Train and passenger and freight path collaborative rescheduling method and system based on space-time network

Abstract

The application discloses a train and passenger and freight path cooperative rescheduling method and system based on a space-time network, and relates to the technical field of railway train scheduling.The application constructs a space-time network based on a target railway physical network, and then establishes a cooperative rescheduling model of three sub-problems, and carries out multi-round iteration operation by combining a Lagrange relaxation method, an alternating direction multiplier method, a linearization method and a dynamic programming method to obtain a final cooperative scheduling scheme.The application deeply studies a train rescheduling problem after interruption of a high-speed rail line, considers passenger and freight path reconstruction when the train is redistributed to a stopping track and is arranged to a departure time, provides a reasonably designed and deeply coupled cooperative rescheduling model, and realizes solution of the model.The application can not only provide a fine train path adjustment strategy and a passenger and freight interchange scheme, but also fully considers differences in transport demands of passengers and freight, and improves real applicability of the final cooperative scheduling scheme.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of railway transportation scheduling, and more particularly, to: 1. a train and passenger and freight path collaborative rescheduling method based on a space-time network; and 2. a train and passenger and freight path collaborative rescheduling system based on a space-time network. BACKGROUND

[0002] With the development of high-speed railways, a passenger and freight mixed transport mode has emerged, in which unused transport capacity is used to integrate freight services into passenger train sets. This passenger and freight mixed transport mode not only helps to alleviate the congestion problem of traditional road transport, but also improves the overall utilization rate of railway resources.

[0003] However, the passenger and freight mixed transport mode also brings complex operational challenges, especially in the context of disruption management. For example, in actual operation, high-speed trains often deviate from the original plan due to external factors such as extreme weather, equipment failure, and foreign object intrusion, disrupting the established transport order, and effective disruption management is required to adjust train operation to mitigate the impact of interference. However, under the passenger and freight mixed transport mode, the complexity of disruption management is significantly increased - because the different service needs of passengers and freight must be taken into account while ensuring normal train operation: passengers prioritize punctuality and comfort, while freight emphasizes timeliness and integrity. Any rearrangement must balance these two needs, and focusing on one side may harm the other, making coordination more difficult than single-service operation.

[0004] However, existing railway disruption management research mostly focuses on rescheduling of passenger-only trains or timetable adjustment of passenger and freight mixed railways, and does not address the special challenges of mixed transport on the same train under disruption. Moreover, the collaborative rescheduling of high-speed train operation and passenger and freight paths under disruption is a deeply coupled problem, and the existing conventional solution method cannot be successfully solved.

[0005] To fill this gap, the present application proposes an effective method for collaborative rescheduling of high-speed train operation and passenger and freight paths under disruption. SUMMARY

[0006] Therefore, it is necessary to provide a train and passenger and freight path collaborative rescheduling method and system based on a space-time network to address the lack of an effective method for collaborative rescheduling of high-speed train operation and passenger and freight paths under disruption.

[0007] The present application adopts the following technical solutions:

[0008] In a first aspect, the present application discloses a train and passenger and freight path collaborative rescheduling method based on a space-time network, comprising:

[0009] The target railway physical network is abstracted and transformed into a directed acyclic graph. G ;

[0010] Will G Expanding into a spatiotemporal network G T It is divided into a train spatiotemporal network. G tr Passenger Spatiotemporal Network G pa Cargo Spatiotemporal Network G ca To simulate the movement of trains, passengers, and goods on railways respectively;

[0011] based on G tr , G pa , G ca A collaborative rescheduling model is established, consisting of three sub-problems: train operation adjustment, passenger route selection, and freight route selection. The expression for the collaborative rescheduling model is: min Z ; s . t . R 1~ R 7; In the formula, Z Indicates the total cost of collaboration; R 1 represents the train flow balance constraint; R 2 is a constraint for passenger flow balance; R 3 represents the constraint of cargo flow balance; R 4. Constraints on station capacity and safe operation of sections; R 5. Restrictions on passenger-booked trains; R 6 represents train capacity constraints; R 7 indicates an interruption interval constraint;

[0012] Will G tr , G pa , G ca belong A D Remove or set the spatiotemporal arc to be unselectable to update min. Z ; s . t . R 1~ R 7 is min Z ; s . t . R 1~ R 6; among which, AD represents an infeasible arc set;

[0013] The min Z is solved by combining the Lagrangian relaxation method, the alternating direction multiplier method, the linearization method and the dynamic programming method. s . t . R 1~ R 6 are iterated until the iteration result converges, and the iteration result at this time is taken as the final collaborative scheduling scheme.

[0014] The train and passenger and freight path collaborative rescheduling method based on the space-time network realizes the method or process according to the embodiments of the present disclosure.

[0015] In a second aspect, the present disclosure discloses a train and passenger and freight path collaborative rescheduling system based on a space-time network, which uses the train and passenger and freight path collaborative rescheduling method based on a space-time network disclosed in the first aspect.

[0016] The train and passenger and freight path collaborative rescheduling system based on a space-time network comprises a railway network conversion module, a network construction module, a model construction module and a model solving module.

[0017] The railway network conversion module is used for abstractly converting a target railway physical network into a directed acyclic graph G .

[0018] The network construction module is used for converting G into a space-time network G T , dividing the space-time network into a train space-time network G tr , a passenger space-time network G pa and a freight space-time network G ca to respectively simulate the running process of trains, passengers and freight on the railway.

[0019] The model construction module is used for establishing a collaborative rescheduling model of the three sub-problems based on G tr , G pa , G ca .

[0020] The model solving module is used for solving G tr , G pa , G ca . A Dspatial arc removal or set as unselectable to update min Z ; s . t . R 1~ R 7 is min Z ; s . t . R 1~ R 6; combined with Lagrange relaxation method, alternating direction multiplier method, linearization method, dynamic programming method to min Z ; s . t . R 1~ R 6 are iterated until the iteration result converges, and the iteration result at this time is taken as the final collaborative scheduling scheme.

[0021] The train and passenger and freight path collaborative rescheduling system based on the space-time network realizes the method or process according to the embodiments of the present disclosure.

[0022] In a third aspect, the present disclosure discloses a computer program product comprising a computer program. The computer program, when executed by a processor, implements the steps of the train and passenger and freight path collaborative rescheduling method based on the space-time network disclosed in the first aspect.

