CN108229725A - A kind of high ferro service chart ledger line optimization method based on mixed-integer programming model - Google Patents
A kind of high ferro service chart ledger line optimization method based on mixed-integer programming model Download PDFInfo
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Abstract
The invention discloses a kind of service chart ledger line methods based on Mixed Integer Multiple Goal Programming model in high-speed railway operation management field.Time window, train dwelling scheme and the acceleration and deceleration that this method has considered the distribution of station station track, the starting station is dispatched a car such as take at the practical factors, to minimize the run time on new ledger line road and the adjustment amplitude of existing line as optimization aim simultaneously, the operation demand of new ledger line road and existing line is taken into account.By the decomposition to original extensive problem, with reference to Preprocessing Algorithm, the present invention can efficiently solve high-speed railway service chart ledger line problem.
Description
Technical field
The invention belongs to the methods of railway transportation planning field more particularly to high-speed railway service chart ledger line.
Background technology
Route map of train is the aggregate plan of railway transportation work and the basis of organization of driving, be coordinate railway each department and
Unit presses the tool of certain procedures carry out activity.Briefly, service chart determines that train reaches and sail out of key facility (such as vehicle
Stand, marshalling yard) at the time of, to ensure that train is not clashed in normal operation on road network, and the utilization rate of resource can
Being optimal.To adapt to the variation of passenger flow, new train line is had sometimes and is added in existing service chart.For new fortune
Row figure, on the one hand, the arriving for service quality needs on new ledger line road ensures；On the other hand, it is contemplated that passenger's is accustomed to by bus, existing
The adjustment of circuit is small as possible.This has resulted in the conflict of new ledger line road and existing line, it is desirable that route map of train is closed
The redesign of reason thereby produces the research of service chart ledger line technology.Currently, China express railway have " the more, line length of point,
It is wide, cross-line passenger flow is more, density of dispatching a car is big " the features such as, and run the train of two kinds of speed, i.e. 300km/h and 250km/
h.When being designed to service chart ledger line, it is necessary to consider the factors such as traffic safety, train overtaking, passenger transference.
In longer in the period of, the design of service chart is based on artificial experience, generally compared with major general's mathematical optimization mostly
Method fusion is entered.Into last century the nineties, with the fast development of information science, area of computer aided operation G- Design is opened
Beginning is used widely.It follows that all kinds of optimization algorithms are gradually integrated into train dispatching system.Towards operation
The Optimization Modeling of figure usually has two class methods：First, time discretization, constructs time-space network, and then establish integer programming model
(integer programming,IP)；Second, dispatching a car sequentially with Boolean variable description, mixed-integer programming model is established
(mixed integer programming,MIP).The problem of route map of train, is converted into the network optimization and asked by first method
Topic, can effectively introduce the ripe algorithm of the network optimization, but shortcoming be time-space network scale with time shaft extension drastically
Increase.Existing scheduling system uses second of Optimization Modeling method mostly.
The mixed-integer programming model established for service chart often has larger scale, existing method for solving master
Will there are three types of.First, design element heuritic approach (metaheuristics), as genetic algorithm (genetic algorithm),
Tabu search algorithm (tabu search algorithm) etc..This kind of algorithm has stronger applicability, but tends not to ensure
As a result quality, and it is longer to calculate the time.Second, using Lagrange relaxation (Lagrange relaxation), column-generation
The algorithm that the more efficients such as (column generation), branch-and-bound (branch and bound) are stablized.But this kind of algorithm
There is higher requirement to the structure of problem, the model that can be solved is often fairly simple.Third, with reference to heuristic rule, to original
Extensive problem decomposed, obtain a series of small-scale problems, recycle the business optimization softwares such as CPLEX or Gurobi by
One solves small-scale problem.The problem of the third method can be solved compared with polymorphic type, adaptability is extensive, can be adjusted flexibly.At present,
With the increase of service chart the complex nature of the problem and the fast development of business optimization software, the third method has obtained more and more
Application.
Based on above-mentioned theory and using present situation, the present invention proposes a kind of height based on Mixed Integer Multiple Goal Programming model
Fast route map of train ledger line method.
Invention content
The object of the present invention is to provide a kind of new ledger line road service chart optimization methods of high-speed railway, and intending realizing is ensuring
While existing line service quality, the run time on new ledger line road is reduced.The present invention is especially considering that station station track distribution, begins
Hair time window, train dwelling scheme and the acceleration and deceleration dispatched a car of station such as take at the practical factors.
