Traffic network hydrogen pricing model construction method based on variational inequality

Abstract

The invention relates to a traffic network hydrogen pricing model construction method based on variational inequality, and belongs to the field of traffic network hydrogen pricing model construction. According to the method, road network user balance containing the charging price is expressed by using a variational inequality, and a unified optimization model of the price regulation and control traffic jam degree is provided. And finally, designing an algorithm to solve the double-layer optimization problem, and converting the variational inequality constraint into an equality constraint through a gap function (GF, gap function). And then, the problem is solved by designing a sequential quadratic programming (SQP) iterative algorithm, and then, the problem is solved by designing a sequential quadratic programming (SQP) iterative algorithm.

Description

Technical Field

[0001] The present invention belongs to the field of construction of hydrogen pricing model for transportation network, and specifically relates to a method for construction of hydrogen pricing model for transportation network based on variational inequality. Background Art

[0002] Faced with the severe social and environmental challenges brought about by large-scale transportation and rapid urbanization, the decarbonization of the transportation industry has become one of the key issues that the automotive industry needs to solve urgently. In order to achieve sustainable travel and zero-emission goals, the industry is urgently seeking breakthroughs. In this context, electric vehicles (EVs), as a green alternative to traditional fuel vehicles, have gained significant market acceptance in recent years. However, even though EVs have achieved significant results in reducing carbon emissions, the growth of personal long-distance travel needs and industrial heavy-duty applications still prompts the industry to explore new ways to extend battery life and rapid replenishment.

[0003] The overall progress of hydrogen energy technology, especially its innovation in production, distribution, storage and application, has injected new vitality into the development of hydrogen-powered vehicles. Among them, hybrid hydrogen electric vehicles (HEV) have become a hot spot for automotive technology innovation due to their unique advantages. The system uses hydrogen fuel cells to efficiently convert hydrogen energy into electrical energy, enhancing the overall performance of the vehicle.

[0004] HEVs have shown broad application prospects due to their high energy density and zero emission characteristics. Compared with pure electric vehicles, they have more advantages in range and refueling speed. However, as the number of vehicles continues to grow, traffic congestion is becoming more and more serious. How to redistribute traffic through hydrogen refueling prices to achieve a lower level of social congestion is a very worthy research issue.

[0005] Most current studies do not take into account the cost of traffic congestion. But in fact, with the development of the economy, the number of vehicles has been growing, which has brought more difficulties to the transportation department to alleviate traffic congestion. As a basic social operation service, hydrogen refueling stations should appropriately bear part of the responsibility for alleviating traffic congestion. Decision makers can alleviate traffic congestion by adjusting the price of hydrogen refueling. Summary of the invention

[0006] The purpose of the present invention is to provide a method for constructing a hydrogen pricing model for a transportation network based on variational inequalities. By using variational inequalities, the user equilibrium of a road network containing charging prices is expressed, and a unified optimization model for price-controlled traffic congestion is proposed. Finally, an algorithm is designed to solve the two-layer optimization problem, and the variational inequality constraint is converted into an equality constraint through a gap function (GF). Then, the problem is solved by designing a sequential quadratic programming (SQP) iterative algorithm.

[0007] To achieve the above object, the technical solution of the present invention is: a method for constructing a transportation network hydrogen pricing model based on variational inequality, comprising:

[0008] Variational inequalities are used to express the user equilibrium of the road network with charging prices, and a general optimization model with variational inequalities for charging price-controlled traffic flow distribution is established.

[0009] In one embodiment of the present invention, it also includes:

[0010] A GF-SQP solving algorithm is designed to solve the general optimization model containing variational inequalities for charging price regulation of traffic flow distribution.

[0011] In one embodiment of the present invention, the GF-SQP solving algorithm converts the variational inequality constraint into an equality constraint through the gap function GF, and then solves the general optimization model containing variational inequalities for charging price regulation of traffic flow distribution by designing a sequential quadratic programming SQP iterative algorithm.

