Research method of urban public transportation network optimization based on complex network theory

Abstract

The present invention belongs to the technical field of urban public transportation systems, and specifically is a research method for optimizing urban public transportation networks based on complex network theory, comprising step 1: firstly calculating the travel cost of passengers and adding it to the network as travel impedance; step 2: then calculating the probability of passengers choosing a travel path based on the travel impedance to obtain the passenger flow demand of different sections, adding the travel impedance, the passenger flow demand and the passenger capacity of public transportation as weights to the network and improving the calculation method of the global efficiency of the network based on the weights; step 3: finally establishing a public transportation network optimization model with the global efficiency of the network as the objective function and using the improved ant colony algorithm for solving the problem, which is reasonably designed, improves the efficiency of urban public transportation, and finally alleviates the problems of unreasonable layout of urban bus lines and low operating efficiency of the bus system.

Description

Technical Field

[0001] The present invention relates to the technical field of urban public transportation systems, and in particular to an urban public transportation network optimization research method based on complex network theory. Background Art

[0002] With the rapid development of computer technology, complex network theory can be applied to the field of transportation. According to complex network theory, the level of public transportation network can be described scientifically and comprehensively, and the connection status of each line and station in the bus line network can also be objectively reflected. As early as 2000, scholars have carried out research on the application of complex networks in transportation networks. In the literature, the study modeled the world aviation network and analyzed the network topology. Finally, the study found that the aviation network topology has scale-free characteristics. A typical study on the application of complex network theory in public transportation systems is the reference literature. The study modeled the public transportation networks of 22 cities in Poland and systematically analyzed the statistical characteristics of the network topology. Finally, it was found that the network degree distribution of different cities is not the same, some obey exponential distribution, and some obey power law distribution.

[0003] Due to the complexity of the public transportation system, unweighted networks cannot show the real public transportation system. Many scholars have studied the empowerment of public transportation networks. Yang Jikai et al. used cross-sectional passenger flow to weight the public transportation network and analyzed the robustness of the weighted network. They concluded that the weighted anti-destruction measurement index can better describe the robustness of the network. Lu Qingchang et al. used passenger travel time and passenger flow as the weights of the rail transit network. The research results show that failures at stations with high time weights and concentrated passenger flow in the rail transit network will cause a large loss of average travel time for users. Zhou Yangyazhi used the PTEW weighting method to assign weights to the public transportation network, introduced the BPR function to reflect the time cost of public travel, and used PTEW weighting to calculate the traffic impedance of each section. Finally, the author used impedance and passing time as weights. Cats O et al. used the passenger flow in the bus line as the weight of the link. Based on the network flow distribution caused by the reduction of local links, the research results show the importance of key links.

[0004] In terms of bus network optimization, Ding Jianxun et al. established a bus network optimization model based on the direct accessibility of bus stops, achieved the dual goals of bus stop optimization and bus route optimization, and optimized the bus network through the shortest path algorithm. Lu Hanyu et al. considered the impact of travel behavior in line layout, and established a two-layer optimization model based on the spatial topological structure of rail transit lines and bus lines while optimizing bus routes and departure intervals. Wang Fei constructed a bus-subway weighted composite network based on bus and subway card swiping data, optimized the network based on the efficiency between nodes with the goal of improving network efficiency, and optimized the network by adding and deleting stations. Hao Yalan proposed the idea of ​​hierarchical optimization of multi-modal bus network. The optimization goal of the trunk network is to reduce the negative impact of travel, and the optimization goal of the branch network is to increase the coverage of the route network. Finally, the ant colony algorithm is used to achieve network optimization.

[0005] So far, most existing studies have considered a single factor, such as cross-sectional passenger flow, travel time or impedance, to assign network weights, but considering only a single factor cannot reflect the actual network operation status; existing studies lack consideration of the overall network when selecting the optimization target of the bus network, or have achieved the optimization of the overall network efficiency, but ignored the influence of the bus line direction. While considering the changes in bus lines, the overall efficiency of the bus network should be optimized. This paper proposes a new bus network optimization method, which determines the probability of passenger travel path selection based on passenger travel impedance, and weights the network according to passenger travel impedance, travel path selection probability and passenger demand, improves the calculation method of bus network efficiency, establishes a bus network optimization model with improving network efficiency as the objective function, and finally uses the ant colony algorithm to solve it, so as to improve the efficiency of urban public transportation, and ultimately alleviate the problems of unreasonable urban bus line layout and low bus system operation efficiency. Summary of the invention

[0006] The purpose of this section is to summarize some aspects of the embodiments of the present invention and briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section and the specification abstract and the invention title of this application to avoid blurring the purpose of this section, the specification abstract and the invention title, and such simplifications or omissions cannot be used to limit the scope of the present invention.

