical applications, reinforcement services can be set as single short-route services, continuous multiple round-trip services, or unidirectional reinforcement services; return-to-track services can be implemented through immediate return, delayed return, or continued standby before return. This invention preferably uses an optimization model to determine the insertion position, arrival and departure times, and return-to-track connection relationships of reinforcement services. In practical applications, rule-based adjustment methods, rolling time-domain adjustment methods, or heuristic insertion methods can also be used to generate an adjusted timetable while meeting the requirements for safety intervals, turnaround times, and service connections. This invention preferably employs a discrete event simulation method involving passenger and vehicle flow coupling. In practical applications, spatiotemporal network passenger flow allocation models, queuing theory models, multi-agent simulation models, or macroscopic simulation models can also be used to evaluate indicators such as passenger waiting time, train load, passenger congestion, and travel time. This invention preferably uses a Bayesian optimization method to search for cross-line shunting solutions. In practical applications, heuristic or intelligent optimization algorithms such as genetic algorithms, simulated annealing algorithms, particle swarm optimization, tabu search algorithms, and reinforcement learning methods can also be used. In small-scale scenarios, enumeration search or mixed integer programming methods can also be used to solve the problem. This invention preferably uses the sum of the average travel time of passengers on all lines of the network and the operating cost of cross-line shunting as the optimization basis. In practical applications, the objective can be replaced or expanded according to operational needs to minimize total passenger waiting time, minimize the number of stranded passengers, minimize train congestion, maximize the capacity supplementation effect, or maximize the overall service improvement rate. This invention evaluates the shunting scheme from the aspects of shunting cost, shunting revenue and comprehensive benefits. In practical applications, indicators such as train punctuality rate, cross-section full load rate, number of passengers staying on the platform, average passenger waiting time, total passenger delay time, vehicle utilization rate and number of cross-line shunting operations can also be added to adapt to different operation and management needs.

[0217] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0218] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0219] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0220] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment, whereby a series of operational steps are performed to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0221] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that, based on the technical solutions disclosed in the present invention, various modifications or variations that can be made by those skilled in the art without creative effort should be included within the scope of protection of the present invention.

Claims

1. A simulation optimization method for urban rail transit cross-line train operation scheduling, characterized in that, include: Acquire basic network data, original train timetables, passenger flow demand data, transfer station connecting line information, train operation constraint parameters, and cross-line shunting operation cost parameters; The period of sustained capacity shortage is divided into several decision windows, and within each decision window, it is determined whether to implement cross-line shunting, from which non-interfering line to allocate which train, and the initial running direction after being transferred to the interfering line. Based on the cross-line shunting decision, reinforcement services and return-to-track services are generated and embedded into the train timetables of the interfering and non-interfering lines, respectively, so that the adjusted timetables meet the constraints of headway, stop time, section travel time, turnaround time and cross-line travel time. A simulation and evaluation model for urban rail passenger and vehicle flow coupling for cross-line shunting is used to calculate the passenger service level under different schemes, and a comprehensive objective function value is formed by combining the cross-line shunting operation cost; among them, Bayesian optimization is used to iteratively search for cross-line shunting schemes. Based on the evaluated schemes, a cross-line train operation scheduling optimization model considering shunting at transfer stations is constructed. The next set of candidate shunting schemes is selected, and the feasibility of the candidate schemes is solved. The scheme effects are calculated and the results are fed back to Bayesian optimization. After multiple iterations, the cross-line train scheduling scheme and the corresponding adjusted train timetable are output.

2. The simulation optimization method for urban rail transit cross-line train operation scheduling according to claim 1, characterized in that, In the cross-line train operation scheduling optimization model considering shunting at transfer stations, the overall passenger service level of the network and the cross-line shunting operation cost are used as the comprehensive optimization basis. An objective function is constructed to achieve a balance between improving passenger service level and controlling shunting cost in the cross-line shunting scheme. The sum of the average travel time of passengers on each line of the network is used as the passenger service level index. This index is obtained by calculating the average travel time of passengers on interfering lines and each non-interfering line separately and summing the results of each line. The cross-line shunting operation cost is converted into equivalent time cost using passenger time value.

3. The simulation optimization method for urban rail transit cross-line train operation scheduling according to claim 2, characterized in that, The model's solution constraints fall into three categories: constraints related to train cross-line dispatching decisions, constraints related to train timetable adjustments on interfering lines, and constraints related to train timetable adjustments on non-interfering lines. The constraints related to train cross-line dispatching decisions determine whether cross-line shunting should be implemented within each decision window, which non-interfering line should dispatch which reinforcement train, and the initial running direction of the reinforcement train after it enters the interfering line. The constraints related to train timetable adjustments on interfering lines generate reinforcement service chains, determine the insertion position and arrival / departure times of reinforcement services, and ensure that the adjusted timetable for the interfering line meets the train operation requirements. The constraints related to train timetable adjustments on non-interfering lines generate return-to-track service chains, determine the insertion position and arrival / departure times of return-to-track services. The constraints for adjusting the train timetable for interfering lines include: when a reinforcement train is transferred to an interfering line, a corresponding reinforcement service chain needs to be inserted into the existing timetable of the interfering line; the reinforcement service chain is embedded into the timetable of the interfering line by adjusting the arrival and departure times of the relevant existing services, and the direction of the first reinforcement service is determined by the cross-line shunting decision, with subsequent reinforcement services connecting in the up and down directions according to the turnaround organization requirements; the constraints for adjusting the train timetable for non-interfering lines include: after completing the reinforcement task on the interfering line, the reinforcement train needs to return to the original non-interfering line via the transfer station connecting line, and a corresponding return service chain is inserted into the existing timetable of the non-interfering line. The return service chain is embedded into the timetable of the non-interfering line by adjusting the arrival and departure times of the relevant existing services to ensure that the reinforcement train can return to the original line to continue its operational tasks.

