CN110135755A - A kind of method of complex optimum section urban public transit timetable establishment and vehicle scheduling - Google Patents

A kind of method of complex optimum section urban public transit timetable establishment and vehicle scheduling Download PDF

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CN110135755A
CN110135755A CN201910432647.4A CN201910432647A CN110135755A CN 110135755 A CN110135755 A CN 110135755A CN 201910432647 A CN201910432647 A CN 201910432647A CN 110135755 A CN110135755 A CN 110135755A
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姜晓红
过秀成
沈涵瑕
龚小林
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Nanjing Forestry University
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Abstract

The invention discloses a kind of methods of complex optimum section urban public transit timetable establishment and vehicle scheduling, comprising the following steps: building Bi-level Programming Models；Upper layer vehicle dispatching model is established using bus operation cost minimization as target based on upper layer planning assumed condition；Assumed condition is planned based on lower layer, is gone on a journey with passenger in section and transfer total time is unsuccessfully punished minimum target with transfer, establishes lower layer's timetable Optimized model；Lower layer's timetable Optimized model solves, and the feasible task shift collection optimized is exported as the satisfactory solution of lower layer's timetable Optimized model；Upper layer vehicle dispatching model solves, and all task chains and corresponding required vehicle number of feasible task shift collection are completed in output；The optimal solution for generating Bi-level Programming Models, completes the output of best vehicle scheduling scheme and corresponding section urban public transit timetable.It not only can intuitively reflect the operational plan of section route tissue, moreover it is possible to effective configuration of the convenient park-and-ride demand of further satisfaction passenger and enterprise's vehicle resources.

Description

A kind of method of complex optimum section urban public transit timetable establishment and vehicle scheduling
Technical field
The present invention relates to a kind of optimization method, more particularly to a kind of establishment of complex optimum section urban public transit timetable with The method of vehicle scheduling belongs to the technical field of optimization urban public transit transport capacity resource.
Background technique
Urban public transit refers mainly to the public transport of connection grass roots, the cities and towns public transport comprising connection city to town (street) Main line, the town village supplementary bus route in town to village, the town town supplementary bus route between adjacent town.Compared to the definition of region public transport, section The range of urban public transit is slightly smaller, positions section, the stronger small towns of relevance to village and village, village with the main line in city to small towns Between can form multiple spot radial pattern or region inner ring type rail network structure so that town-village, village-village's route and cities and towns public transport trunk Line forms a section.Section urban public transit tissue mainly realizes transport capacity resource in section by allotment adjacent lines transport power Integration, be related to section timetable establishment with vehicle scheduling two sub-problems.To guarantee passenger's transfer convenience and enterprise operation Benefit needs to cooperate with the frequency synchronism of transfer point, the allotment of multi-line transport power in the multi-line timetable compilation process of section Vehicle number and empty driving cost are reduced as far as possible on the basis of completing task shift.
Based on the organic connections of both region transit scheduling and vehicle scheduling, domestic and foreign scholars' comprehensive study integrated optimization Way to solve the problem.There are two types of existing methods: 1. sequence is integrated: successively solving timetable or vehicle scheduling subproblem, the party Method is likely to give up total optimization solution when screening the optimal solution of preamble subproblem；2. fully-integrated: one, a model calculation Method disposably solves two sub-problems, and related ends are as follows: Chakroborty etc. has studied the multi-line list under vehicle number constraint Change to the optimization problem of spot net；It is serviced more on the basis of the minimum operation cost that the research such as Castelli is constrained based on vehicle number More passengers；Guihaire etc. be based on existing timetable building comprising operation cost, vehicle number, transfer node quantity and intensity, etc. Interval dispatch a car, the weighted target function of empty driving time；The multi-line bicycle field tune of the research limiting time window such as Ibarra Rojas Degree optimization, to minimize vehicle number and maximize Synchronous Transfer amount as weighted target function；Laporte etc. considers that passenger goes out walking along the street Diameter selects preference and operation cost to limit, and both solves Pareto optimal solution using leash law.Fonseca et al. building transfer Cost and operation cost weighted target function propose that a kind of accurate heuritic approach solves.
Since urban public transit route shift is few, passenger unsuccessfully has the very long waiting time once changing to, and section town and country are public Hand over the Heavenly Stems and Earthly Branches line volume of the flow of passengers, transfer point demand difference obvious, collaboration transfer point to that there need to be sequencing when sending out the time, draw by existing research With describing coefficient of concordance by transfer point route number, or using transfer amount as one of optimization aim, but how preferably according to Sequencing according to transfer amount adjustment transfer point arriving and leaving moment is the content that requires study.In addition, existing model using mathematics, plan strategies for Etc. exact methods or certain heuritic approach are solved, more difficult operation in engineering practice.
Summary of the invention
It is a primary object of the present invention to overcome deficiency in the prior art, provide a kind of complex optimum section town and country public affairs The method for handing over timetable establishment and vehicle scheduling can intuitively reflect that the operational plan of section route tissue, realization meet passenger just Effective configuration of prompt park-and-ride demand and enterprise's vehicle resources, the great utility value having in industry.
