CN106097226A - City Routine Transit Network Design method based on Hierarchical Programming - Google Patents
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Abstract
The invention discloses a kind of City Routine Transit Network Design method based on Hierarchical Programming, the present invention goes out row mode according to passenger and gauze carries out distinguishing hierarchy, and according to " Hierarchical Programming " result, searches for the optional circuit of each level successively, and carry out demand assignment;With demand assignment structure as foundation, build one with departure frequency as variable, with passenger and network operator's cost minimization as object function, with the City Routine Transit Network Design model that the restrictive conditions such as line length, departure frequency, transport capacity, number of, lines are constraint;Use simulated annealing that model is solved, finally can determine rail network structure and circuit departure frequency, it is achieved the once one-tenth net of " Hierarchical Programming " Transit Network Design model simultaneously.Also corresponding to traffic zone in the present invention multiple set out or arrive website, more identical with the actual facilities of traffic zone periphery website, the result of calculation of model is more stable simultaneously.
Description
Technical field
The present invention relates to public transport field, be specifically related to a kind of City Routine Transit Network Design based on Hierarchical Programming
Method.
Background technology
Transit villages design is the key component in public transport development plan, and it is to resident's daily life, work
Trip or even the development of urban economy Community health have very important effect.Regular public traffic is the weight of urban public tranlport system
Want ingredient, thus, the research to City Routine Transit Network Design has important practical significance.City Routine public transport line
The design of net mainly includes determination and the calculating of circuit departure frequency of public bus network structure.Conventional Transit Network Design research
In merely by a traffic zone corresponding to single website, do not correspond with the actual facilities of traffic zone periphery website, can
Bigger error can be caused;Domestic existing " Hierarchical Programming " theory shortage is corresponding can determine that public bus network is tied simultaneously
Structure and the method for departure frequency;And existing " Hierarchical Programming " line net design model lacks the description that passenger changes to behavior;This
Outward, in existing model solution result, the website repetitive rate on circuit is higher, and cannot realize synchronization determine rail network structure and send out
Car frequency.
Summary of the invention
In order to overcome shortcoming that prior art exists with not enough, the present invention provides a kind of City Routine based on Hierarchical Programming
Transit Network Design method.
The present invention adopts the following technical scheme that
As it is shown in figure 1, regular public traffic gauze method for designing based on " Hierarchical Programming ", comprise the following steps:
Known road network is simplified and processes by S1, increases Centroid and distribution node.
S2 uses dijkstra's algorithm to solve the shortest path between each distribution node OD pair, then uses K shortest path to candidate
Circuit expands, and initially screens solving the shortest path obtained according to length constraint, will meet condition
Short-term road, as initial candidate circuit, stores to set A.
Expand, particularly as follows: the K shortest path tried to achieve is screened according to line length constraints, will meet
The K shortest path of constraints is defined as candidate line, and stores in our candidate line set.
As in figure 2 it is shown, the dijkstra's algorithm basic ideas used are:
(1) initialize.Selected search starting point s, makes d (s)=0, prd (s)=0, simultaneously permanent label n node and interim mark
Number node is respectively as follows: P=Φ,For other all nodes: p (i)=-1, d (i)=∞ i=1,2 ... N;Incite somebody to action
Point s is labeled as permanent label n, and is transferred in permanent label n set P, makes k=1, and starts Shortest Path Searching.
(2) search permanent label n.Search smporary label setIn in permanent label n set P labelling point closest
Node i, and the label of node i is become permanent label n, evenMake p (i)=1, and by node i from
Smporary label setIn be transferred in permanent label n set P;K=k+1.
(3) data in road network are updated.To any other nodes j in road network, if (i, j) ∈ A (i), and d (j) > d (i)
+Cij, then d (j)=d (i)+C is madeij, the more distance between new node j and starting point s, and make prd (j)=i.
(4) if all nodes are the most labeled in road network, i.e. k=N, then Shortest Path Searching is complete;If k < N, then return
Step (2), continues the search procedure of permanent label n.
Wherein, the number of nodes during N is road network;I represents that the arbitrary node in road network is numbered, i=1,2 ... N;A (i) table
Show the section being connected in road network;(i, j) represents node i and the section being connected between node j, and arbitrarily (i, j) ∈ A (i);
CijRepresent section (i, length j);P is the set storing permanent label n node;For storing the set of smporary label node;s
Represent the starting point of shortest path, the starting point i.e. searched for;D (i) represents the starting point s length to the shortest path of node i;P (i) is auxiliary
Helping label variable, if p (i)=-1, then node i is smporary label, if p (i)=1, then node i is permanent label n;Prd (j) is
Auxiliary variable, the numbering of the previous node that labelling shortest path is connected with node j, on shortest path, node chases after
Track.