To achieve the above object, technical solution provided by the invention is：One kind is based on Mixed Integer Multiple Goal Programming model
High ferro service chart ledger line optimization method.This method comprises the following steps：
S1, according to the topological characteristic of the target line of input, station platform station track feature, circuit speed limit, existing train
Original service chart, the information of new ledger line road train and adjacent train minimum start interval, the maximum of existing train adjusts width
Degree, newly plus train start time coefficient of relaxation generation stop type constraint, section start time-constrain, the dwell time constraint, begin
The time of departure window constraint of hair station, the constraint of section running interval and station track assignment constraints form constraint set by each constraint；
S2, initial Mixed Integer Multiple Goal Programming model is established according to constraint set and object function；
S3, the circuit speed limit according to existing train in the original service chart of existing train calculate existing train and reach one by one
With leave the earliest of each station and the latest moment, judge whether the sequence of dispatching a car per a pair of existing train at each station may occur
Variation is sequentially generated sequence constraint of dispatching a car, according to traffic rule according to the dispatching a car for existing train pair that sequence of dispatching a car will not change
Traffic rule constraint is generated, and according to sequence constraint and traffic rule constraint and the initial Mixed Integer Multiple Goal Programming mould of dispatching a car
Type establishes Mixed Integer Multiple Goal Programming model；
S4, calculate new ledger line road train it is most short start duration and new ledger line road train be set start the duration upper limit about
Beam, most short according to new ledger line road train start duration and longest starts duration and Mixed Integer Multiple Goal Programming model foundation
First single goal mixed-integer programming model, after solving the first single goal mixed-integer programming model to obtain and export optimization
The service chart of existing train；
S5, according to new ledger line road train it is most short start the time, optimization after existing train service chart and multiple target mix
Close integer programming model and establish the second single goal mixed-integer programming model, solve the second single goal mixed-integer programming model with
Obtain and export the service chart of new ledger line road train.
Preferably, the type constraint that stops is expressed as
Wherein,Plan for train k i AT STATION is stopped scheme, if if train k plans, i stops AT STATIONOtherwise,
xk,iThe scheme that actually stops for train k i AT STATION.
The section is started time-constrain and is expressed as
Wherein,For train k in original service chart get to the station i at the time of；
ak,iGet to the station practical moment of i for train k；
At the time of station i being left for train k in original service chart；
dk,iThe practical moment of station i is left for train k；
σ (k) is the type of train k, σ (k)=0 if train k is bullet train, the σ if train k is ordinary train
(k)=1；
WithThe respectively train k of σ (k) the types upper bound for the duration that average rate is started and lower bound on the i` of section；
τaAnd τdThe respectively acceleration of train and the duration started of deceleration；
The dwell time constraint representation is
xk,i·M≥dk,i-ak,i≥xk,i·si
Wherein, M is the integer of setting；
siMinimum when being parked in station i for train stops duration；
The starting station time of departure window constraint representation is
Wherein, δkThe maximum allowable offset at the time of starting station is left for train k；
For the starting station of train k, whereink∈Ke∪Ka；
For the terminal station of train k, whereink∈Ke∪Ka；
The section running interval constraint representation is
yk,l,i+yl,k,i=1
Wherein,Get to the station the minimum interval of i for adjacent train；
The minimum interval of station i is left for adjacent train；
The station track assignment constraints are expressed as
Wherein, yk,l,iFor if the frequency of train k i AT STATION earlier than train l if yk,l,i=0, otherwise yk,l,i=1；
zk,i,pZ if for i is assigned to station track p AT STATION if train kk,i,p=1, otherwise zk,i,p=0；
PiStation track set for station i.
Preferably, object function described in step S2 is expressed as
Wherein, KeFor existing train set, | Ke|=Ke,i.e.,Ke=1,2 ..., Ke}；
KaTo increase train set newly, | Ka|=Ka,i.e.,Ka={ Ke+1,Ke+2,…,Ke+Ka}；
N gathers for station, | N |=N+1, N={ 0,1 ..., N }；
NkGather for the train k stations passed through, wherein
For the starting station of train k, whereink∈Ke∪Ka；
For the terminal station of train k, whereink∈Ke∪Ka；
Newly to add train k's to start the moment；
It is adjusted for the starting station time of departure；
Start time deviation for section；
For dwell time deviation.
Preferably, initial Mixed Integer Multiple Goal Programming model is expressed as described in step S2
Wherein, Cons is constraint set.
