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

Abstract

The invention discloses a quick method for solving the connection problem of the last train of urban rail transit. The method includes the following steps: S1: establishing a basic database for urban rail transit system decision-making support through on-the-spot research and data collection in large and medium-sized cities at home and abroad; S2: using the network The idea of modeling flow is to build a space-state network with the directional lines as the vertices and the connection relationship as the edge, and to construct the directed weighted graph model of the last train connection scheme with the passenger flow as the weight of the edges; S3 : use the improved Zhu-Liu method to solve the directed weighted graph model; S4: obtain the optimized line connection scheme according to the solution result; S5: calculate the arrival time of other lines to each station according to the optimal connection scheme send time. Aiming at solving the operation plan problem of the last train in a large-scale public transport network, this method can conveniently and quickly formulate a real-time last train schedule according to the passenger flow demand, and improve the accessibility and service level of the last train in urban rail transit.

Description

A Quick Method to Solve the Connection Problem of the Last Train in Urban Rail Transit

technical field

The invention relates to the field of urban rail traffic control. More specifically, it relates to a fast method for solving the connection problem of the last train in urban rail transit.

Background technique

From a global perspective, urban rail transit has become an indispensable mode of urban transportation. The rail transit systems in major cities in my country are also improving day by day, and are gradually transitioning to networked operations. After the urban rail transit network is put into operation, the issue of train operation plan preparation becomes complex and changeable. Coordinating transfer connections within the entire transportation network is the key to dealing with network operation issues. Among them, the operation plan of the last train is the most typical among all kinds of transfer connections. To solve such problems, not only the characteristics of networked operation and passenger flow demand characteristics, but also the allocation of resources such as vehicles and crews in actual operation must be considered. Centralized deployment on the basis of planning, there is no recognized fast and effective method at present.

The scale of the urban rail transit network continues to expand, and the number of transfer nodes continues to increase. Many passengers need to go through one or even multiple transfers to reach their destination stations. Since the end of operation of each line is relatively independent, the time of the last train of each line not only affects the travel of passengers on this line, but also extends the influence to the entire network through the transfer connection relationship of the transfer station. The accessibility of passenger travel routes will change with the change of the last train timetable. Therefore, it is of great significance to compile a reasonable last train timetable to guide the operation practice and benefit more passengers.

From the perspective of the basic requirements of urban rail transit operation, the formulation of its operation plan should match the passenger flow as much as possible, especially in the case of the last train. The accessibility concerns will increase. Since the flow of transfer passengers at each transfer station is determined by the transfer connection relationship between lines, when calculating the arrival and departure time of the last train, the line connection scheme is the most important. Connection relationship, that is, the arrival and departure timing of each last train line at its transfer station. If two last trains can transfer at a transfer station, and one of the last trains A arrives immediately after the last train B, A is called the connection of B. Or A connects to B. In the case of A connecting to B, as long as the time interval between the arrival and departure of the two trains is reasonably arranged, the passenger flow of B can be transferred to A at this station. The connection scheme is a collection of the connection relations of each line in the road network. To calculate the arrival and departure time of the last train, it is first necessary to compile the connection plan of the last train, and then calculate the arrival and departure time of the last train according to the connection plan of the last train.

At present, the preparation of the connection plan of the last train of urban rail transit is often based on empirical judgment and lack of optimization methods, resulting in a disconnect between the plan and the actual passenger demand. In terms of theoretical research, some scholars have proposed a transfer model of the last bus in the network combined with passenger flow demand and used genetic methods to solve it. The method has certain applicability, but in a large-scale network environment, the method takes too long to meet the requirements of practical applications Real-time requirements. Therefore, it has research value and market prospect to formulate a fast and efficient last train operation plan that meets the passenger flow demand.

To sum up, it is necessary to provide a fast method to solve the connection problem of the last train of urban rail transit with large-scale network operation.

Contents of the invention

The purpose of the present invention is to provide a fast method for solving the problem of connecting the last train of urban rail transit with large-scale network operation.

To achieve the above object, the present invention adopts the following technical solutions:

A quick method for solving the connection problem of the last train of urban rail transit, the method comprises the following steps:

S1: Obtain the basic data of the urban rail transit system through field research or data collection. The basic data includes: the topology of the road network, the passenger transfer flow meter of each transfer station in the case of the last train of each line in the road network, and the trains of each line Interval running time.