[0012] In one embodiment of the present invention, a specific method of establishing a general optimization model containing variational inequalities for regulating traffic flow distribution using charging prices is as follows:

[0013] The real traffic network is simplified into a directed graph in is a node set, is a set of directed arcs; directed arcs are the basic elements of a directed graph. A directed edge connecting a pair of nodes is a directed graph. Virtual arcs are introduced to better describe the charging process. 1,v represents the virtual arc introduced, indicating that there is a hydrogen refueling station on the road connecting nodes A and B, and stipulates that the path of the hybrid hydrogen electric vehicle HEV must contain at least one virtual arc. Arc1 represents the real arc, indicating the road connecting nodes A and B in the traffic network. Or O→D is the path of other vehicles that do not need to be charged, is the path of the HEV that needs to be charged, O and D are nodes;

[0014] Feasible domain of transportation network D T As shown below:

[0015]

[0016] in, is the set of real arcs without corresponding virtual arcs, A r is the set of real arcs with corresponding virtual arcs, A v is the set of virtual arcs, S is the set of OD pairs, is the traffic flow at time t corresponding to arc a, is the traffic flow at time t corresponding to path p, δ ap is the incidence matrix of arc a and path p, and are the set of paths with OD ij for HEV and conventional vehicles respectively, and are the demand quantities of conventional vehicles and HEVs with OD ij at time t, respectively;

[0017] The time travel cost of each arc is described by the BPR function, and the charging cost is the product of the charging unit price and the charging size of hydrogen station a:

[0018]

[0019] in, or are the traffic flows of the virtual arc / real arc corresponding to the real arc / virtual arc, is the free travel time of arc a, Ca a is the road capacity corresponding to arc a, α time and α a,charge are the unit driving time cost and the unit charging price of hydrogen filling station a respectively, and E is the charging energy size;

[0020] The travel cost of each path is obtained from the time travel cost of each arc, as shown in the following formula:

[0021]

[0022] Assuming that all HEV and conventional vehicle users in the traffic network are rational, they will minimize the travel cost of their own paths, and through navigation software or other means, they can accurately perceive the time travel cost and charging cost of each road in the corresponding traffic network. Then the corresponding traffic network can achieve mixed user equilibrium, that is, each user cannot reduce his or her own travel cost by changing his or her path choice. The mathematical expression of the user equilibrium state is as follows:

[0023]

[0024] in

[0025] The mathematical programming model of user equilibrium equivalence is shown in the following formula:

[0026]

[0027] The global optimal mathematical programming model and its corresponding formula are shown as follows:

[0028]

[0029] In fact, regulating the distribution of traffic flow by charging additional fees on roads can be regarded as a two-level optimization problem, as shown in the following formula:

[0030]

[0031] The upper-level decision maker is the government, whose goal is to minimize congestion. The decision variable is the additional charge λ for each road. a The decision makers at the lower level are users in the road network, whose goal is to minimize their own travel costs. The decision variables are the vector x composed of the traffic volume of each road.

[0032] The above two-level optimization problem can be viewed as a unified model for regulating traffic flow allocation using price. a Without any constraints, it means that extra charges can be imposed on each road, and the two-level optimization problem degenerates into the optimal model of the system. a If both are constrained to 0, the two-layer optimization problem degenerates into a user equilibrium model;

[0033] Therefore, the two-level optimization problem is added with respect to λ a The constraints of are used to simulate charging only on certain roads, and to study how to minimize traffic congestion under limited conditions. At this time, the two-level optimization problem is in an intermediate state between user equilibrium and system optimality.

[0034] In the hybrid user equilibrium model MUE, there is a factor that affects the cost of transportation, namely, the charging price; therefore, α a,charge E charge cost as lambda a The additional toll costs are used to regulate the distribution of traffic flow within the transportation network, and the additional charges for other sections are all 0.

[0035] In one embodiment of the present invention, the two-layer optimization problem can actually be described as a single-layer optimization problem with a balance constraint MPEC. The user equilibrium of the lower layer is expressed in the form of a variational inequality, which has the following form:

[0036]

[0037] is the maximum value vector corresponding to λ, Ω TN for Feasible domain, h is the flow variable of each path. GF is a method for solving variational inequalities. By constructing a suitable GF, the variational inequality can be transformed. The D-gap function has good differentiable properties. Using this GF, the original equilibrium constraint is replaced by the following formula:

[0038] ζ αβ (h,λ)=0

[0039] where ζ αβ (h,λ)=ζ α (h,λ)-ζ β (h,λ),

[0040] ζ α and β Intermediate variables, α and β are parameters, and z is the variable of the embedded optimization problem. It is the travel cost vector composed of the travel cost of each path, α and β are two positive constants, and 0<α<β.

