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CN111985814A - Method and system for optimizing inter-city train operation scheme with intermittent power supply - Google Patents

Method and system for optimizing inter-city train operation scheme with intermittent power supply Download PDF

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CN111985814A
CN111985814A CN202010846770.3A CN202010846770A CN111985814A CN 111985814 A CN111985814 A CN 111985814A CN 202010846770 A CN202010846770 A CN 202010846770A CN 111985814 A CN111985814 A CN 111985814A
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秦进
张威
柳晓峰
鲁寨军
张宇
谭宇超
聂文斌
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Central South University
CRRC Zhuzhou Locomotive Co Ltd
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CRRC Zhuzhou Locomotive Co Ltd
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Abstract

The invention discloses an optimizing method and a system of an inter-city train operation scheme with intermittent power supply, wherein the method comprises the following steps: dividing an inter-city railway train into a plurality of micro time sections with equal length every day in an operation time period; forming a space-time network directed graph by station nodes on each intercity train line, train stop arcs and train operation arcs of the trains; dividing passengers with the same departure time in the passenger trip demand point set into a passenger group; constructing a relation variable and a decision variable of the passenger group and the train according to whether the passenger group travels by the train or not; setting trip time deviation punishment time and punishment time for passengers not boarding a train; setting constraint conditions by taking the weighted sum of the train running cost and the passenger trip cost as an optimization target; and solving to obtain the optimized inter-city train operation scheme. The method can calculate the actual departure time deviation of the passenger while optimizing, and quantifies the meeting degree of the time-varying requirement of the passenger.

Description

Method and system for optimizing inter-city train operation scheme with intermittent power supply
Technical Field
The invention relates to the technical field of train scheduling, in particular to an optimizing method and system for an inter-city train operation scheme with intermittent power supply.
Background
Intermittent power supply intercity trains are an important mode of next generation intercity traffic, and intermittent power supply vehicles change an energy supply mode on the premise of keeping the advantages of the traditional intercity rail traffic, effectively simplify the spatial distribution of a functional system, but also bring the problems of energy supply shortage and residual energy anxiety. The intermittent power supply intercity train has large passenger flow and time-varying characteristics, obvious fluctuation can occur in the morning and evening peak periods, the train running scheme should meet the time-varying requirement of passengers, and the increase of the energy consumption burden of the train caused by passenger congestion is avoided; meanwhile, railway transportation resources are fully utilized according to actual conditions, and the operation cost of railway enterprises is reduced.
Intercity passenger flow demand has a significant time-varying characteristic, i.e., the magnitude of demand between each pair of origin-destination stations varies over time during the operational period. The traffic may fluctuate during different periods of the same operation day. The existing train driving method does not consider the time distribution of passenger flow, and only optimizes the space (lines, stations and the like) and the time (train arrival time, passenger traveling time and the like).
Therefore, the time distribution of passenger flow needs to be considered in the decision process of the driving scheme, and evaluation is performed from two angles of space (line, station, and the like) and time (train arrival time, passenger traveling time, and the like), so that the overall optimum of the driving scheme of the train is obtained.
Disclosure of Invention
The invention provides an optimization method and system for an inter-city train operation scheme with intermittent power supply, which are used for solving the technical problem that the existing train operation method does not consider the time distribution of passenger flow and only optimizes from two angles of space (lines, stations and the like) and time (train arrival time, passenger travel time and the like).
In order to solve the technical problems, the technical scheme provided by the invention is as follows:
an optimization method of an inter-city train operation scheme with intermittent power supply comprises the following steps:
dividing the operation time period into a plurality of micro time sections with equal length through a plurality of discrete time points according to the daily operation time period of the inter-city railway train;
expanding station nodes on each intercity train line into a plurality of corresponding space-time nodes through a plurality of micro time sections with equal length to form a space-time point set; a train stop arc and a train running arc of the train form a directed arc section set; the space-time point set and the directed arc segment set form a space-time network directed graph;
determining a passenger travel demand point set according to the number of stations on each intercity train line, and dividing passengers with the same departure time in the passenger travel demand point set into a passenger group;
constructing a relation variable and a decision variable of the passenger group and the train according to whether the passenger group travels by the train or not; setting trip time deviation punishment time and punishment time for passengers not boarding a train;
the method comprises the following steps of taking the weighted sum of the train running cost and the passenger trip cost as an optimization target, and taking the train flow and passenger flow conservation characteristics on time-space nodes in a time-space network, time logic between the train flow and the passenger flow, and station departure interval time, train determiners and train running total number required by railway running organizations as constraint conditions; and solving to obtain the optimized inter-city train operation scheme.
