Method and device for coordinating optimization of train departure path and timetable

Abstract

A method and device for optimizing train departure path and timetable cooperatively, the method comprising: constructing a space-time state network for describing the operation of a train bottom; based on the space-time state network, constructing a train departure path and timetable cooperative optimization model; wherein the train departure path and timetable cooperative optimization model comprises a model for minimizing the space-time state path cost of the train bottom leaving a section and corresponding constraint conditions; using a Lagrange relaxation algorithm to transform the train departure path and timetable cooperative optimization model, and using a dynamic programming algorithm to solve the model to obtain an optimal train departure path and timetable. Through the method and device provided in the embodiment of the application, the train operation cost can be effectively reduced while the travel time of passengers is shortened, and the method can be used for assisting actual transportation production and improving the overall quality of train operation plans in departure time periods.

Description

Technical Field

[0001] This invention relates to the field of urban rail transit technology, and more specifically, to a method and apparatus for collaboratively optimizing train departure routes and timetables. Background Technology

[0002] Urban rail transit train section operation modes refer to the operating strategies adopted by trains within a specific line section based on actual operational needs. Based on the type of operating strategy, train section operation modes can be divided into time-saving modes aimed at minimizing train travel time, energy-saving modes aimed at minimizing traction energy consumption, and time-based energy-saving modes that maximize energy savings within a fixed operating time. Considering the passenger flow distribution characteristics during departure periods, adopting a single section operation mode cannot simultaneously address the operational needs of controlling train operating costs under low passenger density and rapidly dispersing passengers under high passenger density. Furthermore, because the total passenger volume during departure periods is relatively small, the headway between trains is relatively large, and the line capacity is relatively sufficient, different trains can adopt different section operation modes during departure periods.

[0003] In the process of compiling urban rail transit train operation plans, the number of trains originating from and terminating at a single turnaround station within a given time period is counted. When the number of terminating trains is less than the number of originating trains, the process of arranging trains to depart from the depot or parking lot to the turnaround station to undertake train transportation tasks is called train departure from the depot. The path from the parking lot or depot (hereinafter referred to as the depot) to the turnaround station is the departure route. Train departure routes can be divided into direct routes and turnaround routes based on whether they involve turnaround operations. If the train can reach its originating station on the main line without turnaround operations, this type of route is called a direct route; otherwise, it is called a turnaround route. As an important part of the train operation plan, the departure route is essentially one (direct route) or multiple (turnaround route) operating trains originating from the depot. Therefore, the train timetable should specify the arrival and departure times of each station through which the departure route passes. To ensure the safety and feasibility of train operation plans, while meeting the capacity of the depot and stations, it is essential to ensure that the train's departure route and timetable do not conflict with the spatial and temporal trajectories of other trains, and that the train arrives at its designated departure time on time.

[0004] Current research primarily focuses on the integrated optimization of train timetables and rolling stock utilization under a single route, aiming to reduce enterprise operating costs by optimizing train arrival and departure times and the continuity between trains. This integrated optimization mostly considers end-of-line depot layouts, where rolling stock entry and exit routes are relatively simple. With the continuous expansion and construction of urban rail lines, the multi-depot layouts with non-end-of-line access and the multi-route train operation organization methods further increase the complexity of train departure routes and timetable compilation. Integrated optimization and trial-and-error methods based on experience cannot meet current needs and cannot ensure the overall quality of train operation plans during departure periods. Summary of the Invention

[0005] In view of this, the present invention proposes a method, apparatus, computer-readable storage medium and electronic device for collaboratively optimizing train departure routes and timetables, in order to solve the problem that existing optimization methods cannot meet the current non-endless access multi-section line layout conditions and multi-routes train operation organization mode, resulting in difficulty in ensuring the overall quality of train operation plans during departure periods.

[0006] In a first aspect, embodiments of the present invention provide a method for collaboratively optimizing train departure routes and timetables. The method includes: constructing a spatiotemporal state network to describe the operation of the train set; building a collaborative optimization model for train departure routes and timetables based on the spatiotemporal state network; wherein the collaborative optimization model for train departure routes and timetables includes a model that minimizes the spatiotemporal state path cost of the train set leaving the depot and its corresponding constraints; transforming the collaborative optimization model for train departure routes and timetables using a Lagrange relaxation algorithm, and solving the model using a dynamic programming algorithm to obtain the optimal train departure routes and timetables.

[0007] Furthermore, the construction of the spatiotemporal state network includes: using Representing a spatiotemporal state network, points Represents physical station In the extension of spatiotemporal state networks, arc Indicates from vertex arrive The effective spatiotemporal state path, where t This represents a uniformly discrete time interval in the planning time dimension. w This indicates the operating status of the vehicle's undercarriage.

[0008] Furthermore, the model for minimizing the spatiotemporal path cost at the bottom of the vehicle exit is as follows:

[0009] ;

[0010] arc The fees are as follows:

[0011] ;

[0012] in, F This indicates the assembly of trains that need to be dispatched from the depot to perform transportation tasks during peak hours. f This indicates the train index that needs to be dispatched from the depot to perform transportation tasks during peak hours. f ∈ F ; A Represents the set of arcs in the spatiotemporal state network. The spatiotemporal state network arc index represents the time at which the train... t From point i Departure in pattern w Run and at time s Arrival point j And reset the train operation mode to w’ ; Represents arc The cost; Indicates train Select Arc As the running path under the vehicle; w This indicates the weight of train operating costs in the calculation of arc costs; c 1 This represents the unit energy consumption cost of train operation. c 2 This represents the cost per unit of waiting time for passengers. Represents arc Train operation energy consumption, Represents arc Total travel time for passengers on board.

[0013] Furthermore, the constraints include spatiotemporal network flow balance constraints, operational constraints, passenger service level constraints, and variable constraints.

[0014] Furthermore, the spatiotemporal network flow balance constraint is as follows:

[0015] ;

[0016] in,( j,s , w’ ) represents the vertex index of the spatiotemporal state network. N Represents the set of network nodes in the spatiotemporal state; Indicates train Select Arc As the running path under the vehicle; o This represents the virtual origin station index for all trains departing from the depot. t This represents a uniformly discrete time interval in the planning time dimension. w Indicates the running status of the vehicle's undercarriage; FThis indicates the assembly of trains that need to be dispatched from the depot to perform transportation tasks during peak hours. f This indicates the train index that needs to be dispatched from the depot to perform transportation tasks during peak hours.

[0017] Furthermore, the operational constraints are as follows:

[0018] ;

[0019] ;

[0020] in, F This indicates the assembly of trains that need to be dispatched from the depot to perform transportation tasks during peak hours. f This index indicates trains that need to be dispatched from the depot to perform transportation tasks during peak hours. The spatiotemporal state network arc index represents the time at which the train... t From point i Departure in pattern w Run and at time s Arrival point j And reset the train operation mode to w’ ; Indicates train Select Arc As the running path under the vehicle; Representing time in a spatiotemporal state network τ Occupying nodes i Conflicting arc sets In the spatiotemporal state network, the starting point is the vehicle depot. i The arc set; n i Indicates field segment i The number of vehicles in use; T Represents the set of times. V Represents the set of spatial nodes of the line; D This represents the set of field segments.