As it is shown on figure 3, the basic ideas of employing K shortest path algorithm are:
(1) shortest path between 1-N is tried to achieve according to Dijkstra methodAnd by it
Store to set A, and make k=1, Num=Nk;
(2) judge whether k≤K sets up, if setting up, then make k=k+1, t=1 and perform step (3), otherwise, calculate knot
Bundle;
(3) inspection AK-1With Aj, j=1,2 ..., front t the node of k-1 is the most identical, if identical, then makes dtq=∞,
Wherein, q represents AjIn the t+1 node;
(4) Q is tried to achieve according to Dijkstra methodtShortest path between-N, during noting this Shortest Path Searching, should arrange
Except AK-1Front t node;
(5) by node 1 to node QtBetween path store to(Part I), node QtRoad between node N
Footpath store to(Part I);
(6) askWillWithMerge, and willStore to set B, and make t=t+1;
(7) t is judged > Nk-1Whether-1 set up, if setting up, then performs step (8), otherwise, return step (3);
(8) path that in search set B, length is the shortest, this path of labelling is AK, and stored to set A, other
Path remains in set B.
Wherein, i is the node serial number in road network, i=1,2 ... N, wherein 1 is starting point, and N is terminal;NkRepresent kth bar
Nodes on short path;1-i-... j, i ≠ j ≠ ... ≠ 1 represents from node 1 to the path of node j, and this path is through node
I ...;Represent the i-th node on kth bar shortest path;
Represent the kth bar shortest path between 1-j, whereinRepresent the 2nd on path, 3 ..., N respectivelyk-1 joint
Point;Represent the A of t node i on kth article shortest pathk-1Set, i.e.With Ak-1From starting point
1 starts to the t node i the most identical, and the node between the t+1 node N to terminal differs;RepresentFirst
Point, i.e. the K shortest path of candidateStarting point 1 to the t node i between path, the node in this set all withIn phase
With;RepresentPart II, i.e. the K shortest path of candidateThe t+1 node i N to terminal between path, this collection
In closing in addition to terminal N, withWithout other same node point;K represents the serial number of shortest path, k=1,2,3 ..., K;dijTable
Show the distance in section between node i-j.
S3 determines the line set of initial solution, public transport network is carried out distinguishing hierarchy, at level by the row mode that goes out of passenger
In partition process, number of transfer and long walking number of times by passenger carry out distinguishing hierarchy, concrete distinguishing hierarchy such as Fig. 6.
S4, according to distinguishing hierarchy result, searches for each optional circuit of level passenger, by always the going out of passenger on each candidate line
The row time carries out demand assignment.Considering under practical situation, passenger is generally biased towards the circuit trip selecting the travel time shorter, only
Retain the travel time circuit less than or equal to minimum Trip Costs 1.3 times.After circuit has screened, further according to the trip of each circuit
Time, the trip requirements between OD is allocated.
1) the first level (0 transfer 0 walking)
The generally central point (Centroid) that also non-selected traffic zone is set of website, but in the traffic zone divided
Periphery arranges bus station, and therefore, the traveler in community, for realizing trip purpose, need to produce point (trip herein from trip
Produce point, attraction refers both to center of housing estate point starting point) walk to periphery bus station.In like manner, after passenger getting off car, the most also need step
Walk to trip purpose ground.Therefore, this goes out under row mode, and the computing formula of total travel time of each circuit is as follows:
Wherein: TTkijFor traffic zone OD to (i, j) between, kth bar 0 changes to total travel time of 0 walking circuit;For
The walking time of origin cell i to a corresponding ik that gets on the bus;Represent the walking time of the kj community j to terminal that gets off;
Wait the average Waiting time of circuit k at the website ik that gets on the bus for passenger;For the time of occupant ride public bus network k, i.e. car
Slave site ik is to the running time of site k j.Calculating formula is respectively as follows:
Wherein, the circuit of occupant ride under k represents this pattern;di,ikRepresent the distance between node i and node i k, dkj,j、
dik,kjImplication be similar to;vwRepresent walking speed;vvRepresent running speed;Aw is Waiting time conversion coefficient, generally takes 0.5;
fkijRepresent that OD is to (i, j) in the departure frequency of kth candidate line of this level.
Total travel time of all candidate lines between each OD pair of this level is calculated, further according to the travel time according to formula (1)
Being allocated demand OD demand, concrete distribution formula is as follows:
Wherein, rkRepresent (i, j) between kth bar candidate line;(qij)rkRepresent that OD is to (i, trip requirements j) is assigned to
Demand on kth bar candidate line therebetween;qijRepresent (i, j) between total trip requirements;RijFor in this level (i, j) between full
The candidate line set of foot condition.
After the search of ground floor secondary line, to this Level Search to can the traffic zone OD of row line to being marked,
Avoid repeat search.
2) the second level
If the road network of the first level cannot meet (i, j) between trip requirements, then for realizing trip purpose, passenger need transfer
Or walking (select 1 transfer 0 walking trip pattern or 0 transfer 1 walking go out row mode), i.e. in the road network of the second level search for
(i, j) between candidate line, and carry out assignment of traffic.Note, in the search procedure of the second level candidate line, should be got rid of
Circuit on level, i.e. straightforward line, therefore in the candidate line search procedure of this level, tackle searching of line sentence
Disconnected, it is to avoid the repeat search of circuit.