Preferably, sequence constraint of dispatching a car described in step S3 further comprises following sub-step：
S3.1, it sorts according to the time sequencing dispatched a car to existing train set Ke, enables k=1；
S3.2, the earliest estimated arrival time respectively stood that existing train k passes through at it is calculatedWith set out the moment earliest
S3.3, the arrival the latest respectively stood and set out the moment the latest that existing train k passes through at it are calculated, be denoted as respectively：
With
If S3.4, k=| Ke |, k=0 is enabled, is transferred to step S3.5；Otherwise k=k+1 is enabled, is transferred to step S3.2；
If S3.5, k=| Ke | -1, it is transferred to step S3.7；Otherwise k=k+1 is enabled, is transferred to step S3.6；
S3.6, sequence constraint of dispatching a car is generated：
S3.6.1, l=k+1 is enabled；
S3.6.2, for train to (k, l), if in starting station i1MeetAnd in terminus i2MeetThen yk,l,i=0；
If S3.6.3, l=| Ke |, turn S3.6；Otherwise l=l+1 is enabled, turns S3.6.2；
S3.7, the y that will be obtainedk,l,i=0 is added to as constraints in set Cons.
Preferably, which is characterized in that traffic rule constraint representation is described in step S3：
zk,i,1=1-xk,i
The traffic rule constraint is added in set Cons.
Preferably, the detailed process of step S4 is：
S4.1, solution the most short of new ledger line road train start duration, and formula is as follows：
Wherein, siThe minimum that station i is parked in for train stops duration.
S4.2, for each new ledger line road train, obtained based on the stage oneThe constraint of the duration upper limit is started in generation
S4.3, according to new ledger line road train it is most short start duration and start the duration upper limit constraint and multiple target mixing it is whole
Number plan model establishes the first single goal mixed-integer programming model：
Wherein, coefficient ρ is relaxation factor；
S4.4, the first single goal mixed-integer programming model, the service chart of the existing train after being optimized are solved.
Preferably, step S5 further comprises following sub-step：
S5.1, according to new ledger line road train it is most short start duration, optimization after existing train service chart and multiple target
Mixed-integer programming model establishes the second single goal mixed-integer programming model：
S5.2, the second single goal mixed-integer programming model is solved, obtains the service chart of new ledger line road train.
Beneficial effects of the present invention are as follows：
This technology invents the technical solution, has considered station station track distribution, time window, the row that the starting station is dispatched a car
Vehicle stops scheme and acceleration and deceleration take and wait practical factors, to minimize the run time on new ledger line road and the tune of existing line simultaneously
Whole picture degree is optimization aim, takes into account the operation demand of new ledger line road and existing line.By the decomposition to original extensive problem,
With reference to Preprocessing Algorithm, which can efficiently solve high-speed railway service chart ledger line problem.On the one hand, it is provided for traveler
To the higher controllability of transit trip time, on the other hand, alleviate urban transportation to improve public transport and sharing and gather around
It is stifled to provide important technology support.
Description of the drawings
The specific embodiment of the present invention is described in further detail below in conjunction with the accompanying drawings:
Fig. 1 is the flow chart that the method for the present invention completes high-speed railway ledger line；
Fig. 2 is platform and station track schematic diagram；
Fig. 3 is inter-city passenger rail conspectus in embodiment 2；
Fig. 4 is the original service chart of inter-city passenger rail in embodiment 2；
Fig. 5 is the new service chart after ledger line in embodiment 2.
Specific embodiment
In order to illustrate more clearly of the present invention, the present invention is done further with reference to preferred embodiments and drawings
It is bright.Similar component is indicated with identical reference numeral in attached drawing.It will be appreciated by those skilled in the art that institute is specific below
The content of description is illustrative and be not restrictive, and should not be limited the scope of the invention with this.