[0021] Furthermore, the passenger service level constraints are as follows:

[0022] ;

[0023] in, F This indicates the assembly of trains that need to be dispatched from the depot to perform transportation tasks during peak hours. f This index indicates trains that need to be dispatched from the depot to perform transportation tasks during peak hours. The spatiotemporal state network arc index represents the time at which the train... t From point i Departure in pattern w Run and at time s Arrival pointj And reset the train operation mode to w’ ; Indicates train Select Arc As the running path under the vehicle; In a spatiotemporal state network, the starting point is the station node. i The arc set; m i This indicates the minimum number of trains that can stop at a station. Q 1 Indicates the meeting point at the line station. Q 2 This represents the set of line turnaround lines.

[0024] Furthermore, the variable constraints are as follows:

[0025] ;

[0026] in, F This indicates the assembly of trains that need to be dispatched from the depot to perform transportation tasks during peak hours. f This index indicates trains that need to be dispatched from the depot to perform transportation tasks during peak hours. The spatiotemporal state network arc index represents the time at which the train... t From point i Departure in pattern w Run and at time s Arrival point j And reset the train operation mode to w’ ; A Represents the set of arcs in a spatiotemporal state network; Indicates if the train Select Arc The value is 1 when it is part of the vehicle's running path, and 0 otherwise.

[0027] Furthermore, the step of transforming the train departure route and timetable collaborative optimization model using the Lagrange relaxation algorithm includes:

[0028] The Lagrange relaxation algorithm is employed, and a non-negative train operation safety multiplier is introduced. α i,τ Resource multipliers β i Service level multiplier γ i By relaxing the difficult constraints into the train departure route and timetable co-optimization model, the transformed train departure route and timetable co-optimization model is obtained as follows:

[0029] ;

[0030] spatiotemporal network flow balance constraints and variable constraints;

[0031] ;

[0032] in, T Represents the set of times. V Represents the set of spatial nodes of the line. Q 1 Indicates the meeting point at the line station. Q 2 This represents the set of line turnaround lines. D Represents the set of field segments; Representing time in a spatiotemporal state network τ Occupying nodes i Conflicting arc sets i ∈ V ; In the spatiotemporal state network, the starting point is the vehicle depot. i arc set, i ∈ D ; In a spatiotemporal state network, the starting point is the station node. i arc set, i ∈ Q 1 ; n i Indicates field segment i The number of vehicles in use, m i This indicates the minimum number of trains that stop at a station.

[0033] Secondly, embodiments of the present invention also provide an apparatus for collaboratively optimizing train departure routes and timetables. The apparatus includes: a spatiotemporal state network construction unit for constructing a spatiotemporal state network to describe the operation of the train carriages; a model construction unit for constructing a collaborative optimization model of train departure routes and timetables based on the spatiotemporal state network; wherein the collaborative optimization model of train departure routes and timetables includes a model that minimizes the spatiotemporal state path cost of the train carriages leaving the depot and its corresponding constraints; and a model solving unit for transforming the collaborative optimization model of train departure routes and timetables using a Lagrange relaxation algorithm and solving the model using a dynamic programming algorithm to obtain the optimal train departure routes and timetables.

[0034] Thirdly, embodiments of the present invention also provide a computer-readable storage medium having a computer program stored thereon, characterized in that the program, when executed by a processor, implements the methods provided in the embodiments of the present invention.

[0035] Fourthly, embodiments of the present invention also provide an electronic device, including: a processor; a memory for storing executable instructions of the processor; the processor being configured to read the executable instructions from the memory and execute the instructions to implement the methods provided in various embodiments of the present invention.

[0036] The method and apparatus for collaboratively optimizing train departure routes and timetables provided in this invention are based on a constructed spatiotemporal state network. Under the condition of satisfying constraints, with the objective of minimizing passenger travel costs and train operating costs, a collaborative optimization model for train departure routes and timetables is constructed. The model is transformed using the Lagrange relaxation algorithm and solved using a dynamic programming algorithm to obtain the optimal train departure routes and timetables. While meeting the passenger travel demand during departure periods, the proposed method can obtain a better train depot departure scheme than existing technologies within a reasonable time. Diverse interval operation modes can effectively reduce train operating costs while shortening passenger travel time. It can be used to assist actual transportation production and improve the overall quality of train operation plans during departure periods. Attached Figure Description

[0037] Figure 1 A flowchart illustrating a method for collaboratively optimizing train departure routes and timetables, provided as an exemplary embodiment of the present invention;

[0038] Figure 2 A circuit diagram provided for an exemplary embodiment of the present invention;

[0039] Figure 3 A schematic diagram of a train departure route provided as an exemplary embodiment of the present invention;

[0040] Figure 4 A schematic diagram of a train running path in a spatiotemporal state network provided as an exemplary embodiment of the present invention;

[0041] Figure 5 A layout diagram of Chongqing Metro Line 3 is provided as an exemplary embodiment of the present invention;

[0042] Figure 6 A schematic diagram of an initial train operation plan provided as an exemplary embodiment of the present invention;

[0043] Figure 7 A schematic diagram of train section operation parameters provided as an exemplary embodiment of the present invention;

[0044] Figure 8 A schematic diagram of route OD passenger flow distribution provided as an exemplary embodiment of the present invention;

[0045] Figure 9A schematic diagram of the train operation result (MOR) obtained by model solving as an exemplary embodiment of the present invention;

[0046] Figure 10 A schematic diagram of a train operation mode provided as an exemplary embodiment of the present invention;

[0047] Figure 11 A schematic diagram of a current experience-based train operation plan (TOP) provided as an exemplary embodiment of the present invention;

[0048] Figure 12 A data graph comparing the full load rate of cross sections provided as an exemplary embodiment of the present invention;

[0049] Figure 13 A data graph illustrating the influence of weighting coefficients provided as an exemplary embodiment of the present invention;

[0050] Figure 14 A schematic diagram of the structure of an apparatus for collaboratively optimizing train departure routes and timetables, provided as an exemplary embodiment of the present invention;

[0051] Figure 15 A block diagram of an electronic device provided as an exemplary embodiment of the present invention. Detailed Implementation

[0052] Exemplary embodiments of the invention will now be described with reference to the accompanying drawings. However, the invention may be embodied in many different forms and is not limited to the embodiments described herein. These embodiments are provided to fully and completely disclose the invention and to fully convey its scope to those skilled in the art. The terminology used in the exemplary embodiments illustrated in the drawings is not intended to limit the invention. In the drawings, the same units / elements are referred to by the same reference numerals.

[0053] Unless otherwise stated, the terms used herein (including technical terms) have their common meaning as understood by one of ordinary skill in the art. Furthermore, it is understood that terms defined in commonly used dictionaries should be understood to have a meaning consistent with the context of their relevant field, and not to be interpreted as having an idealized or overly formal meaning.

[0054] Figure 1This is a flowchart illustrating a method for collaboratively optimizing train departure routes and timetables, provided as an exemplary embodiment of the present invention. The execution subject of this embodiment is a computer device. Optionally, the computer device is a terminal, which can be portable, pocket-sized, handheld, or other types of terminals, such as smartphones, tablets, laptops, and desktop computers. Optionally, the execution subject of this embodiment is a server, which can be an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services.