(1) 1 transfer 0 walking
This goes out under row mode, and the whole trip process of passenger is decomposed into following 4 processes: circuit is walked in origin cell
1 get on the bus website, take circuit 1, take circuit 2, circuit 2 is got off and is a little walked to terminal community.Simultaneously as this goes out row mode
Under, passenger's trip needs carry out 1 transfer, therefore in the calculating of total travel time, penalties at 1 transfer should be increased.Concrete
Total travel time calculating formula is as follows:
Wherein,Represent the second level small area OD (i, j) between total travel time of kth bar circuit;T represents that passenger takes
The circuit 1 taken advantage of;It represents getting on the bus a little of circuit 1;n1Represent transfer website, be circuit 1 get off a little, be again the upper of circuit 2
Che Dian;T ' represents the circuit 2 of occupant ride;Jt ' represents getting off a little of circuit 2;ttransfer_penaltyRepresent penalties at transfer;Its
His symbol due to similar, be not stated otherwise herein.
(2) 0 transfer 1 walkings
This goes out under row mode, and passenger is without transfer, but need to carry out 1 vice-minister's walking, and it may be for starting point to getting on the bus a little
Long walking or the long walking a little located to terminal of getting off.It should be noted that in the search procedure of this pattern, searching for long walking
Time, need to first get rid of the situation that terminus community is adjacent.Therefore, the travel time under this pattern calculates a point following two situation.
When starting point needs long walking:
Wherein, i0Represent the node (distribution node of cell i) that passenger is connected with road network from starting point center of housing estate point;iNTable
Show the terminal of the long walking of starting point, be also getting on the bus a little of occupant ride circuit;K is the circuit of occupant ride;Kj is debarkation stop
Point;For node i0To node iNWalking time;Other symbol implications are with similar.
When destination county needs long walking:
Wherein, ik is for getting on the bus a little;K is the circuit of occupant ride;Kj represents and gets off a little;jNRepresent the long walking of destination county eventually
Point (distribution node of community j);For node kj to node jNWalking time;Other symbol implications are with similar.
In conjunction with result of calculation, according to following demand assignment formula, to this level searched up to OD pair, community between
Demand is allocated, if this level still cannot search minizone up to circuit, then continue the search of next level circuit.
Wherein,Represent the travel time of the second level candidate line;Represent respectively in the second level
1 transfer 0 walking, 0 transfer 1 walking (starting point director's walking), 0 transfer 1 walking (terminal director's walking) go out the candidate under row mode
Line set;Other symbol implications are with above.
This Level Search of labelling is to can OD pair, all traffic zones of row line.
3) third level
This level is number of transfer and the road network layer that long walking number of times summation is 2, if first and second level all cannot search
Between traffic zone up to circuit, then passenger must go out row mode by 2 transfers, 2 walkings or 1 walking of 1 transfer,
Trip purpose could be realized.
(1) 2 transfer 0 walking
In this pattern, passenger need to change to through 2 times could be during starting point cell i reaches home community j, i.e. this trip
Passenger need to take altogether 3 circuits (circuit 1, circuit 2, circuit 3).Wherein, circuit 2 both without starting point community, also without
Terminal community, but it has a common website (transfer point) respectively with circuit 1, circuit 3, and 3 line combinations get up to constitute OD
Travel route between pair.In this research, it is assumed that k1、k2、k3Respectively represent passenger trip during once take circuit 1, circuit
2, circuit 3;ik1For getting on the bus a little of circuit 1;n1For point of getting off, first transfer point of passenger of circuit 1, also it is the upper of circuit 2
Che Dian;n2For point of getting off, second transfer point of passenger of circuit 2, also it is getting on the bus a little of circuit 3;k3J is getting off of circuit 3
Point.Concrete calculating formula is as follows:
Wherein,Represent third level small area OD (i, j) between total travel time of kth bar circuit;Other related symbol
Implication with the most above.
It should be noted that and this pattern needs change to 2 times, therefore, need in the calculating of travel time at plus 2 transfers
Penalties.
(2) 0 transfer 2 walkings
Similar as above, before the search of the travel route of this pattern starts, should first get rid of: terminus cell i, j are adjacent
The situation of community;The situation of a community (neighbor cell is identical) only it is spaced between terminus cell i, j.Then, search terminus
Constitute OD pair of the neighbor cell of community up to circuit, and with the public transport line that circuit is occupant ride under this pattern searched
Road k.It is assumed that i0Distribution node (node being connected with road network) for cell i;Ik be circuit k get on the bus a little, i.e. this node is little
The distribution node point of district's i adjacent node;Kj is getting off a little of circuit k;jNDistribution node for j neighbor cell, community.Total trip
The calculating formula of time is:
Wherein,Represent the long walking spent time at terminus community respectively;Other symbols in formula
Implication is with above.
