Constraint scheduling method, device and product for urban rail transit

Abstract

This application provides a constrained scheduling method and product for urban rail transit. It establishes station passenger flow matching variables based on passenger flow demand at each station under different waiting time slots and travel directions, thereby determining a set of potential train services capable of carrying the corresponding passenger flow. Train service interval variables are used to characterize the operating status and travel interval of each potential train service. Based on this, the arrival interval, turnaround capacity, and train resource allocation of the potential train services are constrained and verified. A set of potential train services that meets actual operating conditions is then selected, and a train operation plan and corresponding train operation plan are generated. This method establishes a direct correlation between fine-grained passenger flow demand and specific train services, and unifies train service generation, travel interval determination, and operational constraint verification within the same scheduling process, thereby improving the passenger flow adaptability, overall coordination, and engineering feasibility of the scheduling results.

Description

Technical Field

[0001] This application relates to the field of urban rail transit technology, specifically to a constrained scheduling method and computer program product for urban rail transit. Background Technology

[0002] With the continuous expansion of urban rail transit networks and the increasing complexity of their operation, passenger demand at different stations, in different directions of travel, and at different times exhibits significant spatial and temporal differences. Current urban rail transit train operation scheduling still primarily relies on pre-prepared fixed timetables, with local adjustments made by adding or suspending trains, adjusting departure intervals, or changing operating sections. However, fixed timetables are typically determined in advance based on predicted passenger flow and established operational experience, making it difficult to respond promptly to dynamic changes in actual passenger demand at each station along the line.

[0003] Existing dispatching methods typically rely on passenger flow at specific points along the line, total passenger flow during a given time period, or overall line capacity demand as the primary basis for train operation organization. This approach provides a coarse-grained representation of passenger demand, failing to capture the differences in passenger flow at different stations during different waiting times and in different directions of travel. Because there is a lack of fine-grained correlation between station passenger demand and specific train services, dispatchers struggle to accurately determine the necessary train services, their starting points, and the operational range they should cover when passenger demand changes. This can easily lead to a mismatch between capacity supply and actual passenger demand at some stations or along certain sections.

[0004] Meanwhile, the setting of train services and their operating range are not solely determined by passenger demand, but are also influenced by a combination of factors, including line operating conditions, station arrival density, terminal turnaround capacity, and train resource allocation. These factors act at different levels, such as stations, sections, train services, and train resources, and are interconnected in terms of operational sequence and spatial scope. With the increasing complexity of railway network structures and operational organization, even partial or single-point adjustments to fixed timetables can trigger cascading changes across multiple stations, multiple operating sections, and different train operations.

[0005] Existing technologies typically base their solutions on predetermined train numbers and operating ranges, then verify different operating conditions separately. This results in a lack of effective coordination between the process of converting passenger demand into train operation organization and various operational constraints. Because different operating conditions are often handled separately, even if local adjustments satisfy some operating conditions, the interrelationships between different constraints may not be uniformly addressed, making it difficult to form a coherent and coordinated train operation plan. Furthermore, the resulting train operation plan may not be compatible with the actual available turnaround capacity and train resources, making it difficult to further transform into an engineering-feasible train operation plan.

[0006] Therefore, how to coordinate and determine train schedules and their operating ranges in response to station passenger flow demands, and how to comprehensively address various operational constraints in order to improve the passenger flow adaptability and project feasibility of scheduling plans, has become an urgent technical problem to be solved. Summary of the Invention

[0007] One objective of this application is to improve the passenger flow adaptability and engineering feasibility of scheduling plans in response to station passenger flow demands.

[0008] A constrained scheduling method for urban rail transit, the method comprising:

[0009] For each station of the target city's rail transit, obtain the station passenger flow matching variable that responds to the passenger flow demand in each waiting time slot. The station passenger flow matching variable corresponding to the direction of travel is used to characterize the train number assigned to the corresponding waiting time slot. The train number carries the station passenger flow in the waiting time slot in the corresponding direction of travel. Based on the passenger flow matching variables of each station under each waiting time slot and driving direction, a set of potential trains that can carry the passenger flow of each station is determined. The potential trains in the set of potential trains are identified by their originating station and train number. For the potential trains in the set of potential trains, a train interval variable is constructed to control the operating section. The train interval variable indicates the operation of the corresponding potential train and the operating section. The constraints of arrival intervals, turnaround capacity, and train resource allocation for potential trains in the potential train set are verified to obtain a set of all verified potential trains. The constraint verification steps for arrival intervals include: for each station, determining the possibility of time conflicts between transit stations based on the arrival time of the potential trains; identifying two potential trains associated with the current station within the same time range, and the possibility of time conflicts between these two potential trains when they pass through the current station; performing an adaptation verification of arrival time and minimum safe interval for these two trains, constraining the arrival times of the two potential trains, and verifying whether the train pairs with the possibility of time conflicts are separated by the minimum safe interval; generating a train operation plan and a corresponding train operation plan for the set of potential trains that have been verified to meet the constraints.

[0010] According to one aspect of the embodiments of this application, a computer device is disclosed, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method as described in any of the preceding claims.

[0011] According to one aspect of the embodiments of this application, a computer program product is disclosed, including a computer program that, when executed by a processor, implements the steps of the method as described in any of the preceding claims.

[0012] According to one aspect of the embodiments of this application, a computer-readable storage medium is disclosed having a computer program stored thereon that, when executed by a processor, implements the steps of the method as described in any of the preceding claims.

[0013] This application establishes station passenger flow matching variables based on station, waiting time slots, and direction of travel, transforming dispersed station passenger flow demand into quantifiable data for train allocation. Based on this, it identifies potential trains and their operating sections to accommodate the corresponding passenger flow, achieving a fine-grained correlation between passenger flow demand and train operation organization. Furthermore, by uniformly constraining and verifying the arrival intervals, turnaround capacity, and train resource allocation of potential trains, train combinations that do not meet actual operating conditions can be simultaneously eliminated during the train operation plan generation process, reducing inconsistencies between passenger flow allocation results and line operating conditions, turnaround capacity, and train resources. This improves the adaptability of train allocation and operating sections to station passenger flow demand and allows the generated train operation plan to further correspond to an executable train operation plan, thereby enhancing the overall coordination and engineering feasibility of urban rail transit scheduling.

[0014] Other features and advantages of this application will become apparent from the following detailed description, or may be learned in part from practice of this application.

[0015] It should be understood that the above general description and the following detailed description are merely exemplary and do not limit this application. Attached Figure Description

[0016] The above and other objectives, features and advantages of this application will become more apparent from a detailed description of exemplary embodiments thereof with reference to the accompanying drawings.

[0017] Figure 1 A flowchart is shown for a scheduling method based on a one embodiment of the present application, which is oriented towards the collaborative constraints of train arrival density and turnaround capacity.

[0018] Figure 2 It is based on Figure 1 The corresponding embodiment shows a flowchart describing the steps of determining the set of potential train services that can carry station passenger flow based on the station passenger flow matching variables corresponding to each station in each waiting time slot and direction of travel.

[0019] Figure 3 It is based on Figure 1 The flowchart described in the corresponding embodiment describes the steps of constructing a train interval variable to control the operating interval for potential trains in the potential train set.

[0020] Figure 4 It is based on Figure 3The corresponding embodiment shows a flowchart describing the steps of constructing train interval variables corresponding to potential trains based on train operation variables.

[0021] Figure 5 It is based on Figure 1 The corresponding embodiment shows a flowchart describing the method for verifying the constraints of arrival interval and train resource usage on potential trains in the potential train set based on the train number interval variable of the potential train number.