Preferably, the train operating cost is the sum of the operating times of the train on the arc segments; the passenger trip cost includes: the sum of travel time of a passenger group on the arc section, the deviation cost of travel time of the passenger and the weighted sum of punishment cost of not boarding the train.
Preferably, the constructing of the relationship variables and decision variables of the passenger population and the train according to whether the passenger population travels by the train comprises:
Figure BDA0002643301990000021
for train f and passenger groups
Figure BDA0002643301990000022
Relation variable, if passenger group
Figure BDA0002643301990000023
F trip rule of train
Figure BDA0002643301990000024
Otherwise
Figure BDA0002643301990000025
The train driving scheme and the traveling situation of passengers adopt the following decision variables:
Figure BDA0002643301990000026
Figure BDA0002643301990000027
wherein E is a directed arc segment set;
Figure BDA0002643301990000028
the method comprises the steps of collecting passenger groups with the same departure time for passenger trip demand points; f is a train;
Figure BDA0002643301990000029
is a directed arc segment, and the train is in the arc segment
Figure BDA00026433019900000210
The running time of (τ -t).
Preferably, the optimization objectives are as follows:
min Z＝1Ψ1+2Ψ2+3Ψ3+4Ψ4 (6)
therein, Ψ1The train operating cost; Ψ2The travel time of the passengers in the arc section; Ψ3Punishing time for the travel time deviation of the passengers; Ψ4Punishing time for passengers not boarding the train;1,2,3,4the weighting parameters of the four are respectively;
wherein the train running cost Ψ1The following were used:
Figure BDA00026433019900000211
wherein the train is in the arc section
Figure BDA00026433019900000212
The run time on is (τ -t); omega is a train running scheme;
the sum of the travel time of the passenger group on the arc segment is calculated as follows:
Figure BDA00026433019900000213
wherein P represents the set of all passenger groups in the network,
Figure BDA00026433019900000214
Preindicating a collection of passengers not boarding the train due to train officer restrictions, i.e. a current passenger population
Figure BDA00026433019900000215
When not boarding a train
Figure BDA00026433019900000216
The total punishment time calculation formula of the departure time deviation of the passengers is as follows:
Figure BDA0002643301990000031
wherein, the passenger group
Figure BDA0002643301990000032
Penalty time value for departure deviation
Figure BDA0002643301990000033
The following were used:
Figure BDA00026433019900000318
wherein,
Figure BDA0002643301990000035
for passenger groups
Figure BDA0002643301990000036
Departure time, lambda, of the train1，λ2Is a positive weighting parameter;
the penalty time calculation function of passengers not boarding the train is as follows:
Figure BDA0002643301990000037
wherein the passenger group not boarding the train
Figure BDA0002643301990000038
Penalty time value of
Figure BDA0002643301990000039
Value is taken as passenger group
Figure BDA00026433019900000310
Minimum train cost between origin and destination.
Preferably, the train flow and passenger flow conservation characteristics at spatiotemporal nodes in the spatiotemporal network include:
constraint of conservation of train flow:
Figure BDA00026433019900000311
Figure BDA00026433019900000312
equation (7) is the train flow conservation constraint at the spatiotemporal point, such that the number of trains arriving at the spatiotemporal point (j, τ) minus the number of trains ending to equal the number of trains leaving the spatiotemporal point (j, τ) minus the number of trains starting;
and (3) passenger flow conservation constraint:
Figure BDA00026433019900000313
Figure BDA00026433019900000314
Figure BDA00026433019900000315
formulas (8) and (9) ensure passenger populations
Figure BDA00026433019900000316
Departure from a starting point and arrival at a corresponding end point, equation (10) ensures passenger populations
Figure BDA00026433019900000317
The number of arrivals and departures in traversing the intermediate node is balanced.