(3) 1 transfer 1 walkings
Long gait processes in this pattern is similar with 0 transfer 1 walking trip pattern, it may occur however that at starting point, destination county
Or between transfer website.Herein for simplifying the search of candidate line, in this goes out row mode, only consider long walking occur in starting point or
The situation of destination county.Therefore, total travel time of this pattern calculates and also should be divided into two kinds of situations.
When starting point needs long walking:
Wherein, i0Represent the node (distribution node of cell i) that passenger is connected with road network from starting point center of housing estate point;iNTable
Show the terminal of the long walking of starting point, be also occupant ride circuit k1Get on the bus a little;k1Circuit 1 for occupant ride;n1For circuit
k1Get off a little, be also the transfer website of passenger;k2Circuit 2 for occupant ride;k2J is circuit k2Get-off stop;Other symbols
Number implication is with similar.
When destination county needs long walking:
Wherein, k1Circuit 1 for occupant ride;ik1For circuit k1Get on the bus a little;n1For circuit k1Get off a little, also take advantage of
The transfer website of visitor;k2Circuit 2 for occupant ride;;k2J is circuit k2Get-off stop;jNFor the long walking of destination county passenger
Terminal, this node is the distribution node of community j;Other symbol implications are with similar.
In sum, the demand assignment formula of this level is as follows:
In above formula,Represent third level small area OD (i, j) between total travel time of kth bar circuit;Other correlative symbol
Number implication with the most above.
S5, so that the Trip Costs of passenger and enterprise operation cost minimization are turned to target, sets up object function, wherein, and passenger
Trip Costs include waiting for bus cost and transfer cost three part in cost, car;
Min TC=CW+CR+CI+Co
Wherein, CWIt is the cost of waiting for bus of passenger, CRFor the transfer cost of passenger, CIIt is cost in the car of passenger, CoVehicle is transported
Battalion's cost;Distinguishing hierarchy in comprehensive S4 and the calculating of each level related data, the calculating formula that can obtain all kinds of cost is as follows:
Wherein: A is candidate line set;fkFrequency for circuit k;αkFor auxiliary variable, if fk≠ 0, then take 1, otherwise,
Take 0;qkFor the flow being assigned on circuit k;βk1、βk2It is auxiliary variable, if current search is to go out row mode containing change to
In circuit, then βk1=0, βk2=1, otherwise, βk1=1, βk2=0;Represent non-transfer mode, transfer mode respectively
Under passenger's unit Waiting time cost;Represent the time of vehicle operation of circuit k;NkStop on circuit k, vehicle is operating
Pull in and count;tdFor vehicle website (without head and the tail website) average stopping time;VI: time cost in passenger's flat vehicle;
βkrFor auxiliary variable, if current search is transfer circuit, then β to circuit kkr=1, otherwise βkr=0;For transfer circuit k's
The average transfer time of average Waiting time, i.e. passenger;diskLength for circuit k;vvTravel speed for vehicle;cFor vehicle
Travel the required unit operation cost paid of 1 km.
In sum, object function expression formula is:
S6 sets relevant constraint, and described constraints includes:
(1) line length lij
200≤lij≤3000
(2) frequency fk
Same circuit bi-directional frequency is equal, and circuit departure frequency need to meet maximum, the constraint of minimum departure frequency (in example
Greatly, minimum departure frequency take 30,0 respectively), meet the restriction of integer condition simultaneously, it may be assumed that
fk=fk+1K=1,3,5 ...
30≥fk≥0
fk is integer
(3) transport capacity constraint
Can the service that transport capacity constraint is gauze and is provided meet all trip requirements in road network.In practical study
In, generally in units of circuit, transport capacity retrained and check, i.e. the transport capacity of circuit can all meet on circuit
Maximum section flow.
qkmax≤fk·cap·load
Wherein, qkmaxFor the maximum stream flow on circuit k, the statement of this parameter is the passenger flow demand on circuit, and equation is right
While be the transport capacity of available transportation service, i.e. circuit in circuit, the meaning of this constraints is the transport energy of circuit
Power must be able to meet passenger flow demand;Cap is vehicle capacity;Load is the maximum load factor allowed.
(4) maximum number of, lines
Obtaining more excellent solution for solving, traffic planners is maximum operating line number in arranging road network generally according to Fleet size
The constraint of amount.The formulation of this constraint plan of arranging an order according to class and grade driver has significant effect.The addition of this constraints, adds optimum
The practicality of gauze solution.
NR≤NRmax
Wherein, NRRepresent the number of, lines in road network;NRmaxRepresent the maximum number of, lines in the road network solution allowed.
S7, by above-mentioned object function and constraints, arranges the nonlinear mathematics programming that can obtain Transit Network Design as follows
Model:
Min TC=CW+CR+CI+CO
s.t.200≤lij≤3000
fk=fk+1K=1,3,5 ...
30≥fk≥0
fk is integer
qkmax≤fk·cap·load
NR≤NRmax
S8 uses simulated annealing to solve above-mentioned nonlinear mathematics programming model, determines the line in public transport network
Line structure and departure frequency.The concrete solution procedure of algorithm is as follows:
S8.1 determines the set A of all shortest paths, makes quantity n=0 of initial candidate circuit.