[0041] In one embodiment of the present invention, when λ a When there are no constraints, that is, when all roads can be charged, the two-layer optimization is completely equivalent to the system optimal model, that is, the two-layer optimization problem degenerates into the system optimal model, and the additional charge The details are as follows:

[0042] First, solve the KKT condition for the equilibrium of the lower-level users, as shown in the following formula:

[0043]

[0044] The KKT condition for solving the optimal system, that is, the upper model does not consider the constraints of the lower model, is as shown in the following formula:

[0045]

[0046] in is the marginal cost MC corresponding to path p p ;

[0047] Since both user equilibrium and system optimization are convex problems, satisfying the KKT condition and the global optimal solution are both sufficient and necessary conditions for these two problems; therefore, for the solution of the two-layer optimization For , it is necessary to satisfy the KKT conditions of user equilibrium and system optimization at the same time; aWithout any constraints, It can satisfy the KKT conditions of both the upper and lower layers at the same time, so the solution to the two-layer optimization problem is

[0048] In one embodiment of the present invention, a GF-SQP solution algorithm is a solution algorithm that combines variational inequality constraints through a gap function GF and sequential quadratic programming SQP.

[0049] In one embodiment of the present invention, a GF-SQP solution algorithm is designed to solve a general optimization model containing variational inequalities for charging price regulation of traffic flow distribution, which is specifically implemented as follows:

[0050] The two-level optimization problem is transformed and written into the following standard form:

[0051]

[0052] F(x) is the abstract objective function, h(x) and g(x) are the equality constraint vector and inequality constraint vector respectively. Then write it in the form of Lagrangian function:

[0053] L(x,λ,μ)=F(x)+λ T h(x)+μ T g(x)

[0054] γ and μ are the Lagrange multipliers corresponding to the equality constraint and inequality constraint respectively. Then, the following quadratic programming subproblems are solved iteratively, and the iteration points are gradually updated to approach the optimal point;

[0055]

[0056] Among them B k is the original Lagrangian function at x k The Hessian matrix at , d is the direction vector, is F(x) at x k The gradient of and are h(x) and g(x)x respectively. k The gradient of

[0057] The specific iteration process is as follows:

[0058] Step 1, initialization: given the initial point x0, Lagrange multipliers λ0, μ0, and Hessian matrix B0;

[0059] Step 2: Solve the quadratic programming sub-problem;

[0060] Step 3: Update variables:

[0061] x k+1 =xk +α k d k

[0062] where α k is the step size, determined by the Goldstein criterion or other methods;

[0063] Step 4: Update the Hessian matrix: The Hessian matrix is ​​approximated using the BFGS method:

[0064]

[0065] in and is the Lagrangian function in (x k+1 ,λ k ,μ k ) and (x k ,λ k ,μ k ), the gradient at x k and x k+1 are the solutions of the kth and k+1th generations respectively, s k and k is an intermediate variable.

[0066] Step 5: Determine whether the convergence condition is met:

[0067]

[0068] ∈1, ∈2 and ∈3 are three convergence thresholds. When the above three termination conditions are met at the same time, it is considered to have converged to the optimal point and the iteration is terminated, otherwise jump to step 2.

[0069] The present invention also provides a system for constructing a transportation network hydrogen pricing model based on variational inequalities, comprising a memory, a processor, and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0070] The present invention also provides a computer-readable storage medium, on which computer program instructions that can be executed by a processor are stored. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0071] Compared with the prior art, the present invention has the following beneficial effects: the double-layer optimization model proposed in the present invention has a significant effect. Without changing the road network, it can significantly improve traffic congestion and improve system efficiency by reasonably adjusting the hydrogen charges at hydrogen refueling stations and regulating vehicle flow distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1It is a schematic diagram of the process of the present invention.

[0073] Figure 2 Schematic diagram of the transportation network with the introduction of virtual arcs. DETAILED DESCRIPTION

[0074] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings.

[0075] The present invention

[0076] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0077] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0078] like Figure 1 As shown, the present invention provides a method for constructing a transportation network hydrogen pricing model based on variational inequality, comprising:

[0079] Variational inequalities are used to express the user equilibrium of the road network with charging prices, and a general optimization model with variational inequalities for charging price-controlled traffic flow distribution is established.