Preferably, the logical constraints on the time between train flow and passenger flow include:
decision variable relationship constraint:
Figure BDA0002643301990000041
Figure BDA0002643301990000042
in the space-time network, passengers can only use the arc sections through which trains pass, namely, on any arc section, the decision variable value of any passenger group cannot be larger than that of any train;
and (3) decision variable value constraint:
Figure BDA0002643301990000043
Figure BDA0002643301990000044
wherein i is a station number; j is the train number.
Preferably, the station departure interval time, the train order and the total train operation number constraints required by the railway train organization comprise:
train officer restraint:
Figure BDA0002643301990000045
Figure BDA0002643301990000046
the number of passengers taking the same train is not more than the number of fixed passengers of the train;
the departure time interval constraint of the departure station is as follows:
Figure BDA0002643301990000047
Figure BDA0002643301990000048
Figure BDA0002643301990000049
the departure time interval of any two trains at the starting station is not less than a fixed value;
and (3) total number of trains constraint:
Y(Ω)≤b (14)
the number of trains used for the train operation scheme omega is not more than a fixed value b.
Preferably, the optimized inter-city train operation scheme is solved, and the method comprises the steps of solving a plurality of optimization solutions which are arranged in the weighted sum from low to high of the train operation cost and the passenger travel cost and are arranged at the front, and taking the optimization solution with the lowest train operation cost as a final result.
The present invention also provides a computer system comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the steps of any of the methods described above when executing the computer program.
The invention has the following beneficial effects:
the optimizing method and the optimizing system of the inter-city train operation scheme with intermittent power supply, disclosed by the invention, have the advantages that the space-time network is constructed according to the conditions and the characteristics of inter-city high-speed rail lines, the variables used in the model and the optimization target are given according to the optimization problem and the characteristics of the space-time network, and the optimization target comprises two parts, namely the train operation cost and the passenger trip cost. The cost of railway enterprises and travelers is comprehensively considered. By means of the time-space network method, the arrival time and departure time of the train at each station can be more conveniently considered, the deviation of the actual departure time of the passengers can be calculated while optimization is carried out, the time-varying requirement meeting degree of the passengers is quantized, and the influence of the time-varying requirement on the formulation of the operation scheme is reflected.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below with reference to the accompanying drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 is a schematic flow chart of a method for optimizing an intermittently powered inter-city train operation scheme in accordance with a preferred embodiment of the present invention;
FIG. 2 is a schematic view of an intercity train line in accordance with a preferred embodiment of the present invention;
figure 3 is a directed schematic diagram of a spatiotemporal network in accordance with a preferred embodiment of the present invention.
Detailed Description
The embodiments of the invention will be described in detail below with reference to the drawings, but the invention can be implemented in many different ways as defined and covered by the claims.
Aiming at the problem of large passenger flow demand of an intercity train, the invention considers that the total operation time period of the intercity railway is divided into a plurality of small time periods, the passenger flow demand in each time period is assumed to be fixed and unchanged, and the time-varying demand is converted into the fixed passenger flow demand, thereby effectively simplifying the problem. In each time interval, the expected departure time of the passengers can be evenly distributed at discrete time points with the same distance or uniformly arranged at the middle point of the time interval according to the number of the passengers in the time interval, so that the calculation is simplified.
By combining the intercity train line and the passenger flow situation, the optimization content of the train operation scheme can be determined to comprise the train operation starting-ending point (the starting station of the train), the operation frequency, the stop scheme and the arrival and departure time of the train at each station along the way. The invention uses the space-time network method for optimization, visually and effectively describes the flow situations of the train flow and the passenger flow on the network from the space and time dimensions, simultaneously considers the limiting conditions and the corresponding cost, displays the corresponding changes, comprehensively considers the mutual influence of the train flow and the passenger flow, and achieves the effect of improving the systematicness optimization.