S2: Construct the directed weighted graph model of the connection scheme of the last train with the line of the sub-direction as the vertex, the connection relationship as the edge, and the passenger flow as the weight of the edge, which specifically includes the following steps:

S21: Under normal circumstances, urban rail transit operating lines are divided into two directions: uplink and downlink. Assuming that the number of lines in the urban rail transit network is n, the number of lines in each direction is 2n, and the lines in each direction are recorded as L=( l ₁ ,l ₂ ,...,l _2i-1 ,l _2i ,...,l _2n-1 ,l _2n ). According to the basic principles of urban rail transit operation, the main purpose of the connection of the last train is to facilitate the travel of passengers and try to make more passengers reach their destinations smoothly. Therefore, the optimization goal of the connection scheme of the last train of urban rail transit can be simplified as making the transfer station in the road network The highest passenger transfer flow can be realized, and the construction model is as follows:

$\mathrm{<span\; class="notranslate">\; max</span>}\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}$

feasible

Among them, 0<i, j<2n, X is a connection scheme including 2n-1 connection relationships, and max Z(X) is the transfer passenger flow completed in all transfer directions in the road network when the connection scheme is X The sum of quantities, f _ij is a variable of 0 and 1, which means that when the connection plan includes l _i → l _j , it takes 1, and when l _i → l _j is not included, it takes 0, and a _ij is the passenger flow of l _j transferring to l _i ;

S22: Abstract each directional line in the road network as a vertex, use a directed graph G to describe the line connection relationship in the urban rail transit network, record G=(V, E, W) as a directed weighted graph The urban rail transit network represented by , where V=(v ₁ ,v ₂ ,…,v _i ,v _i+1 ,…,v _2n-1 ,v _2n ) is a set of vertices, and each vertex v _i represents the In a certain direction of a line of , E is an edge set composed of an ordered pair of elements e _i,j =e(v _i ,v _j ) in V, which represents the set of connection relations between road networks, where i, j∈{1,2,…,2n},i≠j,i+j≠2i+(-1) ⁱ⁺¹ , W is the weight set;

S23: Assign a certain weight w _i,j =w(v _i ,v _j ) to each edge e _i,j in E, then the value of w _i,j is as follows:

${\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}& \mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; E.</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&NotElement;</span>\mathrm{<span\; class="notranslate">\; E.</span>}\end{array}\right.$

Among them, w _i,j is the weight of each edge e _i,j in E, that is, the passenger transfer flow of this station.

Let v _i and v _j represent the r direction of line L _p and the s direction of L _q respectively, then w _i,j is the transfer flow of the last train when the r direction of L _p connects to the s direction of L _q . If there is only one transfer intersection between lines L _p and L _q , then the connection relationship between L _p and L _q can only be completed at this transfer intersection, and the weight w _i,j of this connection relationship is L _p 's Passenger flow in direction s of r direction transfers to L _q at this station. If there are m (m>1) transfer connection points between L _p and L _q , then the connection relationship between L _p and L _q can be completed at any one of these m stations, then w _{i, j} can take any one of them Passenger flow in the r direction of L _p transfers to the s direction of L _q in the station. In general, in order to maximize the flow of passenger transfers that can be achieved by each connection relationship, the station with the largest flow of passenger transfers among the m stations is usually selected as the connection point of the connection relationship. Since the objective function in this paper is Passenger transfer flow achieved by the network is the largest, so this principle is also followed. If other connection points need to be considered under special circumstances, then w _{i, j} should be the transfer flow of passengers at this station.

S24: Find a vertex in the graph G, start from this vertex and traverse each vertex along the direction of the edge to form a tree graph T ^* of a directed graph, and T ^* is all tree graphs in the directed graph The dendrogram with the largest weight, that is, W(T ^* )=max{W(T)|T is the dendrogram of G}, wherein W(T ^* ) is the weight of the dendrogram T ^* of the graph.

