CN106845721A - The optimization method of many beat synthetic operations of train based on Cross-Entropy Algorithm - Google Patents

Abstract

The invention discloses a kind of optimization method of many beat synthetic operations of train based on Cross-Entropy Algorithm, including step：It is optimization aim to minimize each beat unit train overall travel time, limitation etc. is spaced to constrain with the operation of same beat unit train constant duration, with the minimum and maximum run time of beat unit train, builds the Optimized model of many beat unit train synthetic operations；Design the solution coding of many beat synthetic operation timetable schemes of train；The probability parameter of initialization scheme solution；Generate the scheme solution of specified quantity at random based on given probability parameter value；Current each scheme solution is evaluated, wherein a number of high-quality scheme solution is chosen as elite solution, with this update probability parameter, and the new scheme solution of probability generation is pressed based on the probability parameter after renewal, so new scheme solution of continuous renewal probability parameter, generation so far meets any given algorithm end condition.

Description

The optimization method of many beat synthetic operations of train based on Cross-Entropy Algorithm

Technical field

The present invention relates to train operation scheduling or time-table optimization field, more particularly to based on Cross-Entropy Algorithm The optimization method of many beat synthetic operations of train.

Background technology

Time-table optimization is to further determine that train arriving at each station on the basis of given train running scheme Up to the moment of setting out, make its meeting all kinds of drivings and service time require on the premise of maximize train service level.With The aggravation of passenger traffic mode market competition and the carrying for travelling service request such as China Express Railway and aviation, highway Height, improving time-table Compilation Quality can effectively improve travelling service level, and this extends volume growth to high ferro, reality Existing sustainable development has important practical significance.

At present both at home and abroad train operation pattern be commonly divided into periodic duty and it is aperiodic operation two kinds, the former Japan, The countries uses such as Europe are more, and the latter is the method for operation that China's high ferro is mainly used.Existing relevant train schedule Numerous studies in terms of establishment are all to be based respectively on this two kinds of methods of operation and launch.Such as it is directed to the aperiodic time of running table of train Optimization, document (Zhou X., Zhong M..Single-track train timetabling with guaranteed optimality:Branch-and-bound algorithms with enhanced lower bounds[J] .Transportation Research Part B, 2007,41 (3), 320-341.) to minimize the tourist on train time as excellent Change target, devise the branch-bound algorithm of route map of train solution；Document (build up the Army, and dragon builds up Lines for Passenger Transportation row by Xu Hong, horse Research [J] railway societies of car service chart compiling model and computational methods, 2007,29 (2):1-7.) with document (Zhou Wenliang, history Peak, the Line for Passenger Transportation route map of train paving that Chen Yan are based on sequencing optimization draws method [J] railway societies, 2010,32 (1):1-7.) It is target to reduce high-speed railway overline train hourage, it is proposed that the layering superposition side of High Speed Railway Train Diagram optimization Method and sequencing optimization method.Additionally, document (Tang Jinjin, Zhou Leishan, Ran Feng, it is old to carry out into the route map of train that is based on traction simulation Soft Conflict resolution technique study [J] railway societies, 2012,34 (4):1-8.) further contemplate train traction to power influence, using row Car group's integrative simulation method is realized the detection of the soft conflict of service chart and is rejected.

In recent years, for the ease of the joining relation between the different circuit trains for the treatment of, raising passenger transference mass fraction scholar Whole road network route map of train is optimized as overall, such as document (Albrecht A.R., Panton D.M., Lee D.H.,Rescheduling rail networks with maintenance disruptions using Problem Space Search [J] .Computers＆Operations Research, 2013,40 (3), 703-712.) and (Carey M.,Crawford I.,Scheduling trains on a network of busy complex stations[J] .Transportation Research Part B:Methodological, 2007,41 (2), 159-178.) to improve line between Passenger transference quality is target, and globality optimization is carried out to related road network route map of train.For periodicity train operation time table Table, its have it is regular strong, using flexibly, facilitate the advantages such as travelling and organization of station operation, be equally worth everybody deep Research.Document (Willem L.PeetersP., Cyclic Railway Timetable Optimization [D] .Netherlands:Erasmus Research Institute of Management,Erasmus University Rotterdam, 2003.) systematically propose periodic train diagram optimization PESP and CPF models, and document (Caimi G., Fuchsberger M.,Marco L.,Kaspar S.,Periodic railway timetabling with event flexibility[J].Special Issue:Optimization in Scheduled Transportation Networks, 2012,57 (1), 3-18.) on this basis it is further proposed that the elastic PESP models of periodic train diagram.Document (Wang Bo, Yang Hao, Niu Feng, Wang Baohua periodic train diagrams compiling model and algorithm research [J] railway societies, 2007,29 (5):1- 7.) and (Wang Bo, Han Baoming, bright brightness urban mass transit networks periodic train diagram establishment research [J] railway societies of fighting, 2013, 35(4):It is minimum for target sets up inter-city passenger rail with the train dwelling time 9-15.) by network constraint figure and periodic potential differential mode type With urban track traffic periodic train diagram optimization method；(Xie Meiquan, Nie Lei periodicity train diagram establishment models grind document Study carefully [J] railway societies, 2009,31 (4):7-13.) consider train cycling service constraint, set up the periodicity based on sequencing and transport Row figure optimization method；Document (the multi-objective Model of Jia Xiaoqiu, Guan Xiaoyu, Lv Xikui cycle route maps of train and based on Job- The practice of genetic algorithm [J] mathematics of shop and understanding, 2013,43 (10):132-138.) construct high-speed railway cycle row The multi-objective Model of car service chart, and devise the genetic algorithm based on Job-shop；And document (Lee passes guest and is based on matrix table Show high ferro cycle train diagram establishment technique study [D] the Beijing Jiaotong University with maximum algebra method, 2012.) based on matrix Represent and maximum algebra method designs high ferro cycle route map of train optimization method.