In order to achieve the above object, the technical scheme adopted by the invention is that:
A kind of method of complex optimum section urban public transit timetable establishment and vehicle scheduling, comprising the following steps:
1) Bi-level Programming Models are constructed；
The Bi-level Programming Models include upper layer vehicle dispatching model and lower layer's timetable Optimized model, wherein upper deck Scheduling model realizes that the vehicle timing of the more vehicle multi-field models of multi-line by enterprises of public transport's operation cost for the purpose of minimum is assigned, Lower layer's timetable Optimized model, which is realized to go on a journey with passenger in section, unsuccessfully punishes the more of minimum target with transfer transfer total time The optimization of bar urban public transit route timetable；
1-1) construct upper layer vehicle dispatching model；
Upper layer vehicle dispatching model is established using bus operation cost minimization as target based on upper layer planning assumed condition；
1-2) construct lower layer's timetable Optimized model；
Assumed condition is planned based on lower layer, is gone on a journey with passenger in section and transfer total time is unsuccessfully punished minimum mesh with transfer Mark, establishes lower layer's timetable Optimized model；
2) lower layer's timetable Optimized model solves；
Section urban public transit route shift is solved using enumerative technique；
On the basis of existing timetable, optimize timetable by translation operation figure, and be sequentially adjusted in and change according to transfer amount Multiply point moment table, the feasible task shift collection optimized；
The feasible task shift collection optimized is exported as the satisfactory solution of lower layer's timetable Optimized model；
3) upper layer vehicle dispatching model solves；
Using the satisfactory solution of lower layer's timetable Optimized model of output as the feasible input solution of upper layer vehicle dispatching model, adopt With the objective function of Tabu-Search Algorithm upper layer vehicle dispatching model in the value of each feasible task shift, output is completed can All task chains of row task shift collection and corresponding required vehicle number；
4) optimal solution of Bi-level Programming Models is generated；
From all task chains and corresponding required vehicle number of the feasible task shift collection of completion of output, bus operation is selected The optimal solution of task chain corresponding to cost minimization and required vehicle number as Bi-level Programming Models completes best vehicle dispatching party The output of case and corresponding section urban public transit timetable.
The present invention is further arranged to: planning assumed condition in the upper layer are as follows: town and country public bus network is run every in section The each train number of route can be executed according to timetable and arrival on time；All vehicle vehicles are unified；Each route uplink and downlink It is considered independent research object, each train number has and only a public transport executes task；
The upper layer vehicle dispatching model, specifically:
Wherein, Ci,j=cti,j, Ci,M+l=cti,M+l, CM+l,j=ctM+l,j (1)
The constraint condition of upper layer vehicle dispatching model is,
yi,j∈ (0,1), i, j=1,2 ..., M+K, (i, j) ≠ (M+l, M+l '), l, l '=1,2 ..., K (2)
zi,l∈ (0,1), i=1,2 ..., M, l=1,2 ..., K (3)
yM+l,j-zj,l≤ 0, j=1,2 ..., M, l=1,2 ..., K (7)
yi,M+l-zi,l≤ 0, i=1,2 ..., M, l=1,2 ..., K (8)
zi,lyi,j-zj,l≤ 0, i, j=1,2 ..., M, l=1,2 ..., K (9)
ti+ti+1+…+tM+tl,i+ti,i+1+…+tM-1,M+tM,l′≤Tmax,
yl,i·yi,i+1…yM-1,M·yM,l′=1 (10)
In the constraint condition of upper layer vehicle dispatching model, formula (2), formula (3) define yi,j、zi,l；Formula (4) ensures each Bus returns to parking lot waiting after completing train number i or executes next train number j；Formula (5) ensures that each train number has vehicle execution, should Vehicle is executed since parking lot or completing last train number followed by；Formula (6) ensures that each train number only has a parking lot distribution Vehicle；Formula (7) ensures DlVehicle allocation give train number j, and j is first task that vehicle executes after outputing；Formula (8) ensures Parking lot DlVehicle allocation give train number i, and i is that vehicle returns to the last one task executed before parking lot；Formula (9) ensures that vehicle is complete At j is directly executed after train number i, if i is by DlDistribution, then j is also by DlDistribution；Formula (10) is that vehicle continues running time constraint；
In formula, Y is upper layer vehicle dispatching model feasible solution, mapping S (X) → Y is what lower layer's timetable Optimized model generated Task shift forms the feasible input solution of upper layer vehicle dispatching model according to natural number coding, S (X) is that lower layer's timetable optimizes mould Several feasible task shifts that type generates integrate, C is the fixed cost of a bus, V is required vehicle number, M total as shift Number, K are parking lot number, Ci,jRunning cost, c for train number i terminal to train number j starting point are unit time operation cost, ti,jFor vehicle Running time, C of the secondary i terminal to train number j starting pointi,M+lFor train number i terminal to parking lot DlEmpty driving cost, ti,M+lIt is whole for train number i Point arrives parking lot DlRunning time, CM+l,jFor parking lot DlTo the empty driving cost of j starting point, tM+l,jFor parking lot DlTo train number j starting point Running time, TmaxContinue running time for the maximum of a bus；yi,jIf indicating directly to run train number j after completing train number i It is then 1, is otherwise 0；yi,M+lIf indicating to be returned directly to D after train number ilIt is then 1, is otherwise 0；yM+l,jIf indicating train number j is DlFirst train number for issuing vehicle is then 1, is otherwise 0；zi,lIf indicating, train number i is DlThe vehicle of sending is then 1, is otherwise 0； zj,lIf indicating, j is DlThe vehicle of sending is then 1, is otherwise 0；tiFor the time for completing train number i, i=1,2 ..., M；ti,i+1For Running time of the train number i terminal to train number i+1 starting point, i=1,2 ..., M-1；tl,iFor parking lot DlWhen driving to train number i starting point Between, tM,l′For train number M terminal to parking lot Dl'Running time；yM,l′If indicating to be returned directly to parking lot D after completing train number Ml'Then it is 1, it is otherwise 0；yl,iIf indicating from parking lot DlThen it is directly 1 to train number i, is otherwise 0；yi,i+1If after indicating completion train number i directly Running train number i+1 is then 1, is otherwise 0, i=1,2 ..., M-1；
Wherein, model feasible solution Y is,
Y in feasible solution Y in modelM,M+KIf indicating to be returned directly to parking lot D after completing train number MKIt is then 1, is otherwise 0.
