CN114757011A - Method for establishing train operation adjustment model based on space-time network - Google Patents

Method for establishing train operation adjustment model based on space-time network Download PDF

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CN114757011A
CN114757011A CN202210199142.XA CN202210199142A CN114757011A CN 114757011 A CN114757011 A CN 114757011A CN 202210199142 A CN202210199142 A CN 202210199142A CN 114757011 A CN114757011 A CN 114757011A
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CN114757011B (en
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占曙光
石佳娜
戴延泽
修琮
潘槿仪
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Hefei University of Technology
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Abstract

The invention relates to the technical field of train scheduling, in particular to a method for establishing a train operation adjustment model based on a space-time network, which comprises the following steps: (1) constructing a train time-space network to simulate the train running process; (2) constructing a resource space-time network to model space and time resource capacity; (3) and constructing a train adjustment model based on the resource space-time network and the train space-time network. The invention solves the problem of train operation adjustment by balancing and coordinating the space-time resource capacity distribution of different types of railway resources among different types of trains from the perspective of resource guidance.

Description

Method for establishing train operation adjustment model based on space-time network
Technical Field
The invention relates to the technical field of train scheduling, in particular to a method for establishing a train operation adjustment model based on a space-time network.
Background
In a resource contention system, many individuals compete for limited resources. It is important to determine how to allocate these limited resources to individuals in both the spatial and temporal dimensions in order to maximize the profits of all individuals. In practice, many planning, scheduling and control issues may be considered as resource allocation issues, such as transportation planning, machine scheduling, project scheduling, traffic control and information transmission. The key task of such problems is to effectively balance and coordinate the allocation of time and space resources between competitors to achieve a balance between the two parties. It is clear that the available resource capacity is variable and closely related to the resource allocation pattern. For example, if all cars or trains in a transportation system rush into a bottleneck area, the resulting traffic congestion will likely prevent all cars or trains from continuing to operate.
As is well known, few previous studies have explicitly considered the importance of coordinating limited resource capacity in terms of space and time at different supply and demand levels. Furthermore, most studies assume that the capacity of the railway network is constant and the railway capacity is modeled by intervals in road sections or running interval constraints on tracks in stations. The inherent variability of rail capacity is rarely considered. There is therefore a need for a train adjustment model based on spatio-temporal networks.
Disclosure of Invention
The present invention is directed to a method for building a train operation adjustment model based on a spatio-temporal network that overcomes one or more of the deficiencies of the prior art.
The method for establishing the train operation adjustment model based on the spatio-temporal network comprises the following steps:
(1) constructing a train time-space network to simulate the train running process;
(2) constructing a resource space-time network to model space and time resource capacity;
(3) and constructing a train operation adjustment model based on the resource space-time network and the train space-time network.
Preferably, in step (1), in the train space-time network TSTN, the time range may be represented as T ═ δ,2 δ,3 δ,. θ δ }, where θ is the maximum time interval number; the physical node i ∈ N may be extended to a time-dependent node (i, t) ∈ EtrainThe physical link (i, j) e L can be extended to a spatio-temporal arc (i, j, t, t') e Atrain(ii) a The time expansion arc indicates that the train starts from the node i at the time t and arrives at the node j at the time t'; TSTN may be represented by Gtrain＝(Etrain,Atrain)；
The station has an entrance node and an exit node, each track has a start node and an end node, respectively, the train is started from the start point (o)k) Run to endpoint (d)k) A number of different types of arcs are used, as follows:
starting arc with a starting point of
Figure BDA0003528526060000021
The final point is
Figure BDA0003528526060000022
The duration is delta;
entry arc starting point of
Figure BDA0003528526060000023
The final point is
Figure BDA0003528526060000024
Duration of (t' -t) ═ TDacc；
The starting point of the station-entering arc is
Figure BDA0003528526060000025
The final point is
Figure BDA0003528526060000026
Duration of (t' -t) ═ TDent；
Through an arc with a starting point of
Figure BDA0003528526060000027
The final point is
Figure BDA0003528526060000028
Duration of (t' -t) ═ TDpas；
Arc of stopping station with starting point of
Figure BDA0003528526060000029
The final point is
Figure BDA00035285260600000210
Duration of (t' -t) ═ TDdwe；
Starting point of extra waiting arc is
Figure BDA00035285260600000211
The final point is
Figure BDA00035285260600000212
