CN114511143A

CN114511143A - Urban rail transit network generation method based on grouping division

Info

Publication number: CN114511143A
Application number: CN202210110316.0A
Authority: CN
Inventors: 王子甲; 邹林沐; 冯丹泳; 任兵杰
Original assignee: Beijing Jiaotong University
Current assignee: Beijing Jiaotong University
Priority date: 2022-01-29
Filing date: 2022-01-29
Publication date: 2022-05-17

Abstract

The invention provides an urban rail transit network generation method based on an urban space structure, which generates a network scheme matched with an urban space: and selecting a distance-corrected InfoMap algorithm to divide the urban grouping, and generating the wire mesh according to a technical route of 'generation of inter-grouping wire mesh, generation of intra-grouping wire mesh, integration and optimization of wire mesh'. Calculating three parameters of the density of the line network, the passenger flow intensity of the line network and the scale of the line network by adopting the modes of regression analysis, grey correlation degree analysis, entropy value method and the like; generating a connection relation between the groups based on a passenger flow distribution result of a Logit method between the groups; obtaining an alternative road section set in the group by applying an adaptive genetic algorithm; and obtaining the final optimized net layout from the whole net layer according to the connection relation among the groups.

Description

Urban rail transit network generation method based on grouping division

Technical Field

The application relates to the technical field of computers, in particular to a method for generating an urban rail transit network based on grouping division.

Background

The sustainable development of urban rail transit has important strategic significance on the economic development and social stability of China. Through years of urban rail transit construction and operation experience feedback, the later-stage construction and operation and maintenance cost can be greatly reduced by reasonably planning the wire network in the planning stage. However, the current situation of domestic network planning does not form a unified, efficient, objective and automatic planning method. The net planning method at the practical application level tends to be considered from the macroscopic view, namely the view of urban spatial structure, while the net planning method at the theoretical research level focuses on the local optimization view of the net at the microscopic level. Dissimilarity of net planning schemes with city development and extension leads to poor matching of traffic demand with supply in both the time and space dimensions. The existing network planning method is relatively lack of quantitative analysis, and the subjective randomness of the scheme is relatively high, so that the uncertainty of the scheme is relatively high.

Generally, the overall idea of the net planning problem is to set an objective function and constraint conditions and apply an efficient algorithm to solve the problem. For the design of an objective function, Zhao et al carry out wire network optimization on the objective function by minimizing passenger travel time, transfer time and waiting time; nayeem et al introduce an elite operator and apply a multi-objective solution algorithm to solve. The most commonly considered decision variables are line layout and departure frequency, and Ceder and the like develop a mathematical modeling method based on bus station positions and solve by adopting a heuristic algorithm. As for the properties of the constraint variables,

and the public transportation service in multiple periods is researched, and the relation among the urban structure, the daily activity mode and the public transportation service level is disclosed.

When solving the problem of solving the objective function, it is very important to adopt an efficient algorithm for solving, Canca and the like develop an Adaptive Large Neighborhood Search (ALNS) algorithm for solving the problem of network planning; a simulation annealing frame based neighborhood search algorithm solving method is designed by using the firewood tree mountain and the like to establish a net quantification generation mathematical model in an urban rail transit net planning stage. Among a plurality of algorithms, the genetic algorithm has many applications due to the excellent searching capability and the strong practical problem applicability, and an alternative target genetic algorithm (AOGA) is provided by Arbex and the like to effectively solve the problems of multi-target traffic network design and frequency setting; cipriani and the like solve the optimization problem by adopting a genetic algorithm, firstly screen a proper path as an alternative line section by combining passenger flow on the basis of a road network and an urban rail transit network, form an upper chromosome, namely a line, after random generation and feasible line screening, and search an optimal solution by iterative genetic operation.

For the urban public transport network planning problem, the prior invention focuses on solving the problem by an analytic method from a microscopic perspective, and the network focuses on timeliness and economy, but fails to fully consider the interactive relationship between rail transit and urban development and fails to play the roles of rail transit in promoting the urban development level and guiding the urban development direction. In the practical application level, the problem is mainly solved by an analytical method from a macroscopic view, and the long-term effectiveness and the planning property are emphasized by the wire mesh. Although the urban development and the rail transit development are considered comprehensively, the defects are that subjective factors are too strong, and the theoretical research depth of the problem of how to consider urban space structures in the online network planning stage is not enough. And the algorithm used by part of the technologies is still the traditional algorithm, and the improvement of the grouping effect is not obvious. And it is still necessary to determine the number of groups that is superior through a number of experiments, and although there are many studies on how to determine the number of groups, it is not so strong.

Therefore, the invention combines the planning thought of macroscopic and microscopic wire nets, adopts the InfoMap algorithm in the dynamic network partitioning algorithm to research the urban space structure, adopts the genetic algorithm with stronger adaptability to the actual problem to solve, and simultaneously introduces the self-adaptive operator. Reasonable wire network layout and circuit layout are carried out, and the proportion of qualitative analysis in the planning process is reduced.

Disclosure of Invention

In order to realize the purpose of the invention, the technical scheme provided by the invention is as follows: a method for generating an urban rail transit network based on grouping division comprises the following steps:

step 1, determining an alternative layout position;

in the step 1, the concrete steps are as follows:

step 1.1, determining the range of the generation of a wire network according to the current urban development situation;

step 1.2, reserving urban roads with the number of motor vehicle roads of 4 or more, and screening out a main road network;

step 1.3, dividing a research area into grids of 1km by 1km through a conventional public transportation network, counting the number of conventional public transportation stations in each grid, setting alternative anchor points in the planning process of the urban rail transit network in a high-density area of the conventional public transportation stations, and approximating the alternative anchor points to station positions of the urban rail transit lines in the generation process of the online network;

step 1.4, comprehensively considering a road network and an urban conventional public transport network, and determining the position distribution of alternative anchor points of an urban rail transit network; and determining the connection relation between the alternative anchor points according to the trend of the road network, and taking the connection relation as the alternative arrangement position of the urban rail transit.

Step 2, grouping division

Step 2.1, acquiring an all-around rectangular passenger flow exchange matrix between urban data annual traffic cells, and adding the passenger flows of the coming and going between any two traffic cells to obtain a resident travel passenger flow triangular matrix;

step 2.2, knowing the coordinates of any two traffic districts, and solving the distance between any two traffic center-of-mass points;

step 2.3, solving the grouping division result by applying an Infmap grouping division method:

the method for dividing the Infmap group comprises the following steps:

and 2.3.1 defines the transition probability p_α→β: in order to avoid the fact that pure random walk excessively depends on initial solution, penetration probability is introduced

To be provided with

Probability of p_α→βRandom walk of probabilities to

Randomly selects the jump point, i.e. the transition probability is expressed as:

step 2.3.2 solving node n generation probability p_αUsing a defined transition probability p_α→βAnd solving, specifically expressed as:

step 2.3.3 solving the probability of occurrence of the classification criteria and terminators

When the difference between the information contained in the node being processed and the information of the processed node is large in the network structure, a terminator is generated firstly to indicate the end of a group of classes, and then a classification standard symbol is generated to indicate the start of a new group of classes. The probability of the generation of the classification standard and the terminator of the ith classification standard is:

step 2.3.4 use optimization method to solve the classification mode of minimizing the objective function, known from the basic principle of information theory, if a group of information has n elements, each elementProbability of occurrence of element is d_α(d_αE D), the minimum entropy result for this set of information is:

regardless of the encoding scheme, the minimum information entropy of a set of information is known, and therefore equations (2-4) are optimized as the objective function of the encoding scheme.