[0055] like Figure 1 As shown, the method includes:

[0056] Step S101: Construct a spatiotemporal state network to describe the operation of the vehicle undercarriage.

[0057] Furthermore, a spatiotemporal state network is constructed, including:

[0058] use Representing a spatiotemporal state network, points Represents physical station In the extension of spatiotemporal state networks, arc Indicates from vertex arrive The effective spatiotemporal state path, where t This represents a uniformly discrete time interval in the planning time dimension. w This indicates the operating status of the vehicle's undercarriage.

[0059] The coordinated optimization of urban rail train departure routes and timetables considering inter-section operation modes requires simultaneously determining the train's departure depot, departure time, stations along the route, and arrival and departure times at each station. The arrival and departure times at each station are related to the train's operation mode within each section. Given the complex line conditions in actual operation, without loss of generality, this embodiment is based on a line with multiple depots and multiple routes, which can be simplified to a simpler line.

[0060] Specifically, Figure 2 This is a schematic diagram of a circuit provided for an exemplary embodiment of the present invention. Figure 2 The problem is described using the shown line as an example. This line includes 5 stations, 2 depots, and 4 sections. (Stations...) , , , It is a turnaround station, among which , , It is a turnaround station after the station. It is a turnaround station in front of the station. and It can only be used for trains arriving in the upstream direction to turn back. and It can only be used for southbound arriving trains to turn around. (Depot) , Connected to the station via the section connecting line , Connected. Figure 3 The system presents the train groups requiring dispatch during operating hours in the form of a train timetable, and uses one train as an example to illustrate its possible departure routes. It assumes the departure time begins at [time missing]. The end time is . The right side represents the peak period, during which train operation plans are known. Trains without consecutive trains during the peak period (dotted line train operation line) represent the train groups that need to be assigned rolling stock during the departure period, and their departure time from their originating station is the starting point for searching the departure route. The left side represents the train departure time slots, during which train lines are used to meet passenger travel demand. Since there are no connecting trains within a time slot and station arrival and departure times are adjustable, dashed lines (full-dot dashed lines) are used to represent this. The originating station is used as the reference point. Departure time is Taking a non-connecting train as an example, the diagram shows three possible departure routes. Route 1 is a direct route without turning back, while routes 2 and 3 involve one and two turns, respectively. Routes 1 and 3 are both dispatched from the depot. The assigned rolling stock is responsible for transportation tasks, while route 2 is handled by the depot. The assigned vehicles are responsible for transportation tasks. Among the three types of routes, routes numbered 1 and 2 have shorter travel distances, but also provide less capacity for passenger travel during the designated hours. Therefore, when selecting routes during operating hours, it is necessary to consider not only the travel distance of the vehicles but also the travel needs of passengers during those hours.

[0061] A high-dimensional multi-commodity flow modeling framework is adopted to construct a spatiotemporal state network with spatial, temporal, and train operation state dimensions to describe the operation of the train undercarriage. Representing a spatiotemporal state network, points For physical stations In the extension of spatiotemporal state networks, arc Indicates from vertex arrive The effective spatiotemporal state path. Among them, This represents a uniform discrete time interval (e.g., 1 second) in the planning time dimension, which naturally embeds the time window constraint for train departure from the depot. Furthermore, This indicates the running status of the train and is used to record the train's operating mode. When a train leaving the depot changes direction after passing through a turnaround station, the train's running status is reset to [normal]. . Figure 4 This is a schematic diagram of the spatial and temporal state path of a train during operation, provided as an exemplary embodiment of the present invention. For example... Figure 4 As shown, the starting node corresponding to this path is The final node is The spatiotemporal arc is affected by the number of passengers arriving on the route. The passenger flow on the train is relatively small, so the train selects the energy-saving mode. Spacetime arc The passenger flow on the train is relatively large, so the train selects the time-saving mode. .

[0062] Step S102: Based on the spatiotemporal state network, construct a collaborative optimization model for train departure routes and timetables; wherein the collaborative optimization model for train departure routes and timetables includes a model that minimizes the spatiotemporal state path cost of the train depot and its corresponding constraints.

[0063] Furthermore, the model that minimizes the spatiotemporal path cost of exiting the undercarriage is as follows:

[0064] ;

[0065] arc The fees are as follows:

[0066] ;

[0067] in, F This indicates the assembly of trains that need to be dispatched from the depot to perform transportation tasks during peak hours. f This indicates the train index that needs to be dispatched from the depot to perform transportation tasks during peak hours. f ∈ F ; A Represents the set of arcs in the spatiotemporal state network. The spatiotemporal state network arc index represents the time at which the train... t From point i Departure in pattern w Run and at time s Arrival point j And reset the train operation mode to w’ ; Represents arc The cost; Indicates train Select Arc As the running path under the vehicle; w This indicates the weight of train operating costs in the calculation of arc costs; c 1This represents the unit energy consumption cost of train operation. c 2 This represents the cost per unit of waiting time for passengers. Represents arc Train operation energy consumption, Represents arc Total travel time for passengers on board.

[0068] The daily entry and exit routes of train sets for urban rail transit lines can be divided into three categories: train departures before the start of morning and evening peak hours, train returns to the depot after the end of morning and evening peak hours and during the transition to off-peak hours, and concentrated returns after the end of operation. Concentrated returns after the end of operation are usually constrained by the latest operating time and the last train timetable. At the same time, passenger flow is relatively low, train intervals are relatively long, and there are fewer restrictions on train returns. However, for the departure periods before the start of morning and evening peak hours, it is necessary not only to ensure that the train operation plan for peak hours has sufficient train sets to handle transportation tasks, but also to meet the passenger flow demand during this period. Furthermore, the departure capacity of the depot and parking lots is limited, making the determination of train departure routes before peak hours more complex. In this embodiment, based on the morning peak hour train operation plan, the departure periods before the morning peak hour are taken as the object of optimization, and the peak train departure routes and timetables are coordinated. To construct a rigorous mathematical optimization model and facilitate the subsequent method description, the following assumptions are made:

[0069] (1) The train operation plan during peak hours (including the connection relationship between trains within the time period) is known;

[0070] (2) In order to meet the basic transport capacity demand during the departure period, the initial train operation plan (excluding the connection relationship between trains during the period) is known; when the number of arrivals and departures of the depot route combination at each station is greater than or equal to the number of arrivals and departures of the initial train operation plan at each station, the transport capacity demand during the departure period is fully met.

[0071] (3) In order to ensure the universality of the model and method, the impact of the first bus operation mode on the departure route is not considered;

[0072] For ease of description, the symbols and parameters involved in the model in this embodiment and their related definitions are shown in Table 1.