The duration is delta;
the starting point of the outbound arc is
Figure BDA00035285260600000213
The final point is
Figure BDA00035285260600000214
Duration of (t' -t) ═ TDlea；
Arc running: the starting point is
Figure BDA00035285260600000215
The final point is
Figure BDA00035285260600000216
Duration of (t' -t) ═ TDdri；
An outlet arc: the starting point is
Figure BDA00035285260600000217
The final point is
Figure BDA00035285260600000218
Duration of (t' -t) ═ TDegr；
End point arc: starting point is
Figure BDA00035285260600000219
The final point is
Figure BDA00035285260600000220
The duration is delta;
virtual arc: the starting point is
Figure BDA00035285260600000221
The final point is
Figure BDA00035285260600000222
Duration of lk-ek；
Figure BDA00035285260600000223
Is a subset of the nodes of the starting point,
Figure BDA00035285260600000224
is a subset of the destination node(s),
Figure BDA00035285260600000225
is a subset of the ingress node or nodes,
Figure BDA00035285260600000226
is a subset of the starting nodes and,
Figure BDA00035285260600000227
is the end node subset and is,
Figure BDA00035285260600000228
is a subset of egress nodes; parameter TDacc，TDent，TDpas，TDdwe，TDlea，TDdriAnd TDegrIs the desired duration of the corresponding type of arc.
Preferably, in the resource spatio-temporal network, the train spatio-temporal arcs (i, j, t, t ') need to be mapped to the resource spatio-temporal arcs (m, n, τ) in the resource spatio-temporal network RSTN, for each spatio-temporal arc (i, j, t, t') e a of train operationtrainIf the link (i, j) is contained in a resource segment (m, n) and t is contained in a time interval τ, then use the arc (i, j, t, t') ∈ H (m, n, τ); i.e. the train running arc (i, j, t, t') is contained in the track resource space-time segment (m, n, τ).
Preferably, the train operation adjustment model is as follows:
in the objective function, the total utility of all types of trains is maximized, as shown in equation (1):
Max:∑k∈KU(k) (1)
to minimize the total train travel time and total train arrival delay at each station, therefore, the function u (k) is given by equation (2):
Figure BDA00035285260600000229
wherein the first summation is the total travel cost of the train k, and the second summation is the total arrival delay cost of the train k at each passing station s;
on the premise that the following objectives are met:
1) the conservation of train flow constraint (3) is as follows:
Figure BDA0003528526060000031
2) the running interval constraint (4) is as follows:
Figure BDA0003528526060000032
the constraint (4) is the operation interval constraint between any two high-speed trains or medium-speed trains; the constraint can be further modified to a constraint (5) according to the train type, as follows:
Figure BDA0003528526060000033
the running interval constraint between any two trains of the same type can be considered in the constraint (5); the running intervals among the trains of different types can be managed by sequentially adjusting the trains of different types, so that the arcs which are conflicted with the arcs occupied by the trains of the former type cannot be occupied by the trains of the latter type;
3) the resource capacity constraint for one RSTN of trains of type pi and resource r in time interval τ in a section (m, n) is represented by equation (6) as follows:
Figure BDA0003528526060000034
wherein (i, j, t, t ') is ∈ H (m, n, τ) connecting the train spatio-temporal arc (i, j, t, t') in TSTN and the resource spatio-temporal arc (m, n, τ) in RSTN;
equation (6) indicates that the total number of trains of type pi running in the resource section (m, n) in the time interval tau cannot exceed the resource allocated to the train of type pi by the resource r in the time interval tau; the left side of the equation (6) sums the total number of trains of pi type using the resource link (m, n) of the resource type r; the right side of equation (6) allocates the capacity of resource r in link (m, n) in time τ;
4) train regulatory variable field
Figure BDA0003528526060000035
In TSTN as shown in formula (7):
Figure BDA0003528526060000036
5) the shared resource capacity constraint in RSTN is represented by resources shared by various types of trains and cannot exceed available capacity; this is represented by equation (8), as follows:
Figure BDA0003528526060000037
6) the domain of the resource allocation variable is represented by equation (9):
Figure BDA0003528526060000041
in equation (1), the utility of all trains operating from the start point to the end point is maximized; formula (2) is trainDefining a k utility function; equation (3) is the traffic balance constraint for each train K ∈ K in TSTN, which ensures that each train runs from the start to the end; equation (5) is the running interval constraint between trains of the same type; equation (6) is the resource capacity constraints for each resource type in each resource segment for the same type of train, these constraints ensuring that all trains of a particular type that use time-dependent resource arcs in the RSTN cannot exceed the total capacity of the resource arcs allocated to that type of train; equation (7) represents a train track variable
Figure BDA0003528526060000042
A range of (a); equation (8) ensures that the capacity of the resource R e R used by all types of trains cannot exceed the total capacity; equation (9) shows the resource allocation variables in different types of trains
Figure BDA0003528526060000043
In which
Figure BDA0003528526060000044
Is the number of trains of type pi using the resource r in the time interval τ segment (m, n).