[0007] In view of the problems existing in the existing urban public transportation network optimization research methods, the present invention is proposed.

[0008] Therefore, the purpose of the present invention is to provide an urban public transportation network optimization research method based on complex network theory, which can improve the efficiency of urban public transportation and ultimately alleviate the problems of unreasonable layout of urban bus lines and low operating efficiency of the bus system.

[0009] To solve the above technical problems, according to one aspect of the present invention, the present invention provides the following technical solutions:

[0010] The research method of urban public transportation network optimization based on complex network theory includes the following steps:

[0011] Step 1: First calculate the passenger travel cost and add it to the network as travel impedance;

[0012] Step 2: Then, the probability of passengers choosing a travel path is calculated based on the travel impedance to obtain the passenger flow demand of different sections. The travel impedance, passenger flow demand and the passenger capacity of public transportation are added to the network as weights, and the calculation method of the global efficiency of the network is improved based on the weights.

[0013] Step 3: Finally, a public transportation network optimization model is established with the global network efficiency as the objective function, and the improved ant colony algorithm is used for solving it.

[0014] As a preferred solution of the urban public transportation network optimization research method based on complex network theory described in the present invention, wherein: the step 1 uses generalized cost to comprehensively consider the impedance of various factors of public transportation from the origin to the destination, and the generalized travel cost can be expressed as:

[0015] Comprehensive travel cost = waiting time + riding time + transfer time

[0016] Passenger waiting time at the station x a is an uncertain value. This time is mainly related to the number of passenger transfers and the probability distribution of the vehicle headway time at the station. When the passenger chooses a route that does not require transfers, if the arrival of vehicles on line a follows a uniform distribution, the maximum waiting time is the headway time h of vehicles on line a. a , the minimum is 0, and the probability density distribution function of waiting time is:

[0017]

[0018] Waiting time x a The distribution function of is:

[0019]

[0020] When the number of passenger transfers is 1, assume that the passenger takes line a and then transfers to line b. The waiting time for line a and line b is x respectively. a and x b , the headway times are h a and h b ,h b >h a , let the total waiting time be z, then z = x a +x b, assuming that both routes a and b have uniform arrival distribution, the waiting time x a and x b The probability density functions can be expressed as:

[0021]

[0022] According to the convolution formula, the probability density function of the total waiting time z is:

[0023]

[0024] The probability density function is different for different values ​​of z. a Should satisfy: 0≤x a ≤h a ,zh b ≤x a ≤z, on the xOz plane, according to the shaded part f z (z) can be divided into three parts according to the value of z:

[0025] Find the integral f z (z) is calculated as:

[0026]

[0027] When the number of passenger transfers is 2, the probability density functions of the waiting time for the first two lines can be calculated first, and then the probability density function of the total waiting time can be calculated based on the convolution formula.

[0028] As a preferred solution of the urban public transportation network optimization research method based on complex network theory described in the present invention, wherein: the passenger's riding time in step 2 is mainly the vehicle travel time. When the public transportation line is rail transportation, the train is separated from other social vehicles and does not affect each other. The road environment does not affect the vehicle operation. At this time, the vehicle's travel speed is equal to the designed travel speed v s , the intersection delay is 0; when regular buses are driving, they mix with other vehicles, and their driving speed will be affected by the road environment. Assuming α is the congestion coefficient of the road section, it is 1 when the road is unobstructed, and the intersection delay is the same as that of other vehicles. The driving speed of regular buses can be expressed as α·v s ;

[0029] For rail transit, the train travel time between adjacent nodes is:

[0030]

[0031] Where: d od ——The length of the road section from node o to node d, unit: km;

[0032] v s——Speed ​​of public transport vehicles, unit: km / h;

[0033] T——Rail transit vehicle stop time, unit: h;