Applied in a network structure, the probability of occurrence p of a network node_αProbability of occurrence of a classification criterion and probability of occurrence of a terminator

Are different and need to be represented by different expressions. The minimum information entropy of the classification criteria and terminators is expressed as:

the minimum information entropy of the ith classification criterion is expressed as:

finally, H (Q) and H (P)_i) And carrying out weighted average to obtain the minimum value of the network structure information entropy as follows:

and 2.4, obtaining a grouping result, and analyzing the functional area of the city by combining POI distribution of the city.

Step 3, restricting urban traffic scale

Step 3.1, solving the net density of the whole line of the future prediction year, and comprises two methods:

the method A comprises using the density of urban road network and urban rail transit network of known years and performing regression analysis to obtain correlation coefficient R²And judging the correlation between the urban road network density and the urban rail transit network density. The calculation result is similar to the actual situation, and the feasibility of the linear relation is verified;

and B, calculating the line net density by using the population, and respectively counting the population density and the post density of the main domestic city. And calculating the sum of the city population density and the city post density, performing regression analysis on the sum and the city service population calculated wire mesh density to obtain a linear relation between the sum and the city service population calculated wire mesh density, and further obtaining the city service population calculated wire mesh density value.

Step 3.2, solving the intensity of the passenger flow of the whole network;

and 3.2.1, dividing the influence factors influencing the passenger flow intensity of the urban rail transit network into four levels of urban scale, trip characteristics, supply level and urban development level, and selecting corresponding quantitative indexes for analysis under each level.

Step 3.2.2, applying a grey correlation degree analysis method to carry out quantitative sequencing on the correlation between the quantitative indexes and the urban rail transit passenger flow strength to obtain the importance degrees of different influence factors, and calculating to obtain the correlation degree of each quantitative index;

the grey correlation degree analysis method mainly comprises the following steps:

step 3.2.2.1, evaluation indexes are selected: based on subjective cognition and feeling of the evaluation object, selecting an index capable of influencing the change of the evaluation object, determining influence factors of the evaluation object, and establishing an index evaluation system. The quantization index reflecting the purpose of evaluation is called a reference sequence, and the quantization index affecting the purpose of evaluation is called a comparison sequence. Assuming n influencing factors, counting m groups of data, and establishing a data matrix as follows:

in the formula: x_i(i-0, 1.., n) — a data sequence in which X is₀Is a reference sequence, X_i(

i

1, 2.., n) is a comparison sequence.

Step 3.2.2.2 data dimensionless processing: and obtaining the average value of each row of data sequences, and dividing each number in the data sequences by the average value of the data sequences to obtain the dimensionless data sequences. The data sequence after the non-dimensionalization processing is shown in (3-2):

step 3.2.2.3 solving the grey correlation coefficient: the degree of relatedness is the degree of similarity between the curves of the positions of the reference sequence and the comparison sequence. The difference between the reference sequence and the comparison sequence at the corresponding position is calculated. The calculation formula is shown as (3-3):

step 3.2.2.4, find the degree of association: solving the average value of the grey correlation coefficients of the comparison sequence and the reference sequence at each position to obtain the correlation degree of each comparison sequence, wherein the calculation formula is shown as (3-4):

step 3.2.2.5 relevance ranking: and classifying the evaluation indexes according to the grey correlation value, wherein the evaluation indexes are generally classified into significant influence factors, important influence factors and general influence factors. The method comprises the following steps of taking the grey correlation degree as a main influence factor, taking the grey correlation degree as a value range (0.85, 1), taking the grey correlation degree as an important influence factor, taking the grey correlation degree as a value range (0.65, 0.85), taking the grey correlation degree as a value range (0.45, 0.65) as a general influence factor, taking the grey correlation degree as a value range (0, 0.45) as a slight influence factor, and taking the grey correlation degree as a value range.

And 3.2.3, commonly taking values according to the error tolerance, wherein the fluctuation range of the significant influence factors is 3%, the fluctuation range of the important influence factors is 10%, and the fluctuation range of the common influence factors is 15%. Collecting related index data values of different years of domestic city according to the above standard, and selecting the city of specific year with index value in the threshold interval

And 3.2.4, performing regression analysis by using the operation mileage and the average daily passenger capacity of the whole-market passenger flow to finally determine the slope of the whole-market passenger flow.

Step 3.3, solving the scale of the whole network;

weighted average is obtained by four schemes, and the results obtained by solving the 4 algorithms are solved firstly

3.3A: a travel demand deduction algorithm:

according to the general planning and the comprehensive traffic planning, a corresponding data value of a Z city in the forecast year is obtained, the estimation of the rail transit transfer coefficient beta is carried out according to the statistics of the urban rail transfer coefficient and the line number of the urban rail transit city constructed and operated in China, the development condition of the urban rail transit in China is divided into the development initial stage (the urban rail transit line is less than or equal to 3), the rapid development stage (the urban rail transit line is less than or equal to 4) and the suburban extension stage (the urban rail transit line is more than or equal to 10) after the statistics, and the average values of the urban transfer coefficients are respectively counted. Through calculation, the average values of the transfer coefficients of urban rail transit in the cities of three periods are respectively as follows: 1.199,1.373,1.817.

