CN106203708A - A kind of fast method solving urban track traffic last bus connection problem - Google Patents

Abstract

The present invention discloses a kind of fast method solving urban track traffic last bus connection problem, and the method comprises the following steps: S1: set up City Rail Transit System decision support basic database by investigating domestic and international big and medium-sized cities on the spot with data collection；S2: use the idea about modeling of network flow, with the circuit in point direction as summit, with joining relation as limit, sets up spatiality network, and the weights with transfer passenger flow amount as limit, constructs last bus engagement scheme Weighted Directed Diagram model；S3: use the Zhu Liu method improved to solve described Weighted Directed Diagram model；S4: draw the circuit engagement scheme of optimization according to solving result；S5: according to described optimum engagement scheme, extrapolate All other routes to each station to a time.For extensive transit villages last bus operational plan Solve problems, this method conveniently can formulate real-time last bus timetable according to passenger flow demand, promotes accessibility and the service level of urban track traffic last bus.

Description

A kind of fast method solving urban track traffic last bus connection problem

Technical field

The present invention relates to urban track traffic control field.Urban track traffic is solved last more particularly, to one The fast method of car connection problem.

Background technology

From the point of view of world wide, urban track traffic has become indispensable urban transit system mode, each big city of China Rail Transit System also become better and approaching perfection day by day, and gradually to networking run transition.After urban track traffic becomes net operation, train is transported Row planning problem becomes complicated and changeable, and making overall plans and coordinate the transfer in full transportation network is to process network operation problem Key.Wherein, last bus operational plan is most typically in all kinds of transfers, solves problems networking to be considered The feature of operation and passenger flow demand characteristic, it is also contemplated that the configuration of the resource such as vehicle and service on buses or trains of actual operation, transport at each circuit Concentrate allotment on the basis of row plan, there is presently no generally acknowledged method fast and effectively.

Urban Rail Transit scale constantly expands, and transfer node is on the increase, and a lot of passengers need through the most very Purpose station is got to repeatedly transfer.Due to each bar circuit, to terminate the service time relatively independent, the last bus of every circuit Moment not only affects the trip of this line passengers, and impact is expanded to whole by the transfer relation simultaneously also by transfer stop Network.Change with last bus timetable is changed by passenger's trip route accessibility, therefore, works out the rational last bus moment Table, is used for instructing operating practice to make more passenger be benefited significant.

From the point of view of the basic demand of urban track traffic operation, the formulation of its operational plan should as far as possible with passenger flow kissing Closing, especially in the case of last bus, can the arriving and leaving moment of each last bus directly decide passenger and arrive at, passenger couple The accessibility concern of last bus can increase.Due to the transfer passenger flow of each transfer stop be by circuit between transfer relation come certainly Fixed, therefore, when calculating last bus arriving and leaving moment, circuit engagement scheme is the most important thing.Joining relation, the most each last fare A sequential is sent out in arriving of Lu Qi transfer station, if two row last buses can be changed at a transfer station, wherein a last bus A follows closely Arrive after last bus B, just A is called the linking of B, or A is connected B.In the case of A linking B, as long as reasonable arrangement two arranges The passenger flow transfer A that can realize B to a time interval at this station of car.Engagement scheme is the collection of each circuit joining relation in road network Close.Calculate last bus arriving and leaving moment, first have to work out last bus engagement scheme, then extrapolate end according to last bus engagement scheme Regular bus arriving and leaving moment.

At present, establishment urban track traffic last bus engagement scheme the most by virtue of experience judges, lacks optimization method, causes Scheme disconnects with actual passenger demand.In terms of theoretical research, scholar is had to propose to combine the network last bus transfer of passenger flow demand Model also uses genetic method to solve, and method has certain suitability, but under large-scale network environment, during method fortune Long, it is impossible to meet the requirement of real-time of reality application.Therefore, a kind of last bus rapidly and efficiently meeting passenger flow demand is formulated The method of operational plan has researching value and market prospect.

To sum up, it is desirable to provide a kind of urban track traffic last bus connection problem quick solving large scale network operation Method.

Summary of the invention

It is an object of the invention to provide a kind of urban track traffic last bus linking solving large scale network operation to ask The fast method of topic.

For reaching above-mentioned purpose, the present invention uses following technical proposals:

A kind of fast method solving urban track traffic last bus connection problem, the method comprises the following steps:

S1: by investigating on the spot or data collection obtains City Rail Transit System basic data, this basic data includes: The transfer passenger flow scale of each circuit each transfer station in the case of last bus and the train of each circuit in road network topology structure, road network The section operation time.

