A connected vehicle path control method considering travel subsidies

Abstract

The application discloses a kind of considering travel subsidy's net-connected car path control method, comprising the following steps: step 1, abstract road network into directed graph;Step 2, the path selection behavior of user in road network is characterized using hybrid traffic network equilibrium model;Step 3, the path control problem of net-connected car considering travel subsidy is characterized using bi-level programming model;Step 4, the improved Frank-Wolfe algorithm based on sensitivity analysis is used to solve bi-level programming model, and the optimal path control scheme is obtained.The application realizes the improvement of road network traffic efficiency through net-connected car path control, improves the feasibility of path control scheme by providing travel subsidy, and provides reference basis for urban road network traffic congestion analysis and management under intelligent network connection environment.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent transportation, in particular to a path control method for connected vehicles considering travel subsidies. BACKGROUND

[0002] The intelligent connected vehicle (hereinafter referred to as connected vehicle) refers to a new generation of vehicle equipped with advanced vehicle-mounted sensors, controllers, actuators and other devices, which not only has the networking function of real-time information interaction with the road end and cloud end, but also has the automatic driving functions of complex environment perception, intelligent decision-making and cooperative control. The high controllability of the driving behavior of the connected vehicle provides a new idea for traffic congestion management: by planning and controlling the travel paths of part of the connected vehicles to indirectly influence the path selection of other vehicles, the road network flow distribution is adjusted to the expected form, so as to realize the optimization of the road network performance. The above problem is called the connected vehicle path control problem, and the control strategy including the number of connected vehicles to be controlled and the travel path of the controlled connected vehicles is determined by the management department according to its management target.

[0003] The path control scheme requires part of the controlled vehicles to select the system optimal path with longer travel time but less flow to complete the trip, which increases the travel cost of part of the users at the expense of the balanced distribution of the road network flow. This feature may become an obstacle to its implementation in reality. Therefore, how to overcome the above implementation obstacles of the path control and improve the feasibility of the path control scheme is a problem urgently to be solved in the field of intelligent transportation. SUMMARY

[0004] The present application aims to provide a path control method for connected vehicles considering travel subsidies, which indirectly influences the path selection of other users by controlling the path selection of part of the connected vehicle users, realizes the improvement of the road network traffic efficiency, and provides travel subsidies for the users who suffer from the loss of travel utility due to the path control scheme.

[0005] The technical scheme of the present application is a path control method for connected vehicles considering travel subsidies, comprising the following steps:

[0006] Step 1: abstract the road network as a directed graph;

[0007] Step 2: use a mixed traffic network equilibrium model to represent the path selection behavior of the users in the road network;

[0008] Step 3: use a bi-level programming model to represent the path control problem for connected vehicles considering travel subsidies;

[0009] Step 4: use an improved Frank-Wolfe algorithm based on sensitivity analysis to solve the bi-level programming model to obtain the optimal path control scheme.

[0010] Further, step 1 specifically comprises:

[0011] The road network is abstracted as a strongly connected directed graph G = (N, A), where N represents the node set and A represents the link set. According to the path selection behavior, there are two types of users in the road network, namely, equilibrium users who select the shortest path and system optimal users who select the system optimal path. The two types of users are represented by indices 1 and 2, respectively, and the user category set is represented by M = {1, 2}.

[0012] Further, step 2 specifically includes the following process:

[0013] According to the link-path flow relationship and the travel demand-path flow relationship, the flow feasible set of the user category m is represented as:

[0014]

[0015] wherein, represents the travel demand vector of the user category m, represents the total demand vector, and both satisfy W represents the OD pair set of the road network, and the path set r ∈ R of any OD pair w ∈ W w , the set of all paths is R, is the link flow vector of the user category m, is the path flow vector, and the total link flow vector is the total path flow vector is represents the link-path relationship matrix, and the element δ a,r = 1 indicates that the link a belongs to the path r, and δ a,r = 0 indicates that the link a does not belong to the path r; represents the OD-path relationship matrix, and the element λ w,r = 1 indicates that the path r belongs to the OD pair w, and λ w,r = 0 indicates that the path r does not belong to the OD pair w;