Finally, the formula:

in the formula: l is the total length (km) of the track traffic line network;

q-total amount of travel (ten thousand people) of urban residents;

alpha-urban rail transit passenger flow occupation rate;

β -transfer coefficient;

gamma-full network passenger flow intensity (thousands people/(km sun))

Step 3.3B: network service level deduction method

The network service level deduction algorithm is analyzed from two angles of urban rail transit service area and service population, and a formula for deducting the total length of a rail transit network line is as follows:

in the formula: s-area of built-up area of central urban area (km)²)；

Phi-track traffic line network Density (km/km) calculated in service area²)；

P-the general population of cities (ten thousand);

-track traffic net density (km/ten thousand people) calculated as service population;

mid () -taking median

Step 3.3C: infrastructure investment capacity deduction algorithm

The infrastructure investment capacity deduction algorithm mainly calculates the scale of the wire network from the perspective of urban financial burden capacity, and the method is as follows:

in the formula: GDP-Total annual national production value (hundred million yuan);

r-national production gross annual growth rate;

n-planned annual number of copies;

p-sustainable investment accounts for the proportion of urban GDP;

c-cost of net per unit length (Yi Yuan/km)

Step 3.3D regression analysis algorithm

The regression analysis and deduction algorithm is to use key factors capable of influencing the scale of the urban rail transit network as independent variables of a calculation formula, and determine a calculation model through regression analysis and parameter fitting, and the calculation model is as follows:

in the formula: s-area of built-up area of central urban area (km)²)；

P_centerCentral urban population (ten thousand);

GDP-Total value of national production in cities (hundred million yuan);

gamma-intensity of passenger flow of urban rail transit network (ten thousand people/(km x day));

λ_i(i ═ 0,1,2,3,4) — parameters to be determined

② four methods are summarized: comprehensive calculation of the wire mesh scale:

and (3) determining the weight of each wire mesh scale calculation method by applying an entropy method, wherein the final wire mesh calculation formula is represented as follows:

L＝λ₁L_demand+λ₂L_{service_level}+λ₃ L_capacity+λ₄L_regression (3-9)

in the formula: l-total length of track traffic line (km)

L_demandCalculating the total length (km) of the line network according to the travel requirement;

L_{service_level}-calculating the total length (km) of the network line according to the service level of the network;

L_capacitycalculating the total length (km) of the line network circuit according to the basic set investment capacity;

L_regression-calculating the total length (km) of the line network by a function regression method

And (4) predicting the scale L of the rail transit network of a certain city in the year by calculation.

Step 4, generating the net among the groups

Step 4.1 calculate road impedance

Step 4.1.1 generalized travel time cost of conventional public transport in city

The general travel time cost of a conventional bus is represented as:

in the formula: t is t_{bus_related}-travel related time costs (h);

t_{start_bus}-average time to walk to bus stop (h);

t_{bus_destination}-time to walk to destination (h)

L-distance (km) using regular buses;

-average running speed of conventional bus (km/h)

t_wait-average waiting time (h) for regular buses;

t_interval-average departure interval (h) for conventional buses

x is the number of people in the vehicle;

s is the number of seats in the vehicle;

a-area of standing in vehicle (m)²)；

Coefficient of alpha, beta-constant

f_bus-average fare cost (dollar) for regular buses;

x-time cost conversion coefficient (h/yuan)

P_workCase city employment people (people);

T_work-annual working time (h);

GDP-Total value of annual national production in case City (Yuan);

step 4.1.2 generalized travel time cost of the urban taxi;

the generalized travel time cost of the urban taxi comprises the actual time cost on the taxi and the fare cost, and is specifically represented as follows:

in the formula: t is t_taxi-taxi generalized travel time cost (h);

l-taxi trip distance (km);

-mean taxi travel speed (km/h);

f_taxi-average taxi fare cost (dollar);

χ -time cost conversion factor (h/yuan);

step 4.1.3, after the generalized travel time cost of the conventional public transport in the city and the generalized travel time cost of the taxi in the city are determined, weight assignment is carried out on the generalized travel time costs of different travel modes according to the travel sharing rate of different types of traffic modes of the case city, road impedance (which is a function) is determined, and a Dial algorithm is applied to carry out passenger flow distribution;

dial algorithm: the effective path is defined as: the distance between the end point v of the road section (u, v) and the end point j of the OD pair (i, j) is shorter than the distance between the start point u of the road section, and the distance between the end point v and the start point i of the OD pair (i, j) is longer than the distance between the start point u of the road section, namely, each time the road section (u, v) is moved forward, the road user is closer to the end point and farther from the start point.

For OD pair (i, j), starting point is i, ending point is j,

j is an element of N; a link a, starting point u, ending point v,

v ∈ N, the steps of the Dial algorithm are:

step 4.1.3.1 preprocessing;

calculating t_iu,

I.e. the minimum traffic impedance from the starting point i to all nodes; calculating t_uj,

I.e. the minimum traffic impedance of all nodes to end point j; definition of O_uAll the road section end point sets with the node u as a starting point; definition D_uThe method comprises the steps that a node u is used as a starting point set of all road sections of a terminal point; calculating a road section likelihood value L (u, v), wherein the specific calculation formula is as follows:

in the formula: theta is constant, theta is 1

And selecting a path composed of the road sections with the road section likelihood value L (u, v) being more than or equal to 0 as an effective path according to the likelihood value of each road section a.

Step 4.1.3.2 forward calculate road segment weights;

starting from the origin i of OD pair (i, j), according to t_iuConsidering each node in ascending order, calculating the weight value of the road section with i as the starting point, and regarding the node

Weight W (u, v), v ∈ O_uThe calculation formula of (2) is as follows:

step 4.1.3.3 reverse-distributing road traffic volume;

starting from the OD pair (i, j) end point j, according to t_ujThe ascending order considers each node, calculates the traffic volume of the road section taking j as the terminal point, and takes the node as the terminal point

Road traffic F (u, v), u ∈ D_vThe calculation formula of (2) is as follows:

in the formula: f (u, v) -the road section traffic volume taking u as a starting point and v as an end point,

v∈N；

q_ij-the amount of traffic between the OD pair (i, j);

w (u, v) -road segment weight with u as the starting point and v as the ending point,

v∈N

and 4.1.4, distributing the obtained all-around OD passenger flows among the traffic cells to the alternative distribution positions of the urban rail transit lines obtained by screening in the step 1, so as to obtain a whole-network passenger flow distribution result graph.

Step 4.2, arranging wire nets among the clusters;

step 4.2.1 first determines a set of alternative connection relations of the wire network among the groups, namely, the connecting lines among the centroid points of each group. And (4) dividing the predicted passenger flow of the urban rail transit between the groups into alternative connection relations of the inter-group line network by applying the calculated road impedance function value, namely distributing the OD passenger flow of the urban rail transit between the centroids of the groups onto the centroid point connection lines between the groups.