The sharpest edges of periodicity train schedule are that can provide passenger's constant duration regularization operation row Car and facilitate travelling, but for its optimize compilation process, existing research be typically first according to peak period go on a journey need Ask and determine the period train schedule；Then non-peak is obtained by deleting off-peak period part of the train on this basis Period train schedule, its trip requirements amount is adapted to train operation quantity in causing off-peak period.Consequently, it is possible to arrange The regularity of car strict constant duration periodic duty originally will be destroyed to a certain extent.

The content of the invention

Cause that train operation has strict constant duration regular and enables to present invention aim at one kind is provided Different periods train operation quantity train based on the Cross-Entropy Algorithm many beats effectively identical with travelling demand are cooperateed with The optimization method of operation.

To achieve these goals, the invention provides a kind of many beat synthetic operations of train based on Cross-Entropy Algorithm Optimization method, comprises the following steps：

S1：It is optimization aim to minimize each beat unit train overall travel time, with times such as same beat unit trains It is spaced operation, is spaced limitation etc. to constrain with the minimum and maximum run time of beat unit train, builds many beat unit trains The Optimized model of synthetic operation；

S2：It is designed for representing the solution coding of many beat synthetic operation timetable schemes of train；

S3：Initialize the probability parameter for generating many beat synthetic operation timetable scheme solutions of train；

S4：GS scheme solution is generated based on given probability parameter value at random, and based on the optimization of each scheme solution coding information Determine the GS many beat synthetic operation timetables of train；

S5：The Compilation Quality of many beat synthetic operation timetable schemes of each train is evaluated, that is, is calculated in each scheme and is owned Beat unit train overall travel time sum Z；Determine the minimum schemes of tourist on train temporal summation Z as nth iteration simultaneously Optimal case SⁿIf the program is better than current optimal case S^*, then S is made^*=Sⁿ；

S6：By the wherein preceding σ scheme solution of the ascending sequential selections of train overall travel time sum Z in scheme as elite Solution, and then with this each probability parameter value that more newly-generated scheme solution is encoded as follows：

Wherein,WithRespectively beat unit w trains priority gene Q in n-th with n-1 iteration_w The probability of a values is selected,WithRespectively beat unit w trains gene DT in n-th with n-1 iteration_wSelection b The probability of value,WithRespectively beat unit w trains gene D in n-th with n-1 iteration_wSelect the general of c values Rate；Beat unit w train genes Q in respectively k-th elite solution_w,DT_wAnd D_wValue；ES changes for current The elite disaggregation that generation is chosen, parameter ρ is a balance coefficient；

S7：Algorithm end condition judges：If algorithm meets following any one condition, just stop algorithm, output is current most Excellent train synthetic operation timetable S^*；Otherwise, repeat step S4 to step S6, i.e., regenerate GS according to current probability parameter The many beat synthetic operation timetables of train, and quality evaluation, and then update probability parameter are carried out to it；

1. for any beat unit train, its probability parameterMore than 1- ω or less than ω, equally, probability ginseng NumberMore than 1- ω or less than ω, wherein, ω is a very little positive, generally can use ω=0.01；

2. the continuous μ iteration of the corresponding target function value of optimum individual solution for being obtained since algorithm does not improve；

3. current iteration number of times reaches given maximum iteration n_max。

As the further improvement of the method for the present invention：

Step S1, comprises the following steps：

S101：Define decision variable T_wRepresent w-th operation beat unit train run time interval, decision variable a_w,f (i, j) and d_w,f(i, j) is respectively w-th operation beat unit f row train and enters interval (i, j) and leave interval (i, j) Moment；

S102:Determine the constraints that train beat-type is started, including with the operation of beat unit train constant duration about Beam, equal stop with interval run time equated constraint, with beat unit train minimum with the beat unit train station residence time Standing, the time is constrained with interval run time, beat unit train is constrained with the time of departure the latest earliest, beat unit train is minimum With maximum run time spacing constraint, train interval minimum safe arrival time spacing constraint and train it is interval most Small safe departure time spacing constraint：

(1) run with beat unit train constant duration and constrained：Beat unit f+1 arrange with f row train enter with The time interval at interval (i, j) moment is left just for the beat unit train starts time interval, i.e.,：

Wherein, E_wBe w-th operation beat unit train via Interval Set, m_wIt is the # beat unit train operation number Amount；

(2) it is equal with interval run time equated constraint with the beat unit train station residence time：With beat cell columns Car it is same stop with the identical dwell time or do not stop and it is same it is interval there is identical run time, i.e.,：

Wherein, (i, j), it is to be connected two adjacent intervals stood that (j, i ') is respectively with station j；

(3) constrained with interval run time with the beat unit train minimum dwell time：To same beat unit train Speech, as long as so that its 1st row train meets interval run time and requires that remaining train just can meet with the station minimum dwell time This two requirements, therefore only need to set following two constraintss：

Wherein,It is 0-1 indications, if w-th beat unit train i parking AT STATION,Otherwise, It is beat unit w trains i ∈ S AT STATION_wThe minimum dwell time,Respectively beat unit W trains are in interval (i, j) ∈ E_wThe startup additional time-division, pure motion time and stop additional time-division；

(4) beat unit train is constrained with the time of departure the latest earliest：Each first train of beat unit originates the time must not Its regulation time of departure the latest is later than, while must not be earlier than the circuit earliest service time, i.e.,：

Wherein, t_sIt is the circuit earliest service time,It is w-th time of departure the latest of beat unit first train；

(5) the minimum and maximum run time spacing constraint of beat unit train：Each beat unit train run time interval The minimum value of its regulation must not be less than, while its run time interval will ensure that its whole train can be in the range of the service time Set out, therefore：

Wherein,It is w-th minimum run time interval of beat unit train, t_eIt is circuit service time the latest；

(6) train is in interval minimum safe arrival time spacing constraint：Arbitrary neighborhood train reaches car from same interval The time interval stood have to be larger than the minimum value of its defined, i.e.,：

Wherein, AT_i,jEnter the minimum safe time interval of interval (i, j) for two trains；

(7) train is in interval minimum safe departure time spacing constraint：

Wherein, DT_i,jThe minimum safe time interval of interval (i, j), E are left for two trains_w′For beat unit w ' can be via Interval Set, d_w′,f′(i, j) is the moment that the individual operation beat unit the f ' row trains of w ' leave interval (i, j)；

S103：Selection is model optimization target to minimize each beat unit train overall travel time, i.e.,：

Wherein, Z is model objective function value, i.e., each beat unit train overall travel time.