The time-space network is constructed according to the intercity railway line and comprises time-space nodes and directed arcs, wherein the time-space nodes represent departure or arrival events of trains or passenger flows at corresponding stations and corresponding time, the arcs can represent the moving process of the trains or the passenger flows between the two time-space nodes, and the time-space network model of the intercity railway operation scheme increases the information of the arrival and departure time of the trains at each station along the way and can process the time-varying passenger flow distribution problem while the scheme is optimized. Particularly, the method can flexibly adjust the accuracy of the time information according to the actual situation, thereby having good applicability.
Based on the above analysis, the inventive optimization study was based on the following assumptions:
(1) for simple calculation, the train runs between stations only considering the running time division between stations and not considering the starting and stopping additional time division;
(2) the trains adopt fixed marshalling, and the grades of all the trains are the same;
(3) setting an initial terminal to a station on a line according to actual conditions, wherein all the train initial-terminal and final-terminal stations are limited to the initial terminal to the station, and the train is set to be stopped when the train is started and terminated to the station;
(4) the train interval time can reflect the passing capacity of a line and a station, but as the intercity train interval time is of a plurality of types, in order to reduce the calculated amount and obtain a reasonable train running time estimated value, only the train sending interval time of an originating station is considered, so that the possibility of collision of partial train running lines is generated;
(5) the invention does not consider the situation that the railway department sells the station tickets, so the number of passengers taking the same train at the same time does not exceed the number of the fixed passengers.
Based on the assumed conditions and analysis, referring to fig. 1, the method for optimizing the inter-city train operation scheme with intermittent power supply comprises the following steps:
s1: according to the daily operation time period of the inter-city railway train, the operation time period is divided into a plurality of micro time sections with equal length through a plurality of discrete time points.
S2: expanding station nodes on each intercity train line into a plurality of corresponding space-time nodes through a plurality of micro time sections with equal length to form a space-time point set; a train stop arc and a train running arc of the train form a directed arc section set; and the space-time point set and the directed arc segment set form a space-time network directed graph.
S3: and determining a passenger travel demand point set according to the number of stations on each intercity train line, and dividing passengers with the same departure time in the passenger travel demand point set into a passenger group.
S4: constructing a relation variable and a decision variable of the passenger group and the train according to whether the passenger group travels by the train or not; setting trip time deviation punishment time and punishment time for passengers not boarding a train; in this embodiment, the train operation cost is the sum of the operation time of the train on the arc section; the passenger trip cost includes: the sum of travel time of a passenger group on the arc section, the deviation cost of travel time of the passenger and the weighted sum of punishment cost of not boarding the train.
S5: the method comprises the following steps of taking the weighted sum of the train running cost and the passenger trip cost as an optimization target, and taking the train flow and passenger flow conservation characteristics on time-space nodes in a time-space network, time logic between the train flow and the passenger flow, and station departure interval time, train determiners and train running total number required by railway running organizations as constraint conditions; and solving to obtain the optimized inter-city train operation scheme.
An extended embodiment of the above embodiment:
as shown in fig. 2, the research object is a certain intercity high-speed rail line, the set of stations on the line is S, and the number of stations is | S |. Nodes in the graph represent stations, and arcs represent lines between stations.
S1: defining the operation time period of each day of the inter-city railway train as [0, T ], in the space-time network of the operation scheme, the time section is divided into n tiny time sections with equal length by n +1 discrete time points, wherein the length sigma of the time section is T/n. The discrete time points in the network are denoted t, and t e {0,1,2,3, …, n }.
S2: the serial number i belongs to {1,2, …, | S | } of stations on the intercity train line according to the direction sequence. Expanding each station node in a time dimension, namely expanding a station node i into n +1 space-time nodes: (i,0), (i,1), …, (i, t), …, (i, n), all spatio-temporal nodes constitute a set of spatio-temporal points V.
In the spatio-temporal network, the directed arcs represent the movement of the train between stations, i.e. stop and run. The directed arc section between adjacent time nodes (i, t) and (i, t +1) of the same station represents the stop arc of the train, and represents the train in the time period [ t, t +1 ]]Internal station i stops, i.e.