The invention solves the problem of train operation adjustment by balancing and coordinating the space-time resource capacity distribution of different types of railway resources among different types of trains from the perspective of resource guidance. Importantly, this allows the dispatcher's experience to be easily embedded into the resource allocation phase to increase computational efficiency, thereby ensuring that the feasibility of the resulting solution is more comparable to that of previously used price-oriented methods.
Drawings
FIG. 1 is a flowchart of a method for establishing a model for adjusting train operation based on a spatio-temporal network according to embodiment 1;
fig. 2 is a schematic node division diagram of a small railway line including two stations in embodiment 1;
FIG. 3 is a schematic diagram of the division of track resource sections of small and medium-sized railway lines in embodiment 1;
fig. 4 is a schematic diagram of power section division of a small and medium-sized railway line in embodiment 1.
Detailed Description
For a further understanding of the invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples. It is to be understood that the examples are illustrative of the invention and not restrictive.
Example 1
As shown in fig. 1, the embodiment provides a method for establishing a train operation adjustment model based on a spatio-temporal network, which includes the following steps:
(1) constructing a train time-space network to simulate the train running process;
(2) constructing a resource space-time network to model space and time resource capacity;
(3) and constructing a train operation adjustment model based on the resource space-time network and the train space-time network.
(symbol)
The symbols used in the model are given in table 1.
Symbols used in the model of Table 1
Figure BDA0003528526060000051
Figure BDA0003528526060000061
Spatio-temporal networks
Train operation and regulatory issues can be modeled based on a spatiotemporal network, which has been widely used in many previous studies. The time-indexed model helps to eliminate large "M" constraints that would otherwise increase the difficulty of obtaining tight linear relaxation in the traditional Mixed Integer Linear Programming (MILP) model. Furthermore, the time index model has a more decomposition-appropriate structure. The present embodiment uses a spatio-temporal network based formulation, using two types of spatio-temporal networks: TSTN and RSTN.
1. Train space-time network (TSTN)
In spatiotemporal networks, the time is discrete into small time intervals, the time intervals beingThe length of δ may be 1s or 1 min. The time range may be denoted as T ═ δ,2 δ,3 δ,. θ δ }, where θ is the maximum number of time intervals. The physical node i ∈ N may be extended to a time-dependent node (i, t) ∈ EtrainThe physical link (i, j) e L can be extended to a spatio-temporal arc (i, j, t, t') e Atrain. This time-spreading arc represents the train departing from node i at time t and arriving at node j at time t'. TSTN may be represented as Gtrain＝(Etrain,Atrain). In most previous studies, the physical nodes were stations and the physical edges were track sections connecting two consecutive stations. However, in this embodiment, it is desirable to investigate the train adjustment problem in more detail, especially in the station area. Therefore, we consider a station as being composed of a plurality of train operation nodes in one direction, i.e., the station has an entrance node and an exit node, and each track also has a start node and an end node. For example, for S in FIG. 21Station runs to S2Train of stations, S1There are two tracks consisting of six nodes, S2There are three tracks consisting of eight nodes.
According to the node division in fig. 2, a train is started from a starting point (o)k) Run to endpoint (d)k) A number of different types of arcs must be used. To better distinguish between different types of spatio-temporal arcs, several subsets are further defined for the nodes.