Step 4.2.2 urban traffic scale constrained parameter estimation:

firstly, merging traffic cells of the same group, and determining a mass center point of each group as a network node; connecting lines among the grouped mass center points are used as the edges of the network; and calculating the passenger flow exchange quantity between different groups by taking the groups as units to serve as the edge weight. And determining the passenger flow distributed on each edge by applying a 2.3 section passenger flow distribution method, determining the lowest passenger flow requirement according to the practical conditions of case city economy, population and the like, and screening the edges meeting the conditions to form the approximate line network trend. The constraint is expressed as:

in the formula: q. q.s_rsBetween OD pairs (r, s)Passenger flow volume (ten thousand people);

-the amount of traffic between the OD pair (r, s) selects the proportion of the kth path;

-decision variable, if the kth path taken by the traffic between the OD pair (r, s) contains segment a, then

Otherwise, then

γ — net passenger flow intensity (ten thousand people/(km × day));

mu is a nonlinear coefficient, and mu is 1.15-1.4;

l_a-length of section a (km);

step 4.2.3, determining each parameter value in the inter-group line network generation model by combining the parameter calculation result of the urban traffic scale constraint, and determining the approximate form of the urban rail transit line network;

step 4.2.4, calculating the minimum standard of passenger flow screening on the connection relation between each group, and if the passenger flow distribution result is greater than the minimum standard of passenger flow screening, reserving the connection relation between the groups;

step 5, group internal net generation

Step 5.1, applying a cluster internal wire network generation model, and combining the parameter calculation result in the step 3 to obtain a cluster internal wire network generation model;

and 5.2, judging the convergence condition of the group fitness values of each group.

Step 6, wire mesh integration and optimization

And according to the line connection relation among the groups, connecting the internal lines of the groups generated among different groups nearby to form a basic line network in the process of line network integration and optimization, and generating the line network in the whole city range.

Step 7, evaluation of the net scheme

Step 7.1, network generation model result rationality analysis

And respectively calculating indexes in the following index systems for the net generated by the net generation model and the actual net in the forecast year Z city for comparative analysis:

wire mesh size C₂Coverage center urban area ratio C₃Degree of connection with large-scale passenger flow distribution points C₅Number of transfer nodes C₆Coverage population and employment post ratio C₁₈Degree of coordination with urban traffic₂₁

Step 7.2, necessity analysis of grouping

The generation of nets using only net integration and optimization models is compared to the generation of nets using the route of the techniques herein.

The invention has the beneficial effects that: the invention combines the planning thought of macroscopic and microscopic wire nets, adopts the InfoMap algorithm in the dynamic network partitioning algorithm to research the urban space structure, adopts the genetic algorithm with stronger adaptability to the actual problem to solve, and simultaneously introduces the self-adaptive operator. Reasonable wire network layout and circuit layout are carried out, and the proportion of qualitative analysis in the planning process is reduced.

Drawings

FIG. 1 is a schematic diagram of a net generation spatial range;

FIG. 2 is a schematic view of an alternative deployment location;

FIG. 3 is a schematic diagram of the distribution of the density of various POIs;

FIG. 4 is a schematic diagram of a total network Logit passenger flow distribution result;

FIG. 5 is a schematic diagram of an inter-team network topology;

FIG. 6 is a schematic diagram of the arrangement of nets inside a cluster;

FIG. 7 is a diagram illustrating convergence of various groups of blob fitness values;

FIG. 8 is a schematic diagram of a connection relationship between groups;

FIG. 9 is a schematic diagram illustrating a result generated by a whole net according to the present invention;

FIG. 10 is a diagram illustrating the net generation results for non-clustered split nets.

Detailed Description

The technical solution in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings.

The technical scheme of the invention is divided into the following parts: firstly, on the basis of urban traffic cell division results, based on the overall OD passenger flow between traffic cells, a distance-corrected InfoMap algorithm is applied, and the traffic cells are clustered according to the population flow rule between the traffic cells, so that the detection of the urban potential space structure is realized.

Then, based on the Dial effective path searching principle, a Logit passenger flow distribution model taking the travel time cost of the generalized public transport as the utility is established. And carrying out probability distribution on the OD passenger flows of the urban public transport to obtain the passenger flow distribution result among different traffic districts, and preparing for generating a network. And by combining with related data, important parameters related to urban rail transit scale and efficiency in constraint conditions such as line network density, line network passenger flow intensity, line network scale and the like are calculated by applying linear regression, grey correlation degree analysis and an entropy method.

Finally, the process of generating the wire mesh is divided into three layers: inter-cluster wire mesh generation, intra-cluster wire mesh generation and wire mesh integration and optimization. The generation of the inter-group wire network is mainly realized by group division and an inter-group wire network generation model; the inter-group wiring network generation model takes passenger travel time cost and construction cost as objective functions and takes indexes influencing urban rail transit scale as constraint conditions; and adding a line layout variable in the line network integration and optimization model, and simultaneously considering the line network layout and the line layout to obtain the final case urban rail transit network.

The specific steps of the invention are as follows:

a method for generating an urban rail transit network based on grouping division comprises the following steps:

step 1, determining an alternative layout position;

in the step 1, the concrete steps are as follows:

Step 2, grouping division

Step 2.1, acquiring an omnidirectional rectangular passenger flow exchange matrix between urban data year traffic cells, and adding the passenger flows of the coming and going between any two traffic cells to obtain a resident trip passenger flow triangular matrix;

the method for dividing the Infmap group comprises the following steps:

step 2.3.1 defining the transition probability p_α→β: in order to avoid the fact that pure random walk excessively depends on initial solution, penetration probability is introduced

To be provided with

Probability of p_α→βRandom walk of probabilities to

Randomly selecting jump points, i.e. transition profilesThe ratio is expressed as:

step 2.3.4 use optimization method to solve the classification mode of minimizing the objective function, known from the basic principle of information theory, if a group of information has n elements, the probability of each element is d_α(d_αE D), the minimum entropy result for this set of information is:

Applied in a network structure, the probability of occurrence p of a network node_αProbability of occurrence and termination of classification criteriaProbability of occurrence of endstop

and 2.4, obtaining a grouping division result, and analyzing the functional area of the city by combining POI distribution of the city.

Step 3, restricting urban traffic scale

Step 3.2, solving the intensity of the passenger flow of the whole network;

in the formula: x_i(i-0, 1.., n) — a data sequence in which X is₀Is a reference sequence, X_i(i-1, 2., n) is a comparison sequence.

Step 3.2.2.2 data dimensionless processing: and obtaining the average value of each row of data sequence, and dividing each number in the data sequence by the average value of the data sequence to obtain a dimensionless data sequence. The data sequence after the non-dimensionalization processing is shown in (3-2):

Step 3.3, solving the scale of the whole network;

3.3A: the travel demand deduction algorithm comprises the following steps:

Finally, the formula:

in the formula: l is the total length (km) of the track traffic line network;

q-total amount of travel (ten thousand people) of urban residents;

alpha-urban rail transit passenger flow occupation rate;

β -transfer coefficient;

gamma-full network passenger flow intensity (thousands people/(km sun))

Step 3.3B: network service level deduction algorithm

in the formula: s-area of built-up area of central urban area (km)²)；

Phi-calculation by service area, track traffic line network Density (km/km)²)；

P-the general population of cities (ten thousand);

mid () -taking median

Step 3.3C: infrastructure investment capacity deduction algorithm

r-national production gross annual growth rate;

n-planned annual number of copies;

p-sustainable investment accounts for the proportion of urban GDP;

c-cost of net per unit length (Yi Yuan/km)

Step 3.3D regression analysis algorithm

in the formula: s-area of built-up area of central urban area (km)²)；

P_centerCentral urban population (ten thousand);

GDP-Total value of national production in cities (hundred million yuan);

λ_i(i ═ 0,1,2,3,4) — pendingParameter(s)

in the formula: l-total length of track traffic line (km)

And the scale L of the rail transit network of a certain city in the year can be predicted through calculation.