Coding is solved in step S2 to be made up of W coding section, wherein, W is running train beat element number；Each coding section Corresponding to a different beat unit train, for w-th coding section corresponding to train beat unit w=1,2 ..., W, its is total It is made up of 3 encoding genes altogether, respectively：1. priority gene Q_w, 2. first bus frequency gene DT_wAnd when 3. running Between spaced cdna D_w, wherein, priority gene Q_wSpan be 1,2 ..., W, the value determines beat unit w train operations The sequencing of timetable optimization, the beat unit train with larger priority genic value, its time of running table optimization is sequentially Before with smaller priority genic value beat unit train；First bus frequency genic value DT_wBeat unit w is determined The first bus originates the time；Allow run time spaced cdna value D_wDetermine that beat unit w Train Schedules are spaced, that is, limit That has made the beat unit other trains originates the time.

Step S3, comprises the following steps：

S301：NoteIt is beat unit w train priority genes Q_wSelection a=1, the probability parameter of 2 ..., W values should Parameter value is initialized as：

S302：NoteIt is beat unit w train first bus frequency genes DT_wThe probability parameter of b values is selected, should Parameter value is initialized as：

Wherein, b_m9nAnd b_maxRespectively beat unit w first bus frequencys it is earliest with allow value the latest；

S303：NoteIt is the run time spaced cdna D of beat unit w trains_wSelect the probability parameter of c, the parameter Value is initialized as：

Wherein, c_min,c_maxThe minimum and maximum possible value that respectively beat unit w Train Schedules interval allows.

Step S4, comprises the following steps：

S401：According to the probability parameter value that each gene value of each beat unit train is selected, generated at random by probability each Genic value, thus generates a solution coding；This process is repeated until GS solution coding of generation；

S402：Optional one from GS solution coding, according to each beat unit priority valve Q_wDescending sequence, it is determined that The sequencing of each beat unit train timetable establishment；During current beat unit train timetable is worked out, if occurring Train arrival and leaving operation conflict etc., only allows to change current beat unit train station arriving and leaving moment, and can not adjust and work out section Clap unit train timetable；

S403：According to the beat unit train timetable establishment for determining sequentially, a beat unit is selected successively, and note is worked as The beat unit train of preceding selection is w；The first bus according to being given in solution coding originates moment DT_wWith run time spacing value D_w Determine that originating for its all train is constantly respectively：

Wherein,Interval is originated for beat unit w trains；

S404：Since beat unit each trains of w are originated constantly, stopped at each interval run time and each station according to train Time of standing calculates the arriving and leaving moment at other approach stations of each train successively, i.e.,：

a_w,f(j, j+1)=d_w,f(j,j+1)+ST_w(j+1),(j,j+1)∈E_w

Wherein, CT_w(i, i+1) is run time of the beat unit w trains at interval (i, i+1), ST_w(i),ST_w(j+1) Respectively dwell time of beat unit w trains i and j+1 AT STATION；

S405：Judge each train arrival and leaving moments of beat unit w whether with before to determine beat unit train arriving and leaving moment With the presence or absence of operation conflict；If not existing, continue to select next beat unit train, repeat above step S403 and S404 Determine its timetable；Otherwise, conflict set present in note current train schedule is combined into Conflict_w；

S406：From conflict set Conflict_wIn optional one, respectively calculate dissolve the conflict required for beat unit The w first buses originate the minimum adjustment amount Δ t at moment and Train Interval_wWith Δ D_w；And then thus redefine beat unit w The first bus originates the moment and Train Interval is DT_w=DT_w+Δt_wWith D_w=D_w+ΔD_w；On this basis, walked more than Rapid S403 to S405 recalculates arriving and leaving moment of each trains of beat unit w at each approach station；

S407：Above step S402 to S406 is repeated, until obtaining GS solution encodes corresponding many beat trains collaboration fortune Row timetable.

The invention has the advantages that：

The optimization method of the train based on Cross-Entropy Algorithm of the invention many beats synthetic operation, with strong operability, meter The advantages of calculation speed is fast, optimizes many beat train synthetic operation timetables for obtaining and enables to each beat unit by the method Train is strict to be reached and sets out at same station at a fixed time interval, the regularity with the operation of strict constant duration, This greatly facilitates passenger and is familiar with train operation rule, facilitates it to go on a journey；Originated by coordinating each beat unit first bus simultaneously Time is spaced with Train Schedule, enables to different periods to have the running train of varying number, reaches phase commuter rush hour Many drivings, low peak period drive less, and day part train starts the quantity purpose effectively identical with its travelling demand, and this can have Effect improves train attendance, reduces train operation cost.

In addition to objects, features and advantages described above, the present invention also has other objects, features and advantages. Below with reference to accompanying drawings, the present invention is further detailed explanation.

Brief description of the drawings

The accompanying drawing for constituting the part of the application is used for providing a further understanding of the present invention, schematic reality of the invention Apply example and its illustrate, for explaining the present invention, not constitute inappropriate limitation of the present invention.In the accompanying drawings：

Fig. 1 is the stream of many beat synthetic operation optimization methods of train based on cross entropy search of the preferred embodiment of the present invention Journey schematic diagram；

Fig. 2 is the code segment schematic diagram of the solution of the preferred embodiment of the present invention.