S3: Using the improved Zhu-Liu method to solve the directed weighted graph model, which specifically includes the following steps:

S31: Add a vertex v ₀ on the basis of the weighted directed graph G, for There is an edge e _{0, i} (v ₀ , v _i ), whose weight w _{0, i} (v ₀ , v _i ) is greater than the sum of the weights of all edges in graph G, and j≠0, there is w _{0, i} (v ₀ , v _i )=w _{0, j} (v ₀ , v _j ), the directed graph after adding vertex v ₀ is called graph G′, G′=( V', E', W');

S32: Set V ₁ =V', E ₁ =E', W ₁ =-W', G ₁ =(V ₁ , E ₁ , W ₁ ), k=1, where k is a calculation process parameter;

S33: Take a minimum incoming arc of v to form the arc set F _k , if |F _k |<|V _k |-1, stop, the network graph G′ has no supporting tree diagram; if |F _k |=|V _k |- 1. Set F _k ′=F _k , execute step S34; if |F _k |=|V _k |, remove the arc with the largest weight from F _k , record the remaining arc as F _k ′, and execute step S34;

S34: Let H _k = (V _k , F _k ′), if H _k does not contain a circle, then let H _k ′=H _k , H _k ′ is the smallest tree diagram of G _k , and execute step S36; otherwise, in H _k randomly selects a circle C _k , and executes step S35;

S35: Shrink C _k to G _k to obtain a new network graph G _k+1 = (V _k+1 , E _k+1 , W _k+1 ), record the artificial vertex as y _k , let k=k+1, Execute step S33;

S36: If k=1, end, H _k 'is the minimum tree diagram of graph G', otherwise execute step S37;

S37: Let H _{k -1} ′=H _k +C _k-1 -e _k-1 ′, where e _k-1 ′ is an arc in C _k-1 : if y _k-1 has Incoming arc, then e _k-1 ′ takes the arc with the same head as the incoming arc in G _k-1 ; otherwise e _k-1 ′ takes the arc with the largest weight in C _k-1 Let k=k-1, execute step S36.

S4: Obtain the maximum tree graph from the minimum tree graph of G', remove the vertex v ₀ in the maximum tree graph of G', and obtain the maximum tree graph of graph G, that is, the optimal line connection scheme.

S5: According to the optimal connection scheme, in a given urban rail transit running time domain, set the time when the last train in the optimal connection arrives at the terminal station as the right endpoint value of the running time domain, and use this as The calculation of the arrival and departure time of other lines to each station specifically includes the following steps:

S51: Set the optimal connection scheme as:

Among them, L _(i) represents the ith line in the connection scheme, Indicate that line L _(i) connects line L _(i-1) at urban rail transit station S _i ;

S52: Suppose there are r(i) stations on the line L _(i) , respectively numbered as 1, 2,...,i,...r(i), use Indicates the arrival time of line L _(i) at station j, Denotes the departure time of line L _(i) at station j, Indicates the running time of line L _(i) between station k and station k+1, Indicates the transfer connection time of the line at station S _i , Indicates the stop time of line L _(i) at station k;

S53: When the urban rail transit operation time domain is [A, B], the arrival time of L ₍₁₎ at its terminal station is:

${\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; B</span>}$

L ₍₁₎ The arrival and departure time at station j is:

${\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\overset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\overset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

${\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\overset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

It can be obtained that the departure time of L ₍₁₎ at the connecting station S ₁ is and have:

${\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; Z</span>}}$

${\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; Z</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

The arrival time of L (2 ₎ at station S ₁ can be obtained, then the arrival and departure time of L ₍₂₎ at station j is:

When j<S(1):

${\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\overset{\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\overset{\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

${\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\overset{\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

When j>S(1):

${\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\overset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\overset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

${\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\overset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\overset{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

S54: From the above formula, the departure time of station S ₂ can be obtained, from which the arrival time of L (3 ₎ at station S ₂ can be calculated, and then the arrival and departure time of L ₍₃₎ at any station j and L ₍₄ ) can be calculated ₎ , L ₍₅₎ ,…,L _(i) ,…,L _(2n) arrival and departure times at each station.

The beneficial effects of the present invention are as follows:

1. Taking the maximum passenger transfer flow that can be achieved at transfer stations in the road network as the objective function, fully considering the passenger flow demand, and improving the accessibility and service level of the last train of urban rail transit;

2. The complex urban rail transit network is abstracted into a weighted directed graph, which simplifies the original problem, enables large-scale parallel computing, and solves the problem that the operation plan of the last bus in a large-scale public transportation network is difficult to solve.