Figure BDA0003528526060000062
Is a subset of the nodes of the starting point,
Figure BDA0003528526060000063
is a subset of the destination node(s),
Figure BDA0003528526060000064
is a subset of the ingress node(s),
Figure BDA0003528526060000065
is a subset of the starting nodes and,
Figure BDA0003528526060000066
is a subset of the end nodes and,
Figure BDA0003528526060000067
is a subset of egress nodes. These arcs are described in table 2.
TABLE 2 train space-time arc
Figure BDA0003528526060000071
Note that the start-waiting arc, the extra-waiting arc, and the end-waiting arc are all unit arcs. That is, the duration of the arc is one time unit (δ). If the time that the train waits at the start point, station or destination exceeds one unit, several consecutive arcs are used to represent the waiting process. Further, if the train is cancelled due to an interruption, assume that the train is traveling from the origin to the destination in the TSTN using a virtual arc. Parameter TDacc，TDent，TDpas，TDdwe，TDlea，TDdriAnd TDegrIs the desired duration of the corresponding type of arc.
2. Spatio-temporal network representation of complex resource constraints (RSTN)
Trains operating on a railway network must use different types of resources, such as track resources (e.g., inter-block track resources and station track resources), electrical power resources, rolling stock resources, and crew resources. The railway line may be divided into a series of sections according to different resource types. For each resource segment, the resource capacity that can be used within a unit time period τ (e.g., 0.5h or 1h) is limited. Thus, all trains using the particular type of resource in the sector cannot exceed the total available resource capacity in a given time period. To determine the available capacity of each resource in a section within a given time period, it is necessary to divide the railway line/network into resource sections and time periods. Thus, one RSTN is built for each type of railroad resource, which can be used to model resource capacity constraints in the model. In the embodiment, the track resources and the power resources are comprehensively considered, and the resource space-time network is constructed.
To model the resource capability constraint, the train spatio-temporal arc (i, j, t, t ') in TSTN must be mapped to the resource spatio-temporal arc (m, n, τ) in RSTN, which has been constructed in constraint (6) by (i, j, t, t') ∈ H (m, n, τ). Next, we define the track and power RSTN and the mapping between (i, j, t, t') and (m, n, τ).
(1) RSTN of a track
The railway line/network consists of stations and sections between two consecutive stations. The railway line/network is divided into sections and stations, i.e. each track resource section is a section or a station. Modeling the resource capacity R of a track, R ∈ R, where R is the resource type of the track, we divide a line into track resource segments
Figure BDA0003528526060000081
Where a zone is a station or an interval. The railway line shown in fig. 2 may be divided into three track sections; as shown in FIG. 3, where l1,l2And l3Track resource zones 1, 2 and 3, respectively. In the time dimension, the time range T is divided into a number of time intervals, where each time interval is an equal period of time (i.e., τ), e.g., 30 minutes or 1 hour. Capacity of track resource section according to the division of track resource
Figure BDA0003528526060000082
Indicating how many trains in total can use the track of the segment during a period of time (τ), where l ═ (m, n) is a track resource segment and m, n is a node of the track resource. The nodes of the track resources are represented by the large dots in fig. 3.
There is provided an RSTN for track and a TSTN for train operation, which are structurally different from each other as can be seen from fig. 2 and 3. In particular, the structure of TSTN is more detailed than RSTN. Therefore, we need to map the nodes and edges of the TSTN to those of the RSTN. From fig. 3, it can be seen that track resource section 1 includes all edges within station T1. Thus, for each spatio-temporal arc (i, j, t, t') ∈ A of train operationtrainIf it is determined thatThe edge (i, j) is contained in the resource segment (m, n) and t is contained in the time interval τ, then the arc (i, j, t, t') ∈ H (m, n, τ) is used in the resource capacity constraint (6). This means that the train arc (i, j, t, t') is contained in the track resource space-time segment (m, n, τ). In this way, each spatiotemporal arc of train operation in the TSTN can be combined in the model with the spatiotemporal arc of the track resources in the RSTN.
