CN108229725B - High-speed rail operation diagram line-adding optimization method based on mixed integer programming model - Google Patents

High-speed rail operation diagram line-adding optimization method based on mixed integer programming model Download PDF

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CN108229725B
CN108229725B CN201711325219.9A CN201711325219A CN108229725B CN 108229725 B CN108229725 B CN 108229725B CN 201711325219 A CN201711325219 A CN 201711325219A CN 108229725 B CN108229725 B CN 108229725B
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高原
杨立兴
高自友
李树凯
杨凯
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Abstract

The invention discloses a method for adding lines to an operation diagram based on a multi-target mixed integer programming model in the field of high-speed railway operation management. The method comprehensively considers the actual factors of station line distribution, the time window of departure from the starting station, the train stop scheme, time consumption of acceleration and deceleration and the like, takes the minimum running time of the newly added line and the adjustment range of the existing line as optimization targets, and considers the running requirements of the newly added line and the existing line. By decomposing the original large-scale problem and combining a preprocessing algorithm, the method can efficiently solve the problem of the line adding of the high-speed railway operation diagram.

Description

High-speed rail operation diagram line-adding optimization method based on mixed integer programming model
Technical Field
The invention belongs to the field of railway transportation planning, and particularly relates to a method for adding lines to a high-speed railway operation diagram.
Background
The train operation diagram is the basis of comprehensive planning and running organization of railway transportation work and is a tool for coordinating various departments and units of the railway to move according to a certain program. In brief, the operation diagram determines the arrival and departure time of trains at key facilities (such as stations and marshalling stations) so as to ensure that the trains do not conflict when normally operating on the road network and the utilization rate of resources can be optimized. To accommodate changes in passenger flow, new train lines are sometimes added to existing maps. For a new operation diagram, on one hand, the service quality of a newly added line needs to be guaranteed; on the other hand, the existing line is adjusted as small as possible in consideration of the riding habits of passengers. This causes a conflict between the new route and the existing route, and requires a reasonable redesign of the train diagram, thereby leading to a study on the operation diagram line adding technology. At present, the high-speed railway in China has the characteristics of multiple points, long line, wide area, more cross-line passenger flow, high departure density and the like, and trains with two speeds, namely 300km/h and 250km/h, run. When designing the line of the operation diagram, many factors such as driving safety, train overtaking, passenger transfer and the like must be considered.
In a longer period, the design of the operation diagram is mostly based on manual experience, and generally, a mathematical optimization method is less integrated. In the nineties of the last century, with the rapid development of information science, computer aided design of operation diagrams is becoming widely used. It follows that various mathematical optimization algorithms are increasingly integrated into train dispatching systems. The optimization modeling facing the operation diagram generally has two types of methods: firstly, discretizing time, constructing a space-time network, and further establishing an Integer Programming (IP); secondly, describing the departure sequence by Boolean variables, and establishing a Mixed Integer Programming (MIP) model. The first method converts the problem of the train operation diagram into a network optimization problem, can effectively introduce a mature algorithm of network optimization, but has the defect that the scale of a space-time network is sharply increased along with the extension of a time axis. Most of the existing scheduling systems adopt a second optimization modeling method.
The mixed integer programming model established for the operation diagram is often large in scale, and the existing solving methods are mainly three. First, metaheuristic algorithms (metaheuristics) such as genetic algorithm (genetic algorithm), tabu search algorithm (tabu search algorithm) and the like are designed. The algorithm has strong applicability, but the quality of the result cannot be ensured, and the calculation time is long. Secondly, more efficient and stable algorithms such as Lagrange relaxation (Lagrange relaxation), column generation (column generation), branch and bound (branch and bound) are adopted. However, such algorithms have high requirements on the structure of the problem, and the solvable model is often relatively simple. Thirdly, combining heuristic rules to decompose the original large-scale problems to obtain a series of small-scale problems, and then utilizing commercial optimization software such as CPLEX or Gurobi to solve the small-scale problems one by one. The third method can solve more types of problems, has wide adaptability and can be flexibly adjusted. Currently, the third method is increasingly used as the complexity of the runtime diagram problem increases and the business optimization software rapidly develops.
Based on the theory and the current application situation, the invention provides a high-speed train operation diagram line adding method based on a multi-target mixed integer programming model.
Disclosure of Invention
The invention aims to provide a method for optimizing an operation diagram of a newly added line of a high-speed railway, which aims to reduce the operation time of the newly added line while ensuring the service quality of the existing line. The invention especially considers the practical factors of station line distribution, the time window of departure from the starting station, the stop scheme of the train, time consumption of acceleration and deceleration and the like.