S2: with the circuit in point direction as summit, with joining relation as limit, the weights with transfer passenger flow amount as limit, structure end Regular bus engagement scheme Weighted Directed Diagram model, specifically includes following steps:

S21: generally, urban track traffic operating line is divided into uplink and downlink both direction, if urban track traffic In network, number of, lines is n, then the number of, lines in point direction is 2n, and the circuit in point direction is designated as L=(l₁,l₂,…,l_2i-1, l_2i,…,l_2n-1,l_2n).According to the basic principle of urban track traffic operation, the main purpose of last bus linking is to facilitate passenger Trip, makes more passenger arrive at smoothly as far as possible, so the optimization aim of urban track traffic last bus engagement scheme The transfer passenger flow amount that can be reduced to make transfer stop in road network be capable of is maximum, and tectonic model is as follows:

$\max Z\left(X\right)=\underset{i=1}{\overset{2n}{\mathrm{\Σ}}}\underset{j=1}{\overset{2n}{\mathrm{\Σ}}}{f}_{ij}\left(X\right)a_{ij}$

Feasible

Wherein, 0 ＜ i, j ＜ 2n, X are the engagement scheme comprising 2n-1 joining relation, and max Z (X) is in engagement scheme In the case of X, the transfer passenger flow amount sum that in road network, all transfer directions complete, f_ijIt is 0,1 variable, represents and work as engagement scheme In comprise l_i→l_jTime take 1, do not comprise l_i→l_jTime take 0, a_ijFor l_jTransfer l_iThe volume of the flow of passengers；

S22: by abstract for the circuit in every point of direction in road network be a summit, with directed graph G describe city rail hand over Circuit joining relation in open network, note G=(V, E, W) is the urban mass transit network that Weighted Directed Diagram represents, wherein V= (v₁,v₂,…,v_i,v_i+1,…,v_2n-1,v_2n) it is vertex set, each vertex v_iRepresent some side of a circuit in road network To, E is by the Sequential Elements couple e in V_i,j=e (v_i,v_j) the limit collection that constituted, represent the joining relation set between road network, its Middle i, j ∈ 1,2 ..., 2n}, i ≠ j, i+j ≠ 2i+ (-1)ⁱ⁺¹, W is weights set；

S23: to each limit e in E_i,jGive certain weight w_i,j=w (v_i,v_j), then w_i,jValue as follows:

$w_{i,j}=\left\{\begin{array}{cc}{a}_{ij}& if(v_i,v_j)\∈E\\ 0& if(v_i,v_j)\∉E\end{array}\right.$

Wherein, w_i,jFor each limit e in E_i,jWeights, be the transfer passenger flow amount at this station.

If v_iWith v_jRepresent circuit L respectively_pR direction and L_qS direction, then w_i,jFor joining relation L_pR direction linking L_q S direction time last bus in the case of transfer passenger flow amount.If circuit L_pAnd L_qOnly one of which transfer intersection point, then L_pWith L_qBetween Joining relation can only this transfer intersection point complete, the weight w of this joining relation_i,jIt is L_pR direction change at this station Take advantage of L_qThe volume of the flow of passengers in s direction.If L_pAnd L_qThere are m (m ＞ 1) transfer point, then L_pAnd L_qJoining relation can select Any one in this m station completes, then w_i,jL in one station of desirable any of which_pR direction transfer L_qS direction The volume of the flow of passengers.Generally, in order to make the transfer passenger flow amount achieved by each joining relation maximum, it is generally selected this m That station that in station, transfer passenger flow amount is maximum, as the connecting points of this joining relation, is the whole network due to object function herein The transfer passenger flow amount realized is maximum, so also in compliance with this principle, if there being special circumstances to need to consider other connecting points, then w_i,j The transfer passenger flow amount at this station should be taken.

S24: finding a summit in figure G, the direction along limit travels through each summit from this summit, is formed The tree diagram T of one directed graph^*, and T^*For the tree diagram of maximum weight in tree diagrams all in this directed graph, i.e. W (T^*)=max { W (T) Shu T is the tree diagram of G }, wherein W (T^*) it is the tree diagram T to figure^*Weights.

S3: use Zhu-Liu Fangfa improved to solve described Weighted Directed Diagram model, specifically include following steps:

S31: increase a vertex v on the basis of weighted and directed diagraph G₀, rightThere is limit e_{0, i}(v₀, v_i), its power Value w_{0, i}(v₀, v_i) more than the weights sum total on all limits in figure G, and, there is w j ≠ 0_{0, i}(v₀, v_i)=w_{0, j}(v₀, v_j), will increase Vertex v₀After directed graph, be referred to as scheming G ', G '=(V ', E ', W ')；

S32: make V₁=V ', E₁=E ', W₁=-W ', G₁=(V₁, E₁, W₁), k=1, wherein k is calculating process parameter；

S33:The minimum taking v enters arc, forms arc collection F_kIf, | F_k| ＜ | V_k|-1, stop, network G ' does not has There is Spanning Arborescence；If | F_k|=| V_k|-1, make F_k'=F_k, perform step S34；If | F_k|=| V_k|, from F_kIn remove power maximum Arc, remaining arc is designated as F_k', perform step S34；

S34: make H_k=(V_k, F_k'), if H_kWithout circle, then make H_k'=H_k, H_k' it is G_kShortest arborescence, perform step S36；Otherwise, at H_kAppoint and take a circle C_k, perform step S35；

S35: to G_kShrink C_k, obtain new network G_k+1=(V_k+1, E_k+1, W_k+1), remember that artificial summit is y_k, make k=k+ 1, perform step S33；

S36: if k=1, terminate, H_k' it is the shortest arborescence of figure G ', otherwise perform step S37；

S37: make H_k-1'=H_k+C_k-1-e_k-1', wherein e_k-1' it is C_k-1In an arc: if y_k-1At H_kHave in ' into arc, Then e_k-1' take and enter arc at G with this_k-1In have the arc of identical head；Otherwise e_k-1' it is taken as C_k-1The arc that middle weighting is maximumMake k=k- 1, perform step S36.