Fig. 3 is the time-table schematic diagram being made up of 2 operation beat unit trains of the preferred embodiment of the present invention 2；

Fig. 4 is the optimization acquisition of the preferred embodiment of the present invention 2 comprising 5 beat unit train synthetic operation figures.

Specific embodiment

Embodiments of the invention are described in detail below in conjunction with accompanying drawing, but the present invention can be defined by the claims Multitude of different ways with covering is implemented.

In the examples below, the train with identical starting point, terminal, the scheme that stops and speed class is classified as one Class, referred to as one beat unit train.With beat unit train with strict constant duration periodic duty, and different beat units Train can have different run times to be spaced, and then coordinate the time interval and its AT STATION of each beat unit train operation Arrival and departure time cause that all trains are adapted in the operation quantity of different periods with the period travelling demand.

Embodiment 1：

Referring to Fig. 1, the optimization method of many beat synthetic operations of the train based on Cross-Entropy Algorithm of the present embodiment, including with Lower step：

S1：It is optimization aim to minimize each beat unit train overall travel time, with times such as same beat unit trains It is spaced operation, is spaced limitation etc. to constrain with the minimum and maximum run time of beat unit train, builds many beat unit trains The Optimized model of synthetic operation.

S2：The design solution for representing many beat synthetic operation timetable schemes of train as shown in Figure 2 is encoded.

S3：Initialize the probability parameter for generating many beat synthetic operation timetable scheme solutions of train.

S4：GS scheme solution is generated based on given probability parameter value at random, and based on the optimization of each scheme solution coding information Determine the GS many beat synthetic operation timetables of train.

S5：The Compilation Quality of many beat synthetic operation timetable schemes of each train is evaluated, that is, is calculated in each scheme and is owned Beat unit train overall travel time sum Z；Determine the minimum schemes of tourist on train temporal summation Z as nth iteration simultaneously Optimal case SⁿIf the program is better than current optimal case S^*, then S is made^*=Sⁿ。

S6：By the wherein preceding σ scheme solution of the ascending sequential selections of train overall travel time sum Z in scheme as elite Solution, and then with this each probability parameter value that more newly-generated scheme solution is encoded as follows：

Wherein,WithRespectively beat unit w trains priority gene Q in n-th with n-1 iteration_w The probability of a values is selected,WithRespectively beat unit w trains gene DT in n-th with n-1 iteration_wSelection b The probability of value,WithRespectively beat unit w trains gene D in n-th with n-1 iteration_wSelect the general of c values Rate；Beat unit w train genes Q in respectively k-th elite solution_w,DT_wAnd D_wValue；ES changes for current The elite disaggregation that generation is chosen, parameter ρ is a balance coefficient.

S7：Algorithm end condition judges：If algorithm meets following any one condition, just stop algorithm, output is current most Excellent train synthetic operation timetable S^*；Otherwise, repeat step S4 to step S6, i.e., regenerate GS according to current probability parameter The many beat synthetic operation timetables of train, and quality evaluation, and then update probability parameter are carried out to it：

1. for any beat unit train, its probability parameterMore than 1- ω or less than ω, equally, probability ginseng NumberMore than 1- ω or less than ω, wherein, ω is a very little positive, generally can use ω=0.01；

2. the continuous μ iteration of the corresponding target function value of optimum individual solution for being obtained since algorithm does not improve；

3. current iteration number of times reaches given maximum iteration n_max。

Embodiment 2：

Consider high-speed railway circuit L=(S, E) being made up of K station and K-1 multiple line interval, wherein, S is up for its Direction station sequence, and E is its up direction train running interval set.Because the multiple line circuit uplink and downlink direction train is logical Different interval circuits and operation on the station track of station are often arranged in respectively, only consider that the circuit up direction runs beat unit train Timetable optimizes.Assuming that having had determined that the circuit up direction need to run W beat unit in the train running scheme formulation stage Train, for wherein w-th operation beat unit train, its running train quantity is 6_w, all trains have identical inception point r_w ∈ S and terminus s_wIt is ∈ S, identical via station collection S_w∈ S with via Interval Set E_w∈ E, all trains i ∈ S AT STATION_wMost The small dwell time isIn interval (i, j) ∈ E_wThe startup additional time-division, pure motion time and stop additional time-division and be respectively

The optimization of many beat synthetic operations of train is intended to optimize each beat unit train run time interval, and each train AT STATION specific to up to the moment of setting out, make it in the case where all kinds of operations and running time standard conditions are met, each beat unit Train overall travel time reaches minimum.Note decision variable T_wIt is w-th operation beat unit train run time interval, decision-making becomes Amount a_w,f(i, j) and d_w,f(i, j) is respectively w-th operation beat unit f row train and enters interval (i, j) and leave interval The moment of (i, j).In other words, a_w,f(i, j) is that j's train sets out the moment AT STATION, d_w,f(i, j) gets to the station i for train Moment.

For same beat unit train, their periodic duties at equal intervals at definite intervals, this does not mean only that it All trains have the identical dwell time or not parking AT STATION, and require its adjacent train at any station to hair Time interval all same.As shown in figure 3, the train path being represented by solid and broken lines is belonging respectively to two beat cell columns Car, wherein, the 1st beat unit train stops train for station station, and its run time was at intervals of 1 hour；And the 2nd beat cell columns Car only B parkings AT STATION, its run time was at intervals of 1.5 hours.The 1st all trains of beat unit are station station and stop in Fig. 3, And it is equal in the same dwell time stopped, and adjacent train arrive AT STATION hair time interval be 1 hour；Obviously, the 2nd Individual beat unit train is likewise supplied with this moving law feature.

S1：Build train more piece and be afraid of synthetic operation Optimized model.

S101：Determine that the constraints of many beat unit train synthetic operations is as follows：

In order to ensure that each beat unit train is run by above disciplinarian request constant duration, with beat unit train station Arriving and leaving moment first has to meet following constraints.