In order to achieve the purpose, the technical scheme provided by the invention is as follows: a high-speed rail operation diagram line-adding optimization method based on a multi-objective mixed integer programming model is disclosed. The method comprises the following steps:
s1, generating stop type constraints, section start time constraints, stop time constraints, departure time window constraints of an initial station, section travel interval constraints and station line distribution constraints according to input topological features of a target line, station platform line features, line speed limit, an original running chart of an existing train, information of a newly added line train, a minimum start interval of an adjacent train, a maximum adjustment amplitude of the existing train and a start time relaxation coefficient of the newly added train, and forming a constraint set by all the constraints;
s2, establishing an initial multi-target mixed integer programming model according to the constraint set and the objective function;
s3, calculating the earliest and latest moments when the existing trains arrive and leave each station one by one according to the line speed limit of the existing trains in the original operation diagram of the existing trains, judging whether the departure sequence of each pair of existing trains at each station is possible to change, generating departure sequence constraints according to the departure sequence of the existing train pairs of which the departure sequence is not changed, generating driving rule constraints according to driving rules, and establishing a multi-target mixed integer programming model according to the departure sequence constraints, the driving rule constraints and the initial multi-target mixed integer programming model;
s4, calculating the shortest operation duration of the newly added line train and setting the upper limit constraint of the operation duration of the newly added line train, establishing a first single-target mixed integer programming model according to the shortest operation duration and the longest operation duration of the newly added line train and the multi-target mixed integer programming model, and solving the first single-target mixed integer programming model to obtain and output an optimized operation diagram of the existing train;
and S5, establishing a second single-target mixed integer programming model according to the shortest operation time of the newly added line train, the optimized operation diagram of the existing train and the multi-target mixed integer programming model, and solving the second single-target mixed integer programming model to obtain and output the operation diagram of the newly added line train.
Preferably, the station stop type constraint is expressed as
Figure BDA0001505517790000031
Wherein,
Figure BDA0001505517790000032
plan stop plan for train k at station i, if train k plans to stop at station i
Figure BDA0001505517790000033
If not, then,
Figure BDA0001505517790000034
xk,ithe actual stop plan for train k at station i.
The segment open time constraint is expressed as
Figure BDA0001505517790000035
Figure BDA0001505517790000036
Wherein,
Figure BDA0001505517790000037
the time when the train k reaches the station i in the original operation diagram is shown;
ak,ithe actual time when the train k arrives at the station i;
Figure BDA00015055177900000316
the time when the train k leaves the station i in the original operation diagram;
dk,ithe actual moment when the train k leaves the station i;
σ (k) is the type of train k, σ (k) is 0 if the train k is a high-speed train, and σ (k) is 1 if the train k is a normal train;
Figure BDA0001505517790000038
and
Figure BDA0001505517790000039
the upper bound and the lower bound of the time length of the uniform speed running of the sigma (k) type train k on the road section i' respectively;
τaand τdRespectively the duration of the acceleration and deceleration driving of the train;
the stop time constraint is expressed as
xk,i·M≥dk,i-ak,i≥xk,i·si
Wherein M is a set integer;
sithe minimum station stopping time length when the train stops at the station i is obtained;
the origin station departure time window constraint is expressed as
Figure BDA00015055177900000310
Figure BDA00015055177900000311
Wherein, deltakThe maximum allowable deviation of the time when the train k leaves the starting station;
Figure BDA00015055177900000312
is the origin of train k, wherein
Figure BDA00015055177900000313
k∈Ke∪Ka；
Figure BDA00015055177900000314
Is the final station of train k, wherein
Figure BDA00015055177900000315
k∈Ke∪Ka；
The zone headway interval constraint is expressed as
Figure BDA0001505517790000041
Figure BDA0001505517790000042
yk,l,i+yl,k,i＝1
Wherein,
Figure BDA0001505517790000043
the minimum interval for adjacent trains to reach station i;
Figure BDA0001505517790000044
the minimum interval for adjacent trains to leave the station i;
the station line allocation constraint is expressed as
Figure BDA0001505517790000045
Figure BDA0001505517790000046
Figure BDA0001505517790000047
Wherein, yk,l,iY is the departure time of train k at station i is earlier than train l k,l,i0, otherwise yk,l,i＝1；
zk,i,pZ if train k is assigned to station line p at station ik,i,p1, otherwise zk,i,p＝0；
PiIs the station line set of station i.
Preferably, the objective function of step S2 is expressed as
Figure BDA0001505517790000048
Figure BDA0001505517790000049
Wherein, KeFor existing train set, | Ke|＝Ke,i.e.,Ke＝{1,2,…,Ke}；
KaFor newly added train set, | Ka|＝Ka,i.e.,Ka＝{Ke+1,Ke+2,…,Ke+Ka}；
N is station set, | N | ═ N +1, N ═ 0,1, …, N };
Nkset of stations for train k to pass, wherein
Figure BDA00015055177900000418
Figure BDA00015055177900000410
Is the origin of train k, wherein
Figure BDA00015055177900000411
k∈Ke∪Ka；
Figure BDA00015055177900000412
Is the final station of train k, wherein
Figure BDA00015055177900000413
k∈Ke∪Ka；
Figure BDA00015055177900000414
The starting time of a newly added train k is added;
Figure BDA00015055177900000415
adjusting departure time of the starting station;
Figure BDA00015055177900000416
time offsets are opened for the segments;
Figure BDA00015055177900000417
is the station time offset.
Preferably, the initial multi-objective mixed integer programming model of step S2 is expressed as
Figure BDA0001505517790000051
Wherein Cons is a constraint set.