S4: obtained its maximum tree diagram by the shortest arborescence of G ', by the vertex v in the maximum tree diagram of described G '₀Go Fall, obtain the maximum tree diagram of figure G, i.e. optimal route engagement scheme.

S5: according to described optimum engagement scheme, in given urban track traffic runs time domain, during optimum is connected The time that the train of most end is reached terminal is set to run the right-hand member point value of time domain, and as basic point, extrapolates other lines Road specifically includes following steps to each station to the time of sending out:

S51: set optimum engagement scheme as:

Wherein, L_(i)Represent i-th line road in engagement scheme,Represent circuit L_(i)In track traffic station S_iLinking circuit L_(i-1)；

S52: set circuit L_(i)The upper total individual station of r (i), difference numbered 1,2 ..., i ... r (i), usesRepresent circuit L_(i)The due in of j AT STATION,Represent circuit L_(i)The setting out the moment of j AT STATION,Represent circuit L_(i)K AT STATION The operation time interval with station k+1,Represent circuit S AT STATION_iThe transfer time,Represent circuit L_(i)AT STATION The dwell time of k；

S53: when the urban track traffic service time, territory was [A, B], L₍₁₎Due in its terminus is:

$t_{\left(1\right)r\left(i\right)}^D=B$

L₍₁₎In the arriving and leaving moment of station j it is:

$t_{\left(1\right)j}^D=t_{\left(1\right)r\left(i\right)}^D-\underset{k=j}{\overset{r\left(1\right)-1}{\mathrm{\Σ}}}{t}_{\left(1\right)k(k+1)}^Y-\underset{k=j}{\overset{r\left(1\right)-1}{\mathrm{\Σ}}}{t}_{\left(1\right)k}^T$

$t_{\left(1\right)j}^F=t_{\left(1\right)r\left(i\right)}^D-\underset{k=j}{\overset{r\left(1\right)-1}{\mathrm{\Σ}}}{t}_{\left(1\right)k(k+1)}^Y-\underset{k=j-1}{\overset{r\left(1\right)-1}{\mathrm{\Σ}}}{t}_{\left(1\right)k}^T$

L can be obtained₍₁₎At transfer station S₁Frequency beAnd have:

$t_{\left(2\right)S\left(1\right)}^D=t_{\left(1\right)S\left(1\right)}^F-t_{S\left(1\right)}^Z$

$t_{\left(2\right)S\left(1\right)}^F=t_{\left(1\right)S\left(1\right)}^F-t_{S\left(1\right)}^Z+t_{\left(2\right)S\left(1\right)}^T$

L can be obtained₍₂₎At S₁The due in stood, then L₍₂₎In the arriving and leaving moment of station j it is:

When j ＜ S (1):

$t_{\left(2\right)j}^D=t_{\left(2\right)S\left(1\right)}^D-\underset{k=j}{\overset{S\left(1\right)-1}{\mathrm{\Σ}}}{t}_{\left(2\right)k(k+1)}^Y-\underset{k=j}{\overset{S\left(1\right)-1}{\mathrm{\Σ}}}{t}_{\left(2\right)k}^T$

$t_{\left(2\right)j}^F=t_{\left(2\right)S\left(1\right)}^D-\underset{k=j}{\overset{S\left(1\right)-1}{\mathrm{\Σ}}}{t}_{\left(2\right)k(k+1)}^Y-\underset{k=j+1}{\overset{S\left(1\right)-1}{\mathrm{\Σ}}}{t}_{\left(2\right)k}^T$

When j ＞ S (1):

$t_{\left(2\right)j}^D=t_{\left(2\right)S\left(1\right)}^D+\underset{k=S\left(1\right)}{\overset{j-1}{\mathrm{\Σ}}}{t}_{\left(2\right)k(k+1)}^Y+\underset{k=S\left(1\right)}{\overset{j-1}{\mathrm{\Σ}}}{t}_{\left(2\right)k}^T$

$t_{\left(2\right)j}^F=t_{\left(2\right)S\left(1\right)}^D+\underset{k=S\left(1\right)}{\overset{j-1}{\mathrm{\Σ}}}{t}_{\left(2\right)k(k+1)}^Y+\underset{k=S\left(1\right)}{\overset{j}{\mathrm{\Σ}}}{t}_{\left(2\right)k}^T$

S54: S can be obtained by above formula₂The frequency stood, thus can extrapolate L₍₃₎At S₂The due in stood, and then Extrapolate L₍₃₎Arriving and leaving moment and L at arbitrarily station j₍₄₎,L₍₅₎,…,L_(i),…,L_(2n)Arriving and leaving moment at each station.