Figure BDA0002643301990000071
Yt according to train running time between adjacent stations i and i +1i,i+1The train can run between the stations i and i +1 through (i, t) and (i +1, t + yt)i,i+1) Representation of the running arc of the train between two points, i.e.
Figure BDA0002643301990000072
All directed arc segments form a directed arc segment set E, and the E and the V form a space-time network directed graph G (V, E). When yti,i+1＝1,yti+1,i+2When 2, the spatio-temporal network directed graph G (V, E) is as shown in fig. 3.
S3: defining omega as train running scheme, Y (omega) as the number of trains in omega, b as the upper limit of total number of trains in running scheme, and MfDetermining the number of members for the train f belonging to omega; ditRepresenting the number of trains ending at point (i, t), FitRepresents the number of trains originating at point (i, t); s is the set of all stations on the line, R is the set of stations with the ability of starting and ending, SfA set of stations passing by the train f; the minimum departure interval time for the departure station.
The travel demand point set of the passenger is
Figure BDA00026433019900000718
The number of passenger departures between each (O, D) e.g. OD will vary with time, and each OD (O is departure, D is arrival, and an OD pair is a departure arrival behavior) will have the same departure time
Figure BDA00026433019900000716
The passengers are divided into a passenger group
Figure BDA0002643301990000073
The number of passengers in the group, i.e. (o, d) ∈ OD
Figure BDA00026433019900000717
Number of passengers who started
Figure BDA0002643301990000074
P represents the set of all passenger populations in the network,
Figure BDA0002643301990000075
S4：Preindicating a collection of passengers not boarding the train due to train officer restrictions, i.e. a current passenger population
Figure BDA0002643301990000076
When not boarding a train
Figure BDA0002643301990000077
For passenger groups
Figure BDA0002643301990000078
Station sets between origin-destination stations (not involved),
Figure BDA0002643301990000079
for passenger groups
Figure BDA00026433019900000710
Set of all stations between origin-destination stations (inclusive), i.e.
Figure BDA00026433019900000711
For passenger groups
Figure BDA00026433019900000712
The departure time deviation penalty time;
Figure BDA00026433019900000713
for passenger groups not boarding train
Figure BDA00026433019900000714
The penalty time of (d);
Figure BDA00026433019900000715
for train f and passenger groups
Figure BDA0002643301990000081
Relation variable, if passenger group
Figure BDA0002643301990000082
F trip rule of train
Figure BDA0002643301990000083
Otherwise
Figure BDA0002643301990000084
The following decision variables are adopted for clearly determining the train driving scheme and the travel situation of passengers:
Figure BDA0002643301990000085
Figure BDA0002643301990000086
s5: the optimization target of the inter-city high-speed train operation scheme comprises two parts, namely enterprise income and passenger travel cost, wherein the enterprise health development is obtained by improving the enterprise income, and the passenger travel satisfaction is improved by reducing the passenger travel cost. The enterprise income is the difference between the operation income and the operation cost, the intercity train operation income mainly comes from the passenger ticket income, the part can be considered in the travel cost of passengers, and the enterprise operation cost can be reflected by the train operation cost, so that the target letter of the enterprise income part can be includedThe number is determined to minimize train operating costs. In the actual operation process, the train operation cost is represented by train travel time. In a spatiotemporal network, the train operating cost may be calculated by the sum of the train operating times over the arc. Train in arc section
Figure BDA00026433019900000813
The upper running time is (tau-t), the running cost calculation formula of the train is as follows:
Figure BDA0002643301990000087
the travel cost of the passengers mainly comprises three costs of time, expense and comfort. In the analysis of the second chapter, the characteristics of high punctuality rate and less transfer of intercity trains are combined, the time cost can be represented by the travel time of passengers on the trains, and in the spatio-temporal network, the sum of the travel time of the passengers on the arc sections can be calculated. The fare cost of the passengers mainly refers to the fare expenditure of the passengers going out, the fare cost of the passengers on the intercity high-speed rail is mostly related to the riding mileage, and the fare cost of the passengers can be understood as a fixed value in the OD of the same station, so that the influence of the change of the train driving scheme on the fare cost is small, and the fare cost of the passengers can be disregarded. Passenger comfort level in this context mainly means whether passenger's time-varying demand is satisfied, expects that if there is deviation in departure time and the train departure time of taking advantage of, the passenger will feel uncomfortable. Since the situation that the railway enterprises sell the station tickets is not considered in the text, part of passengers can not travel on the train due to the limitation of train determiners, and the passengers also feel uncomfortable. The passenger comfort cost comprises two parts of passenger travel time deviation cost and non-boarding train punishment cost. Based on the above analysis, it is considered that the train operation cost is represented by the operation time, and the passenger trip cost is represented by the trip time of the passenger on the arc section, the trip time deviation punishment time and the passenger punishment time of the passenger not boarding the train.