Preferably, the departure sequence restriction of step S3 further includes the following sub-steps:
s3.1, sequencing the existing train set Ke according to the departure time sequence, and enabling k to be 1;
s3.2, calculating the earliest arrival time of the existing train k at each station where the existing train k passes
Figure BDA0001505517790000052
And earliest departure time
Figure BDA0001505517790000053
S3.3, calculating the latest arrival time and the latest departure time of the existing train k at each station where the existing train k passes through, and respectively recording the latest arrival time and the latest departure time as:
Figure BDA0001505517790000054
and
Figure BDA0001505517790000055
s3.4, if k is | Ke |, making k equal to 0, and then go to step S3.5; otherwise, making k equal to k +1, and going to step S3.2;
s3.5, if k ═ Ke | -1, proceed to step S3.7; otherwise, making k equal to k +1, and going to step S3.6;
s3.6, generating departure sequence constraint:
s3.6.1, let l be k + 1;
s3.6.2 for train pair (k, l), if at the origin station i1Satisfy the requirement of
Figure BDA0001505517790000056
And at terminal i2Satisfy the requirement of
Figure BDA0001505517790000057
Then y isk,l,i＝0；
S3.6.3, if l ═ Ke |, turn S3.6; otherwise, changing l to l +1, and switching to S3.6.2;
s3.7, y to be obtainedk,l,i0 is added to the set Cons as a constraint.
Preferably, the driving rule constraint in step S3 is expressed as:
zk,i,1＝1-xk,i
the driving rule constraints are added to the set Cons.
Preferably, the specific process of step S4 is:
s4.1, solving the shortest running time of the newly-added line train, wherein the formula is as follows:
Figure BDA0001505517790000058
wherein s isiAnd the minimum station-stopping time length of the train at the station i is shown.
S4.2, obtaining each newly added line train based on the stage one
Figure BDA00015055177900000510
Generating an on-line duration upper bound constraint
Figure BDA0001505517790000059
S4.3, establishing a first single-target mixed integer programming model according to the shortest operation duration and the upper limit constraint of the operation duration of the newly added line train and the multi-target mixed integer programming model:
Figure BDA0001505517790000061
wherein the coefficient rho is a relaxation factor;
and S4.4, solving the first single-target mixed integer programming model to obtain an optimized running chart of the existing train.
Preferably, step S5 further includes the following sub-steps:
s5.1, establishing a second single-target mixed integer programming model according to the shortest running time of the newly added line train, the optimized running chart of the existing train and the multi-target mixed integer programming model:
Figure BDA0001505517790000062
and S5.2, solving the second single-target mixed integer programming model to obtain a running chart of the newly added line train.
The invention has the following beneficial effects:
according to the technical scheme, the actual factors of station line distribution, the time window of departure from the starting station, the train stop scheme, acceleration, deceleration, time consumption and the like are comprehensively considered, the running time of the newly added line and the adjustment range of the existing line are simultaneously minimized as optimization targets, and the running requirements of the newly added line and the existing line are considered. By decomposing the original large-scale problem and combining a preprocessing algorithm, the technology can efficiently solve the problem of the line adding of the high-speed railway operation diagram. On one hand, higher controllability of public transportation travel time is provided for travelers, and on the other hand, important technical support is provided for improving public transportation sharing and relieving urban traffic jam.
Drawings
The following detailed description of embodiments of the invention is provided in conjunction with the appended drawings:
FIG. 1 is a flow chart of the method of the present invention for completing the line-adding of a high-speed railway;
fig. 2 is a schematic diagram of a station and station lines;
FIG. 3 is a schematic view of an intercity railway line in embodiment 2;
FIG. 4 is an original operation diagram of an inter-city railway in example 2;
fig. 5 is a new operation diagram after the addition of the wire in embodiment 2.
Detailed Description
In order to more clearly illustrate the invention, the invention is further described below with reference to preferred embodiments and the accompanying drawings. Similar parts in the figures are denoted by the same reference numerals. It is to be understood by persons skilled in the art that the following detailed description is illustrative and not restrictive, and is not to be taken as limiting the scope of the invention.
As shown in fig. 1, the embodiment provides a method for optimizing an operation diagram of a newly added line of a high-speed railway, which includes the following steps:
s1, generating a stop type constraint, a section start time constraint, a stop time constraint, an origin departure time window constraint, a section travel interval constraint and a station line distribution constraint according to input topological characteristics of a target line, station platform station line characteristics, line speed limit, an original running chart of an existing train, information of a newly added line train, a minimum start interval of an adjacent train, a maximum adjustment amplitude of the existing train and a start time relaxation coefficient of the newly added train, wherein the constraint comprises the following specific processes:
s1.1, setting decision variables of the multi-target mixed integer programming model, including:
continuity decision variable ak,iIndicating the time when the train k arrives at the station i;
continuity decision variable dk,iIndicating the time when the train k leaves the station i;
boolean-type decision variable xk,iDenoted as if train k stops at station i, xk,i1, otherwise xk,i＝0；
Boolean decision variable yk,l,iIndicated as at station i, if train k departs earlier than train l,
y k,l,i0, otherwise yk,l,i＝1；
Boolean decision variable zk,i,pDenoted at station i if train k is assigned to station line p, zk,i,p＝1，
Otherwise zk,i,p＝0；
S2.2, generating a constraint set, comprising:
a stop type constraint. If the existing train k stops at the station i in the original operation diagram, the train k must stop at the station i in the new operation diagram; if a newly added train k stops at station i as planned, then train k must stop at station i in the new train diagram. According to xk,iAnd xk,iThe station type constraint is expressed as:
Figure BDA0001505517790000071
wherein,
Figure BDA0001505517790000072
plan stop plan for train k at station i, if train k plans to stop at station i
Figure BDA0001505517790000073
If not, then,
Figure BDA0001505517790000074
xk,ithe actual stop plan for train k at station i.