4. The simulation optimization method for urban rail transit cross-line train operation scheduling according to claim 1, characterized in that, Bayesian optimization is employed to search for cross-line shunting schemes. This includes: using the cross-line shunting decision vector as input, progressively updating candidate schemes through steps such as candidate reinforcement train pool construction, surrogate model fitting, data acquisition function point selection, timetable adjustment and solution, and simulation evaluation feedback, ultimately outputting the cross-line train dispatching scheme with the best overall objective. Specifically, the set of cross-line shunting decision variables is re-encoded, and the th... Each decision window, consisting of a decision vector of multiple binary variables, is compressed into a single integer component, and a complete shunting plan is redefined and encoded into a length of [length missing]. An integer vector.

5. The simulation optimization method for urban rail transit cross-line train operation scheduling according to claim 4, characterized in that, The construction of the candidate pool for reinforcement trains includes: based on the train operation schedule information of each non-interfering line, scanning each decision window for trains that meet the cross-line dispatch conditions to construct the candidate pool for reinforcement trains; for each candidate reinforcement train, recording its line, dispatch direction, transfer station, and the time window in which it can be used to depart from the interfering line after clearing passengers at the transfer station; the candidate pool for reinforcement trains remains unchanged throughout the optimization process, serving as a lookup table for encoding and decoding; for decision windows that do not contain any valid trains, their corresponding decision components are fixed at 0 and do not participate in the Bayesian optimization search process, thereby effectively compressing the search space and improving optimization efficiency.

6. The simulation optimization method for urban rail transit cross-line train operation scheduling according to claim 4, characterized in that, To avoid the initial samples being overly concentrated in local areas, three initial sampling strategies were set up, and initial solutions were generated for different shunting quantities, including: Strategy 1: Diversified Sampling: According to "line" Upward → Line Downstream → Line Upward → Line The order of "downward →..." is rotated, and shunting options are selected sequentially from the available decision windows corresponding to each line and direction, so that the initial sample has a relatively balanced coverage in terms of line and direction dimensions. Strategy 2: Random sampling. Randomly select several windows from all decision windows containing valid candidate trains, and randomly assign a legal shunting option to each selected window to increase sample diversity. Strategy 3, continuous window sampling, is suitable for Timing: Prioritize combinations of decision windows that are consecutive in time to simulate concentrated reinforcement scenarios in actual operations, including: identifying a length no less than the target shunting quantity. From a continuous valid window segment, randomly select a segment and extract a length of [length missing]. A continuous subsequence is then randomly assigned shunting options.

7. A simulation and optimization system for urban rail transit cross-line train operation scheduling, characterized in that, include: The acquisition module is used to acquire basic network data, original train timetables, passenger flow demand data, transfer station connecting line information, train operation constraint parameters, and cross-line shunting operation cost parameters. The cross-line shunting decision module is used to divide the period of continuous capacity shortage into several decision windows, and within each decision window, it determines whether to implement cross-line shunting, from which non-interfering line to dispatch which train, and the initial running direction after being dispatched to the interfering line. The timetable adjustment module is used to generate reinforcement services and return-to-track services based on cross-line shunting decisions, and embed them into the train timetables of interfering and non-interfering lines respectively, so that the adjusted timetable meets the constraints of headway, station dwell time, section travel time, turnaround time and cross-line travel time. The simulation optimization module is used to call the urban rail passenger and train flow coupling simulation evaluation model for cross-line shunting, calculate the passenger service level under different schemes, and form a comprehensive objective function value by combining the cross-line shunting operation cost. Among them, Bayesian optimization is used to iteratively search for cross-line shunting schemes. Based on the evaluated schemes, a cross-line train operation scheduling optimization model considering shunting at transfer stations is constructed, and the next set of candidate shunting schemes is selected. The feasibility of the candidate schemes is solved, the scheme effect is calculated, and the results are fed back to Bayesian optimization. After multiple rounds of iteration, the cross-line train scheduling scheme and the corresponding adjusted train timetable are output.

8. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, which, when executed by a processor, implement the urban rail transit cross-line train operation scheduling simulation optimization method as described in any one of claims 1-6.

9. A computer device, characterized in that, The system includes a memory and a processor, which communicate with each other. The memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the urban rail transit cross-line train operation scheduling simulation optimization method as described in any one of claims 1-6.

10. An electronic device, characterized in that, include: The device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions that implement the urban rail transit cross-line train operation scheduling simulation optimization method as described in any one of claims 1-6.

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