Meanwhile, because same beat unit train requirement AT STATION have the identical dwell time or do not stop, interval have There is identical run time, therefore also need to meet with beat unit train station arriving and leaving moment：

Wherein, (i, j), it is to be connected two adjacent intervals stood that (j, i ') is respectively with station j.

Under effect of contraction of constraint formula (3) with (4), for same beat unit train, as long as so that its 1st row row Car meets interval run time and requires that remaining train just can meet this two requirements, therefore only need to set with the station minimum dwell time Put following two constraintss：

Wherein,It is 0-1 indications, if w-th beat unit train i parking AT STATION,Otherwise,

For any beat unit train, its arriving and leaving moment AT STATION must within the scope of the service time, equally, Under the effect of contraction of constraint formula (1) and (2), need to only enter row constraint to same first train of beat unit and terminal column train arrival and leaving moment .

Wherein, t_s,t_eRespectively train operation time range starting and end time.

Additionally, in order to avoid each beat unit train concentrates on one day because of reasons such as run time interval too smalls, certain is smaller Time range in the morning or afternoon such as run, it is desirable to which each first train of beat unit originates the time must not be later than its regulation and send out the latest The car time, while requiring that each beat unit train run time must not be spaced is less than its minimum value for specifying.Therefore, each is saved Unit train is clapped, also needs to meet following constraint.

Wherein,WithRespectively w-th time of departure the latest of beat unit first train and the beat unit The minimum run time interval of train.

To same beat unit train, arriving and leaving moment has carried out restriction to constraints above formula (1) to (12) AT STATION, except this Outside, also need to ensure to meet between any train minimum safe time interval and the minimum of reaching and set out safe time interval requirement, This is divided between same beat unit train two kinds of situations between different beat unit trains.

For run time interval for being at least 1 times between same beat unit train to hair operation time interval because of it, Therefore only need its run time to be spaced and reached not less than minimum safe or departure time interval.

For between different beat unit trains, it need to meet following constraint to the activity duration is sent out.

Wherein, AT_i,jWith DT_i,jRespectively two trains enter the minimum safe time interval of interval (i, j) and leave interval The minimum safe time interval of (i, j).

S102：It is optimization aim to minimize each beat unit overall travel time, builds many beat unit train collaboration fortune The Optimized model of row timetable is as follows：

Many beat unit train synthetic operation timetable optimizations will be minimum on the basis of all of above constraints is met Change all beat unit train hourage summations, i.e.,：

Wherein, Z is model objective function, i.e., each beat unit train hourage sum.

S2：Optimize many beat unit train synthetic operation timetables using based on Cross-Entropy Algorithm.

The probability parameter that the algorithm is primarily based on initialization generates multiple codings for generating individual solution at random, by each Coding can generate a solution；And then each individual solution quality is weighed, and wherein a certain proportion of elite solution is selected on this basis As the foundation of update probability parameter；Secondly, according to current elite solution update probability parameter, and the thus next iteration of random generation Individual solution coding.Can be with more thus by the coding for being iteratively improved probability parameter and make it possible to generate the individual solution of better quality High probability is generated, and generates the coding of the individual solution of poor quality because its generating probability is relatively low by will eliminate.

S201：Design solution coding.

For any beat unit train, as long as determining that wherein the first bus originates moment and its run time interval, just may be used Arriving and leaving moment of all trains at each station is derived according to train interval run time, station dwell time, but works as beat When element number is more more with train number, because mutually restriction easily occurs without feasible solution between train.In order to avoid each iteration During population influence algorithm search quality in the presence of a large amount of infeasible solutions, design solution coding as shown in Figure 2, wherein each section Clapping unit includes following 5 information：

1. priority valve Q_w；

2. the first bus allows frequency ET earliest_w；

3. the first bus allows frequency LT the latest_w；

4. it is minimum to allow run time to be spaced ED_w；

5. maximum allowable run time is spaced LD_w；

Wherein, priority valve size determines the sequencing of the beat unit train route searching, and its weights is bigger, its Search order more before；The first bus determines first bus operating path scope with frequency is allowed the latest earliest, and it must is fulfilled for The train that constraint formula (7) and (11) require earliest with the service time the latest；And minimum interval with maximum allowable run time determines Beat unit other train operation path domains, equally, its must be fulfilled for constraining (12) and (10) require it is minimum with it is maximum Run time is spaced.

Clearly as increasing the scope of the first bus and run time IV interval, therefore reduce and produce infeasible solution Probability.In actual mechanical process, we can determine suitable hunting zone according to beat unit and train quantity, can so keep away to the greatest extent Exempt to produce infeasible solution, can also avoid causing to calculate overlong time problem because hunting zone is excessive.

S202：Initialization probability parameter, generates initial code.

In the coding of solution, each beat unit train includes 5 integer variable values, and this 5 variate-values will lead to respectively Cross different discrete probability distribution function generations.Note α_w,r,nIt is beat unit w trains selection Q in nth iteration_wThe probability of=r, Now, r=1,2 ..., W；β_w,r,nWith γ_w,r,nBeat unit w trains selection ET respectively in nth iteration_w=r and LT_w=r Probability, and ε_w,r,nWith ∈_w,r,nBeat unit w trains selection ED respectively in nth iteration_w=r and LD_wThe probability of=r.

In initialization procedure, the select probability all same of all values, i.e. equal-probability distribution, if 5 beats altogether Unit, then each beat unit Q_wThe probability that value takes 1,2,3,4,5 is 0.2.

S203：Solution generation is calculated with object function.