The segment open time constraint. The starting time of the train k in the section i consists of pure starting time and acceleration and deceleration time. Since the pure open time has upper and lower bound, the segment open time constraint is expressed as:
Figure BDA0001505517790000081
Figure BDA0001505517790000082
wherein,
Figure BDA0001505517790000083
the time when the train k reaches the station i in the original operation diagram is shown;
akithe actual time when the train k arrives at the station i;
Figure BDA0001505517790000084
the time when the train k leaves the station i in the original operation diagram;
dk,ithe actual moment when the train k leaves the station i;
σ (k) is the type of train k, σ (k) is 0 if the train k is a high-speed train, and σ (k) is 1 if the train k is a normal train;
Figure BDA0001505517790000085
and
Figure BDA0001505517790000086
the upper bound and the lower bound of the time length of the uniform speed running of the sigma (k) type train k on the road section i' respectively;
τaand τdThe acceleration and deceleration driving time lengths of the train are respectively, wherein the acceleration of the train in the acceleration stage is not changed, and the acceleration of the train in the deceleration stage is not changed when the train is in each road section.
And (4) station stop time constraint. If the train k stops at the station i, the stop time of the train k is longer than the minimum stop time; if the train k does not stop at the station i, the stop time is 0. The stop time constraint is expressed as:
xk,i·M≥dk,i-ak,i≥xk,i·si (4)
wherein M is an integer set according to actual requirements;
sithe minimum station stopping time length when the train stops at the station i is obtained;
an origin station departure time window constraint. For an existing train k, from the origin in the new diagram
Figure BDA00015055177900000816
Time of departure
Figure BDA0001505517790000087
The time window constraint that must be satisfied is expressed as:
Figure BDA0001505517790000088
for the newly added train k, the train k is started from the starting station in the new operation diagram
Figure BDA0001505517790000089
Time of departure
Figure BDA00015055177900000810
Time window that must be metThe mouth constraint is expressed as:
Figure BDA00015055177900000811
wherein, deltakThe maximum allowable deviation of the time when the train k leaves the starting station;
Figure BDA00015055177900000812
the starting station of train k, wherein
Figure BDA00015055177900000813
k∈Ke∪Ka；
Figure BDA00015055177900000814
Is the final station of train k, wherein
Figure BDA00015055177900000815
k∈Ke∪Ka；
And (5) driving intervals of the sections. The zone traffic interval constraint includes two parts, namely departure interval constraint and arrival interval constraint. Since the departure sequence is not determined in advance, this type of constraint can be expressed in a linear form by means of the large M method, i.e. for train k and train l, its section traffic interval constraint at the departure interval and arrival interval of station i:
Figure BDA0001505517790000091
Figure BDA0001505517790000092
wherein,
Figure BDA0001505517790000093
the minimum interval for adjacent trains to reach station i;
Figure BDA0001505517790000094
the minimum interval for adjacent trains to leave the station i;
according to the Boolean variable yk,l,iThe following constraints must be satisfied:
yk,l,i+yl,k,i＝1 (9)
station line allocation constraints. If the station line allocated by train k and train l is the same at station i, then their departure-arrival interval must be greater than hda. According to yk,l,iAnd zk,i,pDefinition of (1), station line allocation constraint must be expressed as
Figure BDA0001505517790000095
Figure BDA0001505517790000096
Figure BDA0001505517790000097
Wherein, yk,l,iY is the departure time of train k at station i is earlier than train l k,l,i0, otherwise yk,l,i＝1；
zk,i,pZ if train k is assigned to station line p at station ik,i,p1, otherwise zk,i,p＝0；
PiIs the station line set of station i.
S2, establishing an initial multi-target mixed integer programming model according to the constraint set and the target function, and the specific process is as follows:
the model simultaneously considers two objective functions, and the two objective functions respectively correspond to the total running time of the newly added line train and the adjustment amplitude of the existing line train. The first objective function is expressed as:
Figure BDA0001505517790000098
wherein,
Figure BDA0001505517790000099
indicating the time of the new train k. The second objective function is expressed as:
Figure BDA00015055177900000910
the three items respectively represent departure time adjustment, section starting time deviation and stop time deviation of the starting station.