Passenger population
Figure BDA0002643301990000088
In the arc segment
Figure BDA0002643301990000089
The travel time of the passenger in the arc segment is (tau-t), and the calculation formula of the travel time of the passenger in the arc segment is as follows:
Figure BDA00026433019900000810
introduction of passenger groups
Figure BDA00026433019900000811
Penalty time value for departure deviation
Figure BDA00026433019900000812
The value is calculated by adopting a linear piecewise function, and is expressed as formula (3-3):
Figure BDA0002643301990000091
Figure BDA0002643301990000092
for passenger groups
Figure BDA0002643301990000093
Departure time, lambda, of the train1，λ2Is a positive weighting parameter. Then, the calculation formula of the total punishment time of the departure time deviation of the passengers is as follows (4):
Figure BDA0002643301990000094
introducing passenger groups not boarding train
Figure BDA0002643301990000095
Penalty time value of
Figure BDA0002643301990000096
It has a value ofTaken as passenger group
Figure BDA0002643301990000097
Minimum train cost between origin and destination. The penalty time calculation function of passengers not boarding the train is as follows:
Figure BDA0002643301990000098
for train operation time Ψ1Arc trip time psi for passengers2Punishment time psi of time deviation of passenger trip3And punishment time psi for passengers not boarding train4Introduction of weighting parameters1,2,3,4And combining to generate an optimization target of the train running scheme, as shown in formula (6):
min Z＝1Ψ1+2Ψ2+3Ψ3+4Ψ4 (6)。
constraint conditions of an optimization model of an inter-city high-speed train operation scheme based on a space-time network mainly comprise the characteristics of train flow and passenger flow conservation on space-time nodes in the space-time network, time logic between the train flow and the passenger flow, and constraint conditions of station departure interval time, train determiners, total train operation number and the like required by railway train operation organization, and are specifically as follows:
(1) conservation of train flow
Figure BDA0002643301990000099
Figure BDA00026433019900000910
Equation (7) is the train flow conservation constraint at the spatiotemporal point such that the number of trains arriving at the spatiotemporal point (j, τ) minus the number of trains ending to equal the number of trains leaving the spatiotemporal point (j, τ) minus the number of trains originating.
(2) Conservation of passenger flow
Figure BDA00026433019900000911
Figure BDA0002643301990000101
Figure BDA0002643301990000102
Formulas (8) and (9) ensure passenger populations
Figure BDA0002643301990000103
Departure from a starting point and arrival at a corresponding end point, equation (10) ensures passenger populations
Figure BDA0002643301990000104
The number of arrivals and departures in traversing the intermediate node is balanced.
(3) Decision variable relationship constraint:
Figure BDA0002643301990000105
Figure BDA0002643301990000106
the railway department can only use the train to realize the purpose of passenger transportation, so in the space-time network, passengers can only use the arc sections through which the train passes, namely on any arc section, the decision variable value of any passenger group cannot be larger than that of any train.
(4) Restraint for train passenger
Figure BDA0002643301990000107
Figure BDA0002643301990000108
The number of passengers riding the same train at the same time is not more than the number of fixed passengers of the train.
(5) Departure time interval constraint at originating station
Figure BDA0002643301990000109
Figure BDA00026433019900001010
Figure BDA00026433019900001011
The departure time interval of any two trains at the starting station is not less than a fixed value.