[0022] Figure 6 This is a flowchart illustrating a scheduling method for coordinating train arrival density and turnaround capacity constraints, according to another embodiment.

[0023] Figure 7 yes Figure 1 The corresponding embodiment shows a flowchart describing the method for verifying the constraints of arrival interval and train resource usage on potential trains in the potential train set based on the train number interval variable of the potential train number.

[0024] Figure 8 yes Figure 1 The corresponding embodiment shows a flowchart describing the method for verifying the constraints of arrival interval and train resource usage on potential trains in the potential train set based on the train number interval variable of the potential train number. Detailed Implementation

[0025] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided to make the description of this application more comprehensive and complete, and to fully convey the concept of the exemplary embodiments to those skilled in the art. The drawings are merely illustrative of this application and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted.

[0026] Furthermore, the described features, structures, or characteristics can be combined in any suitable manner in one or more exemplary embodiments. Numerous specific details are provided in the following description to give a full understanding of exemplary embodiments of this application. However, those skilled in the art will recognize that the technical solutions of this application can be practiced with one or more of the specific details omitted, or other methods, components, steps, etc., can be employed. In other instances, well-known structures, methods, implementations, or operations are not shown or described in detail to avoid obscuring various aspects of this application.

[0027] Some of the block diagrams shown in the accompanying drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0028] See Figure 1 , Figure 1 A flowchart illustrating a scheduling method oriented towards the coordinated constraints of train arrival density and turnaround capacity according to an embodiment of this application is shown. An embodiment of this application provides a scheduling method oriented towards the coordinated constraints of train arrival density and turnaround capacity, comprising: Step S110: For each station of the target urban rail transit, obtain the station passenger flow matching variable that responds to the passenger flow demand in each waiting time slot. The station passenger flow matching variable corresponding to the direction of travel is used to characterize the train assigned to the corresponding waiting time slot, which carries the station passenger flow in the corresponding waiting time slot in the corresponding direction of travel. Step S120: Based on the passenger flow matching variables of each station under each waiting time slot and driving direction, determine the set of potential trains that can carry the passenger flow of each station. The potential trains in the set of potential trains are identified by the originating station and the train number. Step S130: For the potential trains in the potential train set, construct a train interval variable to control the operating section. The train interval variable indicates the operation of the corresponding potential train and the operating section. Step S140: Based on the train interval variables of potential trains, perform constraint verification on the arrival interval and train resource usage of potential trains in the potential train set; Step S150: Generate train operation plans and corresponding train operation plans for the set of potential trains that satisfy the constraints.

[0029] These steps are explained in detail below.

[0030] In step S110, for each station and the waiting time slot at each station, a station passenger flow matching variable is constructed in response to the passenger flow demand of the waiting time slot at that station. The station passenger flow matching variable is used to characterize the potential trains allocated to the waiting time slots, so as to achieve the matching between the potential trains and the waiting time slots, and thus determine the potential trains used to carry the passenger demand of the waiting time slots in this direction of travel.

[0031] For example, site passenger flow matching variables are used through variables Representation, Variable The system indicates the train route lno, the direction of travel dir, and the potential train k originating from station m. The arrival time of the potential train k at station i will fall within the waiting time slot t, and it will carry passengers during the waiting time slot t. Here, k is the train number of the potential train.

[0032] For station i, for each travel direction dir, the established station passenger flow matching variables are used. Within the corresponding waiting time slice t, a set of potential train services is determined to accommodate passenger demand. For each potential train service k included in this set, its station passenger flow matching variable... The value assigned is 1.

[0033] For each station and each waiting time slot at the station, a corresponding passenger flow matching variable is constructed to determine the potential trains that can carry passenger flow for the corresponding waiting time slot at the station.

[0034] For example, the construction process of station passenger flow matching variables includes: First, for each station's passenger flow demand in different travel directions and waiting time slots, the required number of trains for that station in the corresponding travel direction and waiting time slot is pre-calculated; then, based on the required number of trains for each station in each travel direction and waiting time slot, corresponding binary variables are constructed as station passenger flow matching variables. It should be clarified that the station passenger flow matching variables... The construction includes the mapping of the corresponding potential train number (m,k) and the assignment of the corresponding value 1.

[0035] The calculation is expected to be performed on each station and the consecutive time slots (i.e., waiting time slots) within each station, thereby obtaining the required number of trains for each station in different travel directions and time slots. For example, the pre-calculation includes: aligning historical passenger flow data at stations and time slots for the consecutively divided time slots after time discretization, obtaining historical passenger flow data for each station in each consecutive time slot; splitting the historical passenger flow data for each station in each consecutive time slot according to travel direction, calculating the historical passenger flow for each station in each time slot along different travel directions; and predicting the number of passengers for each station in the corresponding time slot and travel direction based on the historical passenger flow for each station in the consecutive time slots along the travel direction, and converting this into the required number of trains.

[0036] In this exemplary embodiment, historical passenger flow data can come from the turnstiles, that is, the entry data of each station with a time stamp is used as historical passenger flow data. In addition, OD data (Origin-Destination Data) will be incorporated to determine the passenger flow of each station in each waiting time slot corresponding to the driving line and driving direction, thereby adapting to the complex scheduling structure under multiple lines and multiple driving directions, and accurately determining the passenger flow generated by each station in each driving direction in each time slot.

[0037] It should be understood that OD data, or OD data combined with arrival data, allows for the determination of passenger flow corresponding to the direction of travel in each waiting time slot at each station. For example, OD data describes passenger travel behavior from the originating station to the destination station. OD data includes at least the arrival station, departure station, arrival time, and departure time. The arrival time can be mapped to a time slot, and the arrival and departure stations are mapped to the travel route and the direction of travel along that route. Therefore, the passenger will be part of the passenger flow at that arrival station in the mapped time slot and direction of travel. Similarly, the historical passenger flow at a station corresponding to the travel route and direction of travel in each waiting time slot can be determined.

[0038] For each time slice continuously divided by the station, the historical passenger flow in each direction of travel is predicted based on spatiotemporal characteristics to determine the number of passengers traveling in the corresponding direction of travel at that station in this time slice; By using the number of passengers along the corresponding direction of travel at this station during this time slice and the carrying capacity of a single train, the predicted number of passengers is converted into the required number of trains. The carrying capacity of a single train is determined by the target passenger load factor and the rated passenger capacity of the target urban rail transit system.

[0039] Spatiotemporal features include temporal features and spatial features. Temporal features include lag windows (a number of past time slices), weekdays / hours / whether it is a holiday, and event identifiers. Spatial features include weather and traffic to neighboring stations, which will not be listed here.

[0040] The carrying capacity of a single train depends on the operational objectives. It should be understood that the carrying capacity of a single train is jointly determined by the target load factor of the target urban rail transit system and the train's rated passenger capacity; that is, the product of the target load factor and the train's rated passenger capacity. If the operational objective is passenger experience, the carrying capacity of a single train will be reduced by controlling the target load factor, thereby increasing the number of trains. This ensures that passengers do not fill the entire train capacity while still managing to transport the resulting passenger flow.

[0041] If the operational objective is to reduce operating costs, then the carrying capacity of a single train can be increased by improving the target occupancy rate, thereby ensuring that every train passing through is as full as possible.

[0042] After determining the carrying capacity of a single train in accordance with the operational objectives, the required number of trains can be calculated by dividing the number of passengers at the station along the direction of travel in this time slice by the carrying capacity of the single train.

[0043] Therefore, a station passenger flow matching variable can be constructed based on the required number of trains and assigned a value of 1. When the station passenger flow matching variable is set to 1, it is used to indicate that a potential train (m, k) on the train line lno and the train direction dir arrives at station i in the waiting time slot t. Thus, for the same station i, the same train direction dir, and the same waiting time slot t, the number of station passenger flow matching variables with a value of 1 matches the number of trains required for that station in the current train direction dir and the waiting time slot t.