Wherein, KeFor existing train set, | Ke|＝Ke,i.e.,Ke＝{1,2,…,Ke}；
KaFor newly added train set, | Ka|＝Ka,i.e.,Ka＝{Ke+1,Ke+2,…,Ke+Ka}；
N is station set, | N | ═ N +1, N ═ 0,1, …, N };
Nkset of stations for train k to pass, wherein
Figure BDA0001505517790000101
k∈Ke∪Ka；
Figure BDA0001505517790000102
The starting time of a newly added train k is added;
Figure BDA0001505517790000103
adjusting departure time of the starting station;
Figure BDA0001505517790000104
time offsets are opened for the segments;
Figure BDA0001505517790000105
is the station time offset.
Representing the constraint set of the initial multi-objective mixed integer programming model by the set Cons ═ { constraint (1) - - (12) }, then the initial multi-objective mixed integer programming model is represented as
Figure BDA0001505517790000106
S3, calculating the earliest and latest moments when the existing trains arrive and leave each station one by one according to the line speed limit of the existing trains in the original operation diagram of the existing trains, judging whether the departure sequence of each pair of existing trains at each station is possible to change, generating departure sequence constraints according to the departure sequence of the existing train pairs of which the departure sequence is not changed, generating driving rule constraints according to driving rules, and establishing a multi-target mixed integer programming model according to the departure sequence constraints, the driving rule constraints and the initial multi-target mixed integer programming model, wherein the specific process is as follows:
s3.1, sequencing the existing train set Ke according to the departure time sequence, and enabling k to be 1;
s3.2, calculating the earliest arrival time of the existing train k at each station where the existing train k passes
Figure BDA0001505517790000107
And earliest departure time
Figure BDA0001505517790000108
S3.3, calculating the latest arrival time and the latest departure time of the existing train k at each station where the existing train k passes through, and respectively recording the latest arrival time and the latest departure time as:
Figure BDA0001505517790000109
and
Figure BDA00015055177900001010
s3.4, if k is | Ke |, making k equal to 0, and then go to step S3.5; otherwise, making k equal to k +1, and going to step S3.2;
s3.5, if k ═ Ke | -1, proceed to step S3.7; otherwise, making k equal to k +1, and going to step S3.6;
s3.6, generating departure sequence constraint:
s3.6.1, let l be k + 1;
s3.6.2 for train pair (k, l), if at the origin station i1Satisfy the requirement of
Figure BDA00015055177900001011
And at terminal i2Satisfy the requirement of
Figure BDA00015055177900001012
Then y isk,l,i＝0；
S3.6.3, if l ═ Ke |, proceed to step S3.6; otherwise, if l is l +1, go to step S3.6.2;
s3.7, y to be obtainedk,l,i0 is added to the set Cons as an departure order constraint.
In step S3.2, no other trains are considered, and it is assumed that the existing train k stops according to the stop plan of the original operation diagram, and the stop time is the shortest stop time and runs at the fastest speed. In step S3.3, it is assumed that the existing train k stops at each station passed by and starts at the slowest speed, regardless of other trains. At station i, if the original movement diagram specifies that train k is stopped, then the stop duration at station i in step S3.3 is equal to the stop duration in the original movement diagram, otherwise the stop is the shortest stop duration.
Besides some departure sequences can be predetermined, the relation of some Boolean variables can be determined according to the driving rule. For example, if a train k passes through a station i without stopping, the train k will be assigned to a station line 1 according to fig. 1; otherwise, it will be assigned to other station lines. This relationship can be expressed as a driving rule constraint:
zk,i,1＝1-xk,i.
the constraints described above are also added to the set Cons.
S4, calculating the shortest operation duration of the newly added line train, setting the upper limit constraint of the operation duration of the newly added line train, establishing a first single-target mixed integer programming model according to the shortest operation duration and the longest operation duration of the newly added line train and the multi-target mixed integer programming model, and solving the first single-target mixed integer programming model to obtain and output an optimized operation diagram of the existing train, wherein the specific process is as follows:
since the original model is a dual target, it cannot be directly optimized. In addition, the original model has a large scale, the feasible solution range is too large, and the solver is difficult to find the optimal solution within an acceptable time. Through proper decomposition, a single-target mixed integer programming model with a smaller feasible solution range is obtained, the single-target mixed integer programming model comprises a first single-target mixed integer programming model and a second single-target mixed integer programming model, the single-target mixed integer programming models are solved one by one, an optimal solution can be obtained in a shorter time, and commercial optimization software Gurobi can be borrowed.
S4.1, solving the shortest running time of the newly-added line train, wherein the formula is as follows:
Figure BDA0001505517790000111
wherein s isiAnd the minimum station-stopping time length of the train at the station i is shown.
S4.2, obtaining each newly added line train based on the stage one
Figure BDA0001505517790000114
Generating an on-line duration upper bound constraint
Figure BDA0001505517790000113
S4.3, establishing a first single-target mixed integer programming model according to the shortest operation duration and the upper limit constraint of the operation duration of the newly added line train and the multi-target mixed integer programming model:
Figure BDA0001505517790000121
wherein the coefficient rho is a relaxation factor;
and S4.4, solving the first single-target mixed integer programming model to obtain an optimized running chart of the existing train.