S8.2 determines maximum iteration time L calculated at initial temperature T, global cycle number of times G, each temperature, makes n=n+2,
G=0.
S8.3 randomly chooses n bar initial candidate circuit in shortest path set A, and the frequency of initial candidate circuit is taken maximum
Frequency values, t=T, l=0.
S8.4 according to the current circuit selected and frequency values thereof, by distinguishing hierarchy successively search between OD pair, each community up to
Circuit, is deposited the travel route searched and related data (average Waiting time, website number, time of vehicle operation etc.) thereof by layer
Storage;Further according to Level Search result, OD demand is allocated, and calculating target function TC (S0)。
S8.5 checks level Search Results, if all having up to circuit between OD pair, all communities, if meeting condition, then continuing
Following step;Otherwise, return S8.3.
S8.6 solves the largest cumulative flow of each circuit, and tests the transport capacity of each circuit, if meeting transport
Capacity consistency, then record current target function value and optimal solution, i.e. TC=TC (S0), S=S0;Otherwise, return S8.3.
S8.7, according to the largest cumulative flow of each circuit tried to achieve, recalculates the frequency of candidate line, by newly try to achieve
Frequency carries out Level Search and assignment of traffic again to gauze, and calculates the object function TC (S of correspondenceg) and optimal solution Sg;Relatively
TC(Sg) and TC, if TC is (Sg) < TC then makes TC=TC (Sg), S=Sg, l=l+1.
S8.8t=t/l, if t < ε or l < L, returns S8.4;Otherwise, continue following step.
If S8.9 is g > G, then export current optimal solution, algorithm terminates;Otherwise, if g≤G, g=g+1 return S8.3.
If S8.10 is n > NRmaxThen exporting current optimal solution, algorithm terminates;Otherwise, return S8.2.
Meaning of parameters in Fig. 1 is: g, l, k are auxiliary variable;T represents current temperature;T is initial temperature;ε represents mould
Intend minimum temperature given in annealing algorithm;Sg、TC(Sg), Δ t represent solution that kth time iteration obtains, totle drilling cost, cost respectively
Increment;RbetterRepresent and solve the relatively shortest path set obtained;G, L, K represent that given auxiliary parameter g, the maximum of l, k take respectively
Value, represents under the maximum iteration time at the maximum iteration time of simulated annealing, each temperature, each number of, lines respectively
Candidate line collection maximum search number of times;The line set that R obtains after representing adjustment.
The present invention goes out row mode according to passenger and gauze carries out distinguishing hierarchy, and according to " Hierarchical Programming " result, searches successively
The optional circuit of each level of rope, and carry out demand assignment;With demand assignment structure as foundation, build one with departure frequency for becoming
Amount, with passenger and network operator's cost minimization as object function, limits with line length, departure frequency, transport capacity, number of, lines etc.
Condition processed is the City Routine Transit Network Design model of constraint;Use simulated annealing that model is solved, finally may be used
Determine rail network structure and circuit departure frequency, it is achieved " once becoming net " of " Hierarchical Programming " Transit Network Design model simultaneously;This
Traffic zone is also corresponded to by invention multiple set out or arrive website, with the actual facilities of traffic zone periphery website more
Coincideing, the result of calculation of model is more stable simultaneously.
Beneficial effects of the present invention:
Present invention achieves " Hierarchical Programming " and " once becoming net " of Transit Network Design;The model proposed in the present invention is examined
Consider the transfer behavior of passenger, effectively overcomed the problem that in gauze, on circuit, website repetitive rate is high, it is achieved that synchronized to determine
Line construction in public transport network and the departure frequency of correspondence, and result of calculation is more stable.
Accompanying drawing explanation
Fig. 1 is the workflow diagram of the present invention;
Fig. 2 is the flow chart of dijkstra's algorithm in the present invention;
Fig. 3 is the flow chart of K shortest path algorithm in the present invention;
Fig. 4 is the road network structure figure of the embodiment of the present invention;
Fig. 5 is the road network structure figure after the embodiment of the present invention processes;
Fig. 6 is the gauze distinguishing hierarchy schematic diagram of the embodiment of the present invention;
Fig. 7 is the number of, lines variation diagram in embodiment of the present invention solving result;
Fig. 8 is this variation diagram of system synthesis in embodiment of the present invention solving result.
Detailed description of the invention
Below in conjunction with embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are not
It is limited to this.
Embodiment
Fig. 4 provides a road network being made up of (two-way) 7 traffic zones, 15 nodes (crossover node), 44 sections.