As shown in Figure 1, present embodiments providing a kind of new ledger line road service chart optimization method of high-speed railway, this method includes
Following steps：
S1, according to the topological characteristic of the target line of input, station platform station track feature, circuit speed limit, existing train
Original service chart, the information of new ledger line road train and adjacent train minimum start interval, the maximum of existing train adjusts width
Degree, newly plus train start time coefficient of relaxation generation stop type constraint, section start time-constrain, the dwell time constraint, begin
The time of departure window constraint of hair station, the constraint of section running interval and station track assignment constraints form constraint set, specific mistake by each constraint
Cheng Wei：
S1.1, the decision variable for setting Mixed Integer Multiple Goal Programming model, including：
Continuity decision variable ak,i, represent train k get to the station i at the time of；
Continuity decision variable dk,i, at the time of representing that train k leaves station i；
Boolean type decision variable xk,iIf being expressed as train k is parked in station i, xk,i=1, otherwise xk,i=0；
Boolean type decision variable yk,l,i, be expressed as i AT STATION, if train k frequencys earlier than train l,
yk,l,i=0, otherwise yk,l,i=1；
Boolean type decision variable zk,i,p, i AT STATION is expressed as, if train k is assigned to station track p, zk,i,p=1,
Otherwise zk,i,p=0；
S2.2, generation constraint set, including：
Stop type constraint.If i's existing train k stops AT STATION in original service chart, then in new service chart
I's train k must stop AT STATION；If newly adding train k, i stops AT STATION according to plan, then train k is in vehicle in new service chart
The i that stands must stop.According to xk,iAnd xk,iDefinition, the type constraint that stops is expressed as：
Wherein,Plan for train k i AT STATION is stopped scheme, if if train k plans, i stops AT STATIONOtherwise,
xk,iThe scheme that actually stops for train k i AT STATION.
Section starts time-constrain.Train k starts the time and Acceleration and deceleration time forms in the time of starting of section i by pure.
Start the time due to pure and have bound limitation, section is started time-constrain and is expressed as：
Wherein,For train k in original service chart get to the station i at the time of；
akiGet to the station practical moment of i for train k；
At the time of station i being left for train k in original service chart；
dk,iThe practical moment of station i is left for train k；
σ (k) is the type of train k, σ (k)=0 if train k is bullet train, the σ if train k is ordinary train
(k)=1；
WithThe respectively train k of σ (k) the types upper bound for the duration that average rate is started and lower bound on the i` of section；
τaAnd τdThe respectively acceleration of train and the duration started of deceleration, wherein, train is at each section, in boost phase
Acceleration it is constant, it is also constant in the acceleration in stage in decelerating phase.
Dwell time constrains.If i's train k stops AT STATION, the dwell time must be longer than the minimum dwell time；If
I's train k does not stop AT STATION, then the dwell time is 0.Dwell time constraint representation is：
xk,i·M≥dk,i-ak,i≥xk,i·si (4)
Wherein, M is the integer set according to actual requirement；
siMinimum when being parked in station i for train stops duration；
Starting station time of departure window constraint.For existing train k, from the starting station in new service chartFrequencyThe time window constraint representation that must satisfy is：
For newly adding train k, from the starting station in new service chartFrequencyThe time window that must satisfy
Constraint representation is：
Wherein, δkThe maximum allowable offset at the time of starting station is left for train k；
The starting station of train k, whereink∈Ke∪Ka；
For the terminal station of train k, whereink∈Ke∪Ka；
Section running interval.The constraint of section running interval includes two parts, i.e. departure interval constraint and spacing constraint of arriving at a station.
Due to dispatching a car, sequence is not determined in advance, can be linear forms by such constraint representation by big M method, i.e., for train k and
Train l, AT STATION the section running interval at the departure interval of i and interval of arriving at a station constraint：
Wherein,Get to the station the minimum interval of i for adjacent train；
The minimum interval of station i is left for adjacent train；
According to Boolean variable yk,l,iDefinition, constraint below must satisfy：
yk,l,i+yl,k,i=1 (9)
Station track assignment constraints.Station to distribute corresponding station track to train stop or pass through, if i AT STATION, train k and
The station track that train l is distributed is identical, then they dispatch a car-arrival interval has to be larger than hda.According to yk,l,iAnd zk,i,pDetermine
Justice, station track assignment constraints must be graphed as
Wherein, yk,l,iFor if the frequency of train k i AT STATION earlier than train l if yk,l,i=0, otherwise yk,l,i=1；
zk,i,pZ if for i is assigned to station track p AT STATION if train kk,i,p=1, otherwise zk,i,p=0；
PiStation track set for station i.
S2, initial Mixed Integer Multiple Goal Programming model is established according to constraint set and object function, detailed process is：
Model considers two object functions simultaneously, and correspond to new ledger line road train respectively always starts time and existing line row
The adjustment amplitude of vehicle.First aim function representation is：
Wherein,It represents new plus train k and starts the time.Second target function representation is：
Three therein represent that time deviation, dwell time deviation are started in the adjustment of the starting station time of departure, section respectively.