S5, establishing a second single-target mixed integer programming model according to the shortest operation time of the newly added line train, the optimized operation diagram of the existing train and the multi-target mixed integer programming model, and solving the second single-target mixed integer programming model to obtain and output the operation diagram of the newly added line train, wherein the specific process is as follows:
s5.1, establishing a second single-target mixed integer programming model according to the shortest running time of the newly added line train, the optimized running chart of the existing train and the multi-target mixed integer programming model:
Figure BDA0001505517790000122
and S5.2, solving the second single-target mixed integer programming model to obtain a running chart of the newly added line train.
In order to more clearly illustrate the present invention, the method for adding lines to an operation diagram based on a multi-objective mixed integer programming model provided in this embodiment is further described in the case of adding lines in a single direction and multiple starting-ending stations.
As shown in fig. 3, one-way, multi-origin-terminal addition is the most common addition for inter-city trains. In fig. 3, the shaded squares represent large stations as originating or terminating stations, and the circles represent intermediate stations. It is assumed here that a large station has a sufficient number of station lines allocated to a train, and the station platform and station line structure of a small station is one of fig. 2, in which (1,2) denotes "1-station-2-station line" and (2,3) denotes "2-station-3-station line". Fig. 4 is an original operation diagram of existing trains from 6:00 to 16:00, and there are 60 existing trains in total, wherein the high-speed train is 35 and the normal train is 25.
Assuming that all the acceleration time and the deceleration time are 2 minutes, table 1 lists the upper and lower bounds of the pure opening time of the high-speed train and the ordinary train in each section; the minimum interval of departure of a large station is 5 minutes, the minimum interval of arrival of the large station is 3 minutes, and the minimum stop time is 3 minutes; the minimum departure interval of the small station is 3 minutes, the arrival interval is 2 minutes, and the minimum stop time is 2 minutes; if the two cars share one station line, the minimum interval between the departure of the front car and the arrival of the rear car is 2 minutes; the maximum adjustment range of the departure time of the existing train at the starting station is 5 minutes. The invention will be described below by way of example for this circuit:
table 1: zone pure open-up upper and lower bound (unit: minute)
Segment of High-speed train Ordinary train Segment of High-speed train Ordinary train
1 (12,16) (15,16) 9 (7,8) (7,8)
2 (5,7) (7,9) 10 (7,8) (7,8)
3 (6,9) (7,10) 11 (6,7) (6,7)
4 (9,10) (11,14) 12 (6,7) (6,7)
5 (6,7) (6,7) 13 (6,7) (6,7)
6 (12,13) (12,13) 14 (6,7) (6,7)
7 (10,11) (10,11) 15 (5,6) (5,6)
8 (10,11) (10,11) 16 (7,8) (7,8)
First, 10 newly added line trains listed in table 2 were added to the original operating diagram.
Table 2: newly added line train information
Numbering Type (B) Originating-terminating station Planned stop Time window
1 High speed 0-16 {0,3,5,7,9,11,14,16} [7:00,8:00]
2 General 0-16 {0,2,5,7,9,11,13,16} [7:00,9:00]
3 General 0-16 {0,1,3,5,10,13,15,16} [11:00,12:00]
4 High speed 0-5 {0,3,5} [10:00,12:00]
5 High speed 0-16 {0,2,5,7,11,16} [9:00,10:00]
6 High speed 0-16 {0,3,5,9,13,16} [12:00,13:00]
7 High speed 0-5 {0,3,5} [8:00,9:00]
8 High speed 0-16 {0,5,8,11,13,15,16} [13:00,15:00]
9 General 5-16 {5,6,9,12,14,16} [15:00,16:00]
10 High speed 0-16 {0,2,3,5,7,10,13,14,16} [14:00,15:00]
Secondly, inputting information of a line, an existing train, a newly added train and related parameters in sequence according to the process shown in the figure 1, constructing a constraint condition set and an objective function, and establishing a mixed integer programming model. Then, the existing trains are preprocessed, the departure sequence between part of the train pairs is determined, and the departure sequence is added into the constraint condition.
Subsequently, the model is solved using a three-stage decomposition optimization method.
Stage one: according to the speed limit information shown in the table 1 and the newly added train information shown in the table 2, the shortest running time of the newly added line train can be calculated according to a formula (13)
Figure BDA0001505517790000131
I.e., {160,168, 48,148,48,154,109,166 }.
And a second stage: will be provided with
Figure BDA0001505517790000132
Is input into a single target mixed integer programming model (14), where ρ is 1.2. And solving the model (14) to obtain the running chart of the existing train, wherein the solving model (14) can be realized by calling commercial optimization software Gurobi. Wherein the sum of the adjustment ranges of the existing trains is 14 minutes, namely F 214. Stage twoApproximately 80 seconds.
And a third stage: and inputting the existing train running diagram obtained in the second stage into a mixed integer planning model (15), and solving the model (15) to obtain the running diagram of the newly-added line train, wherein the solving model (15) can be realized by calling commercial optimization software Gurobi. Wherein, the running time sum of the newly added line train is 1439 minutes, namely F11439. Phase three takes approximately 5 seconds.