[0023] Compared with the prior art, the present disclosure has the following beneficial effects:

[0024] 1、The present disclosure deeply studies the train rescheduling problem after the high-speed rail line interruption, considers the passenger and freight path reconstruction when reallocating the stop station track and arranging the arrival and departure time of the train, thereby providing a reasonably designed and deeply coupled collaborative rescheduling model and realizing the solution thereof, solving the problem that the existing method cannot be solved. The present disclosure not only provides a fine train path adjustment strategy and passenger and freight interchange scheme, but also fully considers the difference in transportation demand between passengers and freight, thereby improving the real applicability of the final collaborative scheduling scheme.

[0025] 2、The present disclosure provides a new solution method for the deeply coupled collaborative rescheduling model. The present disclosure first divides the collaborative rescheduling model into three sub-problems through R 6 relaxation processing, thereby redividing the collaborative rescheduling model into three sub-problems to support multi-round iteration operation. In each round of iteration operation, the train operation adjustment problem is first solved for multiple rounds until there is no conflict between trains, and then the result of the train operation adjustment problem is taken as the basis to solve the passenger path selection problem; and then the results of the train operation adjustment problem and the passenger path selection problem are taken as the basis to solve the freight path selection problem, thereby effectively ensuring the conflict-free nature of the collaborative scheduling scheme.

[0026] 3. The application is in the face of train operation adjustment problem, first, the R4 relaxation augmentation is converted, then the decomposition is carried out by using the alternating direction multiplier method, and then the linearization processing is carried out, so as to obtain the linear shortest path problem of each train to support the direct solution by using the dynamic programming method, and high efficient solution can be realized. BRIEF DESCRIPTION OF DRAWINGS

[0027] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0028] Figure 1 The flow chart of the train and passenger and freight path coordinated rescheduling method based on space-time network provided for the embodiment 1 of the present application;

[0029] Figure 2 The schematic diagram of the target railway physical network provided for the embodiment 1 of the present application;

[0030] Figure 3 The train space-time network diagram constructed based on Figure 2 ;

[0031] Figure 4 The passenger space-time network diagram constructed based on Figure 2 ;

[0032] Figure 5 The freight space-time network diagram constructed based on Figure 2 ;

[0033] Figure 6 The principle diagram of solving the min Z ; s . t . R 1~ R 7 provided for the embodiment 1 of the present application. DETAILED DESCRIPTION

[0034] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the protection scope of the present application.

[0035] It should be understood that when an element is referred to as being "on" another element, it can be directly on the other element or intervening elements can also be present. When an element is referred to as being "connected" to another element, it can be directly connected to the other element or intervening elements can also be present. When an element is referred to as being "fixed" to another element, it can be directly fixed to the other element or intervening elements can also be present.

[0036] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used in the description herein is for describing particular embodiments only and is not intended to be limiting of the application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.

[0037] First of all, if the interruption background is not considered, the passenger and freight mixed transport scene is actually only for the planning of the train, that is, the train runs according to the preset timetable, and the passengers and the freight also take the train according to the preset timetable, which does not involve rescheduling.

[0038] Once the interruption background is considered, as described in the background art, the rescheduling problem of train operation, passenger path and freight path will be generated. Moreover, there are inherent complex relationships between trains, passengers and freight, such as taking into account each other's needs and mutual influence, which causes the difficulty of solving the rescheduling problem to be upgraded.

[0039] The present application deeply studies the train rescheduling problem after the line interruption, considers the problems of reassigning the stopping track of the train and arranging the arrival and departure time of the train when reconstructing the passenger and freight transport paths, and provides a specific and effective solving method, which can not only obtain a fine train path adjustment strategy and a passenger and freight interchange scheme, but also fully considers the difference in transport demand between passengers and freight, and improves the real applicability of the scheme.

[0040] Embodiment 1

[0041] Reference Figure 1 The flowchart of the train and passenger and freight path collaborative rescheduling method based on the space-time network provided for the present embodiment 1 includes the following steps:

[0042] Step one, abstractly converting the target railway physical network into a directed acyclic graph G .

[0043] It should be noted that in the target railway physical network, fixed or moving objects include four categories: stations, trains, passengers, and goods. Their movement paths follow routes inside and outside stations, and their operational logic conforms to the requirements of a directed acyclic graph—no loops and directed. Therefore, the railway physical network can be abstracted and transformed into a directed acyclic graph. G Furthermore, for the sake of simplifying the scenario, G The cases of reverse entry and reverse exit were ignored.

[0044] Specifically, G The expression is: G =( N , L );

[0045] in, N express G The set of nodes in; L express G The set of edges in the array.

[0046] I. Regarding N Generally speaking, they can be divided into four categories according to whether they are fixed or active objects:

[0047] ① Station type:

[0048] make S This refers to a set of stations—which includes a series of stations. s express S The first in s Stations (i.e.) s ∈ S );because s There are several tracks in Ω, making Ω s express s The collection of stock channels at the location ω Represents Ω s The first in ω Track (i.e.) ω ∈Ω s ).

[0049] So, s There are two types of nodes:

[0050] (1) Station nodes, which specifically include: s Inbound node , s Outbound node .

[0051] It should be noted that, due to G The cases of reverse entry and reverse exit are ignored, that is... , They are not interchangeable; that is, if a train needs to enter or exit... sAt that time, it could only be from Entering the station, from Exit the station.

[0052] However, each station is equipped with two entry nodes and two exit nodes: one entry node and one exit node form one entry / exit direction; the other entry node and the other exit node form another opposite entry / exit direction; this still ensures the normal operation of the station.

[0053] (2) Track nodes, which specifically include: entry ω The starting point of the stock market ,leave ω The end of the stock market .

[0054] ② Trains:

[0055] make K This refers to a collection of trains—which includes a series of trains. k express K The first in k trains (i.e.) k ∈ K ).

[0056] So, k There are two types of nodes: k virtual starting point o k (express k (originating position) k virtual endpoint d k (express k (The final destination).

[0057] ③ Passenger category:

[0058] make P It represents a collection of passengers—which includes a series of passengers. p express P The first in p One passenger (i.e.) p ∈ P ).

[0059] So, p There are two types of nodes: p virtual starting point o p (express p (originating position) p virtual endpoint d p (express p (The final destination).

[0060] IV. Goods:

[0061] Let C denote a set of goods, which includes a series of goods, c denote C the c th good in c , i.e. C ∈ .

[0062] Then, c there are two kinds of nodes corresponding to: c the virtual start point o c (representing the departure location of c ), and c the virtual end point d c (representing the arrival location of c ).

[0063] Therefore, N can be written as:

[0064] .