[0044] In other words, the number of trains required at a station in a certain waiting time slot in a certain direction of travel is carried by all potential trains corresponding to all station passenger flow matching variables with a value of 1 in that waiting time slot.

[0045] Obtain the station passenger flow matching variables for station i under the corresponding driving direction dir and waiting time slice t. That is, after determining the potential train number it maps to by the time slice it falls into, it can be assigned a value of 1.

[0046] At this point, by executing step S110, the station passenger flow matching variables that correspond to passenger flow demand and match each waiting time slot can be obtained for each station of the target urban rail transit.

[0047] To further explain, the passenger flow matching variables for station i under the corresponding driving direction dir and waiting time slice t. The potential train numbers (m,k) indicated are selected from all potential train numbers that can reach station i within this waiting time slice t, based on the required number of trains.

[0048] It should be added that each time slot is bound to a potential train. Therefore, after the station passenger flow matching variables are constructed, all potential trains bound to the waiting time slots can be selected to generate a set of potential trains.

[0049] In step S120, the passenger flow matching variables of each station in each waiting time slot corresponding to the direction of travel are determined. The potential train numbers (m, k) mapped to these potential train numbers constitute the set of potential train numbers for the target city's rail transit to meet passenger flow demand. The potential train numbers in this set are identified by their originating station m and train number k.

[0050] For the set of potential train numbers obtained in step S120, construct the train number interval variable for each potential train number. The interval variable of this train number This indicates the departure of the corresponding potential train number (m,k) and the operating section (also known as the running section). Specifically, the train number section variable... This is a binary variable used to indicate the operating range of a potential train (m, k) from its originating station m to its destination station n. (Train number range variable) The value can be 0 or 1. For example, if a potential train with train number k is scheduled to run in the operating interval [m,n], then the train interval variable... The value is 1, and the value is 0 otherwise.

[0051] It should be noted that each train route lno has at least one originating station and at least one turnaround station that can serve as the terminal station for each direction of travel. This makes the operating section of the train route lno not unique. Based on this, the operating section of the train route lno will be selected in the corresponding direction dir, and then the train number interval variable will be constructed accordingly. This process will be repeated to obtain the train number interval variable corresponding to each potential train in the potential train set, and the value of the train number interval variable will be 1.

[0052] By constructing the train interval variables corresponding to each potential train in the potential train set, the operating interval can be determined through the train interval variables, and then the constraint verification in step S140 can be performed based on this.

[0053] In addition, as mentioned above, each potential train is bound to a time slice, which indicates the departure time of the bound potential train. Therefore, the arrival and departure times at each station along the route can be determined through the bound time slice. Then, the constraint verification is performed on the obtained set of potential trains through the execution of step S140, so as to finally obtain a set of potential trains that satisfy all constraints, and thereby generate a train operation scheduling plan and a train operation plan corresponding to the train operation scheduling plan.

[0054] See Figure 2 , Figure 2 It is based on Figure 1 The corresponding embodiment shows a flowchart describing the steps of determining the set of potential train services that can carry station passenger flow based on the station passenger flow matching variables corresponding to each station in each waiting time slot and direction of travel.

[0055] The step S120 provided in this application embodiment, which determines the set of potential train services to carry station passenger flow based on the station passenger flow matching variables corresponding to each station in each waiting time slot and direction of travel, includes: Step S121: For the waiting time slots of the station in each direction of travel, extract the mapped train number identifier according to the passenger flow matching variables of the corresponding station. The train number identifier includes a combination of the originating station and the train number. Step S122: Construct a set of potential trains for carrying passenger flow demand along the waiting direction during the waiting time slice, based on the train number identifier.

[0056] The following is a detailed explanation of these two steps.

[0057] As previously mentioned, for each waiting time slot in each direction of travel, the station passenger flow matching variables are obtained by constructing the station passenger flow matching variables in step S110, corresponding to the station, direction of travel, and waiting time slot. For example, regarding the station passenger flow matching variables... This indicates that, under the route lno and the direction dir, the potential train identified by the originating station m and the train number k will arrive at and stop at station i during the waiting time t.

[0058] Therefore, the station passenger flow matching variables obtained in step S110 can be used. The train number identifier (m,k) mapped to the target urban rail transit system is extracted to determine the potential train numbers that can meet the passenger flow demand at the station within the corresponding travel direction and waiting time slot. Based on the collection of train number identifiers, a set of potential train numbers for the target urban rail transit system at each station, each waiting time slot, and each travel direction can be constructed.

[0059] Based on this, in step S121, for each waiting time slot of each station in the target urban rail transit system in each direction of travel, the corresponding station passenger flow matching variables are traversed, and the station passenger flow matching variables with a value of 1 are selected. Each station passenger flow matching variable with a value of 1 corresponds to a unique potential train number, and the train number identifier it maps to is determined by the combination of the originating station m and the train number k.

[0060] Specifically, station passenger flow matching variables Simultaneously, the station i, route lno, direction dir, and waiting time slot t are associated. When the passenger flow matching variable for a station is 1, it indicates that the potential train, identified by the originating station m and train number k, arrives at and stops at station i during waiting time slot t, under route lno and direction dir. Therefore, by parsing the passenger flow matching variable for stations with a value of 1, the corresponding train identifiers (m, k) can be extracted for the station, waiting time slot, and direction of travel.

[0061] In this way, step S121 realizes the mapping of passenger flow demand description from three dimensions of station time slice to potential train identifiers, providing a clear source of train candidates for the subsequent construction of potential train sets.

[0062] In step S122, the potential trains are aggregated based on the train number identifiers extracted in step S121 to construct a set of potential trains to meet the passenger flow demand of the station.

[0063] Specifically, for the same station i, the same driving direction dir, and the same waiting time slice t on the same driving route lno, the corresponding potential trains are included in the currently constructed potential train set based on all train identifiers (m,k) extracted in step S121, so as to perform globally unified constraint verification.

[0064] This aggregation method constructs a set of potential train services that can fully cover the passenger flow capacity requirements of each station in each direction of travel and in each waiting time slot. It also provides a set of basic objects for subsequent constraint verification of potential train services. This is completely different from the existing method of pre-defining train services based on fixed timetables. The set of potential train services is derived from the derivation of station passenger flow matching variables, which makes the selection of potential train services directly related to passenger flow demand in the time and space dimensions, thereby improving the adaptability of train operation scheduling to complex passenger flow distribution.

[0065] See Figure 3 , Figure 3 It is based on Figure 1 The flowchart described in the corresponding embodiment describes the steps of constructing a train interval variable to control the operating interval for potential trains in the potential train set.

[0066] The step S130 of constructing a train interval variable for controlling the operating interval from the potential trains in the potential train set provided in this application embodiment includes: Step S131: For potential trains in the potential train set, construct a train departure variable. The train departure variable is used to indicate that a potential train is in operation. Step S132: Construct the train interval variable corresponding to the potential train number based on the train number operation variable. The train interval variable is used to characterize and control the operating interval of the potential train number.

[0067] The following is a detailed explanation of these two steps.

[0068] Step S131, firstly, should explain the train number operation variable. `<lno>` is a Boolean variable used to indicate whether a potential train (lno, dir, m, k) will depart, given a set of trains with the following parameters: direction of travel (dir) on route lno, originating station m, and train number k. (Train departure variable) A value of 0 indicates that the potential train k originating from station m has not yet run; the train operation variable A value of 1 indicates that the potential train k departs from the originating station m.