Beneficial effects of the present invention is as follows:

1. the transfer passenger flow amount being capable of using transfer stop in road network is maximum as object function, takes into full account that passenger flow needs Ask, promote accessibility and the service level of urban track traffic last bus；

2. by abstract for complicated Urban Rail Transit for weighted and directed diagraph, by former problem reduction, it is possible to realize big rule Mould parallel computation, solves the problem that extensive transit villages last bus operational plan is difficult to solve.

3. Zhu-Liu Fangfa of the improvement used, solution efficiency Gao Bingke accurately solve, and have broken away from conventional heuristic Method for solving can only obtain satisfactory solution and cannot obtain the puzzlement of optimal solution；

4. method for solving operation application is convenient, can Real-time solution, formulate real-time last bus timetable according to passenger flow demand. Meanwhile, when being delayed occurs in last bus or during other emergency situations, it is possible to formulate corresponding last bus operational plan as required, Satisfactory solution is tried to achieve in subrange.

Accompanying drawing explanation

Below in conjunction with the accompanying drawings the detailed description of the invention of the present invention is described in further detail.

Fig. 1 illustrates urban track traffic last bus connection problem fast method flow chart.

Fig. 2 illustrates urban track traffic last bus connection problem fast method modularity flow chart.

Fig. 3 illustrates Urban Rail Transit topology diagram in an embodiment.

Fig. 4 illustrates that oriented tax of last bus engagement scheme that in an embodiment, urban mass transit network example takes out is weighed Figure.

Detailed description of the invention

In order to be illustrated more clearly that the present invention, below in conjunction with preferred embodiments and drawings, the present invention is done further Bright.Parts similar in accompanying drawing are indicated with identical reference.It will be appreciated by those skilled in the art that institute is concrete below The content described is illustrative and be not restrictive, and should not limit the scope of the invention with this.

The present invention is in order to improve the accessibility of road network, and the transfer passenger flow amount making transfer stop in road network be capable of is maximum, if Count the fast method of a kind of urban track traffic last bus connection problem for solving large scale network operation such as Fig. 1, Fig. 2 For the modular division of said method, below in conjunction with accompanying drawing, the inventive method is described in detail: at a specific embodiment In, a kind of fast method solving urban track traffic last bus connection problem, the method comprises the following steps:

S1: set up City Rail Transit System decision support with data collection by domestic and international big and medium-sized cities are investigated on the spot Basic database, this basic data includes: each circuit each transfer station in the case of last bus in road network topology structure, road network The train interval of transfer passenger flow scale and each circuit runs the time.

In one embodiment, Urban Rail Transit topological structure example is as it is shown on figure 3, this road network has four lines Road { L₁,L₂,L₃,L₄, wherein L₄For loop wire, in figure, the direction of arrow represents the down direction of circuit, has 6 transfer stops in road network {A,B,C,D,E,F,G}.Transfer passenger flow scale is as shown in table 1, the first row and the L of first row in table_iUpper and lower expression circuit L_i's Uplink and downlink direction, the cell of row and column intersection is by be expert at L_iUpper and lower transfer is to column L_jThe upper and lower volume of the flow of passengers and institute Transfer stop composition.

Table 1 urban track traffic transfer passenger flow scale

Table 2 is to the explanation of symbol definition in the present invention:

Table 2 symbol definition explanation table

S2: use the idea about modeling of network flow, with the circuit in point direction as summit, with joining relation as limit, set up space- State network, and the weights with transfer passenger flow amount as limit, construct last bus engagement scheme Weighted Directed Diagram model, specifically include with Lower step:

S21: generally, urban track traffic operating line is divided into uplink and downlink both direction, if urban track traffic In network, number of, lines is n, then the number of, lines in point direction is 2n, and the circuit in point direction is designated as L=(l₁,l₂,…,l_2i-1, l_2i,…,l_2n-1,l_2n).According to the basic principle of urban track traffic operation, the main purpose of last bus linking is to facilitate passenger Trip, makes more passenger arrive at smoothly as far as possible, so the optimization aim of urban track traffic last bus engagement scheme The transfer passenger flow amount that can be reduced to make transfer stop in road network be capable of is maximum, and tectonic model is as follows:

$\max Z\left(X\right)=\underset{i=1}{\overset{2n}{\mathrm{\Σ}}}\underset{j=1}{\overset{2n}{\mathrm{\Σ}}}{f}_{ij}\left(X\right)a_{ij}$

Feasible

Wherein, 0 ＜ i, j ＜ 2n, X are the engagement scheme comprising 2n-1 joining relation, and max Z (X) is in engagement scheme In the case of X, the transfer passenger flow amount sum that in road network, all transfer directions complete, f_ijIt is 0,1 variable, represents and work as engagement scheme In comprise l_i→l_jTime take 1, do not comprise l_i→l_jTime take 0, a_ijFor l_jTransfer l_iThe volume of the flow of passengers.