Step 4, generating the net among the clusters

Step 4.1 calculate road impedance

The general travel time cost of a conventional bus is represented as:

in the formula: t is t_{bus_related}-travel related time costs (h);

t_{start_bus}-average time (h) to walk to bus stop;

t_{bus_destination}-time to walk to destination (h)

L-Using conventional bus travel distance (km);

-average running speed of conventional bus (km/h)

t_wait-average waiting time (h) for regular buses;

t_interval-average departure interval (h) for conventional buses

x is the number of people in the vehicle;

s is the number of seats in the vehicle;

a-area of standing in vehicle (m)²)；

Coefficient of alpha, beta-constant

f_bus-average fare cost (yuan) for regular buses;

x-time cost conversion coefficient (h/yuan)

P_workCase city employment people (people);

T_work-annual working time (h);

GDP-Total value (Yuan) of national production in case City;

step 4.1.2 generalized travel time cost of the urban taxi;

in the formula: t is t_taxi-taxi generalized travel time cost (h);

l-taxi trip distance (km);

-mean taxi travel speed (km/h);

f_taxi-average taxi fare cost (dollar);

χ -time cost transformation coefficient (h/yuan);

dial algorithm: the effective path is defined as: the distance between the end point v of the link (u, v) and the end point j of the OD pair (i, j) is shorter than the distance between the start point u of the link, and the distance between the end point v and the start point i of the OD pair (i, j) is longer than the distance between the start point u of the link.

For OD pair (i, j), starting point is i, ending point is j,

j is an element of N; a link a, starting point u, ending point v,

v ∈ N, the steps of the Dial algorithm are:

step 4.1.3.1 preprocessing;

calculating t_iu,

in the formula: theta is constant, theta is 1

Step 4.1.3.2 forward calculates road segment weight;

Weight W (u, v), v ∈ O_uThe calculation formula of (2) is as follows:

step 4.1.3.3 reverse-distributing road traffic volume;

Road traffic F (u, v), u ∈ D_vThe calculation formula of (2) is as follows:

v∈N；

q_ij-the amount of traffic between the OD pair (i, j);

v∈N

Step 4.2, arranging wire nets among the clusters;

Step 4.2.2 urban traffic scale constrained parameter estimation:

firstly, merging traffic cells of the same group, and determining a mass center point of each group as a network node; connecting lines among the grouped mass center points are used as the edges of the network; and calculating the passenger flow exchange quantity between different groups by taking the groups as units to serve as the edge weight. And determining the passenger flow distributed on each edge by applying a 2.3 section passenger flow distribution method, determining the lowest passenger flow requirement according to the practical conditions of case city economy, population and the like, and screening the edges meeting the conditions to form the approximate line network trend. The constraints are expressed as:

in the formula: q. q.s_rs-volume of passengers (ten thousand) between OD pairs (r, s);

Otherwise, then

γ — net passenger flow intensity (ten thousand people/(km × day));

mu is a nonlinear coefficient, and mu is 1.15-1.4;

l_a-length of section a (km);

step 5, group internal net generation

Step 6, wire mesh integration and optimization

Step 7, evaluating the net scheme

Step 7.1, network generation model result rationality analysis

wire mesh size C₂Coverage center urban area ratio C₃And the degree of connection with large-scale passenger flow distribution points C₅Number of transfer nodes C₆Coverage population and employment post ratio C₁₈And cityDegree of coordination of urban traffic C₂₁

Step 7.2, necessity analysis of grouping

The invention is further described below with reference to practical examples:

(3) z market case analysis

1. Case overview

The space range of the case is Z city central urban area, the time range is 2015-2020 years, the data years are 2015 years, and the prediction years are 2020 years. As shown in FIG. 1, the selected net generates a spatial range.

Comprehensively considering a Z-shaped road network and an urban conventional public transport network, determining the position distribution of alternative anchor points of an urban rail transit network, and finally determining the connection relation between the alternative anchor points according to the trend of the Z-shaped road network as the alternative layout position of the urban rail transit, as shown in FIG. 2.

2. Urban space grouping

An InfoMap group division method is applied to an omnidirectional rectangular passenger flow exchange matrix among traffic cells of the Z city data year, 357 traffic cells of the Z city are finally divided into 7 groups, and POI distribution of the Z city is combined, as shown in FIG. 3.

(1) InfoMap group partitioning

The basic idea of grouping division is to quantify the differences among groups as an objective function, and then to make the objective function reach the maximum value through iterative optimization to form a final network group structure.

The method for dividing the Infmap group comprises the following steps:

2.3.1 defining the transition probability p_α→β: in order to avoid the fact that pure random walk excessively depends on initial solution, penetration probability is introduced

To be provided with

Probability of p_α→βRandom walk of probabilities to

Randomly selects a jump point, i.e. the transition probability is expressed as:

2.3.2 solving the node n Generation probability p_αUsing a defined transition probability p_α→βAnd solving, specifically expressed as:

2.3.3 solving Classification Standard symbol and terminator occurrence probabilities

2.3.4 use optimization method to solve the classification mode of minimizing the objective function, known from the basic principle of information theory, if a group of information has n elements, the probability of each element is d_α(d_αE D), the minimum entropy result for this set of information is:

Applied in a network structure, the probability of occurrence p of a network node_αProbability of occurrence of a class criterion and probability of occurrence of a terminator q_iAre different and need to be represented by different expressions. The minimum information entropy of the classification criteria and terminators is expressed as:

the results are as follows:

POIs such as residential buildings, bus stations, shopping malls, supermarkets, schools, banks, hospitals, parks and the like within the group 1 are high in quantity and density, can be used as financial, cultural and commercial centers in Z city, are high in passenger flow attraction, and are obvious in regional advantages.

The train east station in Z city and the CBD center in the east station of the train in Z city are arranged in the group 2 range, the traffic passenger flow exchange is frequent, meanwhile, the construction of a new railway junction provides rich passenger sources for the business of the area, the large passenger flow distribution points of the area are more, and the financial and traffic characteristics are obvious.

The residential buildings in the southern region of the group 3 are dense, typical residential areas, and the government of the province H are located in the range of the group 3 and have certain political functions.

The group 4 has high density of commercial supermarkets and schools, and has twenty-seven square business centers and Z city universities, which are typical business districts and culture centers of Z city.

The POIs in the group 5 are similar and fewer in number, belong to a developing area, and have no obvious characteristics.

The residential buildings in the group 6 have high density and outstanding living functions, and can be positioned as residential areas.