[0073] Table 1. Representation and Definition of Symbols and Parameters

[0074]

[0075] To achieve the joint optimization objective of timetables and vehicle departure routes, the construction of the spatiotemporal network needs to follow these principles:

[0076] (1) For stations that turn back after the station on the line, these stations allow some parallel operations of receiving and dispatching trains and turning back. After the preceding train stops on the turning back track, the receiving route for the following train can be processed. After the preceding train clears the turning back track, the route for the following train to enter the turning back track can be processed. Therefore, it is necessary to set the turning back track after the station as an independent spatial point in the spatiotemporal network, that is, a set. Q 2 Spatial nodes in;

[0077] (2) The preset time period is passed through the time increment Δ t Discretize the data, with the preset start time of the time period being 0, and use an index. t The corresponding time is ;

[0078] (3) Since the train adopts a stop-at-every-station mode after leaving the depot, for the nodes k All satisfactions should be eliminated. arc This is used to ensure that the train is at the node. k parking.

[0079] The train departure path and timetable collaborative optimization model aims to minimize the spatiotemporal path cost of the train leaving the depot, as shown in the equation. The cost of the arc in the spatiotemporal state network includes train operation energy consumption cost and passenger travel cost, as shown in the equation. Passenger travel cost is mainly related to the travel time and stop time of the train selected by the passenger. The train operation energy consumption and travel time under different train operation modes can be obtained through train operation simulation and traction calculation. The number of passengers on the arc, with OD passenger flow as input, can be obtained through a passenger flow allocation algorithm.

[0080] (1)

[0081] (2)

[0082] Furthermore, the constraints include spatiotemporal network flow balance constraints, operational constraints, passenger service level constraints, and variable constraints.

[0083] (1) Spatiotemporal network flow balance constraints

[0084] To describe the departure routes of peak-hour trains in the spatiotemporal network, for each train that requires its rolling stock to undertake transportation tasks... Its departure route begins from the virtual starting point. Ending at point The flow balance constraints are constructed as follows:

[0085] (3)

[0086] (2) Operational constraints

[0087] To ensure the feasibility and rationality of train operation on the spatiotemporal network: at time... interval Only one train can occupy a spatial node. If and only if For ordinary station nodes At time, take at intervals Used to meet the headway between trains; if and only if the node For field segment nodes At time, take at intervals Used to meet the exit interval between car bodies; if and only if the node Abstract nodes for the zigzag line At time, take at intervals This is used to meet the turnaround interval time of trains at the turnaround station, as shown below:

[0088] (4)

[0089] To ensure that the depot has enough operational cars to meet train operation needs: [depot / section] The number of arcs for the initial node should be less than the number of vehicles in operation for that section, as shown below:

[0090] (5)

[0091] (3) Passenger service level constraints

[0092] To meet passenger demand during peak hours and maintain a certain level of service: at the station The number of stop arcs must be greater than the station's minimum service frequency.

[0093] (6)

[0094] (4) Variable constraints

[0095] Variable value constraints:

[0096] (7)

[0097] In summary, the problem of coordinating the train departure routes and timetables of urban rail transit, considering the train section operation modes, can be constructed as the following model:

[0098] (8)

[0099] Step S103: The Lagrange relaxation algorithm is used to transform the train departure route and timetable joint optimization model, and the dynamic programming algorithm is used to solve the model to obtain the optimal train departure route and timetable.

[0100] Using Lagrange relaxation theory, a non-negative train operation safety multiplier is introduced. Resource multipliers Service level multiplier The difficult constraints are relaxed into the objective function. The original problem is transformed into a general shortest path problem for spatiotemporal state networks, as shown in the equation. The definition of the spatiotemporal state arc correction cost is as follows:

[0101] (9)

[0102] (10)

[0103] Urban rail transit train operation and stopping times are generally accurate to the second; therefore, this embodiment selects... The time discreteness is 1 second. The fine time discretization makes the problem's scale difficult to solve in practice. To search for optimal solutions within a reasonable timeframe, an efficient solution algorithm is necessary. The co-optimization of train departure routes and timetables can be viewed as a multi-stage decision problem, where each stage's decision is time-dependent and depends on the current state. Therefore, this embodiment uses a dynamic programming algorithm to solve the model. In this embodiment, solving the departure route of a single train is considered as one stage, with the departure route of its preceding train as the stage state, to optimize the current train's departure route. The proposed method starts with a minimum spatiotemporal network and carefully deletes candidate arcs during the algorithm process by identifying network components important to the current algorithm state.

[0104] The algorithm's input includes information about the train. The constructed spatiotemporal network, train Vertex of the vehicle exit path and the finish line The algorithm outputs the values ​​of each train. The spatiotemporal state path. The specific algorithm steps are as follows:

[0105] Step 1: Initialize the train The cost of any node on the departure route is And set the predecessor node of any node in the path. Set up Lagrange multipliers , , Set the number of Lagrange iterations to 1.

[0106] Step 2: Update the labels using dynamic programming algorithm

[0107] For trains do

[0108] For to do

[0109] For each node do

[0110] For each arc do

[0111] If

[0112] Then ,

[0113] End

[0114] End

[0115] End

[0116] End

[0117] Calculate and record the objective function value of the model. and These serve as the upper and lower bounds for the optimal solution to the original problem.

[0118] Step 3: Obtain the spatiotemporal network of the vehicle departure path that minimizes the objective function.

[0119] For trains do

[0120] Based on the target node The forward nodes sequentially reconstruct the train departure path.

[0121] End

[0122] Step 4: Update the Lagrange multipliers based on the subgradient method

[0123] For , do

[0124]

[0125] End

[0126] For nodes do

[0127]

[0128] End

[0129] For nodes do

[0130]

[0131] End

[0132] in Indicates the first Lagrange subgradient step size during the next iteration.

[0133] Step 5: Algorithm Termination Condition

[0134] If the number of iterations Greater than the predetermined maximum allowed number of iterations If the algorithm fails, it terminates; otherwise, it returns to Step 2.

[0135] It is particularly important to note that high-dimensional complex networks typically have high memory requirements, limiting the algorithm's solution speed. To ensure good optimization results within a reasonable timeframe, when initializing the spatiotemporal state network, a simple set of if-then rules can be used to limit the number of accessible and feasible arcs based on the station's fixed stop times and the train interval running times under alternative operating modes. This narrows the search range and improves solution efficiency.

[0136] The above embodiments, based on the constructed spatiotemporal state network, aim to minimize passenger travel costs and train operation costs under the constraints. A collaborative optimization model for train departure routes and timetables is built, and the model is transformed using the Lagrange relaxation algorithm. Dynamic programming is then used to solve the model, yielding the optimal train departure routes and timetables. While meeting passenger travel demands during departure periods, the proposed method can obtain a better train departure plan than existing technologies within a reasonable timeframe. Diverse interval operation modes can effectively reduce train operation costs while shortening passenger travel time. This approach can be used to assist actual transportation production and improve the overall quality of train operation plans during departure periods.