[0016] Let represent the link travel time, and the link travel time expression is defined as:

[0017]

[0018] wherein, and C a represent the free flow travel time and the road capacity of the link a, respectively, and α and β are function parameters;

[0019] Let represent the path travel time vector, and according to the link-path travel time relationship, it satisfies c = Δ T t;

[0020] Define the marginal travel time expression for a road segment as follows:

[0021]

[0022] The marginal travel time vector of the road segment is in the form of

[0023] The path selection behavior of two types of users, UE and SO, in the road network is characterized by a hybrid traffic network equilibrium model, which can be expressed as the following variational inequality problem:

[0024] Solve Make it meet the following conditions:

[0025]

[0026] The feasible set Ω(d1,d2) in the formula is expressed as follows:

[0027] Ω(d1,d2)=Ω1×Ω2={(x1,x2)|x1∈Ω1(d1),x2∈Ω2(d2)}. (5)

[0028] Furthermore, step 3 specifically includes:

[0029] The connected vehicle routing control problem considering travel subsidies is represented as a bi-level programming model. In the upper-level problem, the control center fully considers the traveler's response behavior to the route planning scheme. In the lower-level problem, a hybrid traffic network equilibrium model is used to characterize the route selection behavior of two types of users, UE and SO, in the road network. The bi-level programming model expression is:

[0030]

[0031]

[0032]

[0033]

[0034] In the formula, This represents the travel demand vector that transitions from a UE user to an SO user after path control is implemented. The travel demand of the remaining UE users is represented as follows: The travel needs of the two types of users under the route control scheme are represented as follows: In the objective function, z1 and z2 represent the total travel time and total subsidy amount of the system, respectively, and their expressions are as follows:

[0035]

[0036]

[0037] In the formula, denotes the minimum travel cost before implementing the route planning scheme, i.e. the minimum travel cost between OD pair w when all users are UE users; denotes the set of paths whose travel cost increases between OD pair w under the planning scheme, i.e. Equations (7) and (8) respectively denote the travel demand vector the upper and lower bounds of constraints, denotes the market penetration rate of connected vehicles.

[0038] Further, the connected vehicle route control method further comprises:

[0039] The values of z1, z2 in the objective function at iteration number n are approximated by:

[0040]

[0041] In the equation, denotes the objective function z k Regarding the gradient of , since the link flow x n is known at iteration number n, z k (x n ) is constant and can be omitted in the objective function, under the approximation of equation (12), the objective function equation (6) at iteration number n is rewritten as:

[0042]

[0043] The above constraints are the same as the constraints of equations (6)-(9) in the bi-level programming model, and equation (13) is the sub-problem to be solved at iteration number n;

[0044] Let denote the path selection matrix of user category m at iteration number n, the value of the element at position (r, w) of the path selection matrix represents the proportion of user category m travelers who select path r between OD pair w to the travel demand of user category m for that OD pair, satisfying m = V m d m ; the mapping Γ in equation (12) is approximated by:

[0045]

[0046] Further, step 4 specifically comprises the following process:

[0047] Step 40, set the convergence threshold to ε d , initialize the parameters, where iteration number n = 1, ​

[0048] Step 41, according to the current travel demand Solve the variational inequality problem (4) by using diagonalization algorithm to get the link flow

[0049] Step 42, determine the most likely path flow form And the corresponding path selection matrix

[0050] Step 43, calculate the path travel time c n , by comparing And The size of the vector Update set Vector And matrix

[0051] Step 44, calculate the objective function gradient by formula (15), formula (16):

[0052]

[0053]

[0054] In the formula, Respectively represent f, c remove all corresponding path Position element vector, Indicates that Replace the element corresponding to the path Position with Vector, Indicates Remove all corresponding path Position row vector matrix, Indicates Δ n Remove all corresponding path Position column vector matrix;