[0080] Also includes:

[0081] A GF-SQP solving algorithm is designed to solve the general optimization model containing variational inequalities for charging price regulation of traffic flow distribution.

[0082] The following is the specific implementation process of the present invention.

[0083] 1. Hybrid User Equilibrium Model for Traffic Network

[0084] The real traffic network can be simplified into a directed graph in is a node set, is a set of directed arcs. Directed arcs are the basic elements of a directed graph. A directed edge connecting a pair of nodes is a directed graph. Virtual arcs are introduced to better describe the charging process, such as Figure 2 As shown. 1,vrepresents the virtual arc introduced, indicating that there is a hydrogen refueling station on the road connecting AB, and stipulates that the path of HEV must contain at least one virtual arc. arc1 is a real arc, indicating the road connecting two nodes in the traffic network. Figure 2 For example, Or O→D is the path of other vehicles that do not need to be charged, The path of the HEV that needs to be charged.

[0085] Feasible domain of transportation network D T As shown in the following formula.

[0086]

[0087] in, is the set of real arcs without corresponding virtual arcs, A r is the set of real arcs with corresponding virtual arcs, A v is the set of virtual arcs, S is the set of OD pairs, is the traffic flow at time t corresponding to arc a, is the traffic flow at time t corresponding to path p, δ ap is the incidence matrix of arc a and path p, and are the set of paths with OD ij for HEV and conventional vehicles respectively, and are the demand quantities at time t for conventional vehicles and HEVs with OD ij respectively.

[0088] The time travel cost of each arc is described by the BPR function, and the charging cost is expressed as the product of the charging unit price and the charging size of hydrogen station a.

[0089]

[0090] in, or are the traffic flows of the virtual arc / real arc corresponding to the real arc / virtual arc, respectively. is the free travel time of arc a, Ca a is the road capacity corresponding to arc a. time and α a,charge are the unit driving time cost and the unit charging price of hydrogen station a respectively.

[0091] The travel cost of each arc can be used to obtain the travel cost of each path, as shown in the following formula.

[0092]

[0093] Assume that all HEV and conventional vehicle users in the traffic network are rational and aim to minimize the travel cost of their own paths. And through navigation software or other means, they can perceive the travel time cost and charging cost of each road in the traffic network without any difference. Then the network can achieve mixed user equilibrium. That is, each user cannot reduce his or her own travel cost by changing his or her path choice. The mathematical expression of the user equilibrium state is as follows.

[0094]

[0095] in

[0096] Beckmann et al. proposed a mathematical programming model equivalent to the above user equilibrium, as shown in the following formula.

[0097]

[0098] The global optimal mathematical programming model and its corresponding formula are shown in the following formula.

[0099]

[0100] In fact, regulating the distribution of traffic flow by charging additional fees on roads can be regarded as a two-level optimization problem, as shown in the following formula:

[0101]

[0102] The upper-level decision maker is the government, whose goal is to minimize congestion. The decision variable is the additional charge λ for each road. a The decision makers at the lower level are users in the road network, whose goal is to minimize their own travel costs. The decision variables are vectors x consisting of the traffic volume of each road.

[0103] Theorem 1: When λ a When there are no constraints, that is, when all roads can be charged, the two-layer optimization is completely equivalent to the system optimality, and the additional charge

[0104] First, we solve the Karush-Kuhn-Tucker (KKT) condition for the lower-level user equilibrium, as shown in the following formula:

[0105]

[0106] Solve the optimal KKT condition of the system (when the upper model does not consider the constraints of the lower model), as shown in the following formula:

[0107]

[0108] in is the marginal cost MC corresponding to path p p .

[0109] Since both user equilibrium and system optimization are convex problems, satisfying the KKT condition and the global optimal solution are both necessary and sufficient conditions for these two problems. For λ, it is necessary to satisfy the KKT conditions of user equilibrium and system optimization at the same time. a Without any constraints, The KKT conditions of the upper and lower layers can be satisfied at the same time. Therefore, the solution to this two-layer optimization problem is

[0110] This model can be viewed as a unified model that uses price to regulate traffic flow allocation. a Without any constraints, it means that extra charges can be imposed on each road, and the two-tier model degenerates into the optimal model. a are all constrained to 0, the problem degenerates into a user equilibrium model. Therefore, we can add a parameter about λ to the model. a The constraints are used to simulate charging only on certain roads, and to study how to minimize traffic congestion under limited conditions. At this time, the model is in an intermediate state between user equilibrium and system optimality.