Fig. 5 shows the final operating diagram with the dashed lines representing the newly added train and the implementation representing the existing train.
Finally, to verify the suitability of the model, we performed 400 additional sets of numerical tests. For the number of new trains | Ka | ═ 5,10,15, and 20, 100 sets of new trains are randomly generated, respectively. And arranging 3 columns of newly added trains at most every hour for each group of generated sets. The time limit (TimeLimit) parameter for Gurobi is set to 1800 seconds, i.e. if the optimal solution has not been obtained at 1800 seconds, the test is aborted.
Table 3 gives statistics of the phase two and phase three calculation times. When | Ka | ═ 5 and 10, all the tested mixed integer programming models can get the optimal solution within 1800 seconds, and the average computation time does not exceed 30 seconds and 120 seconds. When | Ka | > 15, there were 2 sets of trials that did not yield the optimal solution within the specified time, and the remaining 98 sets of trials averaged no more than 230 seconds. When | Ka | ═ 20, there were 6 sets of trials that did not yield the optimal solution within the specified time, and the remaining 94 sets of trials averaged no more than 530 seconds. Considering that more than 10 trains can not be added on one intercity line at the same time in practice, the method of the invention can basically find the optimal solution of the line adding problem of the high-speed railway in a short time.
Table 3: calculating time statistics
Figure BDA0001505517790000141
It should be understood that the above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention, and it will be obvious to those skilled in the art that other variations or modifications may be made on the basis of the above description, and all embodiments may not be exhaustive, and all obvious variations or modifications may be included within the scope of the present invention.

Claims (8)

1. A method for optimizing a running chart of a newly added line of a high-speed railway is characterized by comprising the following steps:
s1, generating stop type constraints, section start time constraints, stop time constraints, departure time window constraints of an initial station, section travel interval constraints and station line distribution constraints according to input topological features of a target line, station platform line features, line speed limit, an original running chart of an existing train, information of a newly added line train, a minimum start interval of an adjacent train, a maximum adjustment amplitude of the existing train and a start time relaxation coefficient of the newly added train, and forming a constraint set by all the constraints;
s2, establishing an initial multi-target mixed integer programming model according to the constraint set and the objective function;
s3, calculating the earliest and latest moments when the existing trains arrive and leave each station one by one according to the line speed limit of the existing trains in the original operation diagram of the existing trains, judging whether the departure sequence of each pair of existing trains at each station is possible to change, generating departure sequence constraints according to the departure sequence of the existing train pairs of which the departure sequence is not changed, generating driving rule constraints according to driving rules, and establishing a multi-target mixed integer programming model according to the departure sequence constraints, the driving rule constraints and the initial multi-target mixed integer programming model;
s4, calculating the shortest operation duration of the newly added line train, setting the upper limit constraint of the operation duration of the newly added line train, establishing a first single-target mixed integer programming model according to the shortest operation duration and the upper limit constraint of the operation duration of the newly added line train and the multi-target mixed integer programming model, and solving the first single-target mixed integer programming model to obtain and output an optimized operation diagram of the existing train;
and S5, establishing a second single-target mixed integer programming model according to the shortest operation time of the newly added line train, the optimized operation diagram of the existing train and the multi-target mixed integer programming model, and solving the second single-target mixed integer programming model to obtain and output the operation diagram of the newly added line train.
2. The method for optimizing the working diagram of the newly added line of the high-speed railway according to claim 1, wherein the stop type constraint is expressed as
Figure FDA0003079703370000011
Wherein,
Figure FDA0003079703370000012
plan stop plan for train k at station i, if train k plans to stop at station i
Figure FDA0003079703370000013
If not, then,
Figure FDA0003079703370000014
xk,ian actual stop scheme of the train k at the station i;
the segment open time constraint is expressed as
Figure FDA0003079703370000021
Figure FDA0003079703370000022
Wherein,
Figure FDA0003079703370000023
the time when the train k reaches the station i in the original operation diagram is shown;
ak,ithe actual time when the train k arrives at the station i;
Figure FDA0003079703370000024
the time when the train k leaves the station i in the original operation diagram;
dk,ithe actual moment when the train k leaves the station i;
σ (k) is the type of train k, σ (k) is 0 if the train k is a high-speed train, and σ (k) is 1 if the train k is a normal train;
Figure FDA0003079703370000025
and
Figure FDA0003079703370000026
the upper bound and the lower bound of the time length of the uniform speed running of the sigma (k) type train k on the road section i' respectively;
τaand τdRespectively the duration of the acceleration and deceleration driving of the train;
the stop time constraint is expressed as
xk,i·M≥dk,i-ak,i≥xk,i·si
Wherein M is a set integer;
sithe minimum station stopping time length when the train stops at the station i is obtained;
if k is an existing train, the departure time constraint of the origin station is expressed as
Figure FDA0003079703370000027
If k is a newly added train, the departure time constraint of the starting station is expressed as
Figure FDA0003079703370000028
Wherein, deltakThe maximum allowable deviation of the time when the train k leaves the starting station;
Figure FDA0003079703370000029
is the origin of train k, wherein
Figure FDA00030797033700000210
Figure FDA00030797033700000211
Is the final station of train k, wherein
Figure FDA00030797033700000212
Figure FDA00030797033700000213
Indicating that newly added train k is at the origin
Figure FDA00030797033700000214
The earliest departure time;
Figure FDA00030797033700000215
indicating that newly added train k is at the origin
Figure FDA00030797033700000216
The latest departure time;
the zone headway interval constraint is expressed as
Figure FDA00030797033700000217
Figure FDA00030797033700000218
yk,l,i+yl,k,i＝1
Wherein,
Figure FDA00030797033700000219
the minimum interval for adjacent trains to reach station i;
Figure FDA0003079703370000031
the minimum interval for adjacent trains to leave the station i;
the station line allocation constraint is expressed as
Figure FDA0003079703370000032
Figure FDA0003079703370000033
Figure FDA0003079703370000034
Wherein, yk,l,iY is the departure time of train k at station i is earlier than train lk,l,i0, otherwise yk,l,i＝1；
zk,i,pZ if train k is assigned to station line p at station ik,i,p1, otherwise zk,i,p＝0；
hdaRepresenting the minimum time interval between the departure of the previous train and the arrival of the next train on the same station line;
Piis the station line set of station i.