For ease of research, need to process former road network (increase dummy node), the road network after process is by 7 traffic zones, 15 joints
Point (crossover node) constitutes 82 sections (two-way 41 sections) and constitutes, and concrete road network structure figure is as shown in Figure 5.In road network respectively
Passenger's the beginning and the end demand between traffic zone, the related data of node and each traffic zone is listed in table 1~table 4 respectively.Public transport
The travel speed of car is 30km/h.It is ready that the passenger's ratio arrived at by transfer is 0.05.Time valency in passenger car
Value 30 (unit/people h) is reluctant that the outer time value 50 (unit/people h) of passenger car of transfer is ready the outer time valency of car of transfer passenger
Value 70 (unit/people h).Vehicle capacity 70 (people/car);The bus stop time is 0.02h every time.Passenger vehicle operating cost mainly includes combustion
Oil consumption, pass cost, personnel's wage etc., add tire consume expense, personal expenditures, enterprise's operating clerical cost etc., equivalent list
Position operation totle drilling cost is that 30 (unit/car km) calculates.Public bus network length is limited between 200m-3000m, and line frequency values limits
System is between 0-30, and maximum load factor takes 1.3.
Table 1 passenger's OD demand
Table 2 traffic zone related data
The traffic zone ownership situation that table 3 distribution node is corresponding
Table 4 crossover node and the coordinate of distribution node
Based on data above, model can synchronize to determine the line construction in optimal gauze and departure frequency.Ask according to model
The departure frequency obtained determines the circuit facilities in road network between each traffic zone.Model calculate gained road network in circuit and
Departure frequency is shown in Table 5.If the departure frequency that circuit is corresponding is 0, then it is not provided with this circuit.Through 300 independent calculating, this example selects
Select one group of result of wherein target function value minimum as route arrangement result.From result of calculation, optimal gauze needs altogether
4 circuits (unidirectional, two-way 8) are set, are specifically shown in Table 5.
Table 5 route arrangement result
The optimal solution of model solution gained is: totle drilling cost 15538 yuan, wherein, cost 2945 yuan of waiting for bus, change to cost 0 yuan,
Time cost 5153 yuan in car, operation cost 7440 yuan.
In this optimal solution, total transfer cost of passenger is 0, and i.e. all passengers in road network are all without transfer, can accept out
Through service between row OD point.Owing to, under this solution throughway, searching for first, second and third level successively, and once at current level
When searching up to travel route, it, to being marked, in other follow-up Level Searchs, is no longer searched by Ji Dui community OD
Rope, which greatly improves the service level of the gauze tried to achieve.
Investigate 300 independent result of calculations, it appeared that the circuit sum in each result of calculation and system synthesis basis
Change is little, and result of calculation is the most stable.Choose 10 the trial result (being shown in Table 6), the stability to result of calculation in this example
It is analyzed as shown in Figure 7.
Table 6 solving result stability analysis
Note: in table, number of, lines is the quantity of one-way line.
As shown in Figure 8, can find according to result of calculation repeatedly, Transit Network Design model solution based on " Hierarchical Programming "
On circuit sum and system synthesis change originally, fluctuate less, i.e. the solving result of model is more stable.
Above-described embodiment is the present invention preferably embodiment, but embodiments of the present invention are not by described embodiment
Limit, the change made under other any spirit without departing from the present invention and principle, modify, substitute, combine, simplify,
All should be the substitute mode of equivalence, within being included in protection scope of the present invention.
Claims (8)
1. a City Routine Transit Network Design method based on Hierarchical Programming, it is characterised in that comprise the steps:
Known public transport network is simplified and processes by S1, particular by increasing Centroid and distribution node, makes each hand over
The corresponding multiple starting points in logical community or arrival website;
S2 uses dijkstra's algorithm to solve the shortest path between each distribution node OD pair, and applies K shortest path algorithm to candidate
Line set expands, and initially screens solving the shortest path obtained according to length constraint, will meet condition
Generic line as initial candidate circuit, store in set A;
S3 determines the set of initial candidate circuit, public transport network is carried out distinguishing hierarchy and flow divides by the row mode that goes out of passenger
Joining, during distinguishing hierarchy, number of transfer and long walking number of times by passenger carry out distinguishing hierarchy;
S4, according to distinguishing hierarchy result, searches for each optional circuit of level passenger, by when always going on a journey of passenger on each candidate line
Between carry out demand assignment;
S5 turns to target with Trip Costs and the enterprise operation cost minimization of passenger, sets up object function, wherein, and the trip of passenger
Cost includes waiting for bus cost and transfer cost three part in cost, car;
Min TC=CW+CR+CI+Co, wherein, CWIt is the cost of waiting for bus of passenger, CRFor the transfer cost of passenger, CIIt it is the car of passenger
Interior cost, CoVehicle operating cost;
S6 sets relevant constraint, and described constraints includes:
(1) line length lijConstraint, 200≤lij≤ 3000, unit is rice;
(2) departure frequency fk, the two-way departure frequency of same circuit is equal, is constrained to:
fk=fk+1K=1,3,5 ...;
30≥fk≥0;
fkis integer;
(3) transport capacity constraint,
qkmax≤fk·cap·load
Wherein, qkmaxIt it is the maximum stream flow on circuit k;Cap is vehicle capacity;Load is the maximum load factor allowed;
(4) maximum number of, lines
NR≤NRmax
Wherein, NRRepresent the number of, lines in road network;NRmaxRepresent the maximum number of, lines in the road network solution allowed;
S7, by above-mentioned object function and constraints, arranges the nonlinear mathematics programming mould that can obtain Transit Network Design as follows
Type:
Min TC=CW+CR+CI+CO
s.t.200≤lij≤3000
fk=fk+1K=1,3,5 ...