(2) RSTN of electric power
Driving a train over an electrified railway line/network requires electrical power. The available power capacity of running trains in the power supply area (section) is limited; thus, the total number of trains operating in a power supply section cannot exceed the total available power capacity of that section at any time. In practice, the power required by the train to run at a certain moment is closely related to the running speed of the train at the moment, and the power consumption process is nonlinear and complex; the present embodiment uses an estimate of the total number of trains operating on the railroad line/network within the power supply area over a period of time τ to represent the total available power capacity of the area. The estimated capacity may be obtained from the experience of the dispatcher. For an electric power system there is also a network where each section is a supply area. Taking the railway line in fig. 2 as an example, if we assume the station S1And a section covered by the electric power district and a station S covered by another electric power district2The power section of the line can be divided as shown in fig. 4.
Each power segment can be considered an edge, and if a time dimension is added, the network shown in fig. 4 can be extended to a spatio-temporal network of the power system. Power segment
Figure BDA0003528526060000083
τ is denoted (m, n, τ) over a time interval, where m and n are nodes in the power RSTN, represented by the large-scale dots in fig. 4. And the total available power capacity of the section (m, n, tau) in the power RSTN
Figure BDA0003528526060000091
To represent the power resource r. The power side shown in fig. 4 is different from the train side shown in fig. 2. Therefore, it is necessary to convert TSTN is mapped into power RSTN. Thus, if edge (i, j) is included in the power edge
Figure BDA0003528526060000092
Then train spatio-temporal arc (i, j, t, t') ∈ A is used in constraint (6)trainAnd t is in the time interval τ, (i, j, t, t') ∈ H (m, n, τ). That is, the spatio-temporal arc (i, j, t, t') is mapped into the power spatio-temporal arc (m, n, τ). The total number of trains running using a train arc (i, j, t, t') ∈ H (m, n, τ) cannot exceed the available power supply capacity
Figure BDA0003528526060000093
3. Train operation adjustment model
Based on the symbols and the constructed space-time network, the resource-oriented train operation adjustment model is called Prd, which is expressed as follows. In the objective function, the total utility of all types of adjustment trains is maximized, as shown in equation (1):
Max:∑k∈KU(k) (1)
to minimize the total train travel time and total train arrival delay at each station, therefore, the function u (k) is given by equation (2):
Figure BDA0003528526060000094
wherein the first summation is the total travel cost of the train k, and the second summation is the total arrival delay cost of the train k at each passing station s;
on the premise that the following objectives are met:
1) the constraint of conservation of train flow (3) is as follows:
Figure BDA0003528526060000095
2) the running interval constraint (4) is as follows:
Figure BDA0003528526060000096
the constraint (4) is the operation interval constraint between any two high-speed trains or medium-speed trains; the constraint can be further modified to a constraint (5) according to the train type, as follows:
Figure BDA0003528526060000097
the running interval constraint between any two trains of the same type can be considered in the constraint (5); different types of trains can be managed by sequentially rearranging different types of trains, while arcs that conflict with arcs occupied by a former type of train cannot be occupied by a latter type of train;
3) the resource capacity constraint for one RSTN of trains of type pi and resource r in time interval τ in a section (m, n) is represented by equation (6) as follows:
Figure BDA0003528526060000101
wherein (i, j, t, t ') is ∈ H (m, n, τ) connecting the train spatio-temporal arc (i, j, t, t') in TSTN and the resource spatio-temporal arc (m, n, τ) in RSTN;
equation (6) represents that the total number of trains of type pi running in the resource zone (m, n) in the time period tau cannot exceed the resources allocated to the trains of type pi by the resource r in the time period tau; the left side of the equation (6) sums the total number of trains of pi type using the resource link (m, n) of the resource type r; the right side of equation (6) allocates the capacity of resource r in link (m, n) in time τ;
4) train regulatory variable field
Figure BDA0003528526060000102
In TSTN as shown by formula (7):
Figure BDA0003528526060000103
5) the shared resource capacity constraint in RSTN is represented by resources shared by various types of trains and cannot exceed available capacity; this is represented by equation (8), as follows:
Figure BDA0003528526060000104
6) the domain of the resource allocation variable is represented by equation (9):
Figure BDA0003528526060000105
in equation (1), the utility of all trains operating from the start point to the end point is maximized; equation (2) is the definition of the utility function of train k; equation (3) is the flow balance constraint for each train K ∈ K in TSTN, which ensures that each train runs from the start point to the end point; equation (5) is the running interval constraint between trains of the same type; equation (6) is the resource capacity constraint for each resource type in each resource segment for the same type of train, these constraints ensuring that all trains of a particular type that use time-dependent resource arcs in the RSTN cannot exceed the total capacity of the resource arcs allocated to that type of train; equation (7) represents a train track variable
Figure BDA0003528526060000106
A range of (d); equation (8) ensures that the capacity of the resource R ∈ R used by all types of trains cannot exceed the total capacity; equation (9) shows the resource allocation variables in different types of trains
Figure BDA0003528526060000107
In which
Figure BDA0003528526060000108
Is the number of trains of type pi using resource r in time interval τ segment (m, n).