[0055] Step 45, calculate the gradient vector p n :

[0056]

[0057] Determine the optimal solution of subproblem (13) by the following formula

[0058]

[0059] In the formula, I (·) Is an indicator vector, when the jth condition in the bracket is true, I j = 1; Otherwise I j= 0; calculate UE user trip demand

[0060] Step 46, according to the current trip demand Solve the variational inequality problem (4) with diagonalization algorithm to get the link flow And the total link flow Determine the step size θ that minimizes Z(x θ ) n ∈ [0, 1], where Let

[0061]

[0062]

[0063] Update the trip demand vector according to the following formula:

[0064]

[0065]

[0066] Step 47, if the trip demand conversion is small enough, that is, it satisfies the following formula (23), then terminate the algorithm and return the trip demand under the combined scheme Otherwise, let And return to step 41,

[0067]

[0068] In the formula, ||·||1 represents the l1 norm of the vector;

[0069] Solve the double-layer programming model (6)-(9) according to the above steps to get the optimal path control scheme That is, accept the number of vehicles that need to be path controlled for each OD pair.

[0070] Further, solve the variational inequality problem with diagonalization algorithm, including the following steps:

[0071] Step 410, set the convergence threshold ε of the diagonalization algorithm x , initialize the parameters, where i = 1, Update the link travel time t i and the link marginal travel time mt i according to

[0072] Step 411, according to the path travel time Δ T t i ​Determine the shortest path for each OD pair, and assign all UE users in that OD pair to that path to obtain the all-inclusive and all-out traffic form for each UE user. Calculate the segment traffic of UE users and search direction

[0073] Step 412, based on the path marginal travel time Δ T mt i Determine the path with the shortest marginal travel time for each OD pair, and assign all SO users of that OD pair to that path, thus obtaining the all-or-nothing flow form for the SO users. Calculate the segment traffic of SO users and search direction

[0074] Step 413, Calculate If it satisfies Stop the algorithm and return the optimal solution. Otherwise, proceed to step 414;

[0075] Step 414, Determine Minimum Optimal iteration step size in make Then return to step 411.

[0076] Beneficial effects: Compared with the prior art, the significant advantages of this invention are: This invention improves the efficiency of road network traffic through connected vehicle route control, and enhances the feasibility of route control schemes by providing travel subsidies, thus providing a reference for the analysis and management of urban road network traffic congestion in an intelligent connected environment. Attached Figure Description

[0077] Figure 1 This is a flowchart of the connected vehicle route control method considering travel subsidies in the embodiment;

[0078] Figure 2 This is a road network structure diagram for an example;

[0079] Figure 3 This example illustrates OD (Original Direct Occupation) travel demand.

[0080] Figure 4 This example illustrates the distribution of SO user proportions across different OD pairs. Detailed Implementation

[0081] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments.

[0082] like Figure 1The diagram shows a flowchart of a connected vehicle route control method considering travel subsidies, as described in this embodiment. The purpose of this method is to improve the overall efficiency of the road network through connected vehicle route control, and to enhance the feasibility of the route control scheme by providing travel subsidies, thus providing a reference for traffic congestion analysis and management of urban road networks in an intelligent connected environment. In this embodiment, it is stipulated that: (i) the management department will implement travel route control for any number of connected vehicles at each origin-destination (OD) based on management objectives; (ii) when the implementation of route control leads to an increase in travel costs for some users, the management department will provide these users with travel subsidies, the amount of which is equal to the increased travel costs.

[0083] The aforementioned method for route control of connected vehicles that considers travel subsidies specifically includes the following steps:

[0084] Step 1: Abstract the road network into a directed graph.