3. The improved Zhu-Liu method adopted has high solution efficiency and accurate solution, which gets rid of the problem that the previous heuristic solution method can only obtain a satisfactory solution but cannot obtain an optimal solution;

4. The solution method is easy to operate and apply, and can be solved in real time, and the real-time last train timetable can be formulated according to the passenger flow demand. At the same time, when the last train is delayed or other emergencies occur, the corresponding last train operation plan can also be formulated according to the needs, and a satisfactory solution can be obtained in a local area.

Description of drawings

The specific implementation manners of the present invention will be further described in detail below in conjunction with the accompanying drawings.

Figure 1 shows the flow chart of the fast method for the connection problem of the last train in urban rail transit.

Figure 2 shows the modular flow chart of the fast method for the connection problem of the last train in urban rail transit.

Fig. 3 shows a topological structure diagram of an urban rail transit road network in an embodiment.

Fig. 4 shows the directed weighted graph of the last train connection scheme abstracted from the urban rail transit network example in one embodiment.

detailed description

In order to illustrate the present invention more clearly, the present invention will be further described below in conjunction with preferred embodiments and accompanying drawings. Similar parts in the figures are denoted by the same reference numerals. Those skilled in the art should understand that the content specifically described below is illustrative rather than restrictive, and should not limit the protection scope of the present invention.

In order to improve the accessibility of the road network and maximize the transfer flow of passengers at the transfer stations in the road network, the present invention designs a fast-moving system as shown in Figure 1 for solving the problem of connecting the last train of urban rail transit in large-scale network operations. Method, Fig. 2 is the modularization division of above-mentioned method, below in conjunction with accompanying drawing, the method of the present invention is described in detail: in a specific embodiment, a kind of fast method that solves the problem of connecting the last train of urban rail transit, the method comprises the following steps:

S1: Establish a basic database for urban rail transit system decision-making support through on-the-spot research and data collection in large and medium-sized cities at home and abroad. The basic data includes: road network topology, and transfers at each transfer station for each line in the road network under the condition of the last train Passenger flow meter and train interval running time of each line.

In one embodiment, an example of the urban rail transit road network topology is shown in Figure 3. The road network has four lines {L ₁ , L ₂ , L ₃ , L ₄ }, wherein L ₄ is a ring line, and the direction of the arrow in the figure Indicates the downlink direction of the line. There are 6 transfer stations {A, B, C, D, E, F, G} in the road network. The passenger flow table is shown in Table 1. The up and down of Li in the first row and the first column in the table indicate the up and down directions of the line L _{i ,} and the cells at the intersection of the row and column are _represented by the upper and lower lines of the line Li , and transfer to the column L _j , the passenger flow on and off and the transfer station where it is located.

Table 1 Passenger Flow Chart of Urban Rail Transit

Table 2 is an illustration to the definition of symbols in the present invention:

Table 2 Symbol Definition Explanation Table

S2: Adopt the modeling idea of network flow, take the directional lines as the vertices, take the connection relationship as the edge, establish a space-state network, and use the passenger flow as the weight of the edge to construct the directional weighting of the last train connection scheme Graphical model, which specifically includes the following steps:

S21: Under normal circumstances, urban rail transit operating lines are divided into two directions: uplink and downlink. Assuming that the number of lines in the urban rail transit network is n, the number of lines in each direction is 2n, and the lines in each direction are recorded as L=( l ₁ ,l ₂ ,...,l _2i-1 ,l _2i ,...,l _2n-1 ,l _2n ). According to the basic principles of urban rail transit operation, the main purpose of the connection of the last train is to facilitate the travel of passengers and try to make more passengers reach their destinations smoothly. Therefore, the optimization goal of the connection scheme of the last train of urban rail transit can be simplified as making the transfer station in the road network The highest passenger transfer flow can be realized, and the construction model is as follows:

$\mathrm{<span\; class="notranslate">\; max</span>}\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}$

feasible

Among them, 0<i, j<2n, X is a connection scheme including 2n-1 connection relationships, and max Z(X) is the transfer passenger flow completed in all transfer directions in the road network when the connection scheme is X The sum of quantities, f _ij is a variable of 0 and 1, which means that when the connection plan includes l _i → l _j , it takes 1, and when l _i → l _j is not included, it takes 0, and a _ij is the passenger flow of l _j transferring to l _i .