And all types of POI in the group 7 are few, and the natural ecological advantages in the area are obvious by combining the urban overall planning of the Z city, thereby belonging to a new development area mainly developing the tourism industry.

3. Urban rail transit scale constraint

According to the method, a calculation model is constructed for key parameters such as net density, net passenger flow strength and net scale from the perspective of quantitative analysis.

I. Net density estimation

The model counts urban road network density and urban rail transit network density of the domestic main city in 2017, and carries out regression analysis on the urban road network density and the urban rail transit network density to obtain Z urban rail transit network density calculated by service area; and calculating the net density by using the population, calculating the sum of the city population density and the city post density, and performing regression analysis on the sum and the net density calculated by using the service population of the city to obtain the net density of the track traffic by using the population of the Z city.

Wire mesh passenger flow intensity estimation

And (4) applying a grey correlation degree analysis method to carry out quantitative sequencing on the correlation between the quantitative indexes and the urban rail transit passenger flow intensity to obtain the importance degrees of different influence factors. And collecting relevant index data values of different years of the domestic city according to the standard, selecting the specific year city with the index value in the threshold interval, performing regression analysis by using the operation mileage and the average daily passenger capacity of the specific year city, and finally determining the passenger flow intensity of the Z city.

Wire mesh Scale estimation

The model comprehensively considers travel requirements, network service levels, infrastructure investment capacity and regression analysis by applying an entropy method, determines the weight of each network scale calculation method, and finally calculates to obtain the Z city rail transit network scale of the forecast year.

TABLE 2 calculation of key parameters

4. Group net generation model

In order to consider the overall arrangement of urban public transport and reduce the dimensionality of the problem, the method firstly researches an urban conventional public transport network and determines an alternative anchor point set of a wire network generation model. And then, an adaptive genetic algorithm is applied to the inside of the cluster to generate an alternative road section set in the cluster, and the passenger time cost and the route construction cost are comprehensively considered for the objective function of the net generation model. And then, according to the connection relation among the groups, connecting the nodes with shorter distance among the groups to obtain an alternative line set in the whole network range. And finally, applying a net integration and optimization model at the whole net layer, and simultaneously considering net layout and line layout to obtain the final urban rail transit network.

Meaning of symbols in the model of Table 1

I. Inter-team wire net generation

1. Inter-group wire network generation model

Inter-cluster wire mesh generation aims at determining wire mesh morphology. And (3) reflecting the contact tightness between different functional areas of the city according to the passenger flow exchange strength between different groups by taking the groups as units, and further determining the macroscopic trend of the wire net. The passenger flow exchange among the groups firstly meets the lowest passenger flow condition for building the rail transit, namely, the passenger flow exchange quantity among the groups reaches a certain quantity, and then the rail transit line can be laid. And secondly, the groups with close passenger flow connection but long distance are penetrated by rail transit to play a role in communicating cities.

The generation of the inter-group net is mainly determined by taking passenger flow as a constraint condition. Firstly, merging traffic cells of the same group, and determining a mass center point of each group as a network node; connecting lines among the grouped mass center points are used as the edges of the network; and calculating the passenger flow exchange quantity between different groups by taking the groups as units to serve as the edge weight. The method comprises the steps of determining passenger flow distributed on each edge by applying a multipath passenger flow distribution method with constant impedance, determining the lowest passenger flow requirement according to the practical conditions of urban economy, population and the like, and screening the edges meeting the conditions to form the approximate line network trend. The constraints are expressed as:

calculating a BPR function to obtain the traffic impedance of a road section, applying a Dial algorithm to perform random passenger flow distribution, distributing the full-formula OD passenger flow among Z urban traffic cells to the screened alternative layout positions of the urban rail transit lines, wherein the distribution result is shown in figure 4:

by combining the urban structure and urban POI distribution, the distribution result of the Logit passenger flow in the whole urban range is more consistent with the actual situation, so the distribution of the passenger flow among groups and the distribution of the passenger flow in the groups can be carried out by using the distribution method of the Logit passenger flow. If the passenger flow distribution result is larger than the minimum standard of passenger flow screening, the connection relationship between the groups is reserved, and finally, the connection relationship between the groups is as shown in fig. 5:

group intranet generation

2. Group internal wire mesh generation model

Solving the problem of the nets in the cluster by adopting a genetic algorithm, wherein the iteration times are 100, the population number is 200, the initial cross probability is 0.8, and the initial mutation probability is 0.05, and the arrangement positions of the nets in the cluster are obtained as shown in FIG. 6:

since the division of the traffic cell mostly takes the urban trunk line as the boundary, the alternative road sections are mostly positioned on the boundary between different groups and belong to a plurality of groups, and therefore, even if the groups generate the wire network, the connectivity of the alternative lines among the groups is good.

Firstly, establishing a generalized travel cost function as an abstract expression of urban rail transit construction cost and passenger travel requirements, then abstracting some construction requirements as constraint conditions, and solving by using an optimization idea and an optimization algorithm to determine the arrangement position of a wire network in a cluster.

I. Generalized travel cost objective function

The generalized travel cost objective function mainly comprises two parts of passenger travel time cost and rail transit construction cost. The passenger travel time cost includes the passenger actual on-board time cost, transfer time cost, and fare cost. The actual on-vehicle time cost is expressed by the road section length and the average operation speed of urban rail transit, and is specifically expressed as follows:

in the formula: z is a radical of₁Is the actual on-board time cost (h) for the passenger;

represents the average operating speed (km/h) of urban rail transit,

the transfer time is expressed by the transfer times, and because the model only considers the whole trend of the line and does not relate to site setting and operation design, an approximation method is adopted for calculation, namely the number of transfer nodes is approximated to the transfer times of passengers.

In the formula: z is a radical of₂Approximate transfer time cost (h) for the passenger;

representing the number of the k-th path passing through the transfer node;

is the average time (h) for each transfer of urban rail transit,

the passenger fare cost is calculated according to the fare calculation mode of the urban rail transit, is a unit of a unified objective function, and is multiplied by a time cost conversion coefficient, and is specifically expressed as:

in the formula: z is a radical of₃Fare the cost (h) for the passenger;

representing a fare calculation function of the urban rail transit; χ is the time cost conversion coefficient (h/yuan)

The line construction cost in the construction cost is expressed by using the average construction cost of urban rail transit with unit length, and is multiplied by a time cost conversion coefficient to be expressed by a unified unit, wherein the specific expression is as follows:

in the formula: z is a radical of₄Cost (h) for line construction; c is the average cost per unit length of the net (Yi Yuan/km)

In summary, the generalized rail transit trip cost objective function is expressed as:

in the formula: xi₁Is a weight coefficient, [0, 1]]Random number between

Constraint conditions

The constraint conditions for urban rail transit network planning are mainly embodied in three layers, namely a network structure layer, a line layer and a network layer. At the network structure level, the rationality of the network structure is constrained. On the line level, the passenger flow distributed on each road section is restricted, namely the highest value of the passenger flow of the road section is set so as to ensure the backbone function and the basic passenger flow benefit of the urban rail transit in the public transport. And at the net layer level, restricting the net scale and the net density of the generated urban rail transit net.