[0137] Example 1

[0138] Taking Chongqing Metro Line 3 (Yudong - Jiangbei Airport T2 Terminal) as an example, the line is 54km long, with 39 stations and 38 sections, numbered sequentially in the downward direction. The interval numbers are as follows: ,like Figure 5 As shown. In actual operation, there are a total of 5 stations along the line that can be used for turnaround, of which... , , Only trains arriving in the upstream direction are allowed to turn back. , Only trains arriving in the downstream direction are allowed to turn back. The minimum operating time for a single train at the turnaround station, i.e., the minimum interval between two adjacent trains occupying the turnaround track, is shown in Table 2. Information on the depot and parking lot of Line 3 and its rolling stock is shown in Table 3. Other input parameters are shown in Table 4. Initial train operation information is shown in... Figure 6 The solid lines represent train timetables and connecting plans during peak hours, while the dashed lines represent train timetables during departure hours (which can be obtained from...). The diagram shows 45 trains without carriages that are used for transportation, requiring the solution of their spatiotemporal paths. Through train operation simulation, the corresponding runtime and energy consumption for different operating modes in each section of the line are obtained (see figure). Figure 7 Passenger flow data from 06:30 to 09:00 on December 6, 2021 (weekday) was used to optimize train departure routes and timetables. OD passenger flow distribution is shown in [link to OD data]. Figure 8 .

[0139] Table 2 Minimum Operating Time for Turnaround Stations

[0140]

[0141] Table 3. Line Section Information

[0142]

[0143] Table 4 Other parameters

[0144]

[0145] Based on the above data and parameter settings, the algorithm is implemented using the C# programming language. The optimal train departure routes and timetables are obtained by iterating and setting the value to 100. This section first analyzes the rationality of the model optimization results. Secondly, it compares the operating costs and passenger travel costs of the model optimization results (MOR) during the operating period (6:30-8:00) with the current experience-based train operation plan (TOP), demonstrating the effectiveness of the proposed model and algorithm.

[0146] Figure 9 This is the train timetable obtained by the algorithm in this embodiment. Detailed information on the train departure routes is shown in Table 5, which only displays the originating and terminating station numbers of the trains traveling on the main line, omitting the train's operation within the depot. Taking the departure route of train 003001 (downward direction) "28-39-39-1-1" as an example, the train... The train departed from the depot and arrived at the station at 05:18:35. And execute the running segment as The downlink transport task, at the turnaround station After the first turnaround, it will continue to operate in the following section: The uplink transport task, at the turnaround station After completing the second turnaround, trains will perform peak-hour transport tasks and complete rolling stock allocation. In the rolling stock departure route display, trains will turn around at a station only if adjacent station numbers are the same. During peak hours, a total of 45 trains need to be assigned rolling stock for corresponding transport tasks, including 25 down-line trains and 20 up-line trains. Four trains will depart in the forward direction without needing to turn around or undertake transport tasks during departure hours. Due to the influence of the non-terminal access depot and to meet passenger travel demands during departure hours, 41 trains will choose to complete their departure by at least one turnaround. Of these, 27 trains will complete their departure by one turnaround, and 14 trains will complete their departure by two turnarounds. The number of trains completing their departure by a maximum of one turnaround accounts for 69%, indicating a high quality of train departure route selection.

[0147] Table 5 Train Departure Route Information

[0148] Outbound train number Exit time Section number Departure route Number of turnarounds 001001 05:04:40 2 28-39-39-1-1 2 002001 05:14:25 1 3-39-39 1 003001 05:18:35 2 28-39-39-1-1 2 004001 05:20:53 1 3-39-39 1 005001 05:32:20 2 28-39-39-1-1 2 006001 05:32:10 1 3-39-39 1 007002 05:40:15 2 28-1-1 1 008001 05:44:05 1 3-39-39 1 009001 05:44:25 2 28-39-39-1-1 2 010001 05:52:15 1 3-39-39 1 011002 05:52:37 2 28-1-1 1 012001 05:56:30 2 28-39-39-1-1 2 013002 05:59:45 1 3-1-1-39-39 2 014001 06:00:05 1 3-39-39 1 015002 06:04:40 2 28-1-1 1 016002 06:07:50 1 3-1-1-39-39 2 017001 06:08:35 2 28-39-39-1-1 2 018001 06:12:20 1 3-39-39 1 019002 06:15:55 1 3-1-1-39-39 2 020001 06:19:10 1 3-39-39 1 021002 06:16:40 2 28-8-8 1 022002 06:27:20 1 3-1-1-28-28 2 023002 06:22:40 2 28-14-14-28-28 2 024002 06:30:05 2 28-8-8 1 025002 06:35:25 1 3-1-1-39-39 2 026002 06:36:05 2 28-14-14-28-28 2 027002 06:44:05 2 28-8-8 1 028002 06:50:10 1 3-1-1 1 029002 06:49:35 2 28-8-8 1 030002 06:57:00 2 28-8-8 1 031002 07:03:00 2 28-14-14 1 032002 07:10:35 2 28-8-8 1 033002 07:15:05 1 3-1-1 1 034002 07:16:35 2 28-8-8 1 035002 07:23:45 2 28-8-8 1 036001 07:23:50 1 3-8 0 037002 07:29:45 2 28-14-14 1 038002 07:36:35 2 28 0 039002 07:41:50 1 3-1-1 1 040002 07:43:25 2 28 0 041002 07:49:55 2 28 0 042001 07:52:55 2 28-39-39 1 043002 08:06:17 1 3-1-1 1 044002 08:07:20 2 28 0 045002 08:31:05 1 3-1-1 1

[0149] Figure 10 Different colors were used to indicate the train's operating mode within the section: green represented energy-saving mode, orange represented timed energy-saving mode, and black represented time-saving mode. Peak-hour train lines, used as input data, all operated in timed energy-saving mode. A total of 53 trains selected their operating mode, making 1117 selections for each section. Table 6 shows the selected operating modes. Energy-saving mode was selected 480 times, accounting for 43% of the total selections, mainly concentrated during periods of low passenger flow (5:00-6:50); timed energy-saving mode was selected 621 times, accounting for 55%, mainly concentrated during periods of increasing passenger flow (6:50-7:30); and time-saving mode was selected 16 times, accounting for 2%, mainly concentrated during periods of relatively high passenger flow (7:30-8:00). The operating section is entirely comprised of trains traveling in the downhill direction. It's worth noting that, as Chongqing Metro Line 3 runs roughly north-south, connecting urban and suburban areas, passenger flow is relatively low during the morning rush hour (outbound). Some uphill trains operating between 7:30 and 8:00 AM will choose energy-saving mode when passing through this section, which aligns with the line's passenger flow distribution characteristics.

[0150] Table 6 Statistical Results of Train Section Operation Mode

[0151]

[0152] Figure 11The current experience-based train operation plan (TOP) for Chongqing Metro Line 3 is used, in which all trains operate in a timed energy-saving mode. The energy consumption cost of train operation and passenger travel costs during the departure period of 6:30-8:00 are compared, and the statistical values ​​of the comparison indicators are shown in Table 7. The train operation cost under the experience-based train operation plan (TOP) is 197,177.31 yuan, while the energy consumption cost under the model optimization result (MOR) is 118,616.67 yuan, representing a reduction of 39.84%. The passenger travel cost under TOP is 100,601.35 yuan, while the passenger travel cost under MOR is 98,237.04 yuan, representing a reduction of 2.35%. Figure 12 The chart compares the occupancy rates of the MOR and TOP models at the 5-minute granularity for both up and down traffic sections. The data shows that, under the condition of not exceeding the expected occupancy rate, the MOR model's occupancy rate is closer to the expected occupancy rate of 1, effectively improving the matching degree between transport capacity and passenger volume. Due to the reduced train departure times and the adoption of energy-saving modes for most train operations, train operating energy consumption has decreased significantly. While the reduced train departure frequency increases passenger waiting time, the overall cost of passenger travel decreases, although the decrease is relatively small, because some trains choose to operate in time-saving modes in sections with high passenger flow. Considering both train operating costs and passenger travel costs, the total cost of train operation plans during the departure time period (6:30-8:00) is reduced by 27.18% compared to TOP after model optimization, demonstrating a significant improvement in model optimization effectiveness.