[0085] Specifically, step 1 above includes:

[0086] The road network is abstracted as a strongly connected directed graph G = (N, A), where N represents the set of nodes and A represents the set of road segments. Based on path selection behavior, there are two types of users in the road network: users who choose the shortest path (UE users) and users who choose the system's optimal path (SO users). The two types of users are represented by subscripts 1 and 2, respectively, and the user category set is represented by M = {1, 2}.

[0087] Step 2: Use a hybrid traffic network equilibrium model to characterize the path selection behavior of users within the road network.

[0088] Specifically, step 2 above includes the following process:

[0089] Step 21: Based on the relationship between road segment and path traffic flow, and the relationship between travel demand and path traffic flow, represent the feasible traffic set for user category m as follows:

[0090]

[0091] in, } represents the travel demand vector of user category m. } represents the total demand vector, and the two satisfy... W represents the set of road network OD pairs, and the set of paths r ∈ R for any OD pair w ∈ W. w Let R be the set of all paths. Let m be the segment traffic vector for user category m. Here is the path flow vector, and the total flow vector for the road segment is... The total path flow vector is This represents the segment-path relationship matrix, where the element δa,r =1 indicates that segment a belongs to path r, δ a,r =0 indicates that segment a does not belong to path r; This represents the OD-path relationship matrix, where the element λ w,r =1 indicates that path r belongs to OD pair w, λ w,r =0 indicates that path r does not belong to OD pair w;

[0092] Step 22, let The segment travel time is represented by the expression:

[0093]

[0094] In the formula, and C a Let α and β represent the free-flow travel time and road capacity of road segment a, respectively, where α and β are function parameters;

[0095] Step 23, let This represents the path travel time vector, where c = Δ is the path travel time relationship between road segments and paths. T t;

[0096] Step 24, define the expression for the marginal travel time of a road segment as follows:

[0097]

[0098] The marginal travel time vector of the road segment is in the form of

[0099] Step 25: Characterize the path selection behavior of UE and SO users in the road network using a hybrid traffic network equilibrium model, expressed as the following variational inequality problem:

[0100] Solve Make it meet the following conditions:

[0101]

[0102] The feasible set Ω(d1,d2) in the formula is expressed as follows:

[0103] Ω(d1,d2)=Ω1×Ω2={(x1,x2)|x1∈Ω1(d1),x2∈Ω2(d2)}. (5)

[0104] Step 3: Use a bi-level programming model to characterize the connected vehicle path control problem considering travel subsidies.

[0105] Specifically, step 3 above includes:

[0106] The connected vehicle routing control problem considering travel subsidies is represented as a bi-level programming model. In the upper-level problem, the control center fully considers the traveler's response behavior to the route planning scheme. In the lower-level problem, a hybrid traffic network equilibrium model is used to characterize the route selection behavior of two types of users, UE and SO, in the road network. The bi-level programming model expression is:

[0107]

[0108]

[0109]

[0110]

[0111] In the formula, This represents the travel demand vector that transitions from a UE user to an SO user after path control is implemented. The travel demand of the remaining UE users is represented as follows: The travel needs of the two types of users under the route control scheme are represented as follows: In the objective function, z1 and z2 represent the total travel time and total subsidy amount of the system, respectively, and their expressions are as follows:

[0112]

[0113]

[0114] In the formula, This represents the minimum travel cost before implementing the route planning scheme, i.e., the minimum travel cost between OD and w when all users are UE users; This represents the set of paths that increase travel costs between OD and w under the planning scheme, i.e. Equations (7) and (8) represent the travel demand vector, respectively. Upper and lower bound constraints, This indicates the market penetration rate of connected vehicles.

[0115] Specifically, z1 and z2 in the above objective function are... The value at that point is approximated by the following formula:

[0116]

[0117] In the formula, Let z represent the objective function z within iteration number n. k about The gradient is due to the road segment flow x within iteration number n. n Since z is known, therefore k (x nThe constant ) can be omitted in the objective function. Under the approximation of equation (12), the objective function equation (6) within the number of iterations n is rewritten as follows:

[0118]

[0119] The constraints in the above formula are the same as those in formulas (6)-(9) in the bi-level programming model. Formula (13) is the sub-problem that needs to be solved within the number of iterations n.