[0065] For the sake of understanding, refer to Figure 2 , which shows a schematic diagram of a railway physical network between 3 stations. Then, for this railway physical network, Figure 2 there are 3 stations S1~S2~S3, which support the uplink direction (S1→S2→S3) and the downlink direction (S3→S2→S1) — two directions use different paths and do not interfere with each other.

[0066] Take S1→S2→S3 as an example: for S1, the entry node is node 1 in Figure 2 and the exit node is node 4 in Figure 2 . S1 has 2 tracks: uplink track 1 and uplink track 2. Then, the track start point of entering uplink track 1 is node 2 in Figure 2 , and the track end point of leaving uplink track 1 is node 3 in Figure 2 ; the track start point of entering uplink track 2 is node 5 in Figure 2 , and the track end point of leaving uplink track 2 is node 6 in Figure 2 . The cases of S2 and S3 are similar to S1 and are not repeated here.

[0067] Take S3→S2→S1 as an example: for S1, the entry node is node 22 in Figure 2 and the exit node is node 21 in Figure 2 . S1 has 2 tracks: downlink track 1 and downlink track 2. Then, the track start point of entering downlink track 1 is node 20 in Figure 2Node 24 in the middle, the end point of the track leaving the downward track 1 is Figure 2 Node 23 in the middle; the starting point of entering the downward channel 2 is Figure 2 Node 26 in the middle, the end point of the track leaving the downward track 2 is Figure 2 Node 25 in the diagram. The cases for S2 and S3 are the same as those for S1, and will not be repeated here.

[0068] II. For L Generally speaking, they can be divided into two categories:

[0069] ① Edges related to the station – These represent the edges between any two nodes that can be directly connected in the actual railway network, including: edges related to entering the station, edges related to leaving the station, and edges related to train stops or passing through the station.

[0070] So, for s The edges associated with it are represented as l in ( s ).

[0071] To aid understanding, let's use... Figure 2 Taking the upward direction as an example:

[0072] For S1, there are 6 edges connecting any two nodes directly: (1→2), (1→5), (3→4), (6→4), (2→3), and (5→6). Among these, the edges related to entering the station are (1→2) and (1→5). The edges related to leaving the station are (3→4) and (6→4). The edges related to train stopping or passing through the station are (2→3) and (5→6). The same applies to S2 and S3, and will not be elaborated further here.

[0073] ② Borders related to the outside of the station – including 3 main categories and 9 types:

[0074] The first category includes edges formed by a train from its virtual origin to the station's entry node (representing a train entering the railway system from the shunting yard); edges formed by a train from the station's exit node to its virtual destination (representing a train entering the shunting yard from the railway system); and edges formed by a train from its virtual origin to its virtual destination (representing train service cancellation).

[0075] The second category includes edges formed by passengers from their virtual origin to the station entry node (representing passengers' entry behavior); edges formed by passengers from the station exit node to their virtual destination (representing passengers' exit behavior); and edges formed by passengers from their virtual origin to their virtual destination (representing passengers' trip cancellation).

[0076] The third category: the edge from the virtual starting point to the station entry node (representing the goods entering the railway system from the warehouse); the edge from the station exit node to the virtual ending point (representing the goods entering the warehouse from the railway system); and the edge from the virtual starting point to the virtual ending point (representing the cancellation of the goods journey).

[0077] In general, for s the edges related to the outside can be represented as l out ( s )。

[0078] Therefore, L can be written as:

[0079] .

[0080] Step two, expand the space-time network G to a space-time network G T , and divide it into train space-time network G tr , passenger space-time network G pa , and goods space-time network G ca to simulate the running process of trains, passengers, and goods on the railway, respectively.

[0081] Since the entire scheduling scenario is related to time, the space-time factor needs to be considered. Then, step two specifically includes:

[0082] S201, add a time dimension to G to obtain T G T ;

[0083] wherein, T ={ η ,2 η ,3 η ,…, n × η}; n represents the total number of time intervals; η represents the basic time interval.

[0084] It should be noted that, η ​The choice of time interval is crucial to the research: smaller time intervals (e.g., 30 seconds to 1 minute) can more accurately capture the dynamic process of trains and scheduling conflicts, but they also significantly increase the model size and computational burden. Larger time intervals (e.g., 5 minutes to 10 minutes), while simplifying model complexity and improving solution efficiency, may not accurately reflect the tight connections and interference characteristics during train operation. Therefore, in Example 1, the time interval is chosen... η =1min.

[0085] So for G any node i ∈ N It can be expanded to include time by adding a time dimension. t Related nodes ( i , t — Indicates that the train (or passengers, or goods) is in t Arrival i .

[0086] Furthermore, due to G It is a directed acyclic entity, so for i ∈ N In other words, it can serve as the starting point of one edge or the ending point of another. i ∈ N There is a corresponding inflow i The edge ( j → i ), outflow i The edge ( i → h It should be noted that... j , h All N The nodes in. And after adding the time dimension, ( j → i ) expands to a spacetime arc ( j , i , t',t )——It is an inflow ( i , t The spacetime arc represents the time it takes for a train (or passenger, or cargo) to travel in space. t' From j Departure, at t Arrival i ;( i → h ) expands to a spacetime arc ( i , h , t,t'' )——It is from ( i , t The outflowing spacetime arc represents the train (or passenger, or cargo) in... t Fromi Departure, at t'' arrival h .

[0087] Such traversal G processing to obtain G T . Then, G T can be written as: G T ( N T , L T ); N T represents the set of space-time nodes in G T ; L T represents the set of space-time arcs in G T .

[0088] S202, according to the target object is divided into G T to obtain G tr , G pa , G ca .

[0089] ①, G tr ( V tr , A tr ); V tr represents the set of space-time nodes related to the train; A tr represents the set of space-time arcs related to the train.

[0090] Specifically, since the train operation in the space-time network depends on the space-time arc, a series of space-time arcs need to be defined to represent k all feasible movements from o k to d k :

[0091] 101, train departure waiting arc : represents the train waiting in the vehicle depot or shunting yard when the train departs late. The running time of the start waiting arc is set as an interval. The train can be described by continuously using multiple departure waiting arcs to describe the continuous waiting process of the train.

[0092] Of course, may be expressed as: .

[0093] 102, Access Arc of Train : indicates the train entering the railway system from the depot or shunting yard.

[0094] Of course, may be expressed as: .

[0095] 103, Inbound Arc of Train : describes the inbound process of the train-connecting the inbound signal of the same station and the starting point of a certain track.

[0096] Of course, may be expressed as: .

[0097] 104, Station Passing Arc of Train : indicates that the station passing arc describes the operation of the train passing through the station directly without stopping, at which time passengers and goods are not allowed to get on and off.