S22: by abstract for the circuit in every point of direction in road network be a summit, with directed graph G describe city rail hand over Circuit joining relation in open network, note G=(V, E, W) is the urban mass transit network that Weighted Directed Diagram represents, wherein V= (v₁,v₂,…,v_i,v_i+1,…,v_2n-1,v_2n) it is vertex set, each vertex v_iRepresent some side of a circuit in road network To, E is by the Sequential Elements couple e in V_i,j=e (v_i,v_j) the limit collection that constituted, represent the joining relation set between road network, its Middle i, j ∈ 1,2 ..., 2n}, i ≠ j, i+j ≠ 2i+ (-1)ⁱ⁺¹, represent the joining relation set between road network, wherein i ≠ j represents Be that the circuit in point direction can not be connected mutually with self, i+j ≠ 2i+ (-1)ⁱ⁺¹Represent be same circuit both direction it Between can not be mutually linked, W is weights set.

S23: to each limit e in E_i,jGive certain weight w_i,j=w (v_i,v_j), then w_i,jValue as follows:

$w_{i,j}=\left\{\begin{array}{cc}{a}_{ij}& if(v_i,v_j)\∈E\\ 0& if(v_i,v_j)\∉E\end{array}\right.$

Wherein, w_i,jFor each limit e in E_i,jWeights, be the transfer passenger flow amount at this station.

If v_iWith v_jRepresent circuit L respectively_pR direction and L_qS direction, then w_i,jFor joining relation L_pR direction linking L_q S direction time last bus in the case of transfer passenger flow amount.If circuit L_pAnd L_qOnly one of which transfer intersection point, then L_pWith L_qBetween Joining relation can only this transfer intersection point complete, the weight w of this joining relation_i,jIt is L_pR direction change at this station Take advantage of L_qThe volume of the flow of passengers in s direction.If L_pAnd L_qThere are m (m ＞ 1) transfer point, then L_pAnd L_qJoining relation can select Any one in this m station completes, then w_i,jL in one station of desirable any of which_pR direction transfer L_qS direction The volume of the flow of passengers.Generally, in order to make the transfer passenger flow amount achieved by each joining relation maximum, it is generally selected this m That station that in station, transfer passenger flow amount is maximum, as the connecting points of this joining relation, is the whole network due to object function herein The transfer passenger flow amount realized is maximum, so also in compliance with this principle, if there being special circumstances to need to consider other connecting points, then w_i,j The transfer passenger flow amount at this station should be taken.

Fig. 4 is that oriented tax of last bus engagement scheme that in an embodiment, urban mass transit network example takes out is weighed Figure.Wherein, L₁On be expressed as v₁, L₁Under be expressed as v₂, L₂On be expressed as v₃, by that analogy.In order to become apparent from representing legibly, With a undirected limit e (v_i,v_j) represent two oriented limit e (v_i,v_j) and e (v_j,v_i), the power on the digitized representation limit on limit Value, wherein the numbering of the starting point of Z representative edge is less than the weights of the directed edge of the numbering of the terminal on limit, the volume of the starting point of F representative edge Number more than the weights of numbering of terminal on limit.

S24: after representing Urban Rail Transit with G, solve one feasible and cover all circuits of road network last Car engagement scheme translates into problems with: finds a summit in figure G, travels through from this summit along the direction on limit Each summit, forms the tree diagram T of a directed graph^*, and T^*For maximum weight tree-like in tree diagrams all in this directed graph Figure, i.e. W (T^*)=max{W (T) Shu T is the tree diagram of G }, wherein W (T^*) it is the tree diagram T to figure^*Weights.

S3: use Zhu-Liu Fangfa improved to solve described Weighted Directed Diagram model, specifically include following steps:

S31: increase a vertex v on the basis of weighted and directed diagraph G₀, rightThere is limit e_{0, i}(v₀, v_i), its weights w_{0, i}(v₀, v_i) more than the weights sum total on all limits in figure G, and, there is w j ≠ 0_{0, i}(v₀, v_i)=w_{0, j}(v₀, v_j), increase is pushed up Point v₀After directed graph, be referred to as scheming G ', G '=(V ', E ', W ').

S32: make V₁=V ', E₁=E ', W₁=-W ', G₁=(V₁, E₁, W₁), k=1, wherein k is calculating process parameter.

S33:The minimum taking v enters arc, forms arc collection F_kIf, | F_k| ＜ | V_k|-1, stop, network G ' does not has There is Spanning Arborescence；If | F_k|=| V_k|-1, make F_k'=F_k, perform step S34；If | F_k|=| V_k|, from F_kIn remove power maximum Arc, remaining arc is designated as F_k', perform step S34.

S34: make H_k=(V_k, F_k'), if H_kWithout circle, then make H_k'=H_k, H_k' it is G_kShortest arborescence, turn S36；No Then, at H_kAppoint and take a circle C_k, perform step S35.

S35: to G_kShrink C_k, obtain new network G_k+1=(V_k+1, E_k+1, W_k+1), remember that artificial summit is y_k, make k=k+ 1, perform step S33.