[0034] ——The travel time of the vehicle on line l from node o to node d, unit: h;

[0035] For conventional public transportation, the vehicle travel time between adjacent nodes is:

[0036]

[0037] Where: α od ——The congestion coefficient of the road section from node o to node d;

[0038] ——The vehicle stop time of node o and line l, unit: h;

[0039] ——The travel time of the vehicle on line l from node o to node d, unit: h;

[0040] The impedance of the edge between adjacent nodes is obtained by adding the vehicle travel time between nodes, node delay and intersection delay:

[0041]

[0042] Where: Z o ——The impedance of the edge connecting node o and node d;

[0043] β——category parameter, if the edge belongs to rail transit, it is 1, otherwise it is 0;

[0044] λ——category parameter, which is 1 if the edge belongs to regular public transportation, and 0 otherwise;

[0045] m——the number of intersections that the edge connecting node o and node d passes through;

[0046] Transfer time can be divided into transfer time at the same station and transfer time at different stations. Transfer time at the same station is the waiting time for the transfer line. Transfer time at different stations includes walking time between stations in addition to waiting time for the transfer line. The impedance of the transfer connection at the same station is:

[0047]

[0048] Where: μ1 is the transfer penalty coefficient, which is 0 if there is no transfer at the same station;

[0049] ——Internal impedance of transfer connection at the same station;

[0050] The impedance of the inter-station transfer connection is:

[0051]

[0052] Where: μ2 is the penalty coefficient for inter-station transfers, which is 0 if there is no inter-station transfer;

[0053] v – walking speed;

[0054] ——Inter-station transfer connection impedance;

[0055] Finally, the travel impedance from node o to node d can be expressed as:

[0056]

[0057] As a preferred solution of the urban public transportation network optimization research method based on complex network theory described in the present invention, in which: since there are multiple lines passing between the stop sites in the process of constructing the composite network model, it is only regarded as one edge between the nodes, in order to reflect the difference of the edges, it is necessary to weight the composite network; there are three types of edges in the public transportation network, the edges between the sites in the conventional bus network, the edges between the sites in the rail transit network and the artificially added transfer edges; the edge weights of the bus composite network are defined as follows:

[0058] (1) Rail transit connection

[0059] The weight of the rail transit edge is defined as the ratio of the inter-node impedance to the rail transit passenger saturation. The weight increases with the increase of the inter-node impedance and decreases with the increase of the saturation. The weight of the edge between rail transit stations i and j can be expressed as:

[0060]

[0061] Where: n is the number of rail transit lines passing through stations i and j;

[0062] ——The passenger capacity of train a on rail transit line, unit: person / day;

[0063] ——The passenger capacity of trains between stations i and j on rail transit line a, unit: person / day;

[0064] (2) Conventional bus connections

[0065] The weight of the conventional bus edge is defined as the ratio of the inter-node impedance to the conventional bus passenger saturation. The weight increases with the increase of the inter-node impedance and decreases with the increase of the saturation. The weight of the edge between conventional bus stops i and j can be expressed as:

[0066]

[0067] Where: n is the number of regular bus routes passing through stations i and j;

[0068] ——The passenger capacity of vehicles on regular bus route a, unit: person / day;

[0069] ——The passenger capacity of vehicles on regular bus route a between stations i and j, unit: person / day;

[0070] (3) Transfer to the side

[0071] The default saturation of the transfer edge is 1, so the weights of the same-station transfer edge and the different-station transfer edge can be expressed as:

[0072]

[0073] The final edge weight is defined as:

[0074]

[0075] As a preferred solution of the urban public transportation network optimization research method based on complex network theory described in the present invention, wherein: to calculate the network efficiency, the shortest path between network nodes must first be calculated. The traditional shortest path search algorithm between nodes is to add 1 to the distance of each node passed through, and then compare all distances and select the one with the smallest value as the shortest path. Considering the actual situation of the public transportation network, the shortest path between nodes is found in a way with the minimum comprehensive impedance;

[0076] Step 1: Based on the comprehensive impedance Z between nodes i and j ij Determine the shortest path a;

[0077] Step 2: Determine the maximum travel time of the shortest path a

[0078] Step 3: Search for other paths to make the comprehensive impedance Z ij Minimum, if there exists a path k such that Less than Then put path k into the set of candidate paths;