30≥fk≥0
fk is integer
qkmax≤fk·cap·load
NR≤NRmax
S8 uses simulated annealing to solve above-mentioned nonlinear mathematics programming model, determines the circuit knot in public transport network
Structure and departure frequency.
City Routine Transit Network Design method the most according to claim 1, it is characterised in that the optional circuit tool of passenger
Body refers to passenger's travel time circuit less than or equal to minimum Trip Costs 1.3 times.
City Routine Transit Network Design method the most according to claim 1, it is characterised in that concrete the solving of described S8
Process is:
S8.1 determines the set A of all shortest paths, makes quantity n=0 of initial candidate circuit;
S8.2 determines maximum iteration time L calculated at initial temperature T, global cycle number of times G, each temperature, makes n=n+2, g=
0;
S8.3 randomly chooses n bar initial candidate circuit in set of minimal paths A, and the frequency of initial candidate circuit takes maximum frequency
Rate value, t=T, l=0;
S8.4 according to the current circuit selected and frequency values thereof, by distinguishing hierarchy successively search between OD pair, each community up to line
Road, is stored the travel route searched and related data thereof by layer;Further according to Level Search result, OD demand is allocated,
And calculating target function TC (S0);
S8.5 checks level Search Results, if all have up to circuit between OD pair, all communities, if meeting condition, then continues following
Step;Otherwise, return S8.3;
S8.6 solves the largest cumulative flow of each circuit, and tests the transport capacity of each circuit, if meeting transport capacity
Constraint, then record current target function value and optimal solution, i.e. TC=TC (S0), S=S0;Otherwise, return S8.3;
S8.7, according to the largest cumulative flow of each circuit tried to achieve, recalculates the frequency of candidate line, by the frequency newly tried to achieve
Again gauze is carried out Level Search and assignment of traffic, and calculates the object function TC (S of correspondenceg) and optimal solution Sg;Relatively TC
(Sg) and TC, if TC is (Sg) < TC then makes TC=TC (Sg), S=Sg, l=l+1;
S8.8t=t/l, if t < ε or l < L, returns S8.4;Otherwise, continue following step;
If S8.9 is g > G, then export current optimal solution, algorithm terminates;Otherwise, if g≤G, g=g+1 return S8.3;
If S8.10 is n > NRmaxThen exporting current optimal solution, algorithm terminates;Otherwise, return S8.2;
Wherein g, l, k are auxiliary variable;T represents current temperature;T is initial temperature;ε represents in simulated annealing given
Minimum temperature;Sg、TC(Sg), Δ t represent solution, totle drilling cost and the cost increase that kth time iteration obtains respectively;RbetterExpression solves
The relatively shortest path set obtained;G, L, K represent given auxiliary parameter g, the maximum occurrences of l, k respectively, represent that simulation is moved back respectively
Maximum iteration time at the fire maximum iteration time of algorithm, each temperature, the candidate line collection under each number of, lines are maximum
Searching times;The line set that R obtains after representing adjustment.
City Routine Transit Network Design method the most according to claim 3, it is characterised in that described related data includes
Average Waiting time, website number and time of vehicle operation.
City Routine Transit Network Design method the most according to claim 1, it is characterised in that described object function, tool
Body is
Min TC=CW+CR+CI+Co
Wherein: A is candidate line set;fkFrequency for circuit k;αkFor auxiliary variable, if fk≠ 0, then take 1, otherwise, take 0;qk
For the flow being assigned on circuit k;βk1、βk2It is auxiliary variable, if the line gone out in row mode for containing transfer of current search
Road, then βk1=0, βk2=1, otherwise, βk1=1, βk2=0;Represent taking advantage of under non-transfer mode, transfer mode respectively
Visitor's unit Waiting time cost;Represent the time of vehicle operation of circuit k;NkFor vehicle operating stop website on circuit k
Number;tdFor vehicle at website, and the average stopping time without head and the tail website;VIRepresent time cost in passenger's flat vehicle;βkr
For auxiliary variable, if current search is transfer circuit, then β to circuit kkr=1, otherwise βkr=0;For putting down of transfer circuit k
All average transfer times of Waiting time, i.e. passenger;diskLength for circuit k;vvTravel speed for vehicle;C is vehicle row
Sail the required unit operation cost paid of 1 km.