[0153] Table 7 Statistical Analysis of Objective Function Values

[0154] objective function TOP MOR change / % Train operating energy consumption cost / yuan 197177.31 118616.67 -39.84 Passenger travel time cost / yuan 100601.35 98237.04 -2.35 Total cost / yuan 297778.66 216853.71 -27.18

[0155] Sensitivity analysis is as follows:

[0156] (1) Train operation mode

[0157] This study further explores the impact of train operation modes on model optimization by changing the set of alternative operation modes for trains within a section. Based on three section operation modes—time-saving, timed energy-saving, and energy-saving—six optimization experiments were conducted under different sets of alternative operation modes. Experiment 6 served as a control, representing the MOR optimization results. The objective function values ​​for each group of experiments are shown in Table 8. A comparison of Experiments 1, 2, 3, and 6 shows that if all departing trains can only choose a single train section operation mode in actual operation, the energy-saving mode should be chosen after comprehensively considering both train operation costs and passenger travel time costs. A comparison of Experiments 4, 5, and 6 shows that the more alternative operation modes available for the train, the better the optimization effect of the train departure route and timetable optimization model. However, the optimization margin of the overall objective decreases as the number of alternative operation modes increases.

[0158] Table 8. Impact of Alternative Operating Modes on Model Optimization Results

[0159]

[0160] (2) Weighting coefficient of arc cost

[0161] Weighting coefficient of spacetime arc This configuration effectively balances train operating costs and passenger travel costs. This article will... The values ​​were set to 0.1-0.9, and the solutions for each example were obtained. The model solution results are as follows: Figure 13 As shown in the figure, the analysis reveals a conflict between operating costs, primarily train energy consumption, and passenger travel costs. When When the value of is equal to 0.1, the train operating cost reaches its minimum, and the passenger travel cost reaches its maximum. With... As trains become more expensive, operating costs increase, while passenger travel costs decrease. When the value equals 0.9, the train operating cost reaches its maximum, and the passenger travel cost reaches its minimum. The objective function value of the optimization model is minimized when the value of is 0.6.

[0162] The analysis results of the above embodiments show that, while meeting the travel demand of passengers during the departure period, the proposed optimization method can obtain a better train depot departure plan than on-site experience within a reasonable time. The diverse interval operation modes can effectively reduce train operation costs while shortening passenger travel time, and can be used to assist actual transportation production.

[0163] Figure 14 This is a schematic diagram of a device for collaboratively optimizing train departure routes and timetables, provided as an exemplary embodiment of the present invention.

[0164] like Figure 14 As shown, the device includes:

[0165] Spatiotemporal state network construction unit 1401 is used to construct a spatiotemporal state network to describe the operation of the vehicle undercarriage.

[0166] Model building unit 1402 is used to build a train departure path and timetable collaborative optimization model based on spatiotemporal state network; the train departure path and timetable collaborative optimization model includes a model that minimizes the spatiotemporal state path cost of the train depot and its corresponding constraints.

[0167] The model solving unit 1403 is used to transform the train departure route and timetable joint optimization model using the Lagrange relaxation algorithm, and to solve the model using the dynamic programming algorithm to obtain the optimal train departure route and timetable.

[0168] Furthermore, a spatiotemporal state network is constructed, including:

[0169] use Representing a spatiotemporal state network, points Represents physical station In the extension of spatiotemporal state networks, arc Indicates from vertex arrive The effective spatiotemporal state path, where t This represents a uniformly discrete time interval in the planning time dimension. w This indicates the operating status of the vehicle's undercarriage.

[0170] Furthermore, the model that minimizes the spatiotemporal path cost of exiting the undercarriage is as follows:

[0171] ;

[0172] arc The fees are as follows:

[0173] ;

[0174] in, F This indicates the assembly of trains that need to be dispatched from the depot to perform transportation tasks during peak hours. f This indicates the train index that needs to be dispatched from the depot to perform transportation tasks during peak hours. f ∈ F ; A Represents the set of arcs in the spatiotemporal state network. The spatiotemporal state network arc index represents the time at which the train... t From point i Departure in pattern w Run and at time s Arrival point j And reset the train operation mode to w’ ; Represents arc The cost; Indicates train Select Arc As the running path under the vehicle; w This indicates the weight of train operating costs in the calculation of arc costs; c 1 This represents the unit energy consumption cost of train operation. c 2 This represents the cost per unit of waiting time for passengers. Represents arc Train operation energy consumption, Represents arc Total travel time for passengers on board.

[0175] Furthermore, the constraints include spatiotemporal network flow balance constraints, operational constraints, passenger service level constraints, and variable constraints.

[0176] Furthermore, the spatiotemporal network flow balance constraints are as follows:

[0177] ;

[0178] in,( j,s , w’ ) represents the vertex index of the spatiotemporal state network. N Represents the set of network nodes in the spatiotemporal state; Indicates train Select Arc As the running path under the vehicle; o This represents the virtual origin station index for all trains departing from the depot. t This represents a uniformly discrete time interval in the planning time dimension. w Indicates the running status of the vehicle's undercarriage; F This indicates the assembly of trains that need to be dispatched from the depot to perform transportation tasks during peak hours. f This indicates the train index that needs to be dispatched from the depot to perform transportation tasks during peak hours.

[0179] Furthermore, the operational constraints are as follows:

[0180] ;

[0181] ;

[0182] in, F This indicates the assembly of trains that need to be dispatched from the depot to perform transportation tasks during peak hours. f This index indicates trains that need to be dispatched from the depot to perform transportation tasks during peak hours. The spatiotemporal state network arc index represents the time at which the train... t From point i Departure in pattern w Run and at time s Arrival point j And reset the train operation mode to w’ ; Indicates train Select Arc As the running path under the vehicle; Representing time in a spatiotemporal state network τ Occupying nodes i Conflicting arc sets In the spatiotemporal state network, the starting point is the vehicle depot. i The arc set; n i Indicates field segment iThe number of vehicles in use; T Represents the set of times. V Represents the set of spatial nodes of the line; D This represents the set of field segments.

[0183] Furthermore, the passenger service level constraints are as follows:

[0184] ;

[0185] in, F This indicates the assembly of trains that need to be dispatched from the depot to perform transportation tasks during peak hours. f This index indicates trains that need to be dispatched from the depot to perform transportation tasks during peak hours. The spatiotemporal state network arc index represents the time at which the train... t From point i Departure in pattern w Run and at time s Arrival point j And reset the train operation mode to w’ ; Indicates train Select Arc As the running path under the vehicle; In a spatiotemporal state network, the starting point is the station node. i The arc set; m i This indicates the minimum number of trains that can stop at a station. Q 1 Indicates the meeting point at the line station. Q 2 This represents the set of line turnaround lines.