[0069] Therefore, in step S131, for each potential train in the potential train set, a corresponding train departure variable is constructed to indicate whether the potential train will be put into operation. In other words, the train departure variable... Corresponding to a set (lno, dir, m, k), it is used to indicate whether a potential train numbered k, originating from station m, is selected as an actual train in operation under the train line lno and the train direction dir.

[0070] When the train number operation variable is 0, it means that the potential train with originating station m and train number k does not participate in actual operation, that is, the potential train (m,k) is not activated; when the train number operation variable is 1, it means that the potential train with originating station m and train number k is selected as the operation train and enters the subsequent constraint verification process.

[0071] Step S131: For each potential train in the potential train set, construct a corresponding train departure variable and assign a uniform value of 1 to the train departure variable to indicate that the potential train is in a candidate state that can be operated, and put it into the subsequent constraint verification process.

[0072] By setting and initializing the train operation variables for all potential trains in the potential train set, all potential trains are qualified to participate in the selection of operating sections and constraint verification in the initial stage of scheduling modeling. This avoids prematurely eliminating trains in the early stage of modeling and facilitates the gradual screening and scheduling decisions of potential trains based on constraint verification and passenger flow matching requirements during the subsequent constraint verification and optimization solution process.

[0073] In step S132, based on the control of the train number operation variable, a corresponding train number interval variable is constructed for each potential train number. The train number interval variable is used to characterize and control the specific travel interval of the potential train number.

[0074] Specifically, train number interval variables This is a binary variable, corresponding to the state of a potential train with train number k operating within the operating interval [m, n], where m represents the originating station of the potential train, and n represents the destination station of the potential train. The train interval variable... This is used to indicate the operating range of a potential train in the actual scheduling range [m,n].

[0075] When train number interval variable When the value is 1, it indicates that the corresponding potential train number (m,k) is scheduled as a section train running from the originating station m to the terminal station n; when the train number section variable When the value is 0, it indicates that the potential train will not operate in the form of a running section.

[0076] Due to train number interval variables Used to process variables related to train departure times. The potential train number indicating its operational status represents its corresponding operating section. Therefore, after completing the train number operation variable for each potential train in the potential train number set... The construction and initialization of the potential train numbers, i.e., after step S131, further involves constructing the corresponding train number interval variables for the potential train numbers. .

[0077] Specifically, based on the originating station and the set of destination stations reachable by each potential train, the possible operating sections of the potential train are enumerated and constructed, and a corresponding train section variable is generated for each possible operating section. During the initialization phase, the train interval variable is assigned a value of 1 to indicate that the potential trains will be used as candidate operating schemes in the corresponding operating intervals during the initial modeling phase and will be incorporated into the subsequent constraint verification process.

[0078] This approach allows potential train services to have a complete candidate space for operating sections in the initial stage, and then to achieve the desired constraints in the subsequent scheduling process, ultimately resulting in a train operation plan that satisfies all constraints.

[0079] For further details, please refer to [link / reference]. Figure 4 , Figure 4 It is based on Figure 3 The corresponding embodiment shows a flowchart describing the steps of constructing train interval variables corresponding to potential trains based on train operation variables.

[0080] The step S132 of constructing the train number interval variable corresponding to the potential train number based on the train number departure variable, as shown in the embodiments of this application, includes: Step S1321: Based on the train number operation variables and the corresponding originating station, determine the destination station of the potential train number for at least one U-turn station distributed along the train route. Step S1322: Construct train interval variables for potential trains based on the destination station. The train interval variables indicate the origin and destination stations of potential trains.

[0081] The following is a detailed explanation of these two steps.

[0082] In step S1321, under the control of the train operation variable, the possible destination station of the potential train along the corresponding travel direction on the train route is determined based on the originating station corresponding to the potential train.

[0083] Specifically, it should be understood that for a potential train, its train number operation variable has a value of 1, thus allowing it to participate in the selection of the operating section under the control of the train number operation variable. At this time, starting from the originating station of the potential train, a search is performed along the train line in the corresponding operating direction to identify at least one usable turning station distributed in that direction. A usable turning station is a station with the conditions for train turnaround or reversal, and is used as a candidate terminal station for the potential train's operating section.

[0084] In this way, for the same potential train service, one or more alternative destinations can be determined based on the route structure and direction of travel, thus forming a set of candidate destinations for the train service's operating section. This process means that the operating section of a potential train service is no longer fixed in advance, but is dynamically determined based on route conditions and scheduling needs, enhancing the adaptability of the implemented operation scheduling to the actual operating conditions of the route.

[0085] In step S1322, based on the candidate terminal stations determined in step S1321, a corresponding train interval variable is constructed for the potential trains to characterize and control the specific operating interval of the potential trains.

[0086] Specifically, for each potential train, a running interval is formed by combining its originating station with each destination station in the candidate destination station set, and a corresponding train interval variable is constructed for each running interval. As mentioned above, the train interval variable is a binary variable used to indicate whether the potential train participates in actual scheduling from the running interval defined by the corresponding originating station to the destination station.

[0087] When the train number interval variable takes a value of 1, it indicates that the potential train is scheduled to run from the originating station to the corresponding destination station. By constructing and controlling the train number interval variable, the same potential train can be selected from multiple candidate running intervals, and the running interval can be screened and determined in the subsequent process by combining constraint verification and the introduced scheduling optimization objective.

[0088] By constructing train interval variables for each potential train in the potential train set in step S130, the potential train can determine its operating range through the mapping of train interval variables to operating range. Then, combined with the train interval variables, step S140 is executed to implement the station interval, i.e., the station arrival density and turnaround capacity of the potential trains in the potential train set. Under the support of the configured turnaround capacity, the constraint verification of train resource allocation is achieved, thereby ensuring that the final train operation plan and train operation plan have engineering feasibility.

[0089] In step S140, based on the train interval variable of the potential train number, the constraints of arrival interval and train resource usage are verified for the potential train numbers in the potential train number set.

[0090] In this step S140, on the one hand, fine-grained constraint verification is performed on the arrival distribution of potential trains at each station to control the arrival density of trains at the station level. Specifically, the lower limit control constraint in the arrival interval constraint will be used to prevent potential trains from arriving at stations too densely, thereby ensuring driving safety. At the same time, the upper limit control constraint in the interval constraint will be used to prevent potential trains from arriving at stations too sparsely, so as to meet the balanced passenger service needs of the stations.

[0091] In addition, step S140 further implements train resource usage constraint control for potential trains arriving at the station. This station is a potential station and also the terminal station of the potential train. Specifically, based on train interval variables and the connection relationship between preceding and subsequent potential trains, constraint verification is performed on train resource usage methods such as turnaround operation, depot entry, and departure from the depot at the terminal station. This ensures that trains operating potential trains prioritize turning around to carry the next potential train while meeting turnaround capacity requirements, and avoids conflicting occupation of the same train resource by multiple potential trains.

[0092] This allows for the coordinated implementation of arrival interval constraints and train resource usage constraints, ensuring that the potential train set meets the engineering operation requirements in terms of station arrival density, terminal turnaround capacity, and train resource allocation. This provides a reliable guarantee for the subsequent generation of train operation plans and corresponding train operation plans that are engineering-executable.

[0093] Given the set of potential train services, the aforementioned process has yielded decisions on train scheduling and operation, including the operating range, departure time, and arrival time at the terminal station for each potential train service. Based on this, corresponding train resource allocation variables will be derived to provide train sources for the operation of potential train services and to control the use and storage of trains.