The present invention is further arranged to: the lower layer plans assumed condition are as follows: the transfer amount at any transfer point is to know , it is not influenced by the departure interval；Because the urban public transit volume of the flow of passengers is small, it can smoothly take in the passenger of transfer point and reach at first Meet the vehicle of condition；
Lower layer's timetable Optimized model, specifically:
The constraint condition of lower layer's timetable Optimized model is,
WMp≤ T, p=1,2 ..., P (13)
In the constraint condition of lower layer's timetable Optimized model, formula (12) is defined from the initial time of period T to first The time of departure is no more than the maximum departure interval of the route；W in formula (13)MpIt dispatches a car for the last one shift of pth route At the moment, the time of departure of the last one shift of dispatching a car in period T is within the termination time of the period；Formula (14) constraint is every The departure interval of route；Formula (15) constrains passenger in the waiting time of transfer point；
In formula, X is lower layer's timetable Optimized model feasible solution, the feasible solution of mapping f (X) → S (X) expression model generation, S It (X) is that feasible task shift integrates, P as public bus network manifolds all in section, M as shift sum, N as transfer point number, T is excellent The change period,To change to from route p ' train number i ' needs to passengers quantity, the W of route p train number iipFor route in period T Frequency, the W of p train number ii'p'For frequency, the T of route p ' train number i ' in period TpnFor the inception point route p to transfer Running time, the T of node np'nFor the inception point route p ' to transfer node n running time,For route p in period T The maximum departure interval,For the minimum departure interval of route p, tw in period TmaxIt is waited for the maximum acceptable transfer of passenger Time, twminIt is penalty factor for minimum time needed for the acceptable transfer of passenger, δ；If indicating the train number i and route p ' of route p Train number i ' when transfer node n can be changed to be 1, be otherwise 0；W1pFor the frequency of route p train number 1 in period T, W(i+1)pFor the frequency of route p train number (i+1) in period T；
Wherein, using uplink and downlink, respectively calculation is calculated all public bus network manifold P in section.
The present invention is further arranged to: the bus operation cost include purchase vehicle fixed cost and vehicle shift with Empty driving cost between parking lot.
The present invention is further arranged to: increases by one when every and fails the passenger smoothly changed to, then bus operation increased costs δ Minute.
The present invention is further arranged to: optimize timetable by translation operation figure in the step 2), specifically,
Step1, selection operation graph type；
Section route operation figure is drawn, using the period as abscissa, using the journey time of each route as ordinate, marks head Terminal point, transfer website；
Step2, selection reference line；
Select that the volume of the flow of passengers is big, a urban public transit main line more than transfer node is benchmark route；
Step3, translation linewise is determined according to the passenger traffic volume and transfer amount size；
Step4, successively translation urban public transit main line operation figure；
The adjustment main line departure interval: if a plurality of main line starting station is identical, guarantee to dispatch a car at equal intervals between route；Otherwise guarantee The time of main line partway transfer stop is identical；
The trunk end residence time is adjusted, is also equally spaced when guaranteeing the main line return set out with website, or is different It also can Synchronous Transfer when the main line return that website sets out；
Step5, successively translation urban public transit branch line operation figure；
The adjustment branch line departure interval is to guarantee itself and main line in the time coordination of transfer point；
The branch line end residence time is adjusted, to ensure that branch line arrival time is identical or slightly before the main line departure time；
Step6, calculate lower layer's timetable Optimized model target function value, and with status scheme comparison,
Optimization is judged whether there is by comparison, is performed the next step if having optimization, if without optimization return step Step4；
Step7, it indicates that seamless exchange node and optimization information form prioritization scheme, and exports and describe the excellent of prioritization scheme Figure is run after change；Wherein, optimization information includes feasible task shift collection, shift sum and frequency.
The present invention is further arranged to: using Tabu-Search Algorithm upper layer vehicle dispatching model in the step 3) Objective function each feasible task shift value, specifically,
3-1) citation form of the natural number coding indicated using structural body as solution indicates parking lot x with " 0 (x) ", natural The shift task that number is completed needed for indicating；
3-2) generate initial solution；
Successively it is ordered pair shift task with the time of departure according to natural number number consecutively, considers maximum lasting running time about Beam, the shift time of departure and runing time, sequence of natural numbers is resequenced；It is inserted into parking lot " 0 (x) ", if parking lot Limited Number Optimal parking lot is then screened one by one；Merge " 0 (x) " that may merge, connects into feasible task chain, the i.e. required vehicle of task chain number Number；
3-3) calculated using 2-top neighborhood operation method；
One group of natural number of random selection forms new sequence to change place every time, reinserts parking lot according to constraint condition and compiles Number, calculating target function value；It, will be candidate using the solution of the target function value maximum/minimum of each grey iterative generation as taboo object Collection is determined as generating the neighborhood space of solution at random, selects the rule based on evaluation of estimate as aspiration criterion, if there is a solution Target value is better than any one optimal candidate solution of front, then specially pardons；Evaluation function so far gained optimal solution with currently solve The difference of target function value；
It 3-4) is terminated and is calculated using target control principle；
If current optimal value is unchanged in given step number, calculating is terminated, and will appoint corresponding to current optimal value Business chain and the output of required vehicle number.