Wherein, KeFor existing train set, | Ke|=Ke,i.e.,Ke=1,2 ..., Ke}；
KaTo increase train set newly, | Ka|=Ka,i.e.,Ka={ Ke+1,Ke+2,…,Ke+Ka}；
N gathers for station, | N |=N+1, N={ 0,1 ..., N }；
NkGather for the train k stations passed through, whereink∈Ke∪Ka；
Newly to add train k's to start the moment；
It is adjusted for the starting station time of departure；
Start time deviation for section；
For dwell time deviation.
The constraint set of initial Mixed Integer Multiple Goal Programming model is represented with set Cons={ constraint (1) -- (12) }, that
Initial Mixed Integer Multiple Goal Programming model is expressed as
S3, the circuit speed limit according to existing train in the original service chart of existing train calculate existing train and reach one by one
With leave the earliest of each station and the latest moment, judge whether the sequence of dispatching a car per a pair of existing train at each station may occur
Variation is sequentially generated sequence constraint of dispatching a car, according to traffic rule according to the dispatching a car for existing train pair that sequence of dispatching a car will not change
Traffic rule constraint is generated, and according to sequence constraint and traffic rule constraint and the initial Mixed Integer Multiple Goal Programming mould of dispatching a car
Type establishes Mixed Integer Multiple Goal Programming model, and detailed process is as follows：
S3.1, it sorts according to the time sequencing dispatched a car to existing train set Ke, enables k=1；
S3.2, the earliest estimated arrival time respectively stood that existing train k passes through at it is calculatedWith set out the moment earliest
S3.3, the arrival the latest respectively stood and set out the moment the latest that existing train k passes through at it are calculated, be denoted as respectively：
With
If S3.4, k=| Ke |, k=0 is enabled, is transferred to step S3.5；Otherwise k=k+1 is enabled, is transferred to step S3.2；
If S3.5, k=| Ke | -1, it is transferred to step S3.7；Otherwise k=k+1 is enabled, is transferred to step S3.6；
S3.6, sequence constraint of dispatching a car is generated：
S3.6.1, l=k+1 is enabled；
S3.6.2, for train to (k, l), if in starting station i1MeetAnd in terminus i2MeetThen yk,l,i=0；
If S3.6.3, l=| Ke |, it is transferred to step S3.6；Otherwise l=l+1 is enabled, is transferred to step S3.6.2；
S3.7, the y that will be obtainedk,l,i=0 is added to as sequence constraint of dispatching a car in set Cons.
In step S3.2, other trains are not considered, it is assumed that existing train k stops according to the scheme of stopping of original service chart
Vehicle, the dwell time is the most short duration that stops, and is started with most fast speed.In step S3.3, other trains are not considered, it is assumed that
Existing train k stops at each station passed through, and is started with most jogging speed.I AT STATION, if original service chart provides
Train k stops, then the parking duration of i is equal to the duration that stops in original service chart AT STATION in step S3.3, otherwise stops
For the most short duration that stops.
In addition to some sequences of dispatching a car can be predefined, according to traffic rule, the pass of some Boolean variables can also be determined
System.I is not parking for example, if train k passes through a station, then according to Fig. 1, train k will be assigned to station track 1；Otherwise, it will be assigned to
Other station tracks.This relationship can be expressed as traffic rule constraint：
zk,i,1=1-xk,i.
Above-mentioned constraint is also added in set Cons.
S4, calculate new ledger line road train it is most short start duration and new ledger line road train be set start the duration upper limit about
Beam, most short according to new ledger line road train start duration and longest starts duration and Mixed Integer Multiple Goal Programming model foundation
First single goal mixed-integer programming model, after solving the first single goal mixed-integer programming model to obtain and export optimization
The service chart of existing train, detailed process are as follows：
Since archetype is Bi-objective, can not directly optimize.In addition, archetype is larger, feasible solution
Range is excessive, and solver is difficult to search out optimal solution within the acceptable time.By appropriate decomposition, feasible solution range is obtained
Smaller single goal mixed-integer programming model, it is whole including the first single goal mixed-integer programming model and the mixing of the second single goal
Number plan model, solves single goal mixed-integer programming model, can obtain optimal solution within a short period of time one by one,
In, business optimization software Gurobi can be borrowed.
S4.1, solution the most short of new ledger line road train start duration, and formula is as follows：
Wherein, siThe minimum that station i is parked in for train stops duration.
S4.2, for each new ledger line road train, obtained based on the stage oneThe constraint of the duration upper limit is started in generation
S4.3, according to new ledger line road train it is most short start duration and start the duration upper limit constraint and multiple target mixing it is whole
Number plan model establishes the first single goal mixed-integer programming model：
Wherein, coefficient ρ is relaxation factor；
S4.4, the first single goal mixed-integer programming model, the service chart of the existing train after being optimized are solved.