[0120] make Let f represent the path selection matrix for user category m within iteration n. The element at position (r, w) in this path selection matrix represents the proportion of user category m travelers who choose path r between OD and w, according to the proportion of travel demand for user category m within that OD, satisfying f m =V m d m The mapping Γ in equation (12) is approximated by the following equation:

[0121]

[0122] Step 4: Solve the bi-level programming model using the improved Frank-Wolfe algorithm based on sensitivity analysis to obtain the optimal path control scheme.

[0123] Specifically, step 4 above includes the following process:

[0124] Step 40, set the convergence threshold to ε d Initialize the parameters, where the number of iterations n = 1.

[0125] Step 41, based on current travel needs The variational inequality problem (4) is solved using the diagonalization algorithm to obtain the road segment flow.

[0126] Step 42: Determine the most likely path flow form. and the corresponding path selection matrix

[0127] Step 43, calculate the path travel time c n By comparison and The size relationship determines the vector Update collection vector sum matrix

[0128] Step 44: Calculate the gradient of the objective function using equations (15) and (16):

[0129]

[0130]

[0131] In the formula, These respectively represent removing all corresponding paths from f and c. The vector following the position element, Indicates will Corresponding path Replace the element at the position with The vector after, express Remove all corresponding paths The matrix following the row vectors of the positions. Indicates Δ n Remove all corresponding paths The matrix following the column vectors of the positions;

[0132] Step 45, calculate the gradient vector p using the following formula. n :

[0133]

[0134] The optimal solution to subproblem (13) is determined by the following formula.

[0135]

[0136] In the formula, I () As an indicator vector, I represents the condition when the j-th condition within the parentheses is true. j =1; otherwise I j =0; Calculate UE user travel demand

[0137] Step 46, based on current travel needs The variational inequality problem (4) is solved using the diagonalization algorithm to obtain the segment flow. and total traffic flow of the road section Determine if Z(x) θ The step size θ for finding the minimum value n ∈[0,1], where make

[0138]

[0139]

[0140] Update the travel demand vector according to the following formula:

[0141]

[0142]

[0143] Step 47: If the travel demand conversion amount is small enough, i.e., satisfies the following equation (23), then terminate the algorithm and return the travel demand under the combined scheme. Otherwise, let Then set n = n + 1 and return to step 41.

[0144]

[0145] In the formula, ||·||1 represents the l1 norm of the vector;

[0146] Solve equations (6) to (9) of the bilevel programming model according to the above steps to obtain the optimal path control scheme. That is, the number of vehicles that need to be routed to each OD pair.

[0147] Specifically, solving variational inequality problems using the diagonalization algorithm includes the following steps:

[0148] Step 410: Set the convergence threshold ε for the diagonalization algorithm. x Initialize the parameters, where i = 1. according to Updated travel time for the route t i and the marginal travel time of the road segment mt i ;

[0149] Step 411, based on the route travel time Δ T t i Determine the shortest path for each OD pair, and assign all UE users in that OD pair to that path to obtain the all-inclusive and all-out traffic form for each UE user. Calculate the segment traffic of UE users and search direction

[0150] Step 412, based on the path marginal travel time Δ T mt i Determine the path with the shortest marginal travel time for each OD pair, and assign all SO users of that OD pair to that path, thus obtaining the all-or-nothing flow form for the SO users. Calculate the segment traffic of SO users and search direction

[0151] Step 413, Calculate If it satisfies Stop the algorithm and return the optimal solution. Otherwise, proceed to step 414;

[0152] Step 414, Determine Minimum Optimal iteration step size in make Then return to step 411.

[0153] To further demonstrate the applicability of the method of the present invention, the following embodiments are used for illustration.