City Routine Transit Network Design method the most according to claim 1, it is characterised in that according to passenger in described S3
The row mode that goes out public transport network is carried out distinguishing hierarchy and assignment of traffic is as follows:
S3-1 searches for the first level, and i.e. 0 changes to 0 Walking Mode,
This goes out under row mode, and the computing formula of total travel time of each circuit is as follows:
Wherein,Wherein, passenger under k represents this pattern
The circuit taken;di,ikRepresent the distance between node i and node i k, vwRepresent walking speed;vvRepresent running speed;Aw is
Car time scale factor, generally takes 0.5;fkijRepresent that OD is to (i, j) in the departure frequency of kth candidate line of this level;
According to total travel time of all candidate lines between each OD pair of this level, OD demand is allocated, specific as follows:
Wherein, rkRepresent (i, j) between kth bar candidate line;Represent that OD is to (i, trip requirements j) is assigned to kth therebetween
Demand on bar candidate line;qijRepresent (i, j) between total trip requirements;RijFor in this level (i, j) between meet condition
Candidate line set;
After the search of ground floor secondary line, to this Level Search to can the traffic zone OD of row line to being marked, it is to avoid
Repeat search;
S3-2 searches for second layer secondary line, and described second level includes 1 transfer 0 Walking Mode and 0 transfer 1 Walking Mode;
When 1 transfer 0 Walking Mode, passenger's trip has only to carry out 1 transfer, its concrete total travel time computing formula
For:
Wherein,Represent the second level small area OD (i, j) between total travel time of kth bar circuit;T represents occupant ride
Circuit 1;It represents getting on the bus a little of circuit 1;n1Represent transfer website, be circuit 1 get off a little, be again getting on the bus a little of circuit 2;
T ' represents the circuit 2 of occupant ride;Jt ' represents getting off a little of circuit 2;ttransfer_penaltyRepresent penalties at transfer;
When 0 transfer 1 walking, passenger is without transfer, but need to carry out 1 vice-minister's walking and be specifically divided into two kinds of situations:
When starting point to the long walking got on the bus a little, its travel time is:
Wherein, i0The distribution node of the cell i that expression passenger is connected with road network from starting point center of housing estate point;iNRepresent starting point
The terminal of long walking, is also getting on the bus a little of occupant ride circuit;K is the circuit of occupant ride;Kj is get-off stop;For joint
Point i0To node iNWalking time;
The long walking a little located to terminal when getting off, its total travel time is:
Wherein,
Ik is for getting on the bus a little;K is the circuit of occupant ride;Kj represents and gets off a little;jNRepresent the long walking terminal i.e. community j of destination county
Distribution node;For node kj to node jNWalking time;
According to the travel time, carry out demand assignment, according to equation below:
Wherein,Represent the travel time of the second level candidate line;Represent in the second level that 1 changes respectively
Take advantage of the candidate line set under 0 walking, starting point director's walking, terminal director's walking trip pattern;
What labelling met that the second layer time searches can all traffic OD pair of row line;
The road network layer that S3-3 third level specially takes advantage of number of times and long walking number of times summation to be 2, if first and second level all cannot be searched
Rope between traffic zone up to circuit, then passenger must be by 2 transfers, 2 walkings or the trip of 1 walking of 1 transfer
Pattern, could realize trip purpose;
Under (1) 2 transfer 0 Walking Mode, total travel time is:
Wherein,Represent third level small area OD(i,j)Between total travel time of kth bar circuit;
(2) 0 transfer 2 walkings:
It is assumed that i0Distribution node for cell i;Ik be circuit k get on the bus a little, i.e. this node be cell i adjacent node distribution joint
Point point;Kj is getting off a little of circuit k;jNFor the distribution node of j neighbor cell, community, the calculating formula of total travel time is:
Wherein,Represent the long walking spent time at terminus community respectively;In formula, the implication of other symbols is same
Above;
(3) 1 transfer 1 walkings:
In this goes out row mode, only consider that long walking occurs the situation at beginning or end, therefore, when always going on a journey of this pattern
Between calculate and also should be divided into two kinds of situations.
When starting point needs long walking:
Wherein, i0Represent the node that passenger is connected with road network from starting point center of housing estate point;iNRepresent the end of the long walking of starting point
Point, is also occupant ride circuit k1Get on the bus a little;k1Circuit 1 for occupant ride;n1For circuit k1Get off a little, be also passenger
Transfer website;k2Circuit 2 for occupant ride;k2J is circuit k2Get-off stop;
When destination county needs long walking:
Wherein, k1Circuit 1 for occupant ride;ik1For circuit k1Get on the bus a little;n1For circuit k1Get off a little, be also passenger
Transfer website;k2Circuit 2 for occupant ride;k2J is circuit k2Get-off stop;jNFor the terminal of the long walking of destination county passenger,
This node is the distribution node of community j;
In sum, the demand assignment formula of this level is as follows:
In above formula,Represent third level small area OD(i,j)Between total travel time of kth bar circuit.
City Routine Transit Network Design method the most according to claim 6, it is characterised in that in the second level, search
During the long walking of rope, to first get rid of starting point and the adjacent situation of terminal.
City Routine Transit Network Design method the most according to claim 1, it is characterised in that described Centroid represents
The center of traffic zone, distribution node the setting out or arriving website as this traffic zone that each community is corresponding.
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