Compared with prior art, the invention has the advantages that:
By the establishment of building Bi-level Programming Models complex optimum section urban public transit timetable and vehicle scheduling, at the middle and upper levels Section urban public transit vehicle dispatching problem realizes the more vehicles of the more vehicles of multi-line using enterprises of public transport's comprehensive operation cost minimization as target The vehicle timing of field is assigned, using Tabu-Search Algorithm；Lower layer's section urban public transit timetable optimization problem is to realize line Minimum is unsuccessfully punished in the transfer total time of all transfer nodes and transfer in road, while ensuring that table collaboration is first at the time of transfer node Order afterwards is solved using operation figure with enumerative technique；On the basis of status timetable, lower layer's timetable Optimized model generates one Group satisfactory solution is selected for upper layer vehicle dispatching model ratio, and then when the best vehicle scheduling scheme of generation and corresponding section urban public transit Table is carved, optimization method provided by the invention can preferably be applied in engineering practice, not only can intuitively reflect section route tissue Operational plan, moreover it is possible to effective configuration of the convenient park-and-ride demand of further satisfaction passenger and enterprise's vehicle resources.
Above content is only the general introduction of technical solution of the present invention, in order to better understand technological means of the invention, under In conjunction with attached drawing, the invention will be further described in face.
Detailed description of the invention
Fig. 1 is the method and step flow chart of the embodiment of the present invention；
Fig. 2 is that operation figure draws flow chart in the method for the embodiment of the present invention；
Fig. 3 is public bus network topological diagram in the exemplary application of the embodiment of the present invention；
Fig. 4 is status operation figure in the exemplary application of the embodiment of the present invention；
Fig. 5 is to run figure after optimizing in the exemplary application of the embodiment of the present invention.
Specific embodiment
With reference to the accompanying drawings of the specification, the present invention is further illustrated.
The present invention provides the method for a kind of complex optimum section urban public transit timetable establishment and vehicle scheduling, such as Fig. 1 institute Show, comprising the following steps:
1) Bi-level Programming Models are constructed；
The Bi-level Programming Models include upper layer vehicle dispatching model and lower layer's timetable Optimized model, wherein upper deck Scheduling model realizes that (including to purchase vehicle fixed cost and vehicle empty between shift and parking lot with enterprises of public transport's operation cost Sail cost) it is minimum for the purpose of the vehicle timing of the more vehicle multi-field models of multi-line assign, lower layer's timetable Optimized model realize with Passenger goes on a journey in section unsuccessfully punishes a plurality of urban public transit route timetable optimization of minimum target transfer total time with transfer.
1-1) construct upper layer vehicle dispatching model；
Upper layer vehicle dispatching model is established using bus operation cost minimization as target based on upper layer planning assumed condition.
The upper layer plan assumed condition are as follows: each train number of every route that town and country public bus network is run in section can be by According to timetable execution and arrival on time；All vehicle vehicles are unified；Each route uplink and downlink is considered independent research object, Each train number has and only a public transport executes task.
The upper layer vehicle dispatching model, specifically:
Wherein, Ci,j=cti,j, Ci,M+l=cti,M+l, CM+l,j=ctM+l,j (1)
The constraint condition of upper layer vehicle dispatching model is,
yi,j∈ (0,1), i, j=1,2 ..., M+K, (i, j) ≠ (M+l, M+l '), l, l '=1,2 ..., K (2)
zi,l∈ (0,1), i=1,2 ..., M, l=1,2 ..., K (3)
yM+l,j-zj,l≤ 0, j=1,2 ..., M, l=1,2 ..., K (7)
yi,M+l-zi,l≤ 0, i=1,2 ..., M, l=1,2 ..., K (8)
zi,lyi,j-zj,l≤ 0, i, j=1,2 ..., M, l=1,2 ..., K (9)
In the constraint condition of upper layer vehicle dispatching model, formula (2), formula (3) define yi,j、zi,l；Formula (4) ensures each Bus returns to parking lot waiting after completing train number i or executes next train number j；Formula (5) ensures that each train number has vehicle execution, should Vehicle is executed since parking lot or completing last train number followed by；Formula (6) ensures that each train number only has a parking lot distribution Vehicle；Formula (7) ensures DlVehicle allocation give train number j, and j is first task that vehicle executes after outputing；Formula (8) ensures Parking lot DlVehicle allocation give train number i, and i is that vehicle returns to the last one task executed before parking lot；Formula (9) ensures that vehicle is complete At j is directly executed after train number i, if i is by DlDistribution, then j is also by DlDistribution；Formula (10) is that vehicle continues running time constraint；
In formula, Y is upper layer vehicle dispatching model feasible solution, mapping S (X) → Y is what lower layer's timetable Optimized model generated Task shift forms the feasible input solution of upper layer vehicle dispatching model according to natural number coding, S (X) is that lower layer's timetable optimizes mould Several feasible task shifts that type generates integrate, C is the fixed cost of a bus, V is required vehicle number, M total as shift Number, K are parking lot number, Ci,jRunning cost, c for train number i terminal to train number j starting point are unit time operation cost, ti,jFor vehicle Running time, C of the secondary i terminal to train number j starting pointi,M+lFor train number i terminal to parking lot DlEmpty driving cost, ti,M+lIt is whole for train number i Point arrives parking lot DlRunning time, CM+l,jFor parking lot DlTo the empty driving cost of j starting point, tM+l,jFor parking lot DlTo train number j starting point Running time, TmaxContinue running time for the maximum of a bus；yi,jIf indicating directly to run train number j after completing train number i It is then 1, is otherwise 0；yi,M+lIf indicating to be returned directly to D after train number ilIt is then 1, is otherwise 0；yM+l,jIf indicating train number j is DlFirst train number for issuing vehicle is then 1, is otherwise 0；zi,lIf indicating, train number i is DlThe vehicle of sending is then 1, is otherwise 0； zj,lIf indicating, j is DlThe vehicle of sending is then 1, is otherwise 0；tiFor the time for completing train number i, i=1,2 ..., M；ti,i+1For Running time of the train number i terminal to train number i+1 starting point, i=1,2 ..., M-1；tl,iFor parking lot DlWhen driving to train number i starting point Between, tM,l′For train number M terminal to parking lot Dl'Running time；yM,l′If indicating to be returned directly to parking lot D after completing train number Ml'Then it is 1, it is otherwise 0；yl,iIf indicating from parking lot DlThen it is directly 1 to train number i, is otherwise 0；yi,i+1If after indicating completion train number i directly Running train number i+1 is then 1, is otherwise 0, i=1,2 ..., M-1；
Wherein, model feasible solution Y is,
Y in feasible solution Y in modelM,M+KIf indicating to be returned directly to parking lot D after completing train number MKIt is then 1, is otherwise 0.