S36: if k=1, terminate, H_k' it is the shortest arborescence of figure G ', otherwise perform step S37.

S37: make H_k-1'=H_k+C_k-1-e_k-1', wherein e_k-1' it is C_k-1In an arc: if y_k-1At H_kHave in ' into arc, Then e_k-1' take and enter arc at G with this_k-1In have the arc of identical head；Otherwise e_k-1' it is taken as C_k-1The arc that middle weighting is maximumMake k=k- 1, perform step S36.

S4: obtained its maximum tree diagram by the shortest arborescence of G ', by the vertex v in the maximum tree diagram of described G '₀Go Falling, obtain the maximum tree diagram of figure G, i.e. optimal route engagement scheme, table 3 is the optimum of Urban Rail Transit shown in Fig. 3 Last bus engagement scheme.

The optimum last bus engagement scheme table of table 3

S5: according to described optimum engagement scheme, in given urban track traffic runs time domain, during optimum is connected The time that the train of most end is reached terminal is set to run the right-hand member point value of time domain, and as basic point, extrapolates other lines Road specifically includes following steps to each station to the time of sending out:

S51: set optimum engagement scheme as:

Wherein, L_(i)Represent i-th line road in engagement scheme,Represent circuit L_(i)In track traffic station S_iLinking circuit L_(i-1)。

S52: set circuit L_(i)The upper total individual station of r (i), difference numbered 1,2 ..., i ... r (i), usesRepresent circuit L_(i)The due in of j AT STATION,Represent circuit L_(i)The setting out the moment of j AT STATION,Represent circuit L_(i)K AT STATION The operation time interval with station k+1,Represent circuit S AT STATION_iThe transfer time,Represent circuit L_(i)At car Stand dwell time of k.

S53: when the urban track traffic service time, territory was [A, B], L₍₁₎Due in its terminus is:

$t_{\left(1\right)r\left(i\right)}^D=B$

L₍₁₎In the arriving and leaving moment of station j it is:

$t_{\left(1\right)j}^D=t_{\left(1\right)r\left(i\right)}^D-\underset{k=j}{\overset{r\left(1\right)-1}{\mathrm{\Σ}}}{t}_{\left(1\right)k(k+1)}^Y-\underset{k=j}{\overset{r\left(1\right)-1}{\mathrm{\Σ}}}{t}_{\left(1\right)k}^T$

$t_{\left(1\right)j}^F=t_{\left(1\right)r\left(i\right)}^D-\underset{k=j}{\overset{r\left(1\right)-1}{\mathrm{\Σ}}}{t}_{\left(1\right)k(k+1)}^Y-\underset{k=j-1}{\overset{r\left(1\right)-1}{\mathrm{\Σ}}}{t}_{\left(1\right)k}^T$

L can be obtained₍₁₎At transfer station S₁Frequency beAnd have:

$t_{\left(2\right)S\left(1\right)}^D=t_{\left(1\right)S\left(1\right)}^F-t_{S\left(1\right)}^Z$

$t_{\left(2\right)S\left(1\right)}^F=t_{\left(1\right)S\left(1\right)}^F-t_{S\left(1\right)}^Z+t_{\left(2\right)S\left(1\right)}^T$

L can be obtained₍₂₎At S₁The due in stood, then L₍₂₎In the arriving and leaving moment of station j it is:

When j ＜ S (1):

$t_{\left(2\right)j}^D=t_{\left(2\right)S\left(1\right)}^D-\underset{k=j}{\overset{S\left(1\right)-1}{\mathrm{\Σ}}}{t}_{\left(2\right)k(k+1)}^Y-\underset{k=j}{\overset{S\left(1\right)-1}{\mathrm{\Σ}}}{t}_{\left(2\right)k}^T$

$t_{\left(2\right)j}^F=t_{\left(2\right)S\left(1\right)}^D-\underset{k=j}{\overset{S\left(1\right)-1}{\mathrm{\Σ}}}{t}_{\left(2\right)k(k+1)}^Y-\underset{k=j+1}{\overset{S\left(1\right)-1}{\mathrm{\Σ}}}{t}_{\left(2\right)k}^T$

When j ＞ S (1):

$t_{\left(2\right)j}^D=t_{\left(2\right)S\left(1\right)}^D+\underset{k=S\left(1\right)}{\overset{j-1}{\mathrm{\Σ}}}{t}_{\left(2\right)k(k+1)}^Y+\underset{k=S\left(1\right)}{\overset{j-1}{\mathrm{\Σ}}}{t}_{\left(2\right)k}^T$

$t_{\left(2\right)j}^F=t_{\left(2\right)S\left(1\right)}^D+\underset{k=S\left(1\right)}{\overset{j-1}{\mathrm{\Σ}}}{t}_{\left(2\right)k(k+1)}^Y+\underset{k=S\left(1\right)}{\overset{j}{\mathrm{\Σ}}}{t}_{\left(2\right)k}^T$

S54: S can be obtained by above formula₂The frequency stood, thus can extrapolate L₍₃₎At S₂The due in stood, and then Extrapolate L₍₃₎Arriving and leaving moment and L at arbitrarily station j₍₄₎,L₍₅₎,…,L_(i),…,L_(2n)Arriving and leaving moment at each station.