In the network structure level, the model adopts a one-way network structure, and road section nodes and road section passenger flow need to be restrained, which is specifically expressed as follows:

and on the line level, the road section passenger flow is determined by the line network passenger flow strength and the road section length, and an ideal passenger flow strength value is obtained by analyzing the importance of the influence factors of the urban rail transit line network passenger flow strength and selecting a city similar to the case city economy and social development conditions for regression analysis. Thus, the line level constraints are:

at the net level, the net size is constrained by calculating the total length of the line. The ideal network scale of the case city can be obtained on the basis of comprehensively considering the travel demand of the case city, the rail transit service level, the infrastructure investment capacity and other city experience values. The net size constraints are therefore:

wherein L is the scale (km) of the urban railway network

In addition, on the line network layer, the line network density of the urban rail transit line network is calculated by combining the area covered by the line network, and the maximum value of the line network density of the case city generation line network is limited. The net density constraints are therefore:

in the formula: iota (iota) type_iAnd

are all variables from 0 to 1, if node i in the initial network is selected, iota _i1, conversely iota _i0; if node i is in traffic cell taz, then

On the contrary, the method can be used for carrying out the following steps,

S_tazrepresenting the surface area (km) of the traffic cell taz²) (ii) a Phi is the net density (km/km) calculated by area²)。

The convergence of the groups of blob fitness values is shown in FIG. 7:

since the number of anchor points within each cluster is different, there is a large difference in chromosome length, i.e., the number of selected line anchor points. The chromosome length is determined by taking a random number from 60% to 90% of the total number of anchor points in the cluster and using the random number as the chromosome length. Because the total number of anchor points of different groups is different, the convergence speed of each group is greatly different, but the convergence is achieved within the range of iteration times. In addition, the genetic algorithm is optimized in the actual algorithm, a self-adaptive strategy is adopted, and the classical genetic algorithm is optimized by respectively adopting improved methods of self-adaptive selection, self-adaptive intersection and self-adaptive variation so as to improve the convergence efficiency of the genetic algorithm and avoid falling into local optimization.

Wire mesh integration and optimization

According to the line connection relationship between the clusters, the internal lines of the clusters generated between different clusters are connected nearby to form a basic line network in the process of line network integration and optimization, as shown in fig. 8, so as to generate the line network within the whole city range.

3. Wire mesh integration and optimization model

On the basis of the overall space form of urban rail transit, the wiring net arrangement positions in each group are integrated and optimized to form wiring net arrangement within an urban range. Unlike the conventional intra-team wiring network generation method, the inclusion relationship between the route and the link is optimized at the same time by taking the route layout into consideration when generating the intra-city-wide wiring network.

The number of transfers is the number of lines passing through the shortest path between the OD pair (r, s), i.e., the number of lines passing through the shortest path, taking into account the layout of the lines

And (4) showing. Thus, the passenger transfer time cost is specifically expressed as:

wherein

And the decision variables represent the passing relationship between the shortest path k and the circuit layout m. Is provided with

If the shortest path k passes through the layout m, then

At the line level, the layout of the lines needs to be constrained because the layout of the lines is considered in the optimization process. Ensuring that each generated line has no branch line, which is specifically represented as:

wherein the content of the first and second substances,

is a variable of 0 to 1, if the line m passes through the section a composed of the nodes (i, j)

Otherwise, then

N (i) represents another node set of a link starting from or ending at node i. Secondly, the number of nodes contained in the generated alternative line is restricted, and the line is ensured to have certain extension, which is specifically expressed as:

then, selecting an effective path for the passenger, namely, constraining the transfer times of the shortest path, which is specifically represented as:

and (3) restricting the passenger flow distributed on the road section, calculating the minimum value of the passenger flow according to the calculated passenger flow intensity, reserving the road section with the passenger flow reaching the standard, and deleting the road section with the smaller passenger flow. And finally obtaining the net layout and the line layout in the city range by taking the limits of the network structure level, the line level and the net level as constraint conditions.

Solving by using a genetic algorithm to obtain the urban intra-area network layout and the line layout as shown in figure 9:

and finally generating 9 track traffic lines in the Z city by applying a line network generation model considering the line layout. The net generation result in the whole city range accords with the obtained connection relationship between the groups, and basically covers the main passenger flow distribution points and important POI points of the city, and the net can play the roles of connecting the main development areas of the city, meeting the traveling demands of residents in different areas and communicating the city.

In order to clarify the necessity of the method, the differences between the generation of the nets between the clusters, the generation of the nets within the clusters, the integration and optimization of the nets and the generation of the nets within the whole net range without the step of dividing the clusters are compared. Nets generated without clique division are shown in FIG. 10.

The resulting net consists of only 6 wires. Compared with the proposed generative model in combination with fig. 9, the coverage center urban area rate is significantly reduced, and almost no urban rail transit lines are covered in the northwest region of the group 3, all regions of the group 5, the southeast region of the group 6, and the north region of the group 7, thereby greatly reducing the effect of urban rail transit in penetrating through the urban area. The reason is that if the grouping division is not carried out, the network integration and optimization model tends to set the network in an area with larger passenger flow demand, the passenger flow demand in the central area of the city is larger than that in the peripheral area, so the power for expanding the network layout to the peripheral area is smaller, and the network layout position is mainly gathered in the core area of the city. Similarly, the coverage population and employment post ratio of the non-clustered generation net is lower.

Therefore, the InfoMap group division method can effectively increase the area rate of covering the central urban area and increase the effect of urban rail transit on penetrating through the urban area. The arrangement positions of the wire nets are not completely mainly gathered in the core area of the city, and the coverage population and employment post proportion of the wire nets generated by grouping and dividing are improved.

The described embodiments are only some embodiments of the present application and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.

Claims

1. A method for generating an urban rail transit network based on grouping division is characterized by comprising the following steps:

step 1, determining an alternative layout position;

step 2, dividing an InfoMap group, based on the division result of urban traffic cells, based on the overall OD passenger flow between traffic cells, applying a distance-corrected InfoMap algorithm, and clustering the traffic cells according to the population flow rule between the traffic cells to realize the detection of the urban potential space structure;

step 3, restricting the urban traffic scale;

step 3.1, solving the net density of the whole line of the future prediction year;

step 3.2, solving the intensity of the passenger flow of the whole network;

step 3.3, solving the scale of the whole network;

step 4, generating a group inter-group wire network;

step 4.1, calculating road impedance;

step 4.2, arranging wire nets among the clusters;

step 5, group internal net generation

step 5.2, judging convergence conditions of the group fitness values;

the generation of the inter-group wire network is realized through group division and an inter-group wire network generation model; the inter-group wiring network generation model takes passenger travel time cost and construction cost as objective functions and takes indexes influencing urban rail transit scale as constraint conditions; and adding a line layout variable in the line network integration and optimization model, and simultaneously considering the line network layout and the line layout to obtain the final urban rail transit network.