S22: Abstract each directional line in the road network as a vertex, use a directed graph G to describe the line connection relationship in the urban rail transit network, record G=(V, E, W) as a directed weighted graph The urban rail transit network represented by , where V=(v ₁ ,v ₂ ,…,v _i ,v _i+1 ,…,v _2n-1 ,v _2n ) is a set of vertices, and each vertex v _i represents the In a certain direction of a line of , E is an edge set composed of an ordered pair of elements e _i,j =e(v _i ,v _j ) in V, which represents the set of connection relations between road networks, where i, j∈{1,2,…,2n}, i≠j, i+j≠2i+(-1) ⁱ⁺¹ , represents the set of connection relations between road networks, where i≠j means that the lines in different directions cannot It is connected with itself, i+j≠2i+(-1) ⁱ⁺¹ means that the two directions of the same line cannot be connected with each other, and W is a set of weights.

S23: Assign a certain weight w _i,j =w(v _i ,v _j ) to each edge e _i,j in E, then the value of w _i,j is as follows:

${\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}& \mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; E.</span>}\\ \mathrm{<span\; class="notranslate">\; 0</span>}& \mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&NotElement;</span>\mathrm{<span\; class="notranslate">\; E.</span>}\end{array}\right.$

Among them, w _i,j is the weight of each edge e _i,j in E, that is, the passenger transfer flow of this station.

Let v _i and v _j represent the r direction of line L _p and the s direction of L _q respectively, then w _i,j is the transfer flow of the last train when the r direction of L _p connects to the s direction of L _q . If there is only one transfer intersection between lines L _p and L _q , then the connection relationship between L _p and L _q can only be completed at this transfer intersection, and the weight w _i,j of this connection relationship is L _p 's Passenger flow in direction s of r direction transfers to L _q at this station. If there are m (m>1) transfer connection points between L _p and L _q , then the connection relationship between L _p and L _q can be completed at any one of these m stations, then w _{i, j} can take any one of them Passenger flow in the r direction of L _p transfers to the s direction of L _q in the station. In general, in order to maximize the flow of passenger transfers that can be achieved by each connection relationship, the station with the largest flow of passenger transfers among the m stations is usually selected as the connection point of the connection relationship. Since the objective function in this paper is Passenger transfer flow achieved by the network is the largest, so this principle is also followed. If other connection points need to be considered under special circumstances, then w _{i, j} should be the transfer flow of passengers at this station.

Fig. 4 is a directed weighted graph of the last train connection scheme abstracted from an example of an urban rail transit network in an embodiment. Wherein, above L ₁ is represented as v ₁ , below L ₁ is represented as v ₂ , above L ₂ is represented as v ₃ , and so on. For a clearer representation, an undirected edge e(v _i ,v _j ) is used to represent two directed edges e(v _i ,v _j ) and e(v _j ,v _i ), the numbers on the edge Represents the weight of the edge, where Z represents the weight of the directed edge whose start number is smaller than the end point of the edge, and F represents the weight of the edge whose start number is greater than the end point of the edge.

S24: After using G to represent the urban rail transit network, solving a feasible connection scheme for the last train that covers all lines in the network is transformed into the following problem: find a vertex in graph G, and traverse along the direction of the edge from this vertex Each vertex forms a tree graph T ^* of a directed graph, and T ^* is the tree graph with the largest weight in all tree graphs in the directed graph, that is, W(T ^* )=max{W(T )丨T is the dendrogram of G}, where W(T ^* ) is the weight of the dendrogram T ^* of the graph.

S3: Using the improved Zhu-Liu method to solve the directed weighted graph model, which specifically includes the following steps:

S31: Add a vertex v ₀ on the basis of the weighted directed graph G, for There is an edge e _{0, i} (v ₀ , v _i ), whose weight w _{0, i} (v ₀ , v _i ) is greater than the sum of the weights of all edges in graph G, and j≠0, there is w _{0, i} (v ₀ , v _i )=w _{0, j} (v ₀ , v _j ), the directed graph after adding vertex v ₀ is called graph G′, G′=( V', E', W').