[0186] Furthermore, the variable constraints are as follows:

[0187] ;

[0188] in, F This indicates the assembly of trains that need to be dispatched from the depot to perform transportation tasks during peak hours. f This index indicates trains that need to be dispatched from the depot to perform transportation tasks during peak hours. The spatiotemporal state network arc index represents the time at which the train... t From point i Departure in pattern w Run and at time s Arrival point j And reset the train operation mode to w’ ; A Represents the set of arcs in a spatiotemporal state network; Indicates if the train Select Arc The value is 1 when it is part of the vehicle's running path, and 0 otherwise.

[0189] Furthermore, the Lagrange relaxation algorithm is used to transform the train departure route and timetable collaborative optimization model, including:

[0190] The Lagrange relaxation algorithm is employed, and a non-negative train operation safety multiplier is introduced. α i,τ Resource multipliers β i Service level multiplier γ i By relaxing the difficult constraints into the train departure route and timetable co-optimization model, the transformed train departure route and timetable co-optimization model is obtained as follows:

[0191] ;

[0192] spatiotemporal network flow balance constraints and variable constraints;

[0193] ;

[0194] in, T Represents the set of times. V Represents the set of spatial nodes of the line. Q 1 Indicates the meeting point at the line station. Q 2 This represents the set of line turnaround lines. D Represents the set of field segments; Representing time in a spatiotemporal state network τ Occupying nodes i Conflicting arc sets i ∈ V ; In the spatiotemporal state network, the starting point is the vehicle depot. i arc set, i ∈ D ; In a spatiotemporal state network, the starting point is the station node. i arc set, i ∈ Q 1 ; n i Indicates field segment i The number of vehicles in use, m i This indicates the minimum number of trains that stop at a station.

[0195] Furthermore, a dynamic programming algorithm is used to solve the model, including:

[0196] Initialize the train fThe cost of any node on the departure route is And set the predecessor node of any node in the path. Set all Lagrange multipliers to 0, and set the number of Lagrange iterations to 0. q =0;

[0197] The upper and lower bounds of the optimal solution of the transformed model are calculated using the dynamic programming algorithm.

[0198] Obtain the spatiotemporal network of the minimum train departure path in the transformed model, and reconstruct the train departure path sequentially based on the forward nodes of the target node;

[0199] Lagrange multipliers are updated based on the subgradient method;

[0200] If the number of iterations q Greater than the predetermined maximum allowed number of iterations q max If the algorithm fails, it terminates; otherwise, it returns to the previous step. The upper and lower bounds of the optimal solution of the transformed model are calculated using dynamic programming.

[0201] The above embodiments, based on the constructed spatiotemporal state network, aim to minimize passenger travel costs and train operation costs under the constraints. A collaborative optimization model for train departure routes and timetables is built, and the model is transformed using the Lagrange relaxation algorithm. Dynamic programming is then used to solve the model, yielding the optimal train departure routes and timetables. While meeting passenger travel demands during departure periods, the proposed method can obtain a better train departure plan than existing technologies within a reasonable timeframe. Diverse interval operation modes can effectively reduce train operation costs while shortening passenger travel time. This approach can be used to assist actual transportation production and improve the overall quality of train operation plans during departure periods.

[0202] It should be noted that the apparatus provided in the above embodiments is only illustrated by the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. In addition, the apparatus and method embodiments provided in the above embodiments belong to the same concept, and their specific implementation process can be found in the method embodiments, which will not be repeated here.

[0203] Figure 15 This is a block diagram of an electronic device provided as an exemplary embodiment of the present invention. (See diagram below.) Figure 5 As shown, the electronic device includes one or more processors 1510 and memory 1520.

[0204] The processor 1510 may be a central processing unit (CPU) or other form of processing unit with data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions.

[0205] The memory 1520 may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may include, for example, random access memory (RAM) and / or cache memory. The non-volatile memory may include, for example, read-only memory (ROM), hard disk, flash memory, etc. One or more computer program instructions may be stored on the computer-readable storage medium, and the processor 1510 may execute the program instructions to implement the methods for collaboratively optimizing train departure routes and timetables, and / or other desired functions of the software programs of the various embodiments of the present invention described above. In one example, the electronic device may also include an input device 1530 and an output device 1540, these components being interconnected via a bus system and / or other forms of connection mechanisms (not shown).

[0206] In addition, the input device 1530 may also include, for example, a keyboard, a mouse, etc.

[0207] The output device 1540 can output various information to the outside. The output device 1540 may include, for example, a display, a speaker, a printer, and a communication network and its connected remote output devices, etc.

[0208] Of course, for the sake of simplicity, Figure 15 Only some of the components of the electronic device relevant to the present invention are shown, omitting components such as buses, input / output interfaces, etc. In addition, the electronic device may include any other suitable components depending on the specific application.

[0209] In addition to the methods and apparatus described above, embodiments of the present invention may also be computer program products and computer-readable storage media, which include computer program instructions that, when executed by a processor, cause the processor to perform the steps in the methods for collaboratively optimizing train departure routes and timetables according to various embodiments of the present invention described in the "Exemplary Methods" section of this specification.

[0210] The computer program product can be written in any combination of one or more programming languages ​​to perform the operations of the embodiments of the present invention. The programming languages ​​include object-oriented programming languages ​​such as Java and C++, as well as conventional procedural programming languages ​​such as C or similar languages. The program code can be executed entirely on the user's computing device, partially on the user's computing device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server.

[0211] Furthermore, embodiments of the present invention may also be computer-readable storage media storing computer program instructions that, when executed by a processor, cause the processor to perform the steps in the method for collaboratively optimizing train departure routes and timetables according to various embodiments of the present invention, as described in the "Exemplary Methods" section above.

[0212] The computer-readable storage medium may be any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof.

[0213] The basic principles of the present invention have been described above with reference to specific embodiments. However, it should be noted that the advantages, benefits, and effects mentioned in the present invention are merely examples and not limitations, and should not be considered as essential features of each embodiment of the present invention. Furthermore, the specific details disclosed above are for illustrative and facilitative purposes only, and are not limitations. These details do not limit the present invention to the necessity of employing the aforementioned specific details.

[0214] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For system embodiments, since they largely correspond to method embodiments, the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments.

[0215] The block diagrams of devices, apparatuses, devices, and systems involved in this invention are merely illustrative examples and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As those skilled in the art will recognize, these devices, apparatuses, devices, and systems can be connected, arranged, and configured in any manner. Words such as “comprising,” “including,” “having,” etc., are open-ended terms meaning “including but not limited to,” and are used interchangeably with them. The terms “or” and “and” as used herein refer to the terms “and / or,” and are used interchangeably with them unless the context clearly indicates otherwise. The term “such as” as used herein refers to the phrase “such as but not limited to,” and is used interchangeably with it.