S5, according to new ledger line road train it is most short start the time, optimization after existing train service chart and multiple target mix
Close integer programming model and establish the second single goal mixed-integer programming model, solve the second single goal mixed-integer programming model with
The service chart of new ledger line road train is obtained and exports, detailed process is as follows：
S5.1, according to new ledger line road train it is most short start duration, optimization after existing train service chart and multiple target
Mixed-integer programming model establishes the second single goal mixed-integer programming model：
S5.2, the second single goal mixed-integer programming model is solved, obtains the service chart of new ledger line road train.
In order to illustrate more clearly of the present invention, in one direction, originate below-the ledger line case of terminal station is to the present embodiment. more
The service chart ledger line method based on Mixed Integer Multiple Goal Programming model provided is described further.
As shown in figure 3, one direction, originate more-ledger line of terminal station is the most common ledger line situation of inter-city train.In Fig. 3,
Rectangular with shade is denoted as originating or the major station of terminal station, and circle represents intermediate station.It is assumed that major station have it is enough
Station track distributes to train, and the platform in small station and station track structure are one kind in Fig. 2, wherein (1,2) represents that " 1- platforms -2- stands
Line ", (2,3) represent " 2- platform -3- station tracks ".Fig. 4 is existing train from 6:00 to 16:00 original service chart, one shares 60
Existing train is arranged, wherein bullet train 35 arranges, and ordinary train 25 arranges.
Assuming that all acceleration time and deceleration time are all 2 minutes, table 1 lists bullet train and ordinary train each
The pure of section starts time bound；The minimum interval of dispatching a car of major station is 5 minutes, and minimum interval of arriving at a station is 3 minutes, and minimum stops
3 minutes time；The minimum interval 3 minutes of dispatching a car in small station, arrival interval 2 minutes, minimum 2 minutes dwell times；If two vehicles are total to
With a station track, then it is 2 minutes that front truck, which is dispatched a car with the minimum interval that rear car reaches,；Existing train is at the starting station time of departure
Adjustment amplitude is up to 5 minutes.By the circuit, for case, the present invention will be described below：
Table 1：Section is pure to start bound (unit：Minute)
| Section | Bullet train | Ordinary train | Section | Bullet 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 groups of new ledger line road trains that addition table 2 is listed in original service chart.
Table 2：New ledger line road train information
| Number | Type | Originate-terminal station | Plan is stopped | Time window |
| 1 | At a high speed | 0-16 | {0,3,5,7,9,11,14,16} | [7:00,8:00] |
| 2 | Commonly | 0-16 | {0,2,5,7,9,11,13,16} | [7:00,9:00] |
| 3 | Commonly | 0-16 | {0,1,3,5,10,13,15,16} | [11:00,12:00] |
| 4 | At a high speed | 0-5 | {0,3,5} | [10:00,12:00] |
| 5 | At a high speed | 0-16 | {0,2,5,7,11,16} | [9:00,10:00] |
| 6 | At a high speed | 0-16 | {0,3,5,9,13,16} | [12:00,13:00] |
| 7 | At a high speed | 0-5 | {0,3,5} | [8:00,9:00] |
| 8 | At a high speed | 0-16 | {0,5,8,11,13,15,16} | [13:00,15:00] |
| 9 | Commonly | 5-16 | {5,6,9,12,14,16} | [15:00,16:00] |
| 10 | At a high speed | 0-16 | {0,2,3,5,7,10,13,14,16} | [14:00,15:00] |
Secondly, flow according to figure 1 sequentially inputs the information of circuit, existing train, new plus train and relevant parameter,
Constraints set and object function are built, establishes mixed-integer programming model.Then, existing train is pre-processed, really
Determine the sequence of dispatching a car between part of the train pair, and be added in constraints.
Then, using three stage decomposition Optimization Method models.
Stage one：New shown in speed-limiting messages and table 2 according to table 1 plus train information, can be with according to formula (13)
The most short of new ledger line road train is calculated and starts the timeI.e. 160,168,168,48,148,148,48,154,109,
166}。
Stage two：It willInformation be input in single goal mixed-integer programming model (14), wherein ρ=1.2.It solves
Model (14), obtains the service chart of existing train, wherein, solving model (14) can call business optimization software Gurobi to realize.
Wherein, the adjustment amplitude summation of existing train is 14 minutes, i.e. F2=14.Stage two probably takes 80 seconds.