The embodiment solves the problem of train operation adjustment by balancing and coordinating the space-time resource capacity allocation of different types of railway resources among different types of trains from the perspective of resource guidance. Importantly, this allows the dispatcher's experience to be easily embedded into the resource allocation phase to increase computational efficiency, thereby ensuring that the feasibility of the resulting solution is more comparable to that of previously used price-oriented methods.
The present invention and its embodiments have been described above schematically, without limitation, and what is shown in the drawings is only one of the embodiments of the present invention, and the actual structure is not limited thereto. Therefore, without departing from the spirit of the present invention, a person of ordinary skill in the art should understand that the present invention shall not be limited to the embodiments and the similar structural modes without creative design.

Claims (4)

1. The method for establishing the train operation adjustment model based on the space-time network is characterized by comprising the following steps of: the method comprises the following steps:
(1) constructing a train time-space network to simulate the train running process;
(2) constructing a resource space-time network to model space and time resource capacity;
(3) and constructing a train operation adjustment model based on the resource space-time network and the train space-time network.
2. The method for building a train operation adjustment model based on a spatio-temporal network according to claim 1, wherein: in the step (1), in the train space-time network TSTN, a time range may be represented as T ═ δ,2 δ,3 δ,. θ δ }, where θ is a maximum time interval number; the physical node i ∈ N may be extended to a time-dependent node (i, t) ∈ EtrainThe physical link (i, j) E L is expandable to a spatio-temporal arc (i, j, t, t') E Atrain(ii) a The time expansion arc indicates that the train starts from the node i at the time t and arrives at the node j at the time t'; TSTN may be represented as Gtrain＝(Etrain,Atrain)；
The station has an entrance node and an exit node, each track has a start node and an end node, respectively, the train starts from the start point (o)k) Run to endpoint (d)k) Make itA variety of different types of arcs are used, as follows:
starting arc with a starting point of
Figure FDA0003528526050000011
The final point is
Figure FDA0003528526050000012
The duration is delta;
entry arc starting point of
Figure FDA0003528526050000013
The final point is
Figure FDA0003528526050000014
Duration of (t' -t) ═ TDacc；
The starting point of the station-entering arc is
Figure FDA00035285260500000111
The final point is
Figure FDA00035285260500000112
Duration of (t' -t) ═ TDent；
Through an arc with a starting point of
Figure FDA00035285260500000113
The final point is
Figure FDA00035285260500000114
Duration of (t' -t) ═ TDpas；
Arc of stopping station with starting point of
Figure FDA00035285260500000115
The final point is
Figure FDA00035285260500000116
Duration of (t' -t) ═ TDdwe；
Starting point of extra waiting arc is
Figure FDA00035285260500000117
The final point is
Figure FDA00035285260500000125
The duration is delta;
the starting point of the outbound arc is
Figure FDA00035285260500000118
The final point is
Figure FDA00035285260500000120
Duration of (t' -t) ═ TDlea；
Arc running: the starting point is
Figure FDA00035285260500000119
The final point is
Figure FDA00035285260500000121
Duration of (t' -t) ═ TDdri；
Outlet arc: starting point is
Figure FDA00035285260500000122
The final point is
Figure FDA00035285260500000123
Duration of (t' -t) ═ TDegr；
And (3) final point arc: starting point is
Figure FDA00035285260500000124
The final point is
Figure FDA00035285260500000126
The duration is delta;
virtual arc: starting point is
Figure FDA00035285260500000127
The final point is
Figure FDA00035285260500000128
Duration of lk-ek；
Figure FDA0003528526050000015
Is a subset of the nodes of the starting point,
Figure FDA0003528526050000016
is a subset of the destination node(s),
Figure FDA0003528526050000017
is a subset of the ingress node or nodes,
Figure FDA0003528526050000018
is a subset of the starting nodes and,
Figure FDA0003528526050000019
is a subset of the end nodes and,
Figure FDA00035285260500000110
is a subset of egress nodes; parameter TDacc，TDent，TDpas，TDdwe，TDlea，TDdriAnd TDegrIs the desired duration of the corresponding type of arc.