[0079] Step 4: Traverse the set of alternative paths and determine the constraints for selecting alternative paths;

[0080] Step 5: Calculate the probability that the alternative paths meet the constraints, sort the alternative paths according to the comprehensive impedance, and output the shortest path set and selection probability;

[0081] Assuming there are two routes to choose from, the probability density distribution function of the total waiting time z1 of route 1 is The probability density distribution function of the total waiting time z2 of path 2 is: Define Z as:

[0082]

[0083] Since Z1 and Z2 are independent of each other, the probability density of (Z1, Z2) is:

[0084]

[0085] Then the probability of Z = 1 is:

[0086]

[0087] Therefore, the probability of choosing path 1 is P{Z=1}, and the probability of choosing path 2 is 1-P{Z=1};

[0088] When there are more than two paths to choose from, the calculation of the probability of selecting each path becomes complicated. This paper uses a simulation method to simulate the calculation of the path selection probability. According to the probability density function of the total waiting time of each path derived in the previous article, the possible waiting time of each path is simulated, and the path is selected according to the simulation time. Finally, the selection probability of different paths is counted.

[0089] The public transportation passenger flow, public transportation passenger capacity and passenger travel impedance are used as weights to assign weights to the network edges, and the shortest path set between nodes is found based on the passenger travel impedance, and finally the global efficiency of the network is improved.

[0090] Assume that there are n paths between nodes i and j, and the probability of selecting each path is P1, P2, ..., P n , then the calculation formula of inter-node efficiency is:

[0091]

[0092] Where: L ij ——The efficiency of nodes i and j;

[0093] P i ——The probability of selecting the i-th path;

[0094] m i ——The number of edges connected to the i-th path;

[0095] W j ——The weight of the jth edge in the i-th path;

[0096] The calculation formula for improving the global efficiency of the network is:

[0097]

[0098] Set constraints in the following aspects:

[0099] (1) Line length

[0100] In bus network planning, the length of bus routes should not be too long or too short. The length of bus trunk lines L g Less than 20km, the length of the bus branch line is L z If the length is less than 10km, the bus route length should be greater than 3km;

[0101] 3km≤L g ≤20km

[0102] 3km≤L z ≤10km

[0103] (2) Line nonlinearity coefficient

[0104] If the non-linear coefficient of conventional bus lines is too high, it will lead to increased operating costs and reduced operating efficiency. Therefore, the non-linear coefficient N l Not greater than 1.4;

[0105]

[0106] Where: d is the shortest distance between the first and last stops of the bus line, unit: m;

[0107] L——actual length of the bus line, unit: m;

[0108] (4) Site spacing

[0109] The distance between public transportation stations in the urban area is 500m, and the distance between adjacent stations i and j is l ij The value range is:

[0110] 300m≤l ij ≤800m

[0111] (4) Road network

[0112] During the optimization process, the route adjustment should adapt to the existing road network, and whether the optimized route can run on the actual road network should be considered during the adjustment process;

[0113]

[0114] Of which: NL line ——Optimized bus route collection;

[0115] NL app ——The collection of roads where buses are allowed to pass;

[0116] (5) Optimized number of lines

[0117] When optimizing lines, there should be an upper limit on the number of lines to be optimized;

[0118]

[0119] Among them: RG line ——Plan to optimize the bus route collection.

[0120] As a preferred solution of the urban public transportation network optimization research method based on complex network theory described in the present invention, the established bus composite network optimization model takes the improved network global efficiency as the optimization target, takes the line length, line non-linear coefficient, station spacing, line passenger capacity and road network status as constraints, and establishes the bus composite network optimization model as follows:

[0121]

[0122] Constraints:

[0123] 3km≤L g ≤20km

[0124] 3km≤L z ≤10km

[0125]

[0126] 300m≤l ij ≤800m

[0127]

[0128] The optimization model is solved using the ant colony algorithm. In the solution process, the initial pheromone is defined as:

[0129]

[0130] Where: z ij ——travel impedance from node i to node j;

[0131] st ij ——Total travel demand of Lianbian ij public transportation;

[0132] The formula for pheromone update is:

[0133]

[0134] Where: E k (G) — the global efficiency of the network composed of paths selected by the kth group of ants in the t+1th iteration;