[0094] For example, the train resource allocation variable is a binary variable, which includes a variable representing the connection between preceding and following trains, a variable representing train departure from the depot, and a variable representing train arrival and entry into the depot. The variable representing the connection between preceding and following trains characterizes the continuity of the same physical train at the terminal station from the arriving train to subsequent departing trains. When the value is 1, it indicates that the same train changes from the previous potential train (m,k), i.e., the train arriving at the destination station n, to the next potential train. (n), which refers to subsequent trains that originate from the terminal station n.

[0095] For a set of potential train services, the construction and values ​​of the connection variables between preceding and following train services for a train operating a potential train service are jointly determined by conditions such as the departure time of subsequent trains that can turn around at the terminal station. The connection variables between preceding and following train services complete the "train-to-train" binding. For example, enumerating and filtering train pairs in the set of potential train services that may have temporal and spatial connections, a connection variable is constructed for the resulting train pairs to represent the connection variables between preceding and following train services when the same train is selected to turn around from the preceding potential train to carry the following potential train.

[0096] Within the potential train set, train pairs with turnaround potential are selected based on the consistency between the destination and origin stations, and the station's turnaround connectivity. Then, the candidate range is further narrowed down based on whether the arrival time (the time the previous potential train arrives at the destination station) and departure time (the departure time of the next potential train) satisfy the minimum turnaround time constraint. For each selected train pair, a variable representing the connection between preceding and following trains is constructed and set to a value of 1. This is the execution process for automatically generating the variable representing the connection between preceding and following trains within the potential train set, and it is used in the constraint verification of subsequent step S140 to verify whether the set of potential trains is a feasible solution.

[0097] After the connection variables between trains are constructed, corresponding warehouse departure variables and train arrival and storage control variables are introduced for each potential train to control the continuous use and recycling of train resources and to verify the constraints in step S140.

[0098] In an exemplary embodiment, the warehouse departure variable is used to characterize whether the corresponding potential vehicle trip is formed by direct warehouse departure. When there is no feasible preceding and following vehicle trip connection variable for a potential vehicle trip as a subsequent potential vehicle trip, that is, the constructed preceding and following vehicle trip connection variable has a value of 0, then the potential vehicle trip is determined to require warehouse departure. Therefore, a corresponding warehouse departure variable can be constructed for the potential vehicle trip, and its value can be set to 1. The warehouse departure variable is constructed based on whether the corresponding potential train can be taken over by existing train resources. This indicates whether the potential train will be dispatched directly from the warehouse and represents the new demand for train resources.

[0099] In another exemplary embodiment, the train arrival and storage control variable is used to indicate the destination of train resources after a train service ends, describing whether the corresponding train service enters the warehouse for storage after its operation at the terminal station. If a potential train service is not connected to any subsequent train service and the terminal station is associated with a warehouse, the corresponding train arrival and storage control variable takes the value of 1, indicating that the corresponding train will be withdrawn from operation and recycled by the warehouse, without forming a "suspended train resource".

[0100] Once the connection variables between trains are determined, it becomes possible to identify which arriving trains are not being used subsequently. These trains will need to be taken out of service at the terminal station and stored in a warehouse. Therefore, a train arrival and warehouse entry control variable is introduced for these trains to indicate whether the train has performed a warehouse entry operation.

[0101] In summary, the train arrival and depot entry control variable is used to characterize the recycling of train resources to prevent situations where the whereabouts of trains are unknown after the train operation ends.

[0102] By introducing variables related to the connection between preceding and following trains, and by constructing train arrival and depot entry control variables and depot departure variables on top of these variables, the continuous use and recycling of train resources are controlled. Furthermore, the turnaround capacity constraints implemented in step S140 ensure that the use of train resources within the overall operation scheduling has a complete closed loop, is conflict-free, and does not exceed the limit.

[0103] See Figure 5 , Figure 5 It is based on Figure 1 The corresponding embodiment shows a flowchart describing the method for verifying the constraints of arrival interval and train resource usage on potential trains in the potential train set based on the train number interval variable of the potential train number.

[0104] The embodiments of this application provide a train number interval variable based on potential train numbers, which implements a constraint verification step S140 on the arrival interval and train resource usage of potential train numbers in the potential train number set, including: Step S141a: Determine the potential trains passing through each station in the potential train set based on the station passenger flow matching variables corresponding to the station, and obtain the arrival time of the potential trains. Step S142a: Construct a continuously sliding lower limit control window and an upper limit control window in the time dimension, and determine the station passenger flow matching variables within the lower limit control window and the station passenger flow matching variables within the upper limit control window, respectively. Step S143a: Based on the station passenger flow matching variables of the lower limit control window and the upper limit control window, verify the legality of the arrival interval constraint for potential trains.

[0105] These steps are explained in detail below.

[0106] For each station, the potential trains passing through that station are determined based on the station passenger flow matching variables of the potential trains, and the planned arrival time of each potential train at that station is obtained. This allows us to obtain the distribution of train arrival times at the station throughout the entire operating period, providing basic data for the verification of the current arrival interval constraint (also for the verification of train arrival density constraint).

[0107] For each station, an upper limit control window is constructed based on the maximum departure interval, and a lower limit control window is constructed based on the minimum departure interval. It should be understood that the station's operating time is discretized into multiple consecutive time slices. For a single station, based on the time slices, a sliding upper limit control window and a sliding lower limit control window are used to determine whether each potential train arrives at the station within the sliding upper limit control window and lower limit control window.

[0108] To further explain, the lower limit control window is used to control the density of trains passing through the station in order to prevent excessively frequent train arrivals; the upper limit control window is used to control the coverage of trains passing through the station in order to prevent excessively sparse train arrivals.

[0109] In the specific implementation, as the upper limit control window and the lower limit control window slide on the continuously divided time slices, the potential trains whose arrival time falls into the sliding upper limit control window and the potential trains whose arrival time falls into the sliding lower limit control window are determined. In this way, the station passenger flow matching variables within the upper limit control window and the station passenger flow matching variables within the lower limit control window are determined.

[0110] In the time dimension, each sliding upper limit control window and each sliding lower limit control window can obtain the potential trains that pass through the current station and fall into the window, and use this to determine the station passenger flow matching variables of the current sliding upper limit control window and the current sliding lower limit control window.

[0111] Based on this, for each sliding upper limit control window and each sliding lower limit control window, it is possible to verify whether the arrivals are too dense to achieve density control; and to verify whether the arrivals are too sparse to achieve control over whether the upper limit control window is covered by a single train. Specifically, the lower limit control window verifies whether the arrivals are too dense, thereby achieving density control of train arrivals at stations; the upper limit control window verifies whether the arrivals are too sparse, thereby preventing excessively sparse train arrivals.

[0112] As the upper and lower control windows of the corresponding operating period of a station slide, the arrival time of potential trains passing through that station will fall into a specific upper and lower control window. At this time, the passenger flow matching variables of the station corresponding to the potential train will be obtained to verify the legality of the arrival interval constraint.

[0113] Therefore, it should be noted that the validity verification of the arrival interval constraint will be used to verify the train arrival density constraint for each station throughout the entire time period. This train arrival density constraint verification includes lower limit control interval constraint verification and upper limit control interval constraint verification, which correspond to the lower limit interval time period and the upper limit interval time period, respectively.

[0114] The lower limit control interval constraint verification is used to verify whether at most one potential train is allowed to pass through the station within any lower limit control window, thereby avoiding platform congestion and operational conflicts caused by too many trains arriving at the station in a short period of time.

[0115] Correspondingly, at this time, based on the station passenger flow matching variable of each upper limit control window, the upper limit control interval constraint verification is performed. Specifically, within any sliding upper limit control window of a station, the maximum arrival interval of at least one potential train passing through the station in the upper limit control window is verified to ensure that passenger waiting time does not exceed the scheduling limit and to meet the requirements of passenger service continuity.