[0098] Of course, may be expressed as: .

[0099] 105, Outbound Arc of Train : describes the outbound process of the train-connecting the end of a certain track of the same station and the exit of the station.

[0100] Of course, may be expressed as: .

[0101] 106, Section Running Arc of Train : indicates the train running between stations.

[0102] Of course, may be expressed as:

[0103] .

[0104] 107, Stopping Arc of Train : indicates that the train stops at the station according to the plan to wait for passengers or goods to get on and off.

[0105] Of course, may be expressed as: .

[0106] It should be noted that, Duration t 1 - t It is determined by the minimum stopping time of the train at that station. The existence of the stopping arc ensures that the train meets the constraint of the minimum stopping time.

[0107] Since the station's passage arc and stopping arc physically represent the same location, they only differ in time on the spatiotemporal network. Therefore... , Use subscripts 1 and 2 to distinguish them.

[0108] 108. Additional stop arc of the train This describes the operation where a train stops at a station for an extended period beyond the planned time.

[0109] certainly, It can be represented as:

[0110] .

[0111] It should be noted that, It is a unit arc. When the train makes an unplanned stop, the appropriate number of arcs is selected based on the corresponding stop time. —— The introduction of this means that the train stops at the station for longer than the planned time.

[0112] 109. Train departure arc This indicates that a train has entered a depot or shunting yard from the railway system.

[0113] certainly, It can be represented as: .

[0114] 110. The waiting arc for the train's final arrival This indicates that the train stops at the depot or shunting yard after arriving at its destination.

[0115] It should be noted that, This is a unit arc with a time interval. In a spatiotemporal network, when a train stops at the terminal for a certain number of minutes, a time interval will be selected. The corresponding number of times.

[0116] certainly, It can be represented as: .

[0117] 111. The virtual path arc of the train : indicates that these trains have been canceled and a virtual path is provided for them, i.e. the train departs from the origin and arrives at the destination on time.

[0118] Of course, can be expressed as: ; In the formula, e k indicates the earliest departure time of k ; l k indicates the latest arrival time of k .

[0119] In summary, A tr The expression of

[0120] .

[0121] Of course, since there is K this train set, then A tr can be used k subset of spatio-temporal arc ; that is, indicates A tr the set of spatio-temporal arcs that can be used in k .

[0122] To assist understanding, taking the uplink direction of Figure 2 as an example, a train spatio-temporal network as shown in Figure 3 is constructed, which is part of G tr , showing part of the nodes and corresponding spatio-temporal arcs.

[0123] ②, G pa ( V pa , A pa ); V pa indicates the set of spatio-temporal nodes related to passengers; A pa indicates the set of spatio-temporal arcs related to passengers.

[0124] A pa Compared with A tr , the arc type is more transfer arc. That is, A pa includes: the passenger's departure waiting arc , the passenger's access arc , the passenger's inbound arc , the passenger's station passing arc , the passenger's outbound arc , the passenger's section running arc , the passenger's stop arc , the passenger's additional stop arc , the passenger's exit arc , the passenger's terminal arrival waiting arc , the passenger's virtual path arc , the passenger's transfer arc .

[0125] That is, A pa The expression of

[0126] .

[0127] Wherein, , , , , , , , , , , The expression of

[0128] For : indicates that the passenger transfers from a track of a station to another track of the same station.

[0129] Of course, Can be expressed as:

[0130] .

[0131] In the formula, ω 1, ω 2 indicates two different tracks in s .

[0132] In addition, similar to A tr , because there is P This passenger set, then A pa The subset p Available spatiotemporal arcs of ; that is, Indicates the set of available spatiotemporal arcs of A pa . p ​

[0133] To assist understanding, take the uplink direction of Figure 2 for example, construct a passenger space-time network as shown in Figure 4 which is part of G , showing some nodes and corresponding space-time arcs. pa

[0134] ③, G ca ( V ca , A ca ); V ca denotes a set of space-time nodes related to goods; A ca denotes a set of space-time arcs related to goods.

[0135] Similar to A pa , A ca compared with A tr , the arc type also has transfer arcs. That is, A ca including: the origin waiting arc of goods , the access arc of goods , the inbound arc of goods , the station passing arc of goods , the outbound arc of goods , the section running arc of goods , the stop station arc of goods , the additional stop station arc of goods , the exit arc of goods , the terminal arrival waiting arc of goods , the virtual path arc of goods , the transfer arc of goods .

[0136] That is, A ca the expression is:

[0137] .

[0138] Among them, , , , , , , , , , , The expression reference ① is not repeated here. The expression reference ② is not repeated here.

[0139] In addition, with A tr , A pa Similarly, due to the existence C of this set of goods, then can be A ca In c the subset of space-time arc available ; that is, represents A ca the set of space-time arc available c

[0140] To assist understanding, in the uplink direction of Figure 2 , a space-time network of goods is constructed as shown in Figure 5 , which is part of G ca , showing some nodes and corresponding space-time arcs.

[0141] Since the subsequent steps involve cost calculation, the corresponding costs need to be set for the different types of space-time arcs described above. The corresponding cost tables are shown in Table 1 and Table 2.

[0142] Table 1 Space-time arc cost related to train

[0143]

[0144] In the table, represents the time cost of additional waiting of the train; r 1 represents the train operation cost per unit time length; t represents the train operation time length; represents the minimum stop time of the train at the station; represents the penalty cost of planned time length.

[0145] Table 2 Space-time arc cost related to passengers and goods

[0146]

[0147] In the formula, δ 1 represents the time cost of additional waiting of the passenger (or goods); r 2 represents the transportation cost per unit time length of the passenger (or goods); δ 2 represents the transfer cost of the passenger; δ 3 represents the transfer cost of the goods.​

[0148] The above Tables 1 and 2 show the costs corresponding to all pairs of space-time arcs.

[0149] Step three, based on G tr , G pa , G ca A collaborative rescheduling model of the three sub-problems is established.

[0150] First of all, it should be noted that the three sub-problems include: I, train operation adjustment problem; II, passenger path selection problem; III, freight path selection problem. Then there are naturally three sub-goals: I, minimizing the total train operation cost; II, minimizing the total passenger travel cost; III, minimizing the total freight transportation cost.

[0151] Therefore, the three sub-problems are considered collaboratively, i.e., the objective function of the collaborative rescheduling model is obtained, which is expressed as:

[0152] ;

[0153] In the formula, Z represents the collaborative total cost; is the weight value; Z tr represents the total train operation cost; Z pa represents the total passenger travel cost; Z ca represents the total freight transportation cost; , , respectively represent the optimal solution of the individual scheduling of the three sub-problems.