[0135] To avoid falling into the local optimum, pheromone has a lower limit τ min,According to the basic principle of ant colony algorithm, the steps for solving the bus network optimization model are as follows:

[0136] Step 1: Divide the selected area into multiple traffic zones, obtain urban public transportation data, road network data, and passenger travel demand between zones;

[0137] Step 2: Use the Space L modeling method to establish a road network and urban public transportation network model;

[0138] Step 3: Place the regular bus routes in the set of routes to be optimized;

[0139] Step 4: Determine the optimization model and constraints;

[0140] Step 5: Determine the starting and ending points and stations of the bus line to be optimized. The starting and ending points are selected as the current starting and ending points by default;

[0141] Step 6: Initialize the network and various parameters, and place m ants at the starting and ending points respectively;

[0142] Step 7: Determine the public transport demand of passengers on each section of the road network, and add the product of the inverse of travel impedance and passenger demand as the initial pheromone to the section;

[0143] Step 8: Calculate the transfer probability of each node and determine the ant's moving direction based on the transfer probability;

[0144] Step 9: After a group of ants completes the path search, they calculate whether the network meets the constraints. If so, they calculate the objective function based on the path given by the ants. If not, the next group of ants will search;

[0145] Step 10: Update the pheromone of each road section and obtain the optimal solution of the objective function after iteration.

[0146] Compared with the prior art, the beneficial effects of the present invention are as follows: the optimization method proposed in this article not only takes into account traditional indicators such as passenger flow demand, line length, non-linear coefficient, etc., but also takes into account the efficiency of the overall operation of the network, reduces the average travel impedance of passengers, alleviates the imbalance between supply and demand, and can improve the efficiency of urban public transportation, and ultimately alleviate the problems of unreasonable layout of urban bus lines and low operating efficiency of the bus system. BRIEF DESCRIPTION OF THE DRAWINGS

[0147] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below in combination with the accompanying drawings and detailed embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative labor. Among them:

[0148] Figure 1 It is a schematic diagram of the structure of the steps of the present invention;

[0149] Figure 2 It is a schematic diagram of the probability density distribution function of the present invention;

[0150] Figure 3 This is a schematic diagram of the value range of the present invention;

[0151] Figure 4 It is a schematic diagram of the probability density distribution function of the present invention;

[0152] Figure 5 This is a schematic diagram of path selection of the present invention;

[0153] Figure 6 This is a schematic diagram of the current bus route of the present invention;

[0154] Figure 7 This is a schematic diagram of the current public transportation network of the present invention;

[0155] Figure 8 This is a schematic diagram of the bus route after optimization according to the present invention. DETAILED DESCRIPTION

[0156] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0157] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0158] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0159] Example 1

[0160] This paper selects the area surrounded by five roads, namely Yan'an Street, Ziyou Road, Linhe Street, Weixing Road and Qianjin Street in Nanguan District, Changchun City, as an example to verify the feasibility of the optimization model and solution algorithm in this paper. The area is divided into 19 traffic zones, with 3 rail transit lines, 19 conventional bus lines, and 128 bus stops. The direction of existing conventional bus lines is shown in the table and figure, and the passenger flow distribution OD table between each traffic zone is shown in the table.

[0161] Table 1 OD matrix

[0162]

[0163] Table 2 Current bus route trends

[0164]

[0165] The road network and bus line network are processed to obtain the road network and public transportation network, and the road network, station distribution and public transportation network in the region are analyzed. Figure 5 , 6 As shown in Table 2, the nodes in the road network are intersections, and the edges are actual roads. The road network includes 77 nodes and 112 edges. The nodes in the bus network are bus stops, and the edges are bus routes and transfer routes. The bus network includes 128 nodes and 160 edges. The existing bus network paths are shown in Table 2. 。

[0166] To facilitate calculation, the following assumptions are made in the application: 1. The stop time at each bus stop is the same; 2. The departure intervals of all bus routes are the same; 3. The waiting time of passengers on different routes is calculated as the expected value; 4. Routes with more than two transfers are not considered; 5. The upstream and downstream passenger flows are merged and the constructed network is an undirected network.