[0116] In one exemplary embodiment, for the station passenger flow matching variable of the lower limit control window, a minimum arrival interval validity verification is performed to ensure that at most one potential train can pass through the station. For example, the lower limit control interval constraint verification is essentially a density constraint verification to prevent excessively dense arrivals and ensure that the minimum departure interval is adhered to. Safe density control is achieved under time-slice discretization, specifically through the following formula:

[0117] in, It is the minimum departure interval between consecutive trains on the same route (lno). It is the train route lno, the departure interval of any originating station; It is the lower limit control window width j; It is a station passenger flow matching variable, which is the potential train (m,k) that falls into the lower limit control window and arrives at station i in time slot t. The arrival time of the potential train (m,k) falls within the time slot t + width j.

[0118] For example, the upper limit control interval constraint verification is essentially a coverage constraint verification to prevent excessively sparse arrivals. This can be achieved through the following formula:

[0119] in, It is the maximum departure interval between consecutive trains on the route lno. The upper limit controls the width j of the window; It is a station passenger flow matching variable used to indicate whether the arrival time of a potential train (m,k) departing from the originating station m falls within the upper limit control window at station i, that is, within the time period corresponding to time slice t + width j.

[0120] Therefore, in a length of Within a continuous time window, i.e. the upper limit control window, at least one train must arrive to ensure that the maximum departure interval is met and passengers do not have to wait too long.

[0121] Under the influence of the upper limit control window and the lower limit control window, the upper limit control interval constraint verification and the lower limit control interval constraint verification are jointly implemented to achieve bidirectional control of the station arrival distribution. That is, based on safety, signaling and station capacity, it should not be too dense or too sparse.

[0122] See Figure 6 , Figure 6 This is a flowchart illustrating a scheduling method for coordinating train arrival density and turnaround capacity constraints, according to another embodiment.

[0123] The scheduling method for coordinating train arrival density and turnaround capacity constraints provided in this application embodiment further includes: Step S210: Obtain the minimum and maximum departure intervals and the train number departure intervals for controlling the departure frequency. The train number departure interval is the departure interval set on the corresponding train line. Step S220: Determine the lower limit control window and upper limit control window for each station distribution to adapt to the minimum departure interval, maximum departure interval, and train departure interval.

[0124] This exemplary embodiment performs adaptive construction of upper and lower limit control windows for constrained verification of train arrival density, adapting them to the stations.

[0125] Minimum departure interval is used to limit the shortest interval between two adjacent potential train departure times to avoid excessively frequent departures that could cause line congestion or platform overload. Maximum departure interval is used to limit the longest interval between two adjacent potential train departure times to avoid excessively long passenger waiting times and reduced transport service quality; train departure interval refers to the departure interval set on its respective route. Minimum departure interval, maximum departure interval, and train departure interval constitute the data basis for verifying train arrival density constraints and for window partitioning.

[0126] The upper and lower control windows are used to implement sliding control along the time dimension. It should be understood that the timeline continuously distributes time slices throughout the entire station operation period based on the continuous divisions performed. Both the upper and lower control windows determine potential train arrival times falling within the window by sliding along the timeline, using the start time of each time slice as a base point, thereby obtaining the corresponding station passenger flow matching variables.

[0127] See Figure 7 , Figure 7 yes Figure 1The corresponding embodiment shows a flowchart describing the method for verifying the constraints of arrival interval and train resource usage on potential trains in the potential train set based on the train number interval variable of the potential train number.

[0128] The embodiments of this application provide a train number interval variable based on potential train numbers, which implements a constraint verification step S140 on the arrival interval and train resource usage of potential train numbers in the potential train number set, including: Step S141b: For each station, determine two potential trains that pass through the station and whose arrival times fall within the same time range, based on the arrival time of the potential train at the station. These two potential trains may have a time conflict when passing through the current station. Step S142b: Two potential trains are associated with the current station within the same time range, and there is a possibility that these two potential trains will have a time conflict when passing through the current station; Step S143b: Perform an adaptation verification of the arrival time and minimum safety interval for the two potential trains, constraining the arrival time interval between the two potential trains to be no less than the preset minimum safety interval.

[0129] In this exemplary embodiment, in order to ensure the safe operation of potential train services at the same station, the arrival times of train services passing through each station are used to verify whether train pairs with potential time conflicts have the minimum safe interval.

[0130] For each station, based on the arrival time of each potential train toward that station during its operation, all potential trains passing through that station are identified, along with the arrival time of each potential train at that station.

[0131] Based on the arrival time of each potential train at the station, two potential trains with similar arrival times within the same time range are further identified, namely, train pairs that are associated with the station within the same time range and thus have a possibility of time conflict.

[0132] This process allows for the early identification of train combinations with potential safety interval risks, enabling the verification of arrival time interval constraints and achieving safety interval control for potential trains.

[0133] At a station, for the two potential trains identified in step S141b, their arrival time interval is specifically constrained to be no less than a preset minimum safety interval. Specifically, if potential trains (m,k) and (mˊ,kˊ) are a train pair with a possible time conflict, then safety interval constraint control is implemented according to the arrival order of these two potential trains to adapt to two different situations.

[0134] It should be further explained that potential train number (m,k) refers to potential train number k departing from originating station m, while potential train number (mˊ,kˊ) refers to potential train number kˊ departing from originating station mˊ.

[0135] Auxiliary Boolean variables and constraint elimination constants are established to adapt to the arrival order of these two potential trains. Constraint control is achieved by adapting the auxiliary Boolean variables and constants to different arrival orders.

[0136] For example, for the identified train pairs with potential time conflicts, namely potential trains (m,k) and potential trains (mˊ,kˊ), the constraint verification for safety interval control is achieved using the following formula: Safety Interval Control Constraint Verification 1:

[0137]

[0138] Verification of safety interval control constraints, part two:

[0139]

[0140] in, It is the arrival time of the potential train (m,k) at station i; It is the arrival time of the potential train (mˊ, kˊ) at station i; It is a constant; This is an auxiliary Boolean variable used to indicate the order in which potential trains (m,k) and (mˊ,kˊ) arrive at station i in a train pair. If potential train (m,k) arrives later than potential train (mˊ,kˊ), then the auxiliary Boolean variable... The value is assigned to 0. If the potential train (m,k) arrives at the station before the potential train (mˊ,kˊ), then the auxiliary Boolean variable is... The value is assigned to 1. It is the minimum safe interval.

[0141] In other words, safety interval control constraint verification one and safety interval control constraint verification two form a symmetrical time-based collision avoidance protection.

[0142] When a potential train (m,k) arrives at a later station than a potential train (mˊ,kˊ), the auxiliary Boolean variable... The value is set to 0, and the constraint verification of these two potential train trips is achieved through the safety interval control constraint verification.

[0143] Verification 2 of the safety interval control constraint, then in the constant It will not be activated under the influence of this condition. The safety interval control constraint is a constant. Amplification and elimination disable the second verification of the safety interval control constraint, thus preventing forced execution.

[0144] When potential train number (m,k) arrives at the station before potential train number (mˊ,kˊ), the auxiliary Boolean variable... Assigning a value of 1, the constraints for these two potential train trips are implemented through safety interval control constraint verification two, and in constant... Under control, the safety interval control constraint verification is turned off and not enabled.

[0145] In summary, by introducing the safety interval control constraint verification, time conflicts between two potential trains at the same station are avoided, thus ensuring the safety of scheduling and operation. This effectively prevents situations where the previous train has not yet departed before the next train arrives at the station, avoids situations where the platform is crowded and the previous train has not yet cleared its passengers before the next train arrives at the station, and also avoids situations where the signal system fails to clear the previous train's signal, causing scheduling chaos.