For any solution coding, train schedule is generated as follows, and calculate corresponding object function：

(1) since beat unit each trains of w are originated constantly, stopped at each interval run time and each station according to train Time calculates the arriving and leaving moment at other approach stations of each train successively, i.e.,：

a_w,f(j, j+1)=d_w,f(j,j+1)+ST_w(j+1),(j,j+1)∈E_w

Wherein, CT_w(i, i+1) is run time of the beat unit w trains at interval (i, i+1), ST_w(i),ST_w(j+1) Respectively dwell time of beat unit w trains i and j+1 AT STATION；

(2) judge each train arrival and leaving moments of beat unit w whether with before to determine that beat unit train arriving and leaving moment is It is no to there is operation conflict；If not existing, continue to select next beat unit train, repeat above procedure and determine its moment Table；Otherwise, conflict set present in note current train schedule is combined into Conflict_w；

(3) from conflict set Conflict_wIn optional one, respectively calculate dissolve the conflict required for beat unit w The first bus originates the minimum adjustment amount Δ t at moment and Train Interval_wWith Δ D_w；And then it is first thus to redefine beat unit w Regular bus originates the moment and Train Interval is DT_w=DT_w+Δt_wWith D_w=D_w+ΔD_w；On this basis, using above step S403 to S405 recalculates arriving and leaving moment of each trains of beat unit w at each approach station；

S204：Update probability parameter.

Above probability parameter will be updated (with parameter beta as follows in each iteration_w,r,nAs a example by, other parameters It is similar)：

Wherein, GS is individual amount in each iteration population, and σ is the ratio for selecting elite solution, and ES chooses for current iteration Elite solution set, ET_wBeat unit w parameters ET in k-th solution in (n, k) expression nth iteration_wValue, parameter ρ is one Individual balance coefficient.

S205：Algorithm end condition judges.

As long as during algorithm iteration, meeting following at least one condition, just can termination algorithm iteration, obtain such as Fig. 4 institutes The many beat synthetic operation timetables of train for showing.

1) for any beat unit train, its probability parameter β_w,r,nWith γ_w,r,nMore than 1- ω or less than ω, equally, Probability parameter ε_w,r,nWith ∈_w,r,nMore than 1- ω or less than ω, wherein, ω is a very little positive, generally desirable ω= 0.01；

2) the continuous μ iteration of the corresponding target function value of optimum individual solution for being obtained since algorithm does not improve；

3) current iteration number of times reaches given maximum iteration n_max。

In summary, the present invention with calculating speed is fast, train have strict constant duration operation it is regular, each when Section train starts the quantity advantage effectively identical with its travelling demand, and this both facilitates travelling, also can effectively carry Train attendance high, reduces train operation cost.

The preferred embodiments of the present invention are these are only, is not intended to limit the invention, for those skilled in the art For member, the present invention can have various modifications and variations.All any modifications within the spirit and principles in the present invention, made, Equivalent, improvement etc., should be included within the scope of the present invention.

Claims (5)

1. the optimization method of a kind of train based on Cross-Entropy Algorithm many beats synthetic operation, it is characterised in that including following step Suddenly：

S1：It is optimization aim to minimize each beat unit train overall travel time, with same beat unit train constant duration Run, be limited to constrain with maximum run time interval with beat unit train is minimum, build many beat unit trains collaboration fortune Capable Optimized model；

S2：It is designed for representing the solution coding of many beat synthetic operation timetable schemes of train；

S3：Initialize the probability parameter for generating many beat synthetic operation timetable scheme solutions of train；

S4：GS scheme solution is generated based on given probability parameter value at random, and determination is optimized based on each scheme solution coding information The GS many beat synthetic operation timetables of train；

S5：The Compilation Quality of many beat synthetic operation timetable schemes of each train is evaluated, that is, calculates all beats in each scheme Unit train overall travel time sum Z；Determine the minimum schemes of tourist on train temporal summation Z as nth iteration most simultaneously Excellent scheme SⁿIf the program is better than current optimal case S^*, then S is made^*=Sⁿ；

S6：By the wherein preceding σ scheme solution of the ascending sequential selections of train overall travel time sum Z in scheme as elite solution, And then with this each probability parameter value that more newly-generated scheme solution is encoded as follows：

${\mathrm{\α}}_w^n\left(a\right)=\mathrm{\ρ}\·\frac{|k:k\∈ES;Q_w^k=a|}{GS\·\mathrm{\σ}}+(1-\mathrm{\ρ})\·{\mathrm{\α}}_w^{n-1}\left(a\right)$

${\mathrm{\β}}_w^n\left(b\right)=\mathrm{\ρ}\·\frac{|k:k\∈ES;{\mathrm{DT}}_w^k=b|}{GS\·\mathrm{\σ}}+(1-\mathrm{\ρ})\·{\mathrm{\β}}_w^{n-1}\left(b\right)$

${\mathrm{\γ}}_w^n\left(c\right)=\mathrm{\ρ}\·\frac{|k:k\∈ES;D_w^k=c|}{GS\·\mathrm{\σ}}+(1-\mathrm{\ρ})\·{\mathrm{\γ}}_w^{n-1}\left(c\right)$

Wherein,WithRespectively beat unit w trains priority gene Q in n-th with n-1 iteration_wSelection a The probability of value,WithRespectively beat unit w trains gene DT in n-th with n-1 iteration_wSelection b values Probability,WithRespectively beat unit w trains gene D in n-th with n-1 iteration_wSelect the probability of c values；Beat unit w train genes Q in respectively k-th elite solution_w,DT_wAnd D_wValue；ES is current iteration The elite disaggregation chosen, parameter ρ is a balance coefficient；

S7：Algorithm end condition judges：If algorithm meets following any one condition, just stop algorithm, export current optimum column Car synthetic operation timetable S^*；Otherwise, repeat step S4 to step S6, i.e., regenerate GS train according to current probability parameter Many beat synthetic operation timetables, and quality evaluation, and then update probability parameter are carried out to it；

1. for any beat unit train, its probability parameterMore than 1- ω or less than ω, equally, probability parameterMore than 1- ω or less than ω, wherein, ω is a very little positive, generally takes ω=0.01；

2. the corresponding target function value of optimum individual solution for being obtained since algorithm is continuous) secondary iteration do not improve；

3. current iteration number of times reaches given maximum iteration n_max。

2. optimization method according to claim 1, it is characterised in that the step S1, comprises the following steps：