S32: Let V ₁ =V', E ₁ =E', W ₁ =-W', G ₁ =(V ₁ , E ₁ , W ₁ ), k=1, where k is a calculation process parameter.

S33: Take a minimum incoming arc of v to form the arc set F _k , if |F _k |<|V _k |-1, stop, the network graph G′ has no supporting tree diagram; if |F _k |=|V _k |- 1. Let F _k ′=F _k , go to step S34; if |F _k |=|V _k |, remove the arc with the greatest weight from F _k , record the remaining arc as F _k ′, go to step S34.

S34: Let H _k = (V _k , F _k ′), if H _k does not contain a circle, then let H _k ′=H _k , H _k ′ is the minimum tree diagram of G _k , turn to S36; otherwise, in H _k randomly selects a circle C _k , and executes step S35.

S35: Shrink C _k to G _k to obtain a new network graph G _k+1 = (V _k+1 , E _k+1 , W _k+1 ), record the artificial vertex as y _k , let k=k+1, Execute step S33.

S36: If k=1, end, H _k ′ is the smallest tree graph of graph G′, otherwise execute step S37.

S37: Let H _{k -1} ′=H _k +C _k-1 -e _k-1 ′, where e _k-1 ′ is an arc in C _k-1 : if y _k-1 has Incoming arc, then e _k-1 ′ takes the arc with the same head as the incoming arc in G _k-1 ; otherwise e _k-1 ′ takes the arc with the largest weight in C _k-1 Let k=k-1, execute step S36.

S4: Obtain the largest dendrogram from the smallest dendrogram of G', remove the vertex v ₀ in the largest dendrogram of G', and obtain the largest dendrogram of graph G, that is, the optimal line connection scheme, Table 3 shows the optimal last train connection scheme of the urban rail transit network shown in Figure 3.

Table 3 Optimal last train connection plan table

S5: According to the optimal connection scheme, in a given urban rail transit running time domain, set the time when the last train in the optimal connection arrives at the terminal station as the right endpoint value of the running time domain, and use this as The calculation of the arrival and departure time of other lines to each station specifically includes the following steps:

S51: Set the optimal connection scheme as:

Among them, L _(i) represents the ith line in the connection scheme, Indicates that line L _(i) connects to line L _(i-1) at urban rail transit station S _i .

S52: Suppose there are r(i) stations on the line L _(i) , respectively numbered as 1, 2,...,i,...r(i), use Indicates the arrival time of line L _(i) at station j, Denotes the departure time of line L _(i) at station j, Indicates the running time of line L _(i) between station k and station k+1, Indicates the transfer connection time of the line at station S _i , Indicates the stop time of line L _(i) at station k.

S53: When the urban rail transit operation time domain is [A, B], the arrival time of L ₍₁₎ at its terminal station is:

${\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; B</span>}$

L ₍₁₎ The arrival and departure time at station j is:

${\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\overset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\overset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

${\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\overset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

It can be obtained that the departure time of L ₍₁₎ at the connecting station S ₁ is and have:

${\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; Z</span>}}$

${\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; Z</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

The arrival time of L (2 ₎ at station S ₁ can be obtained, then the arrival and departure time of L ₍₂₎ at station j is:

When j<S(1):

${\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\overset{\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\overset{\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

${\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\overset{\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

When j>S(1):

${\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\overset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\overset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

${\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; D.</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\overset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; Y</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\overset{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; t</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

S54: From the above formula, the departure time of station S ₂ can be obtained, from which the arrival time of L (3 ₎ at station S ₂ can be calculated, and then the arrival and departure time of L ₍₃₎ at any station j and L ₍₄ ) can be calculated ₎ , L ₍₅₎ ,…,L _(i) ,…,L _(2n) arrival and departure times at each station.

Apparently, the above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those of ordinary skill in the art can also make It is impossible to exhaustively list all the implementation modes here, and any obvious changes or changes derived from the technical solutions of the present invention are still within the scope of protection 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:

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

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:

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

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:

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

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

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):

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

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

When j ＞ S (1):

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

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

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.