1-2) construct lower layer's timetable Optimized model；
Assumed condition is planned based on lower layer, is gone on a journey with passenger in section and transfer total time is unsuccessfully punished minimum mesh with transfer Mark, establishes lower layer's timetable Optimized model.
The lower layer plans assumed condition are as follows: the transfer amount at any transfer point be it is known, not by the shadow of departure interval It rings；Because the urban public transit volume of the flow of passengers is small, the vehicle for meeting condition reached at first can be smoothly taken in the passenger of transfer point.
Lower layer's timetable Optimized model, specifically:
The constraint condition of lower layer's timetable Optimized model is,
WMp≤ T, p=1,2 ..., P (13)
In the constraint condition of lower layer's timetable Optimized model, formula (12) is defined from the initial time of period T to first The time of departure is no more than the maximum departure interval of the route；W in formula (13)MpIt dispatches a car for the last one shift of pth route At the moment, the time of departure of the last one shift of dispatching a car in period T is within the termination time of the period；Formula (14) constraint is every The departure interval of route；Formula (15) constrains passenger in the waiting time of transfer point；
In formula, X is lower layer's timetable Optimized model feasible solution, the feasible solution of mapping f (X) → S (X) expression model generation, S It (X) is that feasible task shift integrates, P as public bus network manifolds all in section, M as shift sum, N as transfer point number, T is excellent The change period,To change to from route p ' train number i ' needs to passengers quantity, the W of route p train number iipFor route p in period T Frequency, the W of train number ii'p'For frequency, the T of route p ' train number i ' in period TpnIt is saved for the inception point route p to transfer Running time, the T of point np'nFor the inception point route p ' to transfer node n running time,Most for route p in period T The big departure interval,For the minimum departure interval of route p, tw in period TmaxWhen being waited for the maximum acceptable transfer of passenger Between, twminFor minimum time needed for the acceptable transfer of passenger, δ be penalty factor (increase by one when every and fail the passenger smoothly changed to, Then bus operation increased costs δ minutes)；If indicating, the train number i ' of the train number i and route p ' of route p can be into transfer node n It is 1 when row transfer, is otherwise 0；W1pFor the frequency of route p train number 1, W in period T(i+1)pFor route p vehicle in period T The frequency of secondary (i+1)；
Wherein, using uplink and downlink, respectively calculation is calculated all public bus network manifold P in section.
2) lower layer's timetable Optimized model solves；
Section urban public transit route shift is solved using enumerative technique；
On the basis of existing timetable, optimize timetable by translation operation figure, and be sequentially adjusted in and change according to transfer amount Multiply point moment table, the feasible task shift collection optimized；
The feasible task shift collection optimized is exported as the satisfactory solution of lower layer's timetable Optimized model.
As shown in Fig. 2, optimize timetable by translation operation figure, specifically,
Step1, selection operation graph type；
Section route operation figure is drawn, using the period as abscissa, using the journey time of each route as ordinate, marks head Terminal point, transfer website；
Step2, selection reference line；
Select that the volume of the flow of passengers is big, a urban public transit main line more than transfer node is benchmark route；
Step3, translation linewise is determined according to the passenger traffic volume and transfer amount size；
Step4, successively translation urban public transit main line operation figure；
The adjustment main line departure interval: if a plurality of main line starting station is identical, guarantee to dispatch a car at equal intervals between route；Otherwise guarantee The time of main line partway transfer stop is identical；
The trunk end residence time is adjusted, is also equally spaced when guaranteeing the main line return set out with website, or is different It also can Synchronous Transfer when the main line return that website sets out；
Step5, successively translation urban public transit branch line operation figure；
The adjustment branch line departure interval is to guarantee itself and main line in the time coordination of transfer point；
The branch line end residence time is adjusted, to ensure that branch line arrival time is identical or slightly before the main line departure time；
Step6, calculate lower layer's timetable Optimized model target function value, and with status scheme comparison,
Optimization is judged whether there is by comparison, is performed the next step if having optimization, if without optimization return step Step4；
Step7, it indicates that seamless exchange node and optimization information form prioritization scheme, and exports and describe the excellent of prioritization scheme Figure is run after change；Wherein, optimization information includes feasible task shift collection, shift sum and frequency.
3) upper layer vehicle dispatching model solves；
Using the satisfactory solution of lower layer's timetable Optimized model of output as the feasible input solution of upper layer vehicle dispatching model, adopt With the objective function of Tabu-Search Algorithm upper layer vehicle dispatching model in the value of each feasible task shift, output is completed can All task chains of row task shift collection and corresponding required vehicle number.
Tabu-Search Algorithm, specifically,
3-1) citation form of the natural number coding indicated using structural body as solution indicates parking lot x with " 0 (x) ", natural The shift task that number is completed needed for indicating；As 0 (1) _ 1_4_0 (1) _ 0 (2) _ 5_9_10_0 (2) indicates two bus difference From parking lot 1 and parking lot 2s, parking lot successively is returned to after execution task.
3-2) generate initial solution；
Successively it is ordered pair shift task with the time of departure according to natural number number consecutively, considers maximum lasting running time about Beam, the shift time of departure and runing time, sequence of natural numbers is resequenced；It is inserted into parking lot " 0 (x) ", if parking lot Limited Number Optimal parking lot is then screened one by one；Merge " 0 (x) " that may merge, connects into feasible task chain, the i.e. required vehicle of task chain number Number.