[0146] This ensures a safe distance between two potential trains, enabling precise scheduling, and is particularly suitable for densely populated subway systems during morning and evening rush hours.

[0147] See Figure 8 , Figure 8 yes Figure 1 The corresponding embodiment shows a flowchart describing the method for verifying the constraints of arrival interval and train resource usage on potential trains in the potential train set based on the train number interval variable of the potential train number.

[0148] The embodiments of this application provide a train number interval variable based on potential train numbers, which implements a constraint verification step S140 on the arrival interval and train resource usage of potential train numbers in the potential train number set, including: Step S141c: For potential trains arriving at the terminal station, when there is a subsequent potential train that continues to depart from the terminal station, obtain the connection relationship variables of the trains before and after the potential trains. The connection relationship variables of the trains before and after the potential trains are used to characterize whether the train turns back from the previous potential train and connects to the subsequent potential train. Step S142c: Based on the connection relationship variables between the preceding and following trains, perform constraint verification on the connection between the preceding and following trains to form a turnaround, constraining the train to continue running the next potential train after completing the turnaround operation at the terminal station.

[0149] In the constraint verification performed on the set of potential trains in this exemplary embodiment, for each potential train, a connection relationship variable of preceding and following trains with a value of 1 is obtained. Based on the connection relationship variable of preceding and following trains with a value of 1, constraint verification is performed on the train running this potential train to verify that the train can run the next potential train in the opposite direction after completing the turnaround operation at the terminal station.

[0150] Therefore, when both trains are scheduled to run, priority will be given to connecting them by turning around, encouraging trains to turn around at the terminal and continue running as much as possible, thereby improving train utilization.

[0151] In urban rail transit dispatching, trains do not only perform a single trip, but make multiple round trips. If the dispatching does not take into account train turnaround connections, it will lead to a decrease in train utilization and an increase in the number of trains required.

[0152] The exemplary embodiments of this application combine train sequence with train operation by using the connection relationship variables of preceding and following trains, so that the scheduling can be optimized in terms of train quantity and operation mode. It is particularly suitable for scenarios with tight train schedules and limited turnaround station capacity, and reduces the number of trains required by optimizing the connection relationship.

[0153] For example, the constraint verification for the connection between trains performing turnarounds can be achieved through the following formula: Sub-constraint verification condition one:

[0154]

[0155] Sub-constraint verification condition two:

[0156]

[0157] in, These are variables relating to the connection between preceding and following train services; It is the station identifier of station m in the up or down direction of a certain train route; yes Stations on the same route in either the downhill or uphill direction Site identifier; For any potential train (m', l), it represents the shortest time for train k departing from station m in the direction of travel dir, including the departure time at station n and the time it takes to turn around at station n to reach the other direction station m' (s(n) = s(m')). The arrival time of train l departing from station m' in the direction of travel dir may overlap with that of train l arriving at station m'.

[0158] As illustrated by example, sub-constraint verification condition one is used to prohibit trains from making illegal U-turns. Only when there is a subsequent train originating from the terminal station after arriving at the terminal station can the train turn back at the terminal station and continue to run in the opposite direction to execute the subsequent train.

[0159] The second sub-constraint verification condition is used to prioritize the establishment of a U-turn connection. That is, if both trains before and after the U-turn are running, then these two potential trains are prioritized to form a U-turn connection.

[0160] Based on this, furthermore, the train sequence connection variable indicates that after completing the turnaround operation at the terminal station, the train executing the potential train continues to run the next potential train; the execution process of step S140 also includes: First, for the previous potential train mapped by the previous train connection relationship variable, obtain its departure time at the terminal station and the arrival time of the corresponding next potential train with the terminal station as the origin station. Secondly, by verifying whether the departure time of the previous potential train at the terminal station and the arrival time of the next potential train with the terminal station as the originating station are compatible with the minimum turning time, the turning and reversing time of the train turnaround operation is constrained.

[0161] In this exemplary embodiment, constraint verification of train turnaround and reversal time requirements is performed to ensure the feasibility of the operational sequence of turnaround trains in the potential train set.

[0162] If the variable indicating the connection between train numbers indicates that a train has changed direction and started the next train, that is, the value of the variable indicating the connection between train numbers is 1, then the operation time of the train at the turnaround station needs to be constrained and verified.

[0163] The time interval between the arrival time of the next potential train and the departure time of the previous potential train is constrained to be no less than the minimum turnaround time. The minimum turnaround time is the shortest operation cycle required for the turnaround operation, which covers necessary operations such as driver end change, train inspection and signal system switching.

[0164] This ensures the feasibility of scheduling, meets the minimum operating time requirements of on-site operations, reduces operational risks caused by insufficient turnaround time, and improves the stability and reliability of train operation, which is especially important for terminal stations with obvious bottlenecks in turnaround capacity.

[0165] In this exemplary embodiment, the verification of train turning-off and reversal constraints for two trains changing direction can be achieved using the following formula:

[0166]

[0167]

[0168] in, It is the minimum turning time. It is the originating station The train number is Potential train arrival stations Time; It is the time when a potential train with originating station m and train number k departs from station n. It is the constraint elimination constant, the potential train number. This represents the next potential train number.

[0169] When consecutive train services are operated by the same train, the departure time of the preceding potential train service (m,k) at the terminal station n is... , and the next potential train At the starting station Arrival time The difference between the two is not less than the minimum turnaround time required.

[0170] Furthermore, by determining the variables related to the connection between the preceding and following parts... and constraint elimination constant To determine whether this constraint is valid, we need to consider the connection variables between preceding and following trains. When it is 0, the constraint elimination constant This sufficiently large value causes the constraint to be enabled but forcibly disabled to adapt to different train usage scenarios.

[0171] In another exemplary embodiment, the execution process of step S140 further includes: First, obtain the warehouse departure variable configured for the next potential train, which is used to indicate whether the next potential train is provided by the warehouse for train operation; Secondly, based on the warehouse departure variable and the connection variable between the preceding and following trains, and combined with the train operation variable indicated by the train interval variable of the next potential train, a uniqueness verification is performed on the source of the train for the next potential train, constraining that the train used to run the next potential train can only be the train that ran the previous potential train, or be provided by the warehouse.

[0172] In this exemplary embodiment, constraint verification is performed on the warehouse departure variables and the connection relationship variables between preceding and following trains configured in the potential train set to ensure consistency between scheduling and train operation.

[0173] Based on the connection variable between preceding and following trains, it is determined whether the train for each potential train is a return trip of the preceding train, or whether it needs to be provided by a warehouse. If the connection variable between preceding and following trains is 0, it indicates that there is no direct connection, and the train running the next potential train is not a return trip of the preceding potential train. It is necessary to further determine whether the originating station of the next potential train is connected to a warehouse. If the next potential train does need to be provided by a warehouse, then its corresponding warehouse departure variable is set to 1. This warehouse departure variable is used to instruct the train to perform a train departure action to run the next potential train.

[0174] Correspondingly, the train arrival and entry control variable is 1, to instruct the train of the previous potential train number to perform the entry action.

[0175] Therefore, under the control of variables such as the connection between trains, the warehouse departure variables, and the train arrival and entry control variables, each train can accurately correspond to the actual entry and exit plans in terms of timing, avoiding situations where trains have no available sources or nowhere to park.