Obviously, the above embodiment of the present invention is only for clearly demonstrating example of the present invention, and is not right The restriction of embodiments of the present invention, for those of ordinary skill in the field, the most also may be used To make other changes in different forms, cannot all of embodiment be given exhaustive here, every belong to this What bright technical scheme was extended out obviously changes or changes the row still in protection scope of the present invention.

Claims (5)

1. the method solving urban track traffic last bus connection problem, the method comprises the following steps:

S1: by investigating on the spot or data collection obtains City Rail Transit System basic data, described basic data includes: road The transfer passenger flow scale of each circuit each transfer station in the case of last bus and the train district of each circuit in net topology structure, road network Between run the time；

S2: with the circuit in point direction as summit, with joining relation as limit, the weights with transfer passenger flow amount as limit, construct last bus Engagement scheme Weighted Directed Diagram model；

S3: use Zhu-Liu Fangfa improved to solve described Weighted Directed Diagram model；

S4: draw optimal route engagement scheme according to solving result；

S5: according to described optimum engagement scheme, in given urban track traffic runs time domain, most end during optimum is connected Time of reaching terminal of train be set to run the right-hand member point value of time domain, and as basic point, extrapolate All other routes and arrive That respectively stands arrives the time of sending out.

Method the most according to claim 1, it is characterised in that described step S2 specifically includes following steps:

S21: set in urban mass transit network number of, lines as n, then the number of, lines in point direction is 2n, will the circuit in point direction It is designated as L=(l₁,l₂,…,l_2i-1,l_2i,…,l_2n-1,l_2n), tectonic model is as follows:

$\max Z\left(X\right)=\underset{i=1}{\overset{2n}{\Σ}}\underset{j=1}{\overset{2n}{\Σ}}{f}_{ij}\left(X\right)a_{ij}$

Wherein, 0 ＜ i, j ＜ 2n, X are the engagement scheme comprising 2n-1 joining relation, and max Z (X) is for being X's in engagement scheme In the case of, the transfer passenger flow amount sum that in road network, all transfer directions complete, f_ijIt is 0,1 variable, represents when engagement scheme is wrapped Containing l_i→l_jTime take 1, do not comprise l_i→l_jTime take 0, a_ijFor l_jTransfer l_iThe volume of the flow of passengers；

S22: note G=(V, E, W) is the urban mass transit network that Weighted Directed Diagram represents, wherein V=(v₁,v₂,…,v_i, v_i+1,…,v_2n-1,v_2n) it is vertex set, each vertex v_iRepresenting some direction of a circuit in road network, E is by V Sequential Elements couple e_i,j=e (v_i,v_j) the limit collection that constituted, represent the joining relation set between road network, wherein i, j ∈ 1, 2,…,2n},i≠j,i+j≠2i+(-1)ⁱ⁺¹, W is weights set；

S23: to each limit e in E_i,jGive certain weight w_i,j=w (v_i,v_j), then w_i,jValue as follows:

$w_{i,j}=\left\{\begin{array}{cc}{a}_{ij}& if(v_i,v_j)\∈E\\ 0& if(v_i,v_j)\∉E\end{array}\right.$

Wherein, w_i,jFor each limit e in E_i,jWeights, be the transfer passenger flow amount at this station；

S24: finding a summit in figure G, the direction along limit travels through each summit from this summit, forms one The tree diagram T of directed graph^*, and T^*For the tree diagram of maximum weight in tree diagrams all in this directed graph, i.e. W (T*)=max{W (T) Shu T is the tree diagram of G }, wherein W (T*) is the weights of the tree diagram T* to figure.

Method the most according to claim 1, it is characterised in that Zhu-Liu Fangfa of described improvement specifically comprises the following steps that

S31: increase a vertex v on the basis of weighted and directed diagraph G₀, rightThere is limit e_{0, i}(v₀, v_i), its weight w_{0, i} (v₀, v_i) more than the weights sum total on all limits in figure G, andThere is w_{0, i}(v₀, v_i)=w_{0, j}(v₀, v_j), summit will be increased v₀After directed graph, be referred to as scheming G ', G '=(V ', E ', W ')；

S32: make V₁=V ', E₁=E ', W₁=-W ', G₁=(V₁, E₁, W₁), k=1, wherein k is calculating process parameter；

S33:The minimum taking v enters arc, forms arc collection F_kIf, | F_k| ＜ | V_k|-1, stop, network G ' does not prop up Support tree diagram；If | F_k|=| V_k|-1, make F_k'=F_k, perform step S34；If | F_k|=| V_k|, from F_kIn to remove power maximum Arc, remaining arc is designated as F_k', perform step S34；

S34: make H_k=(V_k, F_k'), if H_kWithout circle, then make H_k'=H_k, H_k' it is G_kShortest arborescence, perform step S36；No Then, at H_kAppoint and take a circle C_k, perform step S35；