3-3) calculated using 2-top neighborhood operation method；
One group of natural number of random selection forms new sequence to change place every time, reinserts parking lot according to constraint condition and compiles Number, calculating target function value；It, will be candidate using the solution of the target function value maximum/minimum of each grey iterative generation as taboo object Collection is determined as generating the neighborhood space of solution at random, selects the rule based on evaluation of estimate as aspiration criterion, if there is a solution Target value is better than any one optimal candidate solution of front, then specially pardons；Evaluation function so far gained optimal solution with currently solve The difference of target function value.
It 3-4) is terminated and is calculated using target control principle；
If current optimal value is unchanged in given step number, calculating is terminated, and will appoint corresponding to current optimal value Business chain and the output of required vehicle number.
4) optimal solution of Bi-level Programming Models is generated；
From all task chains and corresponding required vehicle number of the feasible task shift collection of completion of output, bus operation is selected The optimal solution of task chain corresponding to cost minimization and required vehicle number as Bi-level Programming Models completes best vehicle dispatching party The output of case and corresponding section urban public transit timetable.
Exemplary application: it is carried out by taking five urban public transit routes (two main lines, three branch lines) of certain city, section, south as an example real Example verifying.Fig. 3 is public bus network topological diagram, and uplink 1 (D1-B-N1-N3-N4-D3) is main line, 2 (B-N1-N3- of route F), route 3 (B-N1-N2-A), route 4 (D2-N2-N3-E) be branch line, route 5 (C-N4-D3) be main line, route 6~10 It respectively corresponds as downgoing line, number journey time (unit: min) between each node in Fig. 3.Each route starting point is changed to four Point (N1, N2, N3, N4), three public transport parking lots (D1, D2, D3) journey time be shown in Table 1, table 1 is each route starting point to each node Between operation duration (unit: min), each node transfer amount is shown in Table 5.Status timetable and operation figure are shown in Table 2 and Fig. 4 respectively, intend The period of optimization is 12:00~15:00.Penalty factor δ is set as 5 through tentative calculation.
Table 1
Table 2
(1) timetable optimizes
Solving two prioritization schemes that lower layer's timetable Optimized model obtains realizes first in the larger line of transfer amount demand The seamless exchange on road, next effectively reduces the waiting time of remaining transfer node；Difference is only handling the few node of transfer amount Sequentially, as scheme one optimizes 8 → 2. → 4, scheme two optimize 6 → 1. → 3, be specifically shown in Table 3 (timetable optimization front and back Change to waiting time comparison).
Table 3
It should be noted that " 1 → 3. → 9 (5,8) " in table 3 indicates 3. passenger changes to route by route 1 in transfer point 9, transfer amount of () the interior digital representation in different train numbers；Change to the waiting time: positive number indicates delay (waiting transfer), negative table Show that (transfer failure), 0 are seamless exchange in advance.
(2) vehicle scheduling
Upper layer vehicle dispatching model sets M=40, K=7, C=100, c=1, T in solvingmax=480min.This example analysis Vehicle scheduling in a certain period, it is assumed that route 5,7,8,9 respectively nearby have distance for 0 virtual parking lot (respectively parking lot 4, 5,6,7), with guarantee vehicle starting at the end of can return to parking lot.Solving result is shown in Table 4 (the model calculations), scheme One vehicle scheduling better effect, operation figure, vehicle scheduling prioritization scheme are shown in Table 5, figure respectively after timetable, optimization after optimization 5, table 6.It should be noted that number is customized shift serial number, black circles in Fig. 5 in () after frequency in table 4 Indicate seamless exchange node.Prioritization scheme reduces 3 buses compared to status, and passenger reduces the transfer waiting time 91.1%.
Table 4
Table 5
Table 6
The method of complex optimum section urban public transit timetable establishment and vehicle scheduling provided by the invention, with urban public transit Transfer time is most short, unsuccessfully punishment is minimum and bus operation cost (purchasing fixed cost, empty driving cost containing vehicle) is minimum for transfer Bi-level Programming Models are established for target, and certain city, section, south urban public transit multi-line tissue is selected to carry out exemplary application, as a result table The Bi-level Programming Models of bright building can meet passenger's trip well and change to convenient demand, while enterprise is integrated in more efficient utilization Vehicle resources, and transfer point arriving and leaving moment can be sequentially adjusted according to transfer amount with enumerative technique, operation graphical method for tran sportation, it can be ensured that Timetable cooperates with primary and secondary, and the operation figure method of use is easy to operate in engineering practice, and visualizes, and can preferably be applied to engineering In practice.
Basic principles and main features and advantage of the invention have been shown and described above.The technical staff of the industry should Understand, the present invention is not limited to the above embodiments, and the above embodiments and description only describe originals of the invention Reason, without departing from the spirit and scope of the present invention, various changes and improvements may be made to the invention, these changes and improvements are all It falls into scope of the claimed invention.The scope of the present invention is defined by the appended claims and its equivalents.