[0216] The methods and apparatus of the present invention may be implemented in many ways. For example, they may be implemented by software, hardware, firmware, or any combination of software, hardware, and firmware. The above-described order of steps for the methods is for illustrative purposes only, and the steps of the methods of the present invention are not limited to the order specifically described above unless otherwise specifically stated. Furthermore, in some embodiments, the present invention may also be implemented as a program recorded on a recording medium, the program comprising machine-readable instructions for implementing the methods according to the present invention. Thus, the present invention also covers recording media storing programs for performing the methods according to the present invention.

[0217] It should also be noted that in the apparatus, device, and method of the present invention, the components or steps can be disassembled and / or recombined. These disassemblies and / or recombinations should be considered equivalents of the present invention. The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use the invention. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein can be applied to other aspects without departing from the scope of the invention. Therefore, the invention is not intended to be limited to the aspects shown herein, but rather to be carried out within the widest scope consistent with the principles and novel features disclosed herein.

[0218] The above description has been given for purposes of illustration and description. Furthermore, this description is not intended to limit the embodiments of the invention to the forms disclosed herein. Although numerous exemplary aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations therein.

Claims

1. A method for collaboratively optimizing train departure routes and timetables, characterized in that, The method includes: Construct a spatiotemporal state network to describe the operation of the vehicle undercarriage; Based on the spatiotemporal state network, a train departure path and timetable collaborative optimization model is constructed; wherein the train departure path and timetable collaborative optimization model includes a model that minimizes the spatiotemporal state path cost of the train depot and its corresponding constraints. The Lagrange relaxation algorithm is used to transform the train departure route and timetable collaborative optimization model, and a dynamic programming algorithm is used to solve the model to obtain the optimal train departure route and timetable; the construction of the spatiotemporal state network includes: use Representing a spatiotemporal state network, points Represents physical station In the extension of spatiotemporal state networks, arc Indicates from vertex arrive The effective spatiotemporal state path is defined as follows: where t represents a uniform discrete time interval in the planning time dimension, and w represents the operating state of the vehicle undercarriage; the model for minimizing the spatiotemporal state path cost of the vehicle undercarriage exit is as follows: ； arc The fees are as follows: ； Where F represents the set of trains that need to be dispatched from the depot to perform transportation tasks during peak hours, f represents the index of the train that needs to be dispatched from the depot to perform transportation tasks during peak hours, f∈F; A represents the set of spatiotemporal state network arcs. The spatiotemporal state network arc index indicates that the train departs from point i at time t, runs in mode w, arrives at point j at time s, and resets the train operation mode to w'. Represents arc The cost; Indicates train Select Arc As the running path of the train; w represents the weight of train operating cost in the arc cost calculation; c1 represents the unit energy consumption cost of train operation; c2 represents the unit waiting time cost of passengers. Represents arc Train operation energy consumption, Represents arc The total travel time of passengers on the platform; the constraints include spatiotemporal network flow balance constraints, operational constraints, passenger service level constraints, and variable constraints.

2. The method according to claim 1, characterized in that, The spatiotemporal network flow balance constraints are as follows: ； Where (j,s,w') represents the vertex index of the spatiotemporal state network, and N represents the set of nodes in the spatiotemporal state network; Indicates train Select Arc As the running path of the train set; o represents the virtual starting station index of all trains leaving the depot, t represents the uniform discrete time interval in the planning time dimension, w represents the running status of the train set; F represents the set of trains that need to leave the depot to undertake transportation tasks during peak hours, and f represents the train index that needs to leave the depot to undertake transportation tasks during peak hours.

3. The method according to claim 2, characterized in that, The operational constraints are as follows: ； ； Where F represents the set of trains that need to be dispatched from the depot to undertake transportation tasks during peak hours, and f represents the train index that needs to be dispatched from the depot to undertake transportation tasks during peak hours; The spatiotemporal state network arc index indicates that the train departs from point i at time t, runs in mode w, arrives at point j at time s, and resets the train operation mode to w'. Indicates train Select Arc As the running path under the vehicle; This represents the set of arcs at time τ that conflict with node i in a spatiotemporal state network. This represents the arc set originating from vehicle segment i in the spatiotemporal state network; n i T represents the number of vehicles in operation for section i; V represents the time set; D represents the set of spatial nodes of the line; and D represents the section set.

4. The method according to claim 2, characterized in that, The passenger service level constraints are as follows: ； Where F represents the set of trains that need to be dispatched from the depot to undertake transportation tasks during peak hours, and f represents the train index that needs to be dispatched from the depot to undertake transportation tasks during peak hours; The spatiotemporal state network arc index indicates that the train departs from point i at time t, runs in mode w, arrives at point j at time s, and resets the train operation mode to w'. Indicates train Select Arc As the running path under the vehicle; This represents the set of arcs originating from station node i in a spatiotemporal state network; m i Q1 represents the minimum number of trains that stop at a station; Q2 represents the set of stations on the line and Q1 represents the set of turnaround lines on the line.

5. The method according to claim 4, characterized in that, The variable constraints are as follows: ； Where F represents the set of trains that need to be dispatched from the depot to undertake transportation tasks during peak hours, and f represents the train index that needs to be dispatched from the depot to undertake transportation tasks during peak hours; A represents the spatiotemporal state network arc index, indicating that the train departs from point i at time t, runs in mode w, arrives at point j at time s, and resets the train operation mode to w'; A represents the set of spatiotemporal state network arcs. Indicates if the train Select Arc The value is 1 when it is part of the vehicle's running path, and 0 otherwise.

6. The method according to claim 5, characterized in that, The method of transforming the train departure route and timetable collaborative optimization model using the Lagrange relaxation algorithm includes: The Lagrange relaxation algorithm is employed, and a non-negative train operation safety multiplier α is introduced. i,τ Resource multiplier β i Service level multiplier γ i By relaxing the difficult constraints into the train departure route and timetable co-optimization model, the transformed train departure route and timetable co-optimization model is obtained as follows: ； spatiotemporal network flow balance constraints and variable constraints; ； Where T represents the time set, V represents the line spatial node set, Q1 represents the line station set, Q2 represents the line turnaround set, and D represents the depot set; Represents the set of arcs that conflict with node i at time τ in a spatiotemporal state network, where i∈V; Let D represent the set of arcs starting from vehicle segment i in the spatiotemporal state network; This represents the set of arcs in the spatiotemporal state network whose starting point is station node i, where i∈Q1; n i m represents the number of vehicles in operation in segment i. i This indicates the minimum number of trains that stop at a station.

7. An apparatus for collaboratively optimizing train departure routes and timetables, the apparatus being based on the method of claim 1, characterized in that, The device includes: Spatiotemporal state network construction unit, used to construct a spatiotemporal state network to describe the operation of the vehicle undercarriage; The model building unit is used to build a train departure path and timetable collaborative optimization model based on the spatiotemporal state network; wherein the train departure path and timetable collaborative optimization model includes a model that minimizes the spatiotemporal state path cost of the train depot and its corresponding constraints. The model solving unit is used to transform the train departure route and timetable joint optimization model using the Lagrange relaxation algorithm, and to solve the model using the dynamic programming algorithm to obtain the optimal train departure route and timetable.

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