[0167] The starting and ending points are determined by referring to the starting and ending points of existing bus lines, and the optimization model is solved using Python programming. The parameter settings are shown in Tables 3 and 4.

[0168] Table 3 Ant colony algorithm parameter settings

[0169]

[0170] Table 4 Constant settings

[0171]

[0172] The optimal bus route network generated after iteration is shown in Table 5 and Figure 7 , some network evaluation indicators are selected to compare with the original bus network. The specific indicator calculation results are shown in Table 6. The global efficiency of the optimized network is improved compared with the original network, and the passenger travel impedance is reduced. Before the optimization, there are 23 edge saturations greater than 1 in the network, with a maximum value of 1.99 and a minimum value of 0.06. After the optimization, there are 8 edge saturations greater than 1 in the network, with a maximum value of 1.92 and a minimum value of 0.15 。

[0173] Table 5 Bus route direction after optimization

[0174]

[0175]

[0176] Table 6 Comparison of indicators before and after optimization

[0177]

[0178]

[0179] Although the present invention has been described above with reference to the embodiments, various modifications may be made thereto and parts thereof may be replaced by equivalents without departing from the scope of the present invention. In particular, as long as there is no structural conflict, the various features in the embodiments disclosed in the present invention may be used in combination with each other in any manner, and the fact that these combinations are not exhaustively described in this specification is only for the sake of omitting space and saving resources. Therefore, the present invention is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A research method for optimizing urban public transportation network based on complex network theory, characterized by: The steps include: Step 1: First calculate the passenger travel cost and add it to the network as travel impedance; Step 2: Then, the probability of passengers choosing a travel path is calculated based on the travel impedance to obtain the passenger flow demand of different sections. The travel impedance, passenger flow demand and the passenger capacity of public transportation are added to the network as weights, and the calculation method of the global efficiency of the network is improved based on the weights. Step 3: Finally, a public transportation network optimization model is established with the global network efficiency as the objective function, and the improved ant colony algorithm is used for solving it.

2. The urban public transportation network optimization research method based on complex network theory according to claim 1 is characterized by: The step 1 uses the generalized cost to comprehensively consider the impedance of various factors of public transportation from the origin to the destination. The generalized travel cost can be expressed as: Comprehensive travel cost = waiting time + riding time + transfer time Passenger waiting time at the station x a is an uncertain value. This time is mainly related to the number of passenger transfers and the probability distribution of the vehicle headway time at the station. When the passenger chooses a route that does not require transfers, if the arrival of vehicles on line a follows a uniform distribution, the maximum waiting time is the headway time h of vehicles on line a. a , the minimum is 0, and the probability density distribution function of waiting time is: Waiting time x a The distribution function of is: When the number of passenger transfers is 1, assume that the passenger takes line a and then transfers to line b. The waiting time for line a and line b is x respectively. a and x b , the headway times are h a and h b ,h b >h a , let the total waiting time be z, then z = x a +x b , assuming that both routes a and b have uniform arrival distribution, the waiting time x a and x b The probability density functions can be expressed as: According to the convolution formula, the probability density function of the total waiting time z is: The probability density function is different for different values ​​of z. a Should satisfy: 0≤x a ≤h a ,zh b ≤x a ≤z, on the xOz plane, according to the shaded part f z (z) can be divided into three parts according to the value of z: Find the integral f z (z) is calculated as: When the number of passenger transfers is 2, the probability density functions of the waiting time for the first two lines can be calculated first, and then the probability density function of the total waiting time can be calculated based on the convolution formula.