Stage three：The existing route map of train that stage two obtains is input to mixed-integer programming model (15), solves mould
Type (15), obtains the service chart of new ledger line road train, wherein, solving model (15) can call business optimization software Gurobi real
It is existing.Wherein, the temporal summation of starting of new ledger line road train is 1439 minutes, i.e. F1=1439.Stage three probably takes 5 seconds.
Final service chart is shown in Fig. 5, and where the dotted line signifies that newly adds train, realizes and represents existing train.
Finally, it is the applicability of testing model, in addition we perform 400 groups of numerical experimentations.For newly adding train quantity | Ka
|=5,10,15 and 20,100 groups are randomly generated respectively newly adds train set.To every group of set of generation, 3 are at most arranged per hour
Lie Xinjia trains.Time restriction (TimeLimit) parameter for setting Gurobi is 1800 seconds, i.e., if when 1800 seconds also
Optimal solution is not obtained, stops the experiment.
Table 3 gives the stage two and the stage three calculates the statistics of time.When | Ka | when=5 and 10, all experiments
Mixed-integer programming model can obtain optimal solution in 1800 seconds, and average calculation times are no more than 30 seconds and 120 seconds.When |
Ka | when=15, there are 2 groups of experiments not obtain optimal solution at the appointed time, remaining 98 groups of experiment average times do not surpass
Spend 230 seconds.When | Ka | when=20, there are 6 groups of experiments not obtain optimal solution at the appointed time, remaining 94 groups of experiments are put down
The equal time is no more than 530 seconds.Considering in practice will not be on an intercity circuit with stylish plus 10 or more trains, present invention side
Method can search out the optimal solution of high-speed railway ledger line problem within a short period of time substantially.
Table 3：Calculate time statistics
Obviously, the above embodiment of the present invention be only to clearly illustrate example of the present invention, and not be pair
The restriction of embodiments of the present invention for those of ordinary skill in the art, may be used also on the basis of the above description
To make other variations or changes in different ways, all embodiments can not be exhaustive here, it is every to belong to this hair
The obvious changes or variations that bright technical solution is extended out are still in the row of protection scope of the present invention.
Claims (8)
1. a kind of service chart optimization method for the new ledger line road of high-speed railway, which is characterized in that this method includes the following steps：
S1, according to the topological characteristic of the target line of input, station platform station track feature, circuit speed limit, existing train it is original
Service chart, the information of new ledger line road train and adjacent train minimum start interval, existing train maximum adjustment amplitude, new
Add train start time coefficient of relaxation generation stop type constraint, section start time-constrain, the dwell time constraint, the starting station hair
The constraint of vehicle time window, the constraint of section running interval and station track assignment constraints form constraint set by each constraint；
S2, initial Mixed Integer Multiple Goal Programming model is established according to constraint set and object function；
S3, the circuit speed limit according to existing train in the original service chart of existing train, calculate one by one existing train reach and from
The earliest of each station and the latest moment are opened, judges whether the sequence of dispatching a car per a pair of existing train at each station may become
Change, sequence constraint of dispatching a car is sequentially generated according to the dispatching a car for existing train pair that sequence of dispatching a car will not change, is given birth to according to traffic rule
Into driving rule constraint, and according to sequence constraint and traffic rule constraint and the initial Mixed Integer Multiple Goal Programming model of dispatching a car
Establish Mixed Integer Multiple Goal Programming model；
S4, calculate new ledger line road train it is most short start duration and set new ledger line road train start the duration upper limit constraint, root
According to new ledger line road train it is most short start duration and start the duration upper limit constraint and Mixed Integer Multiple Goal Programming model foundation
First single goal mixed-integer programming model, after solving the first single goal mixed-integer programming model to obtain and export optimization
The service chart of existing train；
S5, according to new ledger line road train it is most short start the time, optimization after existing train service chart and multiple target mixing it is whole
Number plan model establishes the second single goal mixed-integer programming model, solves the second single goal mixed-integer programming model to obtain
And export the service chart of new ledger line road train.
2. the service chart optimization method according to claim 1 for the new ledger line road of high-speed railway, which is characterized in that described
The type constraint that stops is expressed as
Wherein,Plan for train k i AT STATION is stopped scheme, if if train k plans, i stops AT STATIONIt is no
Then,
xk,iThe scheme that actually stops for train k i AT STATION.