[0154] The network structure diagram used in this example is as follows: Figure 2 As shown, the network comprises 24 nodes, 76 road segments, and 528 origin-destination (OD) pairs. Data on road segment attributes and travel demand can be found on the website (…). https: / / github.com / bstabler / TransportationNetworks The spatial distribution of travel demand is shown in the open-source data (e.g., data from ) Figure 3 As shown, each small square represents an OD pair, with darker colors indicating higher travel demand for that OD pair. The BPR function parameters were chosen as α = 0.15 and β = 4, and other model parameters were selected as follows. Algorithm parameter selection ε x =0.1,ε d =1.0.

[0155] Based on the above settings, we solve the problem of combining route control and travel subsidies for connected vehicles and output the optimal solution. Figure 4 The distribution of SO users in each OD pair is shown. Each small square represents an OD pair, and the darker the color, the higher the SO users (i.e., path control rate) of that OD pair.

[0156] pass Figure 4 It can be seen that the proportion of SO users in some OD pairs is significantly higher than that in other OD pairs, indicating that these OD pairs have a higher path control priority. Through comparison... Figure 4 and Figure 3 It can be seen that OD pairs with high travel demand do not necessarily need a higher route control rate.

[0157] Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. Furthermore, those skilled in the art will recognize that, based on the ideas of this invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A method for route control of connected vehicles considering travel subsidies, characterized in that, Includes the following steps: Step 1: Abstract the road network into a directed graph; Step 2: Use a hybrid traffic network equilibrium model to characterize the path selection behavior of users within the road network; Step 3: Use a bi-level programming model to characterize the connected vehicle route control problem considering travel subsidies; Step 4: Solve the bi-level programming model using the improved Frank-Wolfe algorithm based on sensitivity analysis to obtain the optimal path control scheme; Step 1 specifically includes: Abstract the road network as a strongly connected directed graph. ,in Represents a set of nodes. This represents the set of road segments. Based on path selection behavior, there are two types of users in the road network: users who choose the shortest path (equilibrium users) and users who choose the system's optimal path (system optimal users). These two types of users are represented by subscripts 1 and 2, respectively. The set of user categories is denoted by […]. express; Step 2 specifically includes the following processes: Based on the relationship between road segment and path traffic, and the relationship between travel demand and path traffic, the feasible set of traffic for user category m is represented as: ； in, This represents the travel demand vector for user category m. Represents the total demand vector, and both satisfy... , Let represent the set of OD pairs in a road network, where any OD pair Path set The set of all paths is , Let m be the segment traffic vector for user category m. Here is the path flow vector, and the total flow vector for the road segment is... The total path flow vector is ; This represents the segment-path relationship matrix, whose elements... This indicates that road segment a belongs to path r. This indicates that segment a does not belong to path r; This represents the OD-path relationship matrix, whose elements... This indicates that path r belongs to OD pair w. This indicates that path r does not belong to OD pair w; make The segment travel time is represented by the expression: ； In the formula, and These represent the free-flow travel time and road capacity of road segment a, respectively. and For function parameters; make Represents a path travel time vector, which satisfies the relationship between the travel time of road segments and the path. ; Define the marginal travel time expression for a road segment as follows: ； The marginal travel time vector of the road segment is in the form of ; The path selection behavior of two types of users, UE and SO, in the road network is characterized by a hybrid traffic network equilibrium model, which can be expressed as the following variational inequality problem: Solve Make it satisfy the following conditions: ； The feasible set in the formula The expression is: ； Step 3 specifically includes: The connected vehicle routing control problem considering travel subsidies is represented as a bi-level programming model. In the upper-level problem, the control center fully considers the traveler's response behavior to the route planning scheme. In the lower-level problem, a hybrid traffic network equilibrium model is used to characterize the route selection behavior of two types of users, UE and SO, in the road network. The bi-level programming model expression is: ； s.t. ; ； ； In the formula, This represents the travel demand vector that transitions from a UE user to an SO user after path control is implemented. The