[0154] It should be noted that when constructing Z , considering the large number of passengers and freight, then Z pa , Z ca and Z tr have large differences in scale - larger items may dominate the control process, leading to the neglect of other smaller scale items. Therefore, by the normalization of the cost is realized to eliminate the scale difference.

[0155] In this way, referring to the expression of Z above, it contains three parts: train related items, passenger related items, and freight related items. In order to facilitate expression, use a to represent a space-time arc.

[0156] 1. ForZ tr Its expression is:

[0157] ;

[0158] In the formula, express k use a The specific cost is selected based on Table 1; express k use a Possibility: If k use a ,but =1, otherwise =0.

[0159] 2. For Z pa Its expression is:

[0160] ;

[0161] In the formula, express p use a The specific cost is selected based on Table 2; express p use a Possibility: If p use a ,but =1, otherwise =0; n p express p The number of passengers.

[0162] 3. For Z ca Its expression is:

[0163] ;

[0164] In the formula, express c use a The specific cost is selected based on Table 2; express c use a Possibility: If c use a ,but =1, otherwise =0; n c express c The quantity of goods.

[0165] Therefore, for the cooperative rescheduling model, its expression is: min Z ; s . t . R 1~ R 7.

[0166] In the formula, min represents minimization; R 1~ R 7 are the 7 constraints that the collaborative rescheduling model needs to satisfy.

[0167] The following is about R 1~ R 7. Detailed explanation:

[0168] 1) R 1 represents the train flow balance constraint, which aims to ensure that each train has a feasible path from its virtual starting point to its virtual ending point in the spatiotemporal network.

[0169] R The expression for 1 can be written as:

[0170] ;

[0171] In the formula, j , t' :( j , i , t',t ) indicates in ( j , i , t',t Fixed in) i and t traversal j and t' ; h , t'' :( i , h , t,t'' ) indicates in ( i , h , t,t'' Fixed in) i and t traversal h and t'' ; e k express k The earliest departure time; l k express k The latest arrival time.

[0172] 2) R2 is the passenger flow balance constraint, which is to ensure that there is a feasible path from the virtual origin of each passenger to the virtual destination of each passenger in the space-time network.

[0173] R The expression of 2 can be written as:

[0174] ;

[0175] In the expression, e p denotes the earliest departure time of p ; l p denotes the latest arrival time of p .

[0176] 3) R 3 is the freight flow balance constraint, which is to ensure that there is a feasible path from the virtual origin of each freight to the virtual destination of each freight in the space-time network.

[0177] R The expression of 3 can be written as:

[0178] ;

[0179] In the expression, e c denotes the earliest departure time of c ; l c denotes the latest arrival time of c .

[0180] 4) R 4 is the station capacity and section safety operation constraint, which is to ensure the safe operation of trains in sections and stations: for sections, the operation of two adjacent trains in a section must meet certain departure and arrival intervals and overtaking in sections is prohibited; for stations, each station track can only be used by one train at any given time.

[0181] R The expression of 4 can be written as:

[0182] ;

[0183] In the expression, B denotes the set of sub-conflict arcs, denotes the set of conflict arcs.

[0184] It should be noted that, includes two types of conflict arcs: one type is related to the safe operation of sections; the other type is related to the station capacity. B is A subset of B, satisfying that: any B consists entirely of conflict arcs related to safe operation of the interval, or entirely of incompatible arcs related to station capacity.

[0185] 5) R 5. Passenger-reserved train restrictions, which are to ensure k If not cancelled, all reservations among passengers k Passengers will continue to use the train.

[0186] R The expression for 5 can be written as:

[0187] ;

[0188] In the formula, P k Indicates the original plan to take k The passenger assembly.

[0189] It should be noted that, R 5. This may cause significant delays for some passengers, therefore passengers affected by the disruption will be allowed to transfer to other trains if their original train is not cancelled.

[0190] 6) R 6 represents the train capacity constraint, which ensures that the total number of passengers and cargo on a train does not exceed the train's capacity. Additionally, if the train does not select... a Then passengers and goods will also be unable to use it. a .

[0191] R The expression for 6 can be written as:

[0192] ;

[0193] In the formula, α This represents the train's load factor, used to dynamically adjust the upper limit of the train's load factor.

[0194] In the formula, n k express k The capacity; A couple Let be the set of edges that couple trains, passengers, and goods, indicating that the routes of passengers and goods on these spatiotemporal arcs must be consistent with the trains they ride on.

[0195] Right now, A couple The expression is:

[0196] .

[0197] 7) R7 is the interruption interval constraint, which requires that no train, passenger, and freight is allowed to pass through the interruption interval when the interruption occurs.

[0198] R The expression of 7 can be written as:

[0199] ;

[0200] In the expression, A D denotes the set of infeasible arcs. It is noted that, A D The space-time arcs in 7 are related to the interruption interval, and no train, passenger, and freight is allowed to pass through the interruption interval.

[0201] Since the three sub-problems are closely related to min Z ; s . t . R 1~ R 7, we have:

[0202] I. For the train operation adjustment problem, the model is: Z tr ; s . t . R 1~ R 7.

[0203] Since min Z tr ; s . t . R 1~ R 7 is a linearization problem, we can use the CPLEX solver to solve min Z tr ; s . t . R 1~ R 7 to obtain .

[0204] II. For the passenger path selection problem, the model is: Z pa ; s . t . R 1~ R 7.

[0205] Since min Z pa ; s . t . R 1~ R7 is a linear problem, then the CPLEX solver can be used to solve min Z pa ; s . t . R 1~ R 7 to obtain .

[0206] III. For the goods path selection problem, the model is: min Z ca ; s . t . R 1~ R 7.

[0207] Since min Z ca ; s . t . R 1~ R 7 is a linear problem, then the CPLEX solver can be used to solve min Z ca ; s . t . R 1~ R 7 to obtain .

[0208] Step four, the min Z ; s . t . R 1~ R 7 is solved by combining the Lagrangian relaxation method, the alternating direction multiplier method, the linearization method and the dynamic programming method, to obtain the final collaborative rescheduling scheme.

[0209] The final collaborative rescheduling scheme includes: the final train operation scheme, the passenger path scheme, the goods path scheme and corresponding Z .

[0210] Since the station capacity and the interval safe operation constraint involve different trains, the passenger scheduled train constraint involves passengers and trains, and the train capacity constraint involves trains, passengers and goods, the problems are coupled with each other, and are difficult to be decomposed and solved. Therefore, the Lagrangian relaxation method and the alternating direction multiplier method are combined to decouple the problems in step four, which is an important innovation of the present application.