S101：Define decision variable T_wRepresent w-th operation beat unit train run time interval, decision variable a_w,f(i,j) With d_w,f(i, j) is respectively w-th operation beat unit f row train and enters interval (i, j) and leave the moment of interval (i, j)；

S102:Determine the constraints that train beat-type is started, including with beat unit train constant duration operation constraint, same The beat unit train station residence time is equal with interval run time equated constraint, with the beat unit train minimum dwell time It is minimum and maximum with the constraint of the time of departure the latest, beat unit train earliest with the constraint of interval run time, beat unit train Run time spacing constraint, train are in interval minimum safe arrival time spacing constraint and train in interval minimum safe Departure time spacing constraint：

(1) run with beat unit train constant duration and constrained：Beat unit f+1 row are into and out with f row trains The time interval at interval (i, j) moment just for the beat unit train starts time interval, i.e.,：

$\begin{array}{cc}{a}_{w,f+1}(i,j)=a_{w,f}(i.j)+T_w,& \∀w;f=\mathrm{1,2},...,m_w-1\end{array};(i,j)\∈E_w$

$\begin{array}{cc}{d}_{w,f+1}(i,j)={\text{d}}_{w,f}(i.j)+T_w,& \∀w;f=\mathrm{1,2},...,m_w-1\end{array};(i,j)\∈E_w$

Wherein, E_wBe w-th operation beat unit train via Interval Set, m_wIt is w-th beat unit train operation quantity；

(2) it is equal with interval run time equated constraint with the beat unit train station residence time：Exist with beat unit train It is same stop with the identical dwell time or do not stop and it is same it is interval there is identical run time, i.e.,：

$\begin{array}{c}{a}_{w,f+1}(j,i^{\′})-d_{w,f+1}(i,j)=a_{w,f}(j,i^{\′})-d_{w,f}(i,j),\\ \∀w;f=1,2,\mathrm{...},n_w-1;(i,j)(j,i^{\′})\∈E_w\end{array}$

$\begin{array}{c}{d}_{w,f+1}(i,j)-a_{w,f+1}(i,j)=d_{w,f}(i,j)-a_{w,f}(i,j),\\ \∀w;f=1,2,\mathrm{...},n_w-1;(i,j)\∈E_w\end{array}$

Wherein, (i, j), it is to be connected two adjacent intervals stood that (j, i ') is respectively with station j；

(3) constrained with interval run time with the beat unit train minimum dwell time：For same beat unit train, only Cause that its 1st row train meets interval run time and requires that remaining train just meets this two with the station minimum dwell time It is required that, therefore only need to set following two constraintss：

$\begin{array}{cc}{d}_{w,1}(i,j)-a_{w,1}(i,j)={\mathrm{\δ}}_i^w\×{\mathrm{qt}}_{i,j}^w+{\mathrm{ct}}_{i,j}^w+{\mathrm{\δ}}_j^w\×{\mathrm{tt}}_{i,j}^w,& \∀w;(i,j)\∈E_w\end{array}$

$\begin{array}{cc}{a}_{w,1}(j,i^{\′})-d_{w,1}(i,j)\≥{\mathrm{\τ}}_j^w,& \∀w;(i,j),(j,i^{\′})\∈E_w\end{array}$

Wherein,It is 0-1 indications, if w-th beat unit train i parking AT STATION,Otherwise, It is beat unit w trains i ∈ S AT STATION_wThe minimum dwell time,Respectively beat unit w trains exist Interval (i, j) ∈ E_wThe startup additional time-division, pure motion time and stop additional time-division；

(4) beat unit train is constrained with the time of departure the latest earliest：Each first train of beat unit originates the time must not be later than Its regulation time of departure the latest, while must not be earlier than the circuit earliest service time, i.e.,：

$\begin{array}{cc}{t}_s\≤a_{w,1}(i,j),& \∀w;(i,j)\∈E_w\end{array}$

$\begin{array}{cc}{a}_{w,1}(i,j)\≤t_w^{latest},& \∀w;(i,j)\∈E_w\end{array}$

Wherein, t_sIt is the circuit earliest service time,It is w-th time of departure the latest of beat unit first train；

(5) the minimum and maximum run time spacing constraint of beat unit train：Each beat unit train run time must not be spaced Less than the minimum value that it specifies, while its run time interval will ensure that its whole train can go out in the range of the service time Hair, therefore：

$\begin{array}{cc}{T}_w\≥T_w^{min},& \∀w\end{array}$

$\begin{array}{cc}{T}_w\≤\frac{t_e-t_s}{m_w},& \∀w\end{array}$

Wherein,It is w-th minimum run time interval of beat unit train, t_eIt is circuit service time the latest；

(6) train is in interval minimum safe arrival time spacing constraint：Arbitrary neighborhood train gets to the station from same interval Time interval have to be larger than the minimum value of its defined, i.e.,

$\begin{array}{cc}{T}_w\≥{\mathrm{AT}}_{i,j},& \∀w;(i,j)\∈E_w\end{array}$

$\begin{array}{cc}|a_{w,f}(i,j)-a_{w^{\′},f^{\′}}(i,j)|\≥{\mathrm{AT}}_{i,j},& \∀w\≠w^{\′};\∀f,f^{\′};(i,j)\∈E_w\∩E_{w^{\′}}\end{array}$

Wherein, AT_i,jEnter the minimum safe time interval of interval (i, j) for two trains；

(7) train is in interval minimum safe departure time spacing constraint

$\begin{array}{cc}{T}_w\≥{\mathrm{DT}}_{i,j},& \∀w;(i,j)\∈E_w\end{array}$

$\begin{array}{cc}|d_{w,f}(i,j)-d_{w^{\′},f^{\′}}(i,j)|\≥{\mathrm{DT}}_{i,j},& \∀w\≠w^{\′};\∀f,f^{\′};(i,j)\∈E_w\∩E_{w^{\′}}\end{array}$