[0176] Based on this, the execution process of step S140 further includes: obtaining the train arrival and depot entry control variable configured for the previous potential train, the train arrival and depot entry control variable being used to indicate whether the train running the previous potential train performs the depot entry action after arriving at the terminal station; based on the connection relationship variable between the preceding and following trains and the train arrival and depot entry control variable, and combined with the train interval variable of the previous potential train, performing a uniqueness verification on the destination of the train running the previous potential train, constraining the train used to run the previous potential train to only choose to continue connecting to the next potential train or perform the depot entry action after arriving at the terminal station.

[0177] As step S140 completes the constraint verification of the arrival interval, turnaround capacity and train resource allocation of each potential train in the potential train set, the final set of all verified potential trains is obtained, and then step S150 is used to generate the train operation plan and train operation plan.

[0178] The set of potential trains obtained through constraint verification in step S140 clarifies the operating section, arrival and departure times, and connection relationships between trains before and after each potential train. Therefore, it is possible to generate a train operation plan that can be directly executed to clarify the actual operation arrangement of each potential train.

[0179] Based on the train connection, turnaround, departure and arrival results determined in the train operation plan, a corresponding train operation plan is further generated to complete the unified allocation of specific train resources throughout the entire scheduling cycle.

[0180] It should be understood that if the constraint verification in step S140 fails, the potential train set constructed driven by passenger flow demand will be rejected by the constraints. At this time, the process will return to step S110 to start the reconstruction of the potential train set until a potential train set that satisfies all constraints is obtained. Then, step S150 will be executed to fully ensure the reliability and engineering feasibility of train operation scheduling and the use of trains.

[0181] In one exemplary embodiment, this application also provides a computer device including a memory, a processor, and a computer program stored in the memory, the processor executing the computer program to implement the steps of the method as described above.

[0182] In one exemplary embodiment, this application also provides a computer program product including a computer program that, when executed by a processor, implements the steps of the method as described above.

[0183] In one exemplary embodiment, this application also provides a computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps of the method as described above.

[0184] Furthermore, although the steps of the method in this application are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in that specific order, or that all the steps shown must be performed to achieve the desired result. Additional or alternative steps may be omitted, multiple steps may be combined into one step, and / or a step may be broken down into multiple steps.

[0185] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this application are indicated by the appended claims.

Claims

1. A constrained scheduling method for urban rail transit, characterized in that, The method includes: For each station of the target city's rail transit, obtain the station passenger flow matching variable that responds to the passenger flow demand in each waiting time slot. The station passenger flow matching variable corresponding to the direction of travel is used to characterize the train number assigned to the corresponding waiting time slot. The train number carries the station passenger flow in the waiting time slot in the corresponding direction of travel. Based on the passenger flow matching variables of each station under each waiting time slot and driving direction, a set of potential trains that can carry the passenger flow of each station is determined. The potential trains in the set of potential trains are identified by their originating station and train number. For the potential trains in the set of potential trains, a train interval variable is constructed to control the operating section. The train interval variable indicates the operation of the corresponding potential train and the operating section. The constraints of arrival intervals, turnaround capacity, and train resource allocation for potential trains in the potential train set are verified to obtain a set of all verified potential trains. The constraint verification steps for arrival intervals include: for each station, determining the possibility of time conflicts between transit stations based on the arrival time of the potential trains; identifying two potential trains associated with the current station within the same time range, and the possibility of time conflicts between these two potential trains when they pass through the current station; performing an adaptation verification of arrival time and minimum safe interval for these two trains, constraining the arrival times of the two potential trains, and verifying whether the train pairs with the possibility of time conflicts are separated by the minimum safe interval; generating a train operation plan and a corresponding train operation plan for the set of potential trains that have been verified to meet the constraints.

2. The method according to claim 1, characterized in that, The step of determining the potential set of train services to carry station passenger flow based on the station passenger flow matching variables corresponding to each waiting time slot and direction of travel includes: For the waiting time slots of stations in each direction of travel, the mapped train number identifier is extracted based on the passenger flow matching variables of the corresponding stations. The train number identifier includes a combination of the originating station and the train number. For the train number identifier, construct a set of potential train numbers for the station to accommodate passenger flow demand along the waiting direction during the waiting time slice.

3. The method according to claim 1, characterized in that, The step of constructing a train interval variable for controlling the operating section for the potential trains in the potential train set includes: For the potential trains in the set of potential trains, a train departure variable is constructed, which indicates that the potential train is in operation. Based on the train departure variables, a train interval variable is constructed for the corresponding potential train. The train interval variable is used to characterize and control the travel interval of the potential train.

4. The method according to claim 3, characterized in that, The step of constructing the train number interval variable corresponding to the potential train number based on the train number departure variable includes: Based on the train departure variables and the corresponding originating station, determine the destination station of the potential train for at least one U-turn station distributed along the train route in terms of train direction. Based on the destination station, a train number interval variable is constructed for the potential train number, and the train number interval variable indicates the origin and destination stations of the potential train number.

5. The method according to claim 1, characterized in that, The constraint verification of the turnaround capability includes: For potential trains arriving at the terminal station, when there is a subsequent potential train that departs from the terminal station, the connection relationship variable between the trains that run the potential train is obtained. The connection relationship variable between the trains is used to characterize whether the train turns back from the previous potential train and connects to the subsequent potential train. Based on the variables relating to the preceding and following trains, a constraint verification is performed on the train to ensure that the preceding and following trains form a turnaround connection, constraining the train to continue running the next potential train after completing the turnaround operation at the terminal station.

6. The method according to claim 1, characterized in that, Potential train numbers (m,k) and (mˊ,kˊ) are train pairs that may have time conflicts. The process of performing an adaptation verification between the arrival time and the minimum safe interval for these two trains, constraining the arrival times of the two potential trains, and verifying whether the train pairs with potential time conflicts are within the minimum safe interval includes: An auxiliary Boolean variable and a constraint elimination constant are established to adapt to the arrival order of these two potential trains. The auxiliary Boolean variable is used to indicate the arrival order of potential trains (m,k) and (mˊ,kˊ) at station i. If potential train (m,k) arrives after potential train (mˊ,kˊ), the auxiliary Boolean variable is assigned a value of 0; if potential train (m,k) arrives after potential train (mˊ,kˊ), the auxiliary Boolean variable is assigned a value of 0. If the destination arrives first, the auxiliary Boolean variable is assigned the value 1; For the arrival time of trains passing through each station, the minimum safe interval is verified under the control of the auxiliary Boolean variable and the constraint elimination constant. The verification is used to implement symmetric time collision avoidance protection of the safe interval control constraint.

7. The method according to claim 1, characterized in that, The variable indicating the connection between preceding and following train numbers indicates that after a potential train completes a turnaround operation at the terminal station, it continues to run the next potential train. The constraint verification of the turnaround capability includes: For the preceding potential train mapped to the preceding train connection relationship variable with a value of 1, obtain its departure time at the terminal station and the arrival time of the corresponding following potential train with the terminal station as its origin. By verifying whether the departure time of the previous potential train at the terminal station and the arrival time of the subsequent potential train with the terminal station as the originating station are compatible with the minimum turning time, the turning and reversing time of the train turnaround operation is constrained.

8. The method according to claim 1, characterized in that, The constraint verification of the train resource allocation includes: Obtain the warehouse departure variable configured for the next potential train, the warehouse departure variable is used to indicate whether the next potential train is provided by the warehouse for train operation; Based on the warehouse departure variable and the connection variable between the preceding and following trains, and combined with the train operation variable indicated by the train interval variable of the next potential train, a uniqueness verification is performed on the source of the train running the next potential train. The train used to run the next potential train is constrained to be either the train running the previous potential train or provided by the warehouse.

9. An electronic device comprising a computer program, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method as described in any one of claims 1 to 8.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1-8.

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