3. The urban public transportation network optimization research method based on complex network theory according to claim 2 is characterized by: The passenger's travel time in step 2 is mainly the vehicle travel time. When the public transportation line is rail transportation, the train is separated from other social vehicles and does not affect each other. The road environment does not affect the vehicle operation. At this time, the vehicle's travel speed is equal to the designed travel speed v s , the intersection delay is 0; when regular buses are driving, they mix with other vehicles, and their driving speed will be affected by the road environment. Assuming that α is the congestion coefficient of the road section, it is 1 when the road is unobstructed, and the intersection delay is the same as that of other vehicles. The driving speed of regular buses can be expressed as α·v s ; For rail transit, the train travel time between adjacent nodes is: Where: d od ——The length of the road section from node o to node d, unit: km; v s ——Speed ​​of public transport vehicles, unit: km / h; T——Rail transit vehicle stop time, unit: h; ——The travel time of the vehicle on line l from node o to node d, unit: h; For conventional public transportation, the vehicle travel time between adjacent nodes is: Where: α od ——The congestion coefficient of the road section from node o to node d; ——The vehicle stop time of node o and line l, unit: h; ——The travel time of the vehicle on line l from node o to node d, unit: h; The impedance of the edge between adjacent nodes is obtained by adding the vehicle travel time between nodes, node delay and intersection delay: Where: Z o ——The impedance of the edge connecting node o and node d; β——category parameter, if the edge belongs to rail transit, it is 1, otherwise it is 0; λ——category parameter, which is 1 if the edge belongs to regular public transportation, and 0 otherwise; m——the number of intersections that the edge connecting node o and node d passes through; Transfer time can be divided into transfer time at the same station and transfer time at different stations. Transfer time at the same station is the waiting time for the transfer line. Transfer time at different stations includes walking time between stations in addition to waiting time for the transfer line. The impedance of the transfer connection at the same station is: Where: μ1 is the transfer penalty coefficient, which is 0 if there is no transfer at the same station; ——Internal impedance of transfer connection at the same station; The impedance of the inter-station transfer connection is: Where: μ2 is the penalty coefficient for inter-station transfers, which is 0 if there is no inter-station transfer; v – walking speed; ——Inter-station transfer connection impedance; Finally, the travel impedance from node o to node d can be expressed as:

4. The urban public transportation network optimization research method based on complex network theory according to claim 1 is characterized by: Since there are multiple lines passing between the stop sites in the process of building the composite network model, it is only considered that there is one edge between the nodes. In order to reflect the difference in edges, the composite network needs to be weighted. There are three types of edges in the public transportation network, the edges between stations in the conventional bus network, the edges between stations in the rail transit network, and the artificially added transfer edges. The edge weights of the bus composite network are defined as follows: (1) Rail transit connection The weight of the rail transit edge is defined as the ratio of the inter-node impedance to the rail transit passenger saturation. The weight increases with the increase of the inter-node impedance and decreases with the increase of the saturation. The weight of the edge between rail transit stations i and j can be expressed as: Where: n is the number of rail transit lines passing through stations i and j; ——The passenger capacity of train a on rail transit line, unit: person / day; ——The passenger capacity of trains between stations i and j on rail transit line a, unit: person / day; (2) Conventional bus connections The weight of the conventional bus edge is defined as the ratio of the inter-node impedance to the conventional bus passenger saturation. The weight increases with the increase of the inter-node impedance and decreases with the increase of the saturation. The weight of the edge between conventional bus stops i and j can be expressed as: Where: n is the number of regular bus routes passing through stations i and j; ——The passenger capacity of vehicles on regular bus route a, unit: person / day; ——The passenger capacity of vehicles on regular bus route a between stations i and j, unit: person / day; (3) Transfer to the side The default saturation of the transfer edge is 1, so the weights of the same-station transfer edge and the different-station transfer edge can be expressed as: The final edge weight is defined as:

5. The urban public transportation network optimization research method based on complex network theory according to claim 1 is characterized by: To calculate network efficiency, we must first calculate the shortest path between network nodes. The traditional shortest path search algorithm between nodes adds 1 to the distance of each node passed, then compares all distances and selects the one with the smallest value as the shortest path. Considering the actual situation of the public transportation network, the shortest path between nodes is found by minimizing the comprehensive impedance. Step 1: Based on the comprehensive impedance Z between nodes i and j ij Determine the shortest path a; Step 2: Determine the maximum travel time of the shortest path a Step 3: Search for other paths to make the comprehensive impedance Z ij Minimum, if there exists a path k such that Less than Then put path k into the set of candidate paths; Step 4: Traverse the set of alternative paths and determine the constraints for selecting alternative paths; Step 5: Calculate the probability that the alternative paths meet the constraints, sort the alternative paths according to the comprehensive impedance, and output the shortest path set and selection probability; Assuming there are two routes to choose from, the probability density distribution function of the total waiting time z1 of route 1 is The probability density distribution function of the total waiting time z2 of path 2 is: Define Z as: Since Z1 and Z2 are independent of each other, the probability density of (Z1, Z2) is: Then the probability of Z = 1 is: Therefore, the probability of choosing path 1 is P{Z=1}, and the probability of choosing path 2 is 1-P{Z=1}; When there are more than two paths to choose from, the calculation of the probability of selecting each path becomes complicated. The simulation method is selected to simulate the calculation of the path selection probability. The possible waiting time of each path is simulated according to the probability density function of the total waiting time of each path derived in the previous article. The path is selected according to the simulation time, and finally the selection probability of different paths is counted. The public transportation passenger flow, public transportation passenger capacity and passenger travel impedance are used as weights to assign weights to the network edges, and the shortest path set between nodes is found based on the passenger travel impedance, and finally the global efficiency of the network is improved. Assume that there are n paths between nodes i and j, and the probability of selecting each path is P1, P2, ..., P n , then the calculation formula of inter-node efficiency is: Where: L ij ——The efficiency of nodes i and j; P i ——The probability of selecting the i-th path; m i ——The number of edges connected to the i-th path; W j ——The weight of the jth edge in the i-th path; The calculation formula for improving the global efficiency of the network is: Set constraints in the following aspects: (1) Line length In bus network planning, the length of bus routes should not be too long or too short. The length of bus trunk lines L g Less than 20km, the length of the bus branch line is L z If the length is less than 10km, the bus route length should be greater than 3km; 3km≤L g ≤20km 3km≤L z ≤10km (2) Line nonlinearity coefficient If the nonlinear coefficient of conventional bus lines is too high, it will lead to increased operating costs and reduced operating efficiency. Therefore, the nonlinear coefficient N l Not greater than 1.4; Where: d is the shortest distance between the first and last stops of the bus line, unit: m; L——actual length of the bus line, unit: m; (4) Site spacing The distance between public transportation stations in the urban area is 500m, and the distance between adjacent stations i and j is l ij The value range is: 300m≤l ij ≤800m (4) Road network During the optimization process, the route adjustment should adapt to the existing road network, and whether the optimized route can run on the actual road network should be considered during the adjustment process; Of which: NL line ——Optimized bus route collection; NL app ——The collection of roads where buses are allowed to pass; (5) Optimized number of lines When optimizing lines, there should be an upper limit on the number of lines to be optimized; Among them: RG line ——Plan to optimize the bus route collection.

6. The urban public transportation network optimization research method based on complex network theory according to claim 5 is characterized by: The established bus composite network optimization model takes the improved network global efficiency as the optimization goal, and takes the line length, line non-linear coefficient, station spacing, line passenger capacity and road network status as constraints. The bus composite network optimization model is established as follows: Constraints: 3km≤L g ≤20km 3km≤L z ≤10km 300m≤l ij ≤800m The optimization model is solved using the ant colony algorithm. In the solution process, the initial pheromone is defined as: Where: z ij ——travel impedance from node i to node j; st ij ——Total travel demand of Lianbian ij public transportation; The formula for pheromone update is: Where: E k (G) — the global efficiency of the network composed of paths selected by the kth group of ants in the t+1th iteration; To avoid falling into the local optimum, pheromone has a lower limit τ min ,According to the basic principle of ant colony algorithm, the steps for solving the bus network optimization model are as follows: Step 1: Divide the selected area into multiple traffic zones, obtain urban public transportation data, road network data, and passenger travel demand between zones; Step 2: Use the Space L modeling method to establish a road network and urban public transportation network model; Step 3: Place the regular bus routes in the set of routes to be optimized; Step 4: Determine the optimization model and constraints; Step 5: Determine the starting and ending points and stations of the bus line to be optimized. The starting and ending points are selected as the current starting and ending points by default; Step 6: Initialize the network and various parameters, and place m ants at the starting and ending points respectively; Step 7: Determine the public transport demand of passengers on each section of the road network, and add the product of the inverse of travel impedance and passenger demand as the initial pheromone to the section; Step 8: Calculate the transfer probability of each node and determine the ant's moving direction based on the transfer probability; Step 9: After a group of ants completes the path search, they calculate whether the network meets the constraints. If so, they calculate the objective function based on the path given by the ants. If not, the next group of ants will search; Step 10: Update the pheromones of each section of the road, and obtain the optimal solution of the objective function after iteration.

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