S35: to G_kShrink C_k, obtain new network G_k+1=(V_k+1, E_k+1, W_k+1), remember that artificial summit is y_k, make k=k+1, hold Row step S33；

S36: if k=1, terminate, H_k' it is the shortest arborescence of figure G ', otherwise perform step S37；

S37: make H_k-1'=H_k+C_k-1-e_k-1', wherein e_k-1' it is C_k-1In an arc: if y_k-1At H_kHave in ' into arc, then e_k-1' take and enter arc at G with this_k-1In have the arc of identical head；Otherwise e_k-1' it is taken as C_k-1The arc that middle weighting is maximumMake k=k-1, Perform step S36.

Method the most according to claim 3, it is characterised in that obtained its maximum tree diagram by the shortest arborescence of G ', by institute State the vertex v in the maximum tree diagram of G '₀Remove, obtain the maximum tree diagram of figure G, i.e. optimal route engagement scheme.

Method the most according to claim 1, it is characterised in that described step S5 specifically includes following steps:

S51: set optimum engagement scheme as:

Wherein, L_(i)Represent i-th line road in engagement scheme,Represent circuit L_(i)In track traffic station S_iRank Link L_(i-1)；

S52: set circuit L_(i)The upper total individual station of r (i), difference numbered 1,2 ..., i ... r (i), usesRepresent circuit L_(i)? The due in of station j,Represent circuit L_(i)The setting out the moment of j AT STATION,Represent circuit L_(i)K and station AT STATION The operation time that k+1 is interval,Represent circuit S AT STATION_iThe transfer time,Represent circuit L_(i)The stopping of k AT STATION Stand the time；

S53: when the urban track traffic service time, territory was [A, B], L₍₁₎Due in its terminus is:

$t_{\left(1\right)r\left(i\right)}^D=B$

L₍₁₎In the arriving and leaving moment of station j it is:

$t_{\left(1\right)j}^D=t_{\left(1\right)r\left(i\right)}^D-\underset{k=j}{\overset{r\left(1\right)-1}{\Σ}}{t}_{\left(1\right)k(k+1)}^Y-\underset{k=j}{\overset{r\left(1\right)-1}{\Σ}}{t}_{\left(1\right)k}^T$

$t_{\left(1\right)j}^F=t_{\left(1\right)r\left(i\right)}^D-\underset{k=j}{\overset{r\left(1\right)-1}{\Σ}}{t}_{\left(1\right)k(k+1)}^Y-\underset{k=j-1}{\overset{r\left(1\right)-1}{\Σ}}{t}_{\left(1\right)k}^T$

L can be obtained₍₁₎At transfer station S₁Frequency beAnd have:

$t_{\left(2\right)S\left(1\right)}^D=t_{\left(1\right)S\left(1\right)}^F-t_{S\left(1\right)}^Z$

$t_{\left(2\right)S\left(1\right)}^F=t_{\left(1\right)S\left(1\right)}^F-t_{S\left(1\right)}^Z+t_{\left(2\right)S\left(1\right)}^T$

L can be obtained₍₂₎At S₁The due in stood, then L₍₂₎In the arriving and leaving moment of station j it is:

When j ＜ S (1):

$t_{\left(2\right)j}^D=t_{\left(2\right)S\left(1\right)}^D-\underset{k=j}{\overset{S\left(1\right)-1}{\Σ}}{t}_{\left(2\right)k(k+1)}^Y-\underset{k=j}{\overset{S\left(1\right)-1}{\Σ}}{t}_{\left(2\right)k}^T$

$t_{\left(2\right)j}^F=t_{\left(2\right)S\left(1\right)}^D-\underset{k=j}{\overset{S\left(1\right)-1}{\Σ}}{t}_{\left(2\right)k(k+1)}^Y-\underset{k=j+1}{\overset{S\left(1\right)-1}{\Σ}}{t}_{\left(2\right)k}^T$

When j ＞ S (1):

$t_{\left(2\right)j}^D=t_{\left(2\right)S\left(1\right)}^D+\underset{k=S\left(1\right)}{\overset{j-1}{\Σ}}{t}_{\left(2\right)k(k+1)}^Y+\underset{k=S\left(1\right)}{\overset{j-1}{\Σ}}{t}_{\left(2\right)k}^T$

$t_{\left(2\right)j}^F=t_{\left(2\right)S\left(1\right)}^D+\underset{k=S\left(1\right)}{\overset{j-1}{\Σ}}{t}_{\left(2\right)k(k+1)}^Y+\underset{k=S\left(1\right)}{\overset{j}{\Σ}}{t}_{\left(2\right)k}^T$

S54: S can be obtained by above formula₂The frequency stood, thus can extrapolate L₍₃₎At S₂The due in stood, and then calculate Go out L₍₃₎Arriving and leaving moment and L at arbitrarily station j₍₄₎,L₍₅₎,…,L_(i),…,L_(2n)Arriving and leaving moment at each station.