[0211] In general, referring to Figure 6 , step four includes:

[0212] S401, the min G tr ,G pa 、 G ca belongs to A D spatial arc is removed or set as unselectable (i.e. the min G tr 、 G pa 、 G ca ) is updated to update the min Z ; s . t . R 1~ R 7 is min Z ; s . t . R 1~ R 6.

[0213] Through the setting of S401, the train, the passenger and the cargo cannot select the unfeasible arc, so that the min R 7 is satisfied, thereby realizing the elimination of the min R 7.

[0214] S402, in combination with the Lagrange relaxation method, the alternating direction multiplier method, the linearization method and the dynamic programming method, performs a multi-round iteration operation on the min Z ; s . t . R 1~ R 6 until the iteration result converges, and takes the iteration result at this time as the final collaborative scheduling scheme.

[0215] Specifically, the process of each round of iteration operation is as follows:

[0216] S4021, introduces R6 into the min Z by the Lagrange relaxation method to realize relaxation, and updates the min Z ; s . t . R 1~ R 6 is min ; wherein, denotes the updated collaborative total cost.

[0217] Specifically, the expression of the min is as follows:

[0218] ;

[0219] In the formula, ω 2( a ) denotes the corresponding Rthe Lagrange multiplier of 6, which is adjustable.

[0220] Thus, by R 6, the three sub-problems are decoupled to some extent.

[0221] S4022, the updated model is decomposed into three sub-problems.

[0222] After the processing of S4021, the three sub-problems can be decomposed into three relatively independent models: the updated model of the train operation adjustment problem, the updated model of the passenger path selection problem, and the updated model of the freight path selection problem.

[0223] Specifically:

[0224] 1. The updated model of the train operation adjustment problem is:

[0225] ;

[0226] In the formula, denotes the updated total train operation cost.

[0227] wherein, the expression of is:

[0228] ;

[0229] In the formula, denotes the fixed value of the freight decision variable; denotes the fixed value of the passenger decision variable.

[0230] 2. The updated model of the passenger path selection problem is:

[0231] ;

[0232] In the formula, denotes the updated total passenger travel cost.

[0233] wherein, the expression of is:

[0234] ;

[0235] In the formula, denotes the fixed value of the freight decision variable; denotes the fixed value of the train decision variable.

[0236] 3. The updated model of the freight path selection problem is:

[0237] ;

[0238] In the formula, represents the updated total freight transportation cost.

[0239] wherein, the expression of is:

[0240] ;

[0241] In the formula, represents a fixed value of the passenger decision variable; represents a fixed value of the train decision variable.

[0242] After the model decomposition and update of the three sub-problems are realized through S4022, the next step is to solve.

[0243] Since train operation is the basis of passenger travel and freight transportation, and the priority of passenger travel is higher than that of freight transportation in the passenger-freight mixed operation mode, the solution has mutual order: first solve , then solve , and finally solve . In this way, the feasibility and efficiency of the overall scheme can be ensured.

[0244] S4023, multiple rounds of are solved until there is no conflict between trains, i.e., the train operation scheme of this round of iteration is obtained.

[0245] Overall, S4023 includes:

[0246] First, the is converted into an enhanced Lagrangian relaxation model of R 4 through 4 relaxation augmentation transformation , and then the is decomposed to obtain the nonlinear problem of each train using the alternating direction multiplier method, followed by linearization to convert each nonlinear problem into a simpler linear form to obtain the shortest path problem of each train (there are shortest path problems of trains, representing the total number of trains in ), and then the dynamic programming method is used to solve each train's shortest path problem to obtain the current train operation scheme; K If there is a train conflict in the current train operation scheme, return to S4023 and adjust

[0247] to re-solve; otherwise, the current train operation scheme is taken as the train operation scheme of this round of iteration, and S4024 is performed. In S4023,

[0248] the conversion method includes: ​

[0249] Let R 4be introduced by Lagrangian relaxation method in order to realize relaxation and get the Lagrangian relaxation model of ; then introduce the relaxation variable u a Let R 4be converted into equality constraints R' 4, then based on R' 4build the quadratic penalty term and add it into to get .

[0250] Wherein, the expression of

[0251] ;

[0252] In the formula, f LR indicates the objective function of ; 1( ω ) indicates the Lagrange multiplier corresponding to B 4, which is adjustable. R

[0253] R' The expression of 4is: .

[0254] The quadratic penalty term is: ; μ indicates the quadratic penalty term coefficient, the value of which is adjustable to make the quadratic penalty term also adjustable.

[0255] The expression of

[0256] ;

[0257] In the formula, f ALR indicates the objective function of .

[0258] For , it is nonlinear and cannot be directly separated. The alternating direction multiplier method is suitable for processing it: it removes the constant term in which does not affect (that is, ), and then decomposes into a nonlinear problem. Next, by linearizing each nonlinear problem, the shortest path problem of each train is obtained. At this point, the shortest path problem of each train has the condition of independent solution, and can be solved efficiently by using dynamic programming method.

[0259] wherein, k the shortest path problem of each train can be expressed as:

[0260] ;

[0261] wherein, represents the running cost of k; represents the correction cost term of k ; Q 1 is a constant term.

[0262] It should be noted that for the current train running scheme solved, it is still necessary to consider whether there is a conflict between trains - if there is a conflict, return to S4023, and adjust (adjustable ω 1( B ) or / and μ to achieve) to perform a new round of solution; otherwise, no need to loop, i.e. the train running scheme of this round of iteration is obtained.

[0263] S4024, first simplify into the shortest path problem of each passenger; then solve the shortest path problem of each passenger based on the train running scheme of this round of iteration by using dynamic programming method to obtain the passenger path scheme of this round of iteration.

[0264] The difference between S4024 and S4023 is that S4024 does not need to be solved in multiple rounds, but is directly solved by using dynamic programming method based on the train running scheme of this round of iteration after simplification.

[0265] Specifically, the method for simplifying includes:

[0266] remove the constant term (i.e. ) in , and introduce a seat reservation restriction coefficient ξ a to ignore R 5, so as to convert and decompose it into the shortest path problem of each passenger (a total of shortest path problems of passengers, denotes the total number of passengers in P ).

[0267] wherein, pThe shortest path problem can be represented as:

[0268] ;

[0269] In the formula, express p Travel costs; express p The adjusted cost item.

[0270] It is important to note that ξ a Satisfy: 0≤ ξ a ≤1, which simulates passengers' preferences for their originally booked trains in the seat reservation system, reflects passengers' tendency to avoid temporary transfers in the event of traffic disruption.