travel demand of the remaining UE users is represented as follows: The travel needs of the two types of users under the route control scheme are represented as follows: In the objective function , Representing the total travel time and total subsidy amount, respectively, the expressions are as follows: ； ； In the formula, This represents the minimum travel cost before implementing the route planning scheme, i.e., the minimum travel cost between OD and w when all users are UE users; This represents the set of paths that increase travel costs between OD and w under the planning scheme, i.e. Equations (7) and (8) represent the travel demand vectors, respectively. Upper and lower bound constraints, Indicates the market penetration rate of connected vehicles; This method also includes: In the objective function , exist The value at that point is approximated by the following formula: ； In the formula, Describes the objective function within iteration number n. about The gradient is due to the road segment flow rate within iteration number n. Since it is known, therefore Since is a constant, it can be omitted in the objective function. Under the approximation of equation (12), the objective function equation (6) within the number of iterations n is rewritten as follows: ； The constraints in the above equation are the same as those in equations (6) to (9) of the bilevel programming model. Equation (13) is the subproblem that needs to be solved within the number of iterations n. make This represents the path selection matrix for user category m within iteration number n. The element value of the location represents the proportion of user category m travelers who choose path r between OD pairs w, accounting for the travel demand of user category m for that OD pair, satisfying... The mapping in equation (12) Approximated by the following formula: ； Step 4 specifically includes the following processes: Step 40, set the convergence threshold as Initialize the parameters, including the number of iterations. , , , ; Step 41, based on current travel needs The variational inequality problem (4) is solved using the diagonalization algorithm to obtain the traffic flow of the road segment. ; Step 42: Determine the most likely path flow form. and the corresponding path selection matrix ; Step 43, calculate the route travel time By comparison and The size relationship determines the vector Update the set ,vector sum matrix ; Step 44, calculate the gradient of the objective function using equations (15) and (16): ； ； In the formula, , They represent , Remove all corresponding paths The vector following the position element, Indicates will Corresponding path Replace the element at the position with The vector after, express Remove all corresponding paths The matrix following the row vectors of the positions. express Remove all corresponding paths The matrix following the column vectors of the positions; Step 45: Calculate the gradient vector using the following formula. : ；； The optimal solution to subproblem (13) is determined by the following formula. : ； In the formula, As an indicator vector, when the j-th condition in parentheses is true, ;otherwise ; Calculate UE user travel demand ; Step 46, based on current travel needs Solving variational inequality problems using the diagonalization algorithm To obtain the traffic flow of the road segment and total traffic flow of the road section ; Determine Step size for finding the minimum value ,in ,make ； ； Update the travel demand vector according to the following formula: ； ； Step 47: If the travel demand conversion amount is small enough, i.e., satisfies the following formula (23), then terminate the algorithm and return the travel demand under the combined scheme. Otherwise, let , And return to step 41, ； In the formula, Representing vectors Norm; Solve equations (6)-(9) of the bilevel programming model according to the above steps to obtain the optimal path control scheme. That is, the number of vehicles that need to be routed to each OD pair; Solving variational inequality problems using the diagonalization algorithm includes the following steps: Step 410: Set the convergence threshold for the diagonalization algorithm. Initialize the parameters, among which , , ,according to Updated travel time for the route and the marginal travel time of the road segment ; Step 411, based on route travel time Determine the shortest path for each OD pair, and assign all UE users in that OD pair to that path to obtain the all-inclusive and all-out traffic form for each UE user. Calculate the segment traffic of UE users and search direction ; Step 412, based on path marginal travel time Determine the path with the shortest marginal travel time for each OD pair, and assign all SO users of that OD pair to that path, thus obtaining the all-or-nothing flow form for the SO users. Calculate the segment traffic of SO users and search direction ; Step 413, Calculate , If it satisfies Stop the algorithm and return the optimal solution. , Otherwise, proceed to step 414; Step 414, Determine Minimum Optimal iteration step size ,in ,make , Then return to step 411.

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