(6) Total number of trains constraint
Y(Ω)≤b (14)
The total train use number has an important influence on the transportation efficiency and the capacity of an enterprise, trains running too much inevitably increase the train running cost, and meanwhile, the capacity of a line interval and a station is close to saturation, so that the train running efficiency is reduced, and therefore, the train use number is limited, namely, the train number used by the train running scheme omega is not more than a fixed value b.
(7) Decision variable value constraint
Figure BDA00026433019900001012
Figure BDA0002643301990000111
According to the analysis, the optimization model of the inter-city high-speed train operation scheme based on the space-time network is as follows:
min Z＝1Ψ1+2Ψ2+3Ψ3+4Ψ4
s.t. formula (7) -formula (16);
the model is a 0-1 integer planning model, and the cost of railway enterprises and trip passengers is comprehensively considered. During implementation, a plurality of optimization solutions which are arranged in the low-to-high sequence and are positioned at the front of the weighted sum of the train running cost and the passenger trip cost can be solved, and the optimization solution with the lowest train running cost is taken as a final result.
The present invention also provides a computer system comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the steps of any of the above embodiments being implemented when the computer program is executed by the processor.
In conclusion, the arrival and departure time of the train at each station can be more conveniently considered through the space-time network method, the deviation of the actual departure time of the passengers can be calculated while optimization is carried out, the time-varying requirement meeting degree of the passengers is quantized, and the influence of the time-varying requirement on the formulation of the operation scheme is reflected.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (9)

1. An optimization method for an inter-city train operation scheme with intermittent power supply is characterized by comprising the following steps:
dividing the operation time period into a plurality of micro time sections with equal length through a plurality of discrete time points according to the daily operation time period of the inter-city railway train;
expanding station nodes on each intercity train line into a plurality of corresponding space-time nodes through the plurality of micro time sections with equal length to form a space-time point set; a train stop arc and a train running arc of the train form a directed arc section set; the space-time point set and the directed arc segment set form a space-time network directed graph;
determining a passenger travel demand point set according to the number of stations on each intercity train line, and dividing passengers with the same departure time in the passenger travel demand point set into a passenger group;
constructing a relation variable and a decision variable of the passenger group and the train according to whether the passenger group travels by the train or not; setting trip time deviation punishment time and punishment time for passengers not boarding a train;
the method comprises the following steps of taking the weighted sum of the train running cost and the passenger trip cost as an optimization target, and taking the train flow and passenger flow conservation characteristics on time-space nodes in a time-space network, time logic between the train flow and the passenger flow, and station departure interval time, train determiners and train running total number required by railway running organizations as constraint conditions; and solving to obtain the optimized inter-city train operation scheme.
2. The method of claim 1, wherein the train operating cost is the sum of the operating times of the train over the arc; the passenger trip cost includes: the sum of travel time of a passenger group on the arc section, the deviation cost of travel time of the passenger and the weighted sum of punishment cost of not boarding the train.
3. The method for optimizing an inter-city train operation scheme with intermittent power supply according to claim 1 or 2, wherein the construction of the relationship variables and decision variables between the passenger groups and the train according to whether the passenger groups travel on the train comprises:
Figure FDA0002643301980000011
for train f and passenger groups
Figure FDA0002643301980000012
Relation variable, if passenger group
Figure FDA0002643301980000013
F trip rule of train
Figure FDA0002643301980000014
Otherwise
Figure FDA0002643301980000015
The train driving scheme and the traveling situation of passengers adopt the following decision variables:
Figure FDA0002643301980000016
Figure FDA0002643301980000017
wherein E is a directed arc segment set;
Figure FDA0002643301980000018
the method comprises the steps of collecting passenger groups with the same departure time for passenger trip demand points; f is a train;
Figure FDA0002643301980000019
is a directed arc segment, and the train is in the arc segment
Figure FDA00026433019800000110
The running time of (τ -t).