[0271] S4025, first... The problem is simplified into a shortest path problem for each cargo. Then, dynamic programming is used to solve the shortest path problem for each cargo based on the train operation plan and passenger route plan of the current iteration, so as to obtain the cargo route plan for the current iteration.

[0272] The difference between S4025 and S4023 is that S4025 does not require multiple rounds of solution. Instead, after simplification, it directly uses dynamic programming to solve the train operation scheme and passenger route scheme of the current iteration.

[0273] Specifically, for Methods for simplifying the process include:

[0274] Remove The constant term in (i.e.) (soon) Transform and decompose it into the shortest path problem for each item (total) The shortest path problem for a quantity of goods. express C (Total quantity of goods in China).

[0275] So, c The shortest path problem can be represented as:

[0276] ;

[0277] In the formula, express c Transportation costs; express c The adjusted cost item.

[0278] This yields the train operation plan, passenger route plan, and freight route plan for this iteration, which are then substituted into... Z The total collaborative cost value corresponding to this iteration is obtained—these are all considered as the results of this iteration.

[0279] S4026, If the iteration result converges, then the iteration result at this point is taken as the final cooperative scheduling scheme; otherwise, return to S4021 and adjust... (Can be adjusted) ω 2( a This will enable a new round of iterations.

[0280] After passing through S401~S402, the final train operation plan, passenger route plan, and freight route plan were obtained, and then substituted into... Z The corresponding total cost of coordination can be obtained from the expression, and the coordinated rescheduling is thus completed.

[0281] In summary, this invention provides a specific and feasible solution to the problem of coordinated rescheduling of high-speed train operation and passenger and freight routes under interruption background. On the one hand, it achieves a breakthrough from being difficult to solve to being easily solved. On the other hand, the entire method process takes less time (generally around 300 seconds), which can be considered as achieving efficient solution in a short time.

[0282] Example 2

[0283] This embodiment 2 provides a train and passenger / freight route collaborative rescheduling system based on a spatiotemporal network, which uses the train and passenger / freight route collaborative rescheduling method based on a spatiotemporal network provided in embodiment 1.

[0284] The train and passenger / freight route collaborative rescheduling system based on spatiotemporal networks includes: a railway network conversion module, a network construction module, a model construction module, and a model solving module.

[0285] The railway network conversion module is used to: abstract the target railway physical network into a directed acyclic graph. G .

[0286] The network building module is used to: G Expanding into a spatiotemporal network G T It is divided into a train spatiotemporal network. G tr Passenger Spatiotemporal Network G pa Cargo Spatiotemporal Network G ca This simulates the movement of trains, passengers, and goods on railways.

[0287] The model building module is used for: based onG tr 、 G pa 、 G ca The three sub-problems are cooperatively rescheduled.

[0288] The model solving module is configured to: G tr 、 G pa 、 G ca The space-time arcs belonging to the set of A D are removed or set as unselectable to update the min Z ; s . t . R 1~ R 7 is the min Z ; s . t . R 1~ R 6; the min Z ; s . t . R 1~ R 6 is iterated multiple rounds until the iteration result converges, and the iteration result at this time is taken as the final cooperative scheduling scheme.

[0289] Since the system uses the train and passenger and freight path cooperative rescheduling method based on the space-time network in Embodiment 1, it also has the same effect, which is not repeated here.

[0290] Embodiment 3

[0291] Embodiment 3 discloses a computer device comprising a memory and a processor, the memory storing a computer program, and the processor implementing the steps of the train and passenger and freight path cooperative rescheduling method based on the space-time network disclosed in Embodiment 1 when executing the computer program.

[0292] Embodiment 3 also discloses a readable storage medium, which stores computer program instructions. When the computer program instructions are read and run by a processor, the steps of the train and passenger and freight path cooperative rescheduling method based on the space-time network disclosed in Embodiment 1 are executed.

[0293] Embodiment 3 also discloses a computer program product comprising a computer program. When the computer program is executed by a processor, the steps of the train and passenger and freight path cooperative rescheduling method based on the space-time network disclosed in Embodiment 1 are implemented.

[0294] The above embodiments only express several implementation manners of the present application, which are described in a more specific and detailed manner, but cannot be understood as a limitation on the patent scope of the present application. It should be noted that, for ordinary skilled persons in the art, several modifications and improvements can be made without departing from the concept of the present application, which all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application should be subject to the appended claims.