3. The method according to claim 2, wherein the objective function of step S2 is expressed as
Figure FDA0003079703370000035
Figure FDA0003079703370000036
Wherein, KeFor existing train set, | Ke|＝Ke,i.e.,Ke＝{1,2,…,Ke}；
KaFor newly added train set, | Ka|＝Ka,i.e.,Ka＝{Ke+1,Ke+2,…,Ke+Ka}；
N is station set, | N | ═ N +1, N ═ 0,1, …, N };
Nkset of stations for train k to pass, wherein
Figure FDA0003079703370000037
Figure FDA0003079703370000038
The starting time of a newly added train k is added;
Figure FDA0003079703370000039
adjusting departure time of the starting station;
Figure FDA00030797033700000310
time offsets are opened for the segments;
Figure FDA00030797033700000311
is the station time offset.
4. The method of claim 3, wherein the initial multi-objective mixed integer programming model of step S2 is represented as
Figure FDA0003079703370000041
Wherein Cons is a constraint set.
5. The method of claim 4, wherein the departure sequence constraint of step S3 further comprises the sub-steps of:
s3.1, sequencing the existing train set Ke according to the departure time sequence, and enabling k to be 1;
s3.2, calculating the earliest arrival time of the existing train k at each station where the existing train k passes
Figure FDA0003079703370000042
And earliest departure time
Figure FDA0003079703370000043
S3.3, calculating the latest arrival time and the latest departure time of the existing train k at each station where the existing train k passes through, and respectively recording the latest arrival time and the latest departure time as:
Figure FDA0003079703370000044
and
Figure FDA0003079703370000045
s3.4, if k is | Ke |, making k equal to 0, and then go to step S3.5; otherwise, making k equal to k +1, and going to step S3.2;
s3.5, if k ═ Ke | -1, proceed to step S3.7; otherwise, making k equal to k +1, and going to step S3.6;
s3.6, generating departure sequence constraint:
s3.6.1, let l be k + 1;
s3.6.2 for train pair (k, l), if at the origin station i1Satisfy the requirement of
Figure FDA0003079703370000046
And at terminal i2Satisfy the requirement of
Figure FDA0003079703370000047
Then y isk,l,i＝0；
S3.6.3, if l ═ Ke |, proceed to step S3.6; otherwise, if l is l +1, go to step S3.6.2;
s3.7, y to be obtainedk,l,i0 is added to the set Cons as a constraint.
6. The method according to claim 4 or claim 5, wherein the driving rule constraint of step S3 is expressed as:
zk,i,1＝1-xk,i
the driving rule constraints are added to the set Cons.
7. The method according to claim 6, wherein the specific process of step S4 is as follows:
s4.1, solving the shortest running time of the newly-added line train, wherein the formula is as follows:
Figure FDA0003079703370000051
wherein s isiThe minimum station stopping time length of the train at the station i is obtained;
s4.2, obtaining f based on the stage one for each newly added line train1 k*Generating an upper bound f on the duration of the run1 (k)≤ρ·f1 (k*)；
S4.3, establishing a first single-target mixed integer programming model according to the shortest operation duration and the upper limit constraint of the operation duration of the newly added line train and the multi-target mixed integer programming model:
Figure FDA0003079703370000052
wherein the coefficient rho is a relaxation factor;
and S4.4, solving the first single-target mixed integer programming model to obtain an optimized running chart of the existing train.
8. The method of claim 1, wherein step S5 further comprises the sub-steps of:
s5.1, establishing a second single-target mixed integer programming model according to the shortest running time of the newly added line train, the optimized running chart of the existing train and the multi-target mixed integer programming model:
Figure FDA0003079703370000053
and S5.2, solving the second single-target mixed integer programming model to obtain a running chart of the newly added line train.
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