3. The method for building a train operation adjustment model based on a spatio-temporal network according to claim 2, wherein: in the resource space-time network, the train space-time arcs (i, j, t, t ') need to be mapped to the resource space-time arcs (m, n, tau) in the resource space-time network RSTN, and each train space-time arc (i, j, t, t') belongs to AtrainIf the link (i, j) is contained in a resource segment (m, n) and t is contained in a time interval τ, then an arc is used(i, j, t, t') ∈ H (m, n, τ); namely train operating arcs (i, j, t, t') are contained in the track resource space-time segments (m, n, tau).
4. The method for building a train operation adjustment model based on a spatio-temporal network according to claim 3, wherein: the train operation adjustment model is as follows:
in the objective function, the total utility of all types of trains is maximized, as shown in equation (1):
Max:∑k∈KU(k) (1)
to minimize the total train travel time and total train arrival delay at each station, therefore, the function u (k) is given by equation (2):
Figure FDA0003528526050000021
wherein the first summation is the total travel cost of the train k, and the second summation is the total arrival delay cost of the train k at each passing station s;
on the premise that the following objectives are met:
1) the constraint of conservation of train flow (3) is as follows:
Figure FDA0003528526050000022
2) the train running interval constraint (4) is as follows:
Figure FDA0003528526050000023
the constraint (4) is the operation interval constraint between any two high-speed trains or medium-speed trains; the constraint can be further modified to a constraint (5) according to the train type, as follows:
Figure FDA0003528526050000024
the running interval constraint between any two trains of the same type can be considered in the constraint (5); the operation intervals among the trains of different types can be managed by sequentially adjusting the trains of different types, so that arcs which are occupied by the trains of the former type and conflict with each other are ensured to be unavailable in the adjustment of the trains of the latter type;
3) the resource capacity constraint for one RSTN of trains of type pi and resource r in time interval τ in a section (m, n) is represented by equation (6) as follows:
Figure FDA0003528526050000025
wherein (i, j, t, t ') is ∈ H (m, n, τ) connecting the train spatio-temporal arc (i, j, t, t') in TSTN and the resource spatio-temporal arc (m, n, τ) in RSTN;
equation (6) represents that the total number of trains of type pi running in the resource zone (m, n) in the time period tau cannot exceed the resources allocated to the trains of type pi by the resource r in the time period tau; the left side of the equation (6) sums the total number of trains of pi type using the resource link (m, n) of the resource type s; the right side of equation (6) allocates the capacity of resource r in link (m, n) in time τ;
4) train regulatory variable field
Figure FDA0003528526050000031
In TSTN as shown in formula (7):
Figure FDA0003528526050000032
5) the shared resource capacity constraint in RSTN is represented by resources shared by various types of trains and cannot exceed available capacity; this is represented by equation (8), as follows:
Figure FDA0003528526050000033
6) the domain of the resource allocation variable is represented by equation (9):
Figure FDA0003528526050000034
in equation (1), the utility of all trains operating from the start point to the end point is maximized; equation (2) is the definition of the utility function of train k; equation (3) is the traffic balance constraint for each train K ∈ K in TSTN, which ensures that each train runs from the start to the end; equation (5) is the operating interval constraint between trains of the same type; equation (6) is the resource capacity constraints for each resource type in each resource segment for the same type of train, these constraints ensuring that all trains of a particular type that use time-dependent resource arcs in the RSTN cannot exceed the total capacity of the resource arcs allocated to that type of train; equation (7) represents a train track variable
Figure FDA0003528526050000035
A range of (d); equation (8) ensures that the capacity of the resource R ∈ R used by all types of trains cannot exceed the total capacity; equation (9) shows the resource allocation variables in different types of trains
Figure FDA0003528526050000036
In which
Figure FDA0003528526050000037
Is the number of trains of type pi using the resource r in the time interval τ segment (m, n).
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