Claims

1. A train and passenger and freight path collaborative rescheduling method based on a space-time network, characterized in that, Comprise: Converting target railway physical network abstraction into a directed acyclic graph G ; wherein, G The expression of G ( N , L ) ; N denotes a set of nodes in G ; L denotes a set of edges in G ; wherein N The expression for ; wherein S denotes a set of stations; s denotes S the i-th station in s Ω s denotes s a set of tracks at ω denotes the i-th track in s Ω ω denotes an inbound node of s ; denotes an outbound node of s ; denotes a track start into ω ; denotes a track end out of ω ; K denotes a set of trains; k denotes K the i-th train in k ; o k denotes a virtual start of k ; d k denotes a virtual end of k ; P denotes a set of passengers; p denotes P the i-th passenger in p ; o p denotes a virtual start of p ; d p denotes a virtual end of p ; C denotes a set of goods; c denotes C the i-th good in c ; o c denotes a virtual start of c ; d c denotes a virtual end of c ;​ wherein L The expression for is: ； In the formula, l in ( s ) represents the edge related to s inside; l out ( s ) represents the edge related to s outside; and G is extended to a space-time network G T , which is divided into train space-time network G tr , passenger space-time network G pa , and freight space-time network G ca to simulate the running process of trains, passengers, and freight on the railway, respectively. wherein G tr , G pa , G ca the construction method comprising: S201, to G add a time dimension T to obtain G T ; wherein T ={ η ,2 η ,3 η ,…, n × η}; n denotes the total number of time intervals; η denotes the basic time interval; G T =( N T , L T ); N T representing G T a set of spatio-temporal nodes in L T representing G T a set of spatio-temporal arcs in S202, according to the target object G T carrying out division to obtain G tr , G pa , G ca ; wherein G tr ( V tr , A tr ), G pa ( V pa , A pa ), G ca ( V ca , A ca ) ; In the formula, V tr denotes a set of space-time nodes related to the train; A tr denotes a set of space-time arcs related to the train; V pa denotes a set of space-time nodes related to the passenger; A pa denotes a set of space-time arcs related to the passenger; V ca denotes a set of space-time nodes related to the goods; A ca denotes a set of space-time arcs related to the goods; Based on G tr , G pa , G ca A collaborative rescheduling model of three sub-problems is established; wherein, the three sub-problems include: train operation adjustment problem, passenger path selection problem, and freight path selection problem; the expression of the collaborative rescheduling model is: min Z ; s . t . R 1~ R 7; in the formula, Z denotes collaborative total cost; R 1 is train flow balance constraint; R 2 is passenger flow balance constraint; R 3 is freight flow balance constraint; R 4 is station capacity and section safe operation constraint; R 5 is passenger scheduled train constraint; R 6 is train capacity constraint; R 7 denotes interrupted section constraint; Z The expression is: ； In the formula, is a weight value; Z tr represents the total train operation cost; Z pa represents the total passenger travel cost; Z ca represents the total freight transport cost; respectively represent the optimal solution of the individual scheduling of the three sub-problems; represents A tr in the formula k a set of space-time arcs available; represents A pa in the formula p a set of space-time arcs available; represents A ca in the formula c a set of space-time arcs available; a characterizes a space-time arc; represents k the cost of using a ; represents k the possibility of using a ; represents p the cost of using a ; represents p the possibility of using a ; n p represents p the number of passengers; represents c the cost of using a ; represents c the possibility of using a ; n c represents c the number of goods;​​ Will G tr , G pa , G ca belong A D Remove or set the spatiotemporal arc to be unselectable to update min. Z ; s . t . R 1~ R 7 is min Z ; s . t . R 1~ R 6; among which, A D Represent the set of infeasible arcs; The min Z ; s . t . R 1~ R 6 are iterated until the iteration result converges, and the iteration result at this time is taken as the final cooperative scheduling scheme. Wherein, the method of each round of iterative operation comprises: S4021, to R 6min is introduced by Lagrangian relaxation method Z in order to realize relaxation, and min is updated Z ; s . t . R 1~ R 6is ; wherein, denotes the updated total cost of cooperation; S4022, to updating the model decomposed into three sub-problems; Wherein, the updated model of the train operation adjustment problem is: ； In the formula, denotes the updated total train operation cost; The updated model of the passenger path selection problem is: ； In the formula, represents the updated total passenger trip cost; The updated model of the freight path selection problem is: ； In the formula, denotes the updated total freight transportation cost; S4023, to perform multiple rounds of solving until there is no conflict between trains, i.e., obtain the train operation scheme of this round of iteration; S4024, first... The problem is simplified to the shortest path problem for each passenger. Then, dynamic programming is used to solve the shortest path problem for each passenger based on the train operation plan of this iteration, so as to obtain the passenger path plan for this iteration. S4025, first... The problem is simplified into a shortest path problem for each cargo. Then, dynamic programming is used to solve the shortest path problem for each cargo based on the train operation plan and passenger route plan of the current iteration, so as to obtain the cargo route plan for the current iteration. S4026, if the iteration result converges, the iteration result at this time is taken as the final cooperative scheduling scheme; otherwise, return to S4021, and adjust and a new round of iteration is thus performed.

2. The space-time network based train and passenger-freight path coordinated rescheduling method according to claim 1, characterized in that, The model of the train operation adjustment problem is min Z tr ; s . t . R 1~ R 7; The calculation method comprises the following steps: solving min Z tr ; s . t . R 1~ R 7 by using a CPLEX solver to obtain ; The model of the passenger route selection problem is: min Z pa ; s . t . R 1~ R 7; The calculation method of the min Z pa ; s . t . R 1~ R 7 includes: solving the min by using a CPLEX solver to obtain The model of the cargo path selection problem is: min Z ca ; s . t . R 1~ R 7; The calculation method of the min Z ca ; s . t . R 1~ R 7 is solved by using a CPLEX solver to obtain .

3. The space-time network based train and passenger-freight path coordinated rescheduling method according to claim 1, characterized in that, S4023 comprises: Firstly By solving R 4 Relaxation augmented transformation into Enhanced Lagrangian relaxation model , and then using the alternating direction multiplier method to decompose to get each train nonlinear problem, then using linearization method to convert each nonlinear problem into a simpler linear form to get each train shortest path problem, and then using dynamic programming method to solve each train shortest path problem to get the current train operation scheme; If there is a train conflict in the current train operation scheme, return to S4023 and adjust to re-solve; otherwise, take the current train operation scheme as the train operation scheme of this round of iteration, and proceed to S4024.

4. The train and passenger and freight path coordinated rescheduling method based on space-time network according to claim 3, characterized in that, In S4023, The conversion methods include: will be introduced into R 4 by Lagrangian relaxation method in order to realize relaxation and obtain the Lagrangian relaxation model of ; then the relaxation variable u a will be converted into equality constraints R 4 R' 4, and then the quadratic penalty term R' 4 is constructed based on and added into to obtain or / and, in S405, to The method of simplifying processing includes: remove the constant term in the equation ξ a ignoring R 5, so as to convert and decompose into a shortest path problem for each passenger or / and, S406, to The method of simplifying processing includes: remove the constant term, i.e., to convert and decompose into a shortest path problem for each cargo.

5. A train and passenger and freight path collaborative rescheduling system based on a space-time network, characterized in that, It uses the train and passenger and freight path collaborative rescheduling method based on a space-time network as claimed in any one of claims 1-4; The train and passenger and freight path collaborative rescheduling system based on a space-time network comprises: A railway network conversion module for converting a target railway physical network abstraction into a directed acyclic graph G ; a network construction module, configured to: G expand into a space-time network G T , and divide into a train space-time network G tr , a passenger space-time network G pa , and a cargo space-time network G ca to respectively simulate the running process of the train, the passenger, and the cargo on the railway. a model construction module, configured to: construct a model based on the three sub-problems G tr , G pa , G ca establish a cooperative rescheduling model of the three sub-problems; and a model solving module, configured to: G tr , G pa , G ca spatial and temporal arcs belonging to A D are removed or set as unselectable, to update min Z ; s . t . R 1~ R 7 is min Z ; s . t . R 1~ R 6; in combination with Lagrange relaxation method, alternating direction multiplier method, linearization method, dynamic programming method, min Z ; s . t . R 1~ R 6 is subjected to multiple rounds of iterative operation until the iterative result converges, and the iterative result at this time is taken as the final collaborative scheduling scheme.

6. A computer program product, characterised in that, It comprises a computer program; when the computer program is executed by a processor, the steps of the train and passenger and freight path collaborative rescheduling method based on a space-time network as claimed in any one of claims 1-4 are realized.

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