Claims (7)

1. a kind of method of complex optimum section urban public transit timetable establishment and vehicle scheduling, which is characterized in that including following Step:
1) Bi-level Programming Models are constructed；
The Bi-level Programming Models include upper layer vehicle dispatching model and lower layer's timetable Optimized model, wherein upper layer vehicle tune The vehicle timing for spending multi-line more vehicle multi-field models of the model realization by enterprises of public transport's operation cost for the purpose of minimum is assigned, lower layer Timetable Optimized model realizes a plurality of city for going on a journey with passenger in section and changing to and total time unsuccessfully punishing minimum target with transfer The optimization of township's public bus network timetable；
1-1) construct upper layer vehicle dispatching model；
Upper layer vehicle dispatching model is established using bus operation cost minimization as target based on upper layer planning assumed condition；
1-2) construct lower layer's timetable Optimized model；
Assumed condition is planned based on lower layer, is gone on a journey with passenger in section and transfer total time is unsuccessfully punished minimum target with transfer, Establish lower layer's timetable Optimized model；
2) lower layer's timetable Optimized model solves；
Section urban public transit route shift is solved using enumerative technique；
On the basis of existing timetable, optimize timetable by translation operation figure, and be sequentially adjusted in transfer point according to transfer amount Timetable, the feasible task shift collection optimized；
The feasible task shift collection optimized is exported as the satisfactory solution of lower layer's timetable Optimized model；
3) upper layer vehicle dispatching model solves；
Using the satisfactory solution of lower layer's timetable Optimized model of output as the feasible input solution of upper layer vehicle dispatching model, using taboo Avoid value of the objective function in each feasible task shift that searching algorithm solves upper layer vehicle dispatching model, output completes feasible All task chains of business shift collection and corresponding required vehicle number；
4) optimal solution of Bi-level Programming Models is generated；
From all task chains and corresponding required vehicle number of the feasible task shift collection of completion of output, bus operation cost is selected The optimal solution of task chain corresponding to minimum and required vehicle number as Bi-level Programming Models, complete best vehicle scheduling scheme and The output of corresponding section urban public transit timetable.
2. the method for a kind of complex optimum section urban public transit timetable establishment and vehicle scheduling according to claim 1, It is characterized by: assumed condition is planned on the upper layer are as follows: each train number of every route that town and country public bus network is run in section It can be according to timetable execution and arrival on time；All vehicle vehicles are unified；Each route uplink and downlink is considered independent research Object, each train number has and only a public transport executes task；
The upper layer vehicle dispatching model, specifically:
Wherein, Ci,j=cti,j, Ci,M+l=cti,M+l, CM+l,j=ctM+l,j (1)
The constraint condition of upper layer vehicle dispatching model is,
yi,j∈ (0,1), i, j=1,2 ..., M+K, (i, j) ≠ (M+l, M+l '), l, l '=1,2 ..., K (2)
zi,l∈ (0,1), i=1,2 ..., M, l=1,2 ..., K (3)
yM+l,j-zj,l≤ 0, j=1,2 ..., M, l=1,2 ..., K (7)
yi,M+l-zi,l≤ 0, i=1,2 ..., M, l=1,2 ..., K (8)
zi,lyi,j-zj,l≤ 0, i, j=1,2 ..., M, l=1,2 ..., K (9)
ti+ti+1+…+tM+tl,i+ti,i+1+…+tM-1,M+tM,l′≤Tmax,
yl,i·yi,i+1…yM-1,M·yM,l′=1 (10)
In the constraint condition of upper layer vehicle dispatching model, formula (2), formula (3) define yi,j、zi,l；Formula (4) ensures each public transport Vehicle returns to parking lot waiting after completing train number i or executes next train number j；Formula (5) ensures that each train number has vehicle execution, the vehicle It is executed since parking lot or completing last train number followed by；Formula (6) ensures that each train number only has a parking lot distribution vehicle； Formula (7) ensures DlVehicle allocation give train number j, and j is first task that vehicle executes after outputing；Formula (8) ensures parking lot Dl Vehicle allocation give train number i, and i is that vehicle returns to the last one task executed before parking lot；Formula (9) ensures that vehicle completes train number J is directly executed after i, if i is by DlDistribution, then j is also by DlDistribution；Formula (10) is that vehicle continues running time constraint；
In formula, Y is upper layer vehicle dispatching model feasible solution, the task that mapping S (X) → Y is the generation of lower layer's timetable Optimized model It is raw for lower layer's timetable Optimized model that shift forms the feasible input solution of upper layer vehicle dispatching model, S (X) according to natural number coding At several feasible task shifts integrate, C is the fixed cost of a bus, V be required vehicle number, M as shift sum, K For parking lot number, Ci,jRunning cost, c for train number i terminal to train number j starting point are unit time operation cost, ti,jIt is whole for train number i Point arrives running time, the C of train number j starting pointi,M+lFor train number i terminal to parking lot DlEmpty driving cost, ti,M+lFor train number i terminal to vehicle Field DlRunning time, CM+l,jFor parking lot DlTo the empty driving cost of j starting point, tM+l,jFor parking lot DlWhen driving to train number j starting point Between, TmaxContinue running time for the maximum of a bus；yi,jExpression is 1 if directly running train number j after completing train number i, It otherwise is 0；yi,M+lIf indicating to be returned directly to D after train number ilIt is then 1, is otherwise 0；yM+l,jIf indicating, train number j is DlIt issues First train number of vehicle is then 1, is otherwise 0；zi,lIf indicating, train number i is DlThe vehicle of sending is then 1, is otherwise 0；zj,lTable If showing, j is DlThe vehicle of sending is then 1, is otherwise 0；tiFor the time for completing train number i, i=1,2 ..., M；ti,i+1For train number i Running time of the terminal to train number i+1 starting point, i=1,2 ..., M-1；tl,iFor parking lot DlTo the running time of train number i starting point, tM,l′For train number M terminal to parking lot Dl'Running time；yM,l′If indicating to be returned directly to parking lot D after completing train number Ml'It is then 1, it is no It is then 0；yl,iIf indicating from parking lot DlThen it is directly 1 to train number i, is otherwise 0；yi,i+1If indicating directly to run after completing train number i Train number i+1 is then 1, is otherwise 0, i=1,2 ..., M-1；
Wherein, model feasible solution Y is,
Y in feasible solution Y in modelM,M+KIf indicating to be returned directly to parking lot D after completing train number MKIt is then 1, is otherwise 0.