2. The method for generating an urban rail transit network based on grouping division according to claim 1, wherein in step 1, the specific steps of determining the alternative deployment positions are as follows:

step 1.3, dividing a research area into grids of 1km multiplied by 1km through a conventional public transportation network, counting the number of conventional public transportation stations in each grid, setting alternative anchor points in the planning process of an urban rail transit line network in a high-density area of the conventional public transportation stations, and approximating the alternative anchor points to station positions of the urban rail transit line in the generation process of the line network;

3. The method for generating an urban rail transit network based on grouping according to claim 1, wherein in the step 2,

the method for dividing the Infmap group comprises the following steps:

To be provided with

Probability of p_α→βRandom walk of probabilities to

4. The method for generating urban rail transit network based on grouping division according to claim 1, wherein in step 3, step 3.1, there are two methods for solving the network density of the whole line in the predicted year in the future:

method A, combining the urban road network density and the urban rail transit network density of the known yearIt performs regression analysis to solve the correlation coefficient R²And judging the correlation between the urban road network density and the urban rail transit network density. The calculation result is similar to the actual condition, and the feasibility of the linear relation is verified;

5. The urban rail transit line network generation method based on grouping division according to claim 1, wherein in step 3, step 3.2, the passenger flow intensity of the whole network is solved;

in the formula：X_i(i-0, 1.., n) — a data sequence in which X is₀Is a reference sequence, X_i(i 1, 2.., n) is a comparison sequence.

6. The method for generating an urban rail transit network based on grouping according to claim 1, wherein the step 4.1 of calculating the road impedance comprises the following steps:

step 4.1.1 generalized travel time cost of the conventional public transport in the city;

the general travel time cost of a conventional bus is represented as:

in the formula: t is t_{bus_related}-travel related time costs (h);

t_{start_bus}-average time to walk to bus stop (h);

t_{bus_destination}-time to walk to destination (h)

L-Using conventional bus travel distance (km);

-average running speed of conventional bus (km/h)

t_wait-average waiting time (h) for regular buses;

t_interval-average departure interval (h) for conventional buses

x is the number of people in the vehicle;

s is the number of seats in the vehicle;

a-area of standing in vehicle (m)²)；

Coefficient of alpha, beta-constant

f_bus-average fare cost (dollar) for regular buses;

x-time cost conversion coefficient (h/yuan)

P_workCase city employment people (people);

T_work-annual working time (h);

GDP-Total value (Yuan) of national production in case City;

step 4.1.2 generalized travel time cost of the urban taxi;

in the formula: t is t_taxi-taxi generalized travel time cost (h);

l-taxi trip distance (km);

-mean taxi travel speed (km/h);

f_taxi-average taxi fare cost (dollar);

χ -time cost transformation coefficient (h/yuan);

4.1.3, after determining the generalized travel time cost of the conventional public transport in the city and the generalized travel time cost of the taxi in the city, carrying out weight assignment on the generalized travel time costs in different travel modes according to the travel sharing rate of different types of traffic modes of the case city, determining the road impedance as a function, and applying a Dial algorithm to carry out passenger flow distribution;

7. The method for generating an urban rail transit network based on grouping division according to claim 6, wherein in step 4.1.3, the Dial algorithm specifically comprises:

the distance between the end point v of the road section (u, v) and the end point j of the OD pair (i, j) is shorter than the distance between the start point u of the road section, and the distance between the end point v and the start point i of the OD pair (i, j) is longer than the distance between the start point u of the road section, namely, each time the road section (u, v) is moved forward, the road user is closer to the end point and farther from the start point.

For OD pair (i, j), starting point is i, ending point is j,

a link a, starting point u, ending point v,

the Dial algorithm comprises the following steps:

step 4.1.3.1 preprocessing;

calculating t_iu,

in the formula: theta is constant, theta is 1

Step 4.1.3.2 forward calculates road segment weight;

Weight W (u, v), v ∈ O_uThe calculation formula of (2) is as follows:

step 4.1.3.3, reversely distributing road traffic volume;

Road traffic F (u, v), u ∈ D_vThe calculation formula of (2) is as follows:

q_ij-the amount of traffic between the OD pair (i, j);

。

8. the method for generating the urban rail transit network based on the grouping division according to claim 1, wherein in the step 4.2, the specific steps of the inter-group network layout are as follows:

step 4.2.1, firstly, determining a group inter-group wire network alternative connection relation set, namely a connecting line between centroid points of each group; distributing the predicted passenger flow of the urban rail transit between the groups to alternative connection relations of the inter-group wire network by applying the calculated road impedance function value, namely distributing the passenger flow of the urban rail transit OD between the centroids of the groups to the centroid point connection lines between the groups;

step 4.2.2 urban traffic scale constrained parameter estimation:

firstly, merging traffic cells of the same group, and determining a mass center point of each group as a network node; connecting lines among the grouped mass center points are used as the edges of the network; calculating passenger flow exchange capacity between different groups by taking the groups as units, and taking the passenger flow exchange capacity as an edge weight; determining passenger flow distributed on each edge by applying a passenger flow distribution method, determining the lowest passenger flow requirement according to the practical conditions of case urban economy, population and the like, and screening the edges meeting the conditions to form a general line network trend; the constraint is expressed as:

Otherwise, then

γ — wire mesh passenger flow intensity (thousands of people/(km × day));

mu is a nonlinear coefficient, and mu is 1.15-1.4;

l_a-length of section a (km);

and 4.2.4, calculating the minimum standard of passenger flow screening on the connection relation among each group, and if the passenger flow distribution result is greater than the minimum standard of passenger flow screening, keeping the connection relation among the groups.

9. The method for generating a wire mesh of urban rail transit based on grouping division according to claim 1, further comprising step 6, wire mesh integration and optimization, wherein the wires in groups generated between different groups are connected nearby according to the wire connection relationship between the groups to form a basic wire mesh in the wire mesh integration and optimization process, and the wire mesh generation within the whole city is performed.

10. The urban rail transit network generation method based on grouping division according to claim 1, further comprising step 7, network scheme evaluation;

step 7.1, analyzing the rationality of a net generation model result;

wire mesh size C₂Coverage center urban area ratio C₃Degree of connection with large-scale passenger flow distribution points C₅Number of transfer nodes C₆Coverage population and employment post ratio C₁₈Degree of coordination with urban traffic₂₁；

7.2, analyzing necessity of grouping;