4. The method of claim 3, wherein the optimization objective is as follows:
min Z＝1Ψ1+2Ψ2+3Ψ3+4Ψ4 (6)
therein, Ψ1The train operating cost; Ψ2For the travel time of passengers in arc section；Ψ3Punishing time for the travel time deviation of the passengers; Ψ4Punishing time for passengers not boarding the train;1,2,3,4the weighting parameters of the four are respectively;
wherein the train running cost Ψ1The following were used:
Figure FDA0002643301980000021
wherein the train is in the arc section
Figure FDA0002643301980000022
The run time on is (τ -t); omega is a train running scheme;
the sum of the travel time of the passenger group on the arc segment is calculated as follows:
Figure FDA0002643301980000023
wherein P represents the set of all passenger groups in the network,
Figure FDA0002643301980000024
Preindicating a collection of passengers not boarding the train due to train officer restrictions, i.e. a current passenger population
Figure FDA0002643301980000025
When not boarding a train
Figure FDA0002643301980000026
The total punishment time calculation formula of the departure time deviation of the passengers is as follows:
Figure FDA0002643301980000027
wherein, the passenger group
Figure FDA0002643301980000028
Penalty time value for departure deviation
Figure FDA0002643301980000029
The following were used:
Figure FDA00026433019800000210
wherein,
Figure FDA00026433019800000211
for passenger groups
Figure FDA00026433019800000212
Departure time, lambda, of the train1，λ2Is a positive weighting parameter;
the penalty time calculation function of passengers not boarding the train is as follows:
Figure FDA00026433019800000213
wherein the passenger group not boarding the train
Figure FDA00026433019800000214
Penalty time value of
Figure FDA00026433019800000215
Value is taken as passenger group
Figure FDA00026433019800000216
Minimum train cost between origin and destination.
5. The method of claim 3, wherein the characteristics of conservation of traffic and passenger flow at the time-space nodes in the space-time network comprise:
constraint of conservation of train flow:
Figure FDA0002643301980000031
Figure FDA0002643301980000032
equation (7) is the train flow conservation constraint at the spatiotemporal point, such that the number of trains arriving at the spatiotemporal point (j, τ) minus the number of trains ending to equal the number of trains leaving the spatiotemporal point (j, τ) minus the number of trains starting;
and (3) passenger flow conservation constraint:
Figure FDA0002643301980000033
Figure FDA0002643301980000034
Figure FDA0002643301980000035
formulas (8) and (9) ensure passenger populations
Figure FDA0002643301980000036
Departure from a starting point and arrival at a corresponding end point, equation (10) ensures passenger populations
Figure FDA0002643301980000037
The number of arrivals and departures in traversing the intermediate node is balanced.
6. The method of claim 3 wherein the time logic constraints between train flow and passenger flow comprise:
decision variable relationship constraint:
Figure FDA0002643301980000038
Figure FDA0002643301980000039
in the space-time network, passengers can only use the arc sections through which trains pass, namely, on any arc section, the decision variable value of any passenger group cannot be larger than that of any train;
and (3) decision variable value constraint:
Figure FDA00026433019800000310
Figure FDA00026433019800000311
wherein i is a station number; j is the train number.
7. The method of claim 3 for optimizing an inter-city train operation scheme with intermittent power supply, wherein the station departure interval time, train determiners and total train operation number constraints required by the railway train operation organization comprise:
train officer restraint:
Figure FDA00026433019800000312
Figure FDA00026433019800000313
the number of passengers taking the same train is not more than the number of fixed passengers of the train;
the departure time interval constraint of the departure station is as follows:
Figure FDA0002643301980000041
Figure FDA0002643301980000042
Figure FDA0002643301980000043
the departure time interval of any two trains at the starting station is not less than a fixed value;
and (3) total number of trains constraint:
Y(Ω)≤b (14)
the number of trains used for the train operation scheme omega is not more than a fixed value b.
8. The method for optimizing an inter-city train operation scheme with intermittent power supply according to any one of claims 1 to 7, wherein solving to obtain the optimized inter-city train operation scheme comprises solving a plurality of optimization solutions which are weighted by train operation cost and passenger operation cost and are arranged from low to high and are arranged at the front, and taking the optimization solution with the lowest train operation cost as a final result.
9. A computer system comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the steps of the method of any one of claims 1 to 8 are performed when the computer program is executed by the processor.
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CN112766650A (en) * 2020-12-31 2021-05-07 北京嘀嘀无限科技发展有限公司 Method and device for determining scheduling scheme
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