3. the method for a kind of complex optimum section urban public transit timetable establishment and vehicle scheduling according to claim 2, It is characterized by: the lower layer plans assumed condition are as follows: the transfer amount at any transfer point be it is known, not by the departure interval It influences；Because the urban public transit volume of the flow of passengers is small, the vehicle for meeting condition reached at first can be smoothly taken in the passenger of transfer point；
Lower layer's timetable Optimized model, specifically:
The constraint condition of lower layer's timetable Optimized model is,
WMp≤ T, p=1,2 ..., P (13)
In the constraint condition of lower layer's timetable Optimized model, formula (12) is defined dispatches a car from the initial time of period T to first Time is no more than the maximum departure interval of the route；W in formula (13)MpFor the frequency of the last one shift of pth route, The time of departure of the last one shift of dispatching a car in period T is within the termination time of the period；Formula (14) constrains every line The departure interval on road；Formula (15) constrains passenger in the waiting time of transfer point；
In formula, X is lower layer's timetable Optimized model feasible solution, the feasible solution of mapping f (X) → S (X) expression model generation, S (X) Integrate for feasible task shift, P as public bus network manifolds all in section, M as shift sum, N be transfer point number, T as optimization Period,To change to from route p ' train number i ' needs to passengers quantity, the W of route p train number iipFor route p vehicle in period T Frequency, the W of secondary ii'p'For frequency, the T of route p ' train number i ' in period TpnFor the inception point route p to transfer node Running time, the T of np'nFor the inception point route p ' to transfer node n running time,For the maximum of route p in period T Departure interval,For the minimum departure interval of route p, tw in period TmaxFor passenger's maximum acceptable transfer waiting time, twminIt is penalty factor for minimum time needed for the acceptable transfer of passenger, δ；If indicating the vehicle of the train number i and route p ' of route p Secondary i ' is 1 when transfer node n can be changed to, and is otherwise 0；W1pFor the frequency of route p train number 1 in period T, W(i+1)pFor the frequency of route p train number (i+1) in period T；
Wherein, using uplink and downlink, respectively calculation is calculated all public bus network manifold P in section.
4. the method for a kind of complex optimum section urban public transit timetable establishment and vehicle scheduling according to claim 1, It is characterized by: the bus operation cost include purchase vehicle fixed cost and vehicle between shift and parking lot empty driving at This.
5. the method for a kind of complex optimum section urban public transit timetable establishment and vehicle scheduling according to claim 3, It is characterized by: when every increase by one fails the passenger smoothly changed to, then bus operation increased costs δ minutes.
6. the method for a kind of complex optimum section urban public transit timetable establishment and vehicle scheduling according to claim 1, It is characterized by: optimize timetable by translation operation figure in the step 2), specifically,
Step1, selection operation graph type；
Section route operation figure is drawn, using the period as abscissa, using the journey time of each route as ordinate, marks first and last station Point, transfer website；
Step2, selection reference line；
Select that the volume of the flow of passengers is big, a urban public transit main line more than transfer node is benchmark route；
Step3, translation linewise is determined according to the passenger traffic volume and transfer amount size；
Step4, successively translation urban public transit main line operation figure；
The adjustment main line departure interval: if a plurality of main line starting station is identical, guarantee to dispatch a car at equal intervals between route；Otherwise guarantee main line Partway the time of transfer stop is identical；
The trunk end residence time is adjusted, is also equally spaced when guaranteeing the main line return set out with website, or different websites It also can Synchronous Transfer when the main line return set out；
Step5, successively translation urban public transit branch line operation figure；
The adjustment branch line departure interval is to guarantee itself and main line in the time coordination of transfer point；
The branch line end residence time is adjusted, to ensure that branch line arrival time is identical or slightly before the main line departure time；
Step6, calculate lower layer's timetable Optimized model target function value, and with status scheme comparison,
Optimization is judged whether there is by comparison, is performed the next step if having optimization, if without optimization return step Step4；
Step7, indicate that seamless exchange node and optimization information form prioritization scheme, and after exporting and describing the optimization of prioritization scheme Operation figure；Wherein, optimization information includes feasible task shift collection, shift sum and frequency.
7. the method for a kind of complex optimum section urban public transit timetable establishment and vehicle scheduling according to claim 1, It is characterized by: the objective function using Tabu-Search Algorithm upper layer vehicle dispatching model in the step 3) is each The value of feasible task shift, specifically,
3-1) citation form of the natural number coding indicated using structural body as solution indicates parking lot x, natural number table with " 0 (x) " The shift task completed needed for showing；
3-2) generate initial solution；
Successively be ordered pair shift task with the time of departure according to natural number number consecutively, consider it is maximum continue running time constraint, The shift time of departure and runing time, sequence of natural numbers is resequenced；Be inserted into parking lot " 0 (x) ", if the Limited Number of parking lot by The one optimal parking lot of screening；Merge " 0 (x) " that may merge, connects into feasible task chain, the i.e. required vehicle number of task chain number；
3-3) calculated using 2-top neighborhood operation method；
One group of natural number of random selection forms new sequence to change place every time, reinserts parking lot number according to constraint condition, Calculating target function value；It is using the solution of the target function value maximum/minimum of each grey iterative generation as taboo object, Candidate Set is true It is set to the random neighborhood space for generating solution, selects the rule based on evaluation of estimate as aspiration criterion, if there is the target of a solution Value is better than any one optimal candidate solution of front, then specially pardons；Evaluation function is gained optimal solution so far and the target currently solved The difference of functional value；
It 3-4) is terminated and is calculated using target control principle；
If current optimal value is unchanged in given step number, calculating is terminated, and by task chain corresponding to current optimal value It is exported with required vehicle number.
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