Wherein, DT_i,jThe minimum safe time interval of interval (i, j), E are left for two trains_w′For beat unit w ' can be via interval Collection, d_w′,f′(i, j) is the moment that the individual operation beat unit the f ' row trains of w ' leave interval (i, j)；

S103：Selection is model optimization target to minimize each beat unit train overall travel time, i.e.,：

$\min Z=\underset{w=1}{\overset{W}{\Σ}}\underset{f=1}{\overset{m_w}{\Σ}}\{\underset{(i,j)\∈E_w}{\mathrm{\Σ}}\left(d_{w,f}\right(i,j)-a_{w,f}(i,j\left)\right)+\underset{(i,j),(j,i^{\′})\∈E_w}{\mathrm{\Σ}}\left(a_{w,f}\right(j,i^{\′})-d_{w,f}(i,j\left)\right)\}$

Wherein, Z is model objective function value, i.e., each beat unit train overall travel time.

3. optimization method according to claim 1, it is characterised in that coding is solved in the step S2 by W coding section structure Into, wherein, W is running train beat element number；Each coding section corresponds to a different beat unit train, for correspondence In w-th coding section of train beat unit w=1,2 ..., W, it is made up of 3 encoding genes altogether, respectively：1. priority Gene Q_w, 2. first bus frequency gene DT_wAnd 3. run time spaced cdna D_w, wherein, priority gene Q_wTake Value scope is 1,2 ..., and W, the value determines the sequencing of beat unit w train schedules optimization, with larger preferential The beat unit train of genic value is weighed, its time of running table optimization order is with smaller priority genic value beat unit train Before；First bus frequency genic value DT_wThe beat unit w first buses are determined originates the time；Run time is allowed to be spaced Genic value D_wDetermine that beat unit w Train Schedules are spaced, that is, limit the beat unit other trains originates the time.

4. optimization method according to claim 1, it is characterised in that the step S3, comprises the following steps：

S301：NoteIt is beat unit w train priority genes Q_wSelection a=1, the probability parameter of 2 ..., W values, the parameter Value is initialized as：

${\mathrm{\α}}_w^0\left(a\right)=\frac{1}{W},a=1,2,...,W$

S302：NoteIt is beat unit w train first bus frequency genes DT_wSelect the probability parameter of b values, the parameter value It is initialized as：

${\mathrm{\β}}_w^0\left(b\right)=\frac{1}{b_{max}-b_{min}+1}b=b_{min},b_{min}+1,...,b_{max}$

Wherein, b_minAnd b_maxRespectively beat unit w first bus frequencys it is earliest with allow value the latest；

S303：NoteIt is the run time spaced cdna D of beat unit w trains_wAt the beginning of selecting the probability parameter of c, the parameter value Beginning turns to：

${\mathrm{\γ}}_w^0\left(c\right)=\frac{1}{c_{max}-c_{min}+1},c=c_{min},b_{min}+1,...,c_{max}$

Wherein, c_min,c_maxThe minimum and maximum possible value that respectively beat unit w Train Schedules interval allows.

5. optimization method according to claim 2, it is characterised in that the step S4, comprises the following steps：

S401：According to the probability parameter value that each gene value of each beat unit train is selected, each gene is generated at random by probability Value, thus generates a solution coding；This process is repeated until GS solution coding of generation；

S402：Optional one from GS solution coding, according to each beat unit priority valve Q_wDescending sequence, determines each section Clap the sequencing of unit train timetable establishment；During current beat unit train timetable is worked out, if there is train To breaking-out industry conflict, only allow to change current beat unit train station arriving and leaving moment, and can not adjust and work out beat unit Time-table；

S403：According to the beat unit train timetable establishment for determining sequentially, a beat unit, the current choosing of note are selected successively The beat unit train selected is w；The first bus according to being given in solution coding originates moment DT_wWith run time spacing value D_wRespectively Determine that originating for its all train is constantly：

$a_{w,f}(i_w^0,i_w^0+1)={\mathrm{DT}}_w+(f-1)\×D_w,f=1,2,...,m_w$

Wherein,Interval is originated for beat unit w trains；

S404：Since beat unit each trains of w are originated constantly, according to train when each interval run time stops with each station Between calculate arriving and leaving moment at other approach stations of each train successively, i.e.,：

$d_{w,f}(j,j+1)=a_{w,f}(i_w^0,i_w^0+1)+\underset{i=i_w^0}{\overset{j}{\Σ}}{\mathrm{CT}}_w(i,i+1)+\underset{i=i_w^0}{\overset{j-1}{\Σ}}{\mathrm{ST}}_w\left(i\right),(j,j+1)\∈E_w$

a_w,f(j, j+1)=d_w,f(j,j+1)+ST_w(j+1),(j,j+1)∈E_w

Wherein, CT_w(i, i+1) is run time of the beat unit w trains at interval (i, i+1), ST_w(i),ST_w(j+1) respectively It is the dwell time of beat unit w trains i and j+1 AT STATION；

S405：Judge each train arrival and leaving moments of beat unit w whether with before whether to determine beat unit train arriving and leaving moment There is operation conflict；If not existing, continue to select next beat unit train, repeat above step S403 and S404 and determine Its timetable；Otherwise, conflict set present in note current train schedule is combined into Conflict_w；

S406：From conflict set Conflict_wIn optional one, calculate respectively dissolve it is first to beat unit w required for the conflict Car originates the minimum adjustment amount Δ t at moment and Train Interval_wWith Δ D_w；And then thus redefine the beat unit w first buses Moment and Train Interval are originated for DT_w=DT_w+Δt_wWith D_w=D_w+ΔD_w；On this basis, using above step S403 Arriving and leaving moment of each trains of beat unit w at each approach station is recalculated to S405；

S407：Above step S402 to S406 is repeated, until when obtaining the GS solution corresponding many beat train synthetic operation of coding Carve table.