The section is started time-constrain and is expressed as
Wherein,For train k in original service chart get to the station i at the time of；
ak,iGet to the station practical moment of i for train k；
At the time of station i being left for train k in original service chart；
dk,iThe practical moment of station i is left for train k；
σ (k) is the type of train k, σ (k)=0 if train k is bullet train, the σ (k) if train k is ordinary train
=1；
WithThe respectively train k of σ (k) the types upper bound for the duration that average rate is started and lower bound on the i` of section；
τaAnd τdThe respectively acceleration of train and the duration started of deceleration；
The dwell time constraint representation is
xk,i·M≥dk,i-ak,i≥xk,i·si
Wherein, M is the integer of setting；
siMinimum when being parked in station i for train stops duration；
The starting station time of departure window constraint is expressed as
Wherein, δkThe maximum allowable offset at the time of starting station is left for train k；
For the starting station of train k, wherein
For the terminal station of train k, wherein
The section running interval constraint representation is
yk,l,i+yl,k,i=1
Wherein,Get to the station the minimum interval of i for adjacent train；
The minimum interval of station i is left for adjacent train；
The station track assignment constraints are expressed as
Wherein, yk,l,iFor if the frequency of train k i AT STATION earlier than train l if yk,l,i=0, otherwise yk,l,i=1；
zk,i,pZ if for i is assigned to station track p AT STATION if train kk,i,p=1, otherwise zk,i,p=0；
PiStation track set for station i.
3. according to the method described in claim 2, it is characterized in that, object function described in step S2 is expressed as
Wherein, KeFor existing train set, | Ke|=Ke,i.e.,Ke=1,2 ..., Ke}；
KaTo increase train set newly, | Ka|=Ka,i.e.,Ka={ Ke+1,Ke+2,…,Ke+Ka}；
N gathers for station, | N |=N+1, N={ 0,1 ..., N }；
NkGather for the train k stations passed through, wherein
Newly to add train k's to start the moment；
It is adjusted for the starting station time of departure；
Start time deviation for section；
For dwell time deviation.
4. according to the method described in claim 3, it is characterized in that, initial Mixed Integer Multiple Goal Programming model described in step S2
It is expressed as
Wherein, Cons is constraint set.
5. according to the method described in claim 4, it is characterized in that, sequence constraint of dispatching a car described in step S3 further comprise it is as follows
Sub-step：
S3.1, it sorts according to the time sequencing dispatched a car to existing train set Ke, enables k=1；
S3.2, the earliest estimated arrival time respectively stood that existing train k passes through at it is calculatedWith set out the moment earliest
S3.3, the arrival the latest respectively stood and set out the moment the latest that existing train k passes through at it are calculated, be denoted as respectively：With
If S3.4, k=| Ke |, k=0 is enabled, is transferred to step S3.5；Otherwise k=k+1 is enabled, is transferred to step S3.2；
If S3.5, k=| Ke | -1, it is transferred to step S3.7；Otherwise k=k+1 is enabled, is transferred to step S3.6；
S3.6, sequence constraint of dispatching a car is generated：
S3.6.1, l=k+1 is enabled；
S3.6.2, for train to (k, l), if in starting station i1MeetAnd in terminus i2Meet
Then yk,l,i=0；
If S3.6.3, l=| Ke |, it is transferred to step S3.6；Otherwise l=l+1 is enabled, is transferred to step S3.6.2；
S3.7, the y that will be obtainedk,l,i=0 is added to as constraints in set Cons.
6. according to the method described in claim 4, claim 5, which is characterized in that traffic rule constraint representation described in step S3
For：
zk,i,1=1-xk,i
The traffic rule constraint is added in set Cons.
7. according to the method described in claim 6, it is characterized in that, the detailed process of step S4 is：
S4.1, solution the most short of new ledger line road train start duration, and formula is as follows：
Wherein, siThe minimum that station i is parked in for train stops duration.
S4.2, for each new ledger line road train, obtained based on the stage oneThe constraint of the duration upper limit is started in generation
S4.3, according to new ledger line road train it is most short start duration and start the duration upper limit constraint and multiple target MIXED INTEGER advise
Draw model foundation the first single goal mixed-integer programming model：
Wherein, coefficient ρ is relaxation factor；
S4.4, the first single goal mixed-integer programming model, the service chart of the existing train after being optimized are solved.
8. according to the method described in claim 1, it is characterized in that, step S5 further comprises following sub-step：
S5.1, according to new ledger line road train it is most short start duration, optimization after existing train service chart and multiple target mix
Integer programming model establishes the second single goal mixed-integer programming model：
S5.2, the second single goal mixed-integer programming model is solved, obtains the service chart of new ledger line road train.
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