[0111] In the mixed user equilibrium model (MUE), there is a factor that affects the cost of transportation, namely the charging price. a,charge E charge cost as lambda a The additional toll costs are used to regulate the distribution of traffic flow within the transportation network, and the additional charges for other sections are all 0.

[0112] 2. Transformation of the two-layer model

[0113] This two-layer problem can actually be described as a single-layer optimization problem with equilibrium constraints (MPEC, mathematical program with equilibrium constraints). The user equilibrium of the lower layer is expressed in the form of variational inequalities, which is as follows.

[0114]

[0115] is the maximum value vector corresponding to λ. GF is a method for solving variational inequalities. By constructing a suitable GF, variational inequalities can be transformed. D-gap function has good differentiable properties. Using this GF, the original equilibrium constraint can be replaced by the following formula.

[0116] ζ αβ (h,λ)=0 (12)

[0117] where ζ αβ (h,λ)=ζ α (h,λ)-ζ β (h,λ),

[0118] C(x,λ) is the travel cost vector composed of the travel cost of each path, α,β are two positive constants, and 0<α<β. However, in general, since GF also embeds a maximization optimization problem, it is impossible to directly obtain the explicit expression of GF, but we can use its good differentiability to solve it through numerical iteration.

[0119] 3. Solution Algorithm

[0120] The present invention considers designing GF and Sequential Quadratic Programming (SQP) to solve the model. SQP is an iterative algorithm for solving nonlinear problems. It approximates the nonlinear objective function and constraints through quadratic functions, and solves this approximate quadratic programming to obtain update points, repeating the cycle and gradually approaching the optimal solution. It has the advantages of fast convergence speed, good effect on differentiable problems, and effective processing of equality and inequality constraints.

[0121] The original two-layer model can be transformed into the following standard form:

[0122]

[0123] Then write it in the form of Lagrangian function:

[0124] L(x,λ,μ)=f(x)+λ T h(x)+μ T g(x) (14)

[0125] Then, the following quadratic programming subproblems are solved through continuous iterations, and the iteration points are gradually updated to approach the optimal point.

[0126]

[0127] Among them B kis the original Lagrangian function at x k The Hessian matrix at .

[0128] The specific iteration process is as follows:

[0129] 1. Initialization: given the initial point x0, Lagrange multipliers λ0, μ0, Hessian matrix B0

[0130] 2. Solve the quadratic programming subproblem: as shown in formula (14).

[0131] 3. Update variables:

[0132] x k+1 =x k +α k d k (17)

[0133] where α k is the step size, which can be determined by the Goldstein criterion or other methods.

[0134] 4. Update the Hessian matrix: In actual calculations, since the amount of computation required to directly calculate the Hessian matrix is ​​too large, the BFGS method is usually used to approximate it.

[0135]

[0136] 5. Determine whether the convergence conditions are met:

[0137]

[0138] When the three termination conditions are met at the same time, it is considered to have converged to the optimal point and the iteration is terminated. Otherwise, jump to step 2.

[0139] The present invention also provides a system for constructing a transportation network hydrogen pricing model based on variational inequalities, comprising a memory, a processor, and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0140] The present invention also provides a computer-readable storage medium, on which computer program instructions that can be executed by a processor are stored. When the processor executes the computer program instructions, the method steps described above can be implemented.

[0141] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0142] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0143] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0144] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0145] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

Claims

1. A method for constructing a hydrogen pricing model for a transportation network based on variational inequality, characterized in that: include: Variational inequalities are used to express the user equilibrium of the road network with charging prices, and a general optimization model with variational inequalities for charging price-controlled traffic flow distribution is established.

2. The method for constructing a transportation network hydrogen pricing model based on variational inequality according to claim 1, characterized in that: Also includes: A GF-SQP solving algorithm is designed to solve the general optimization model containing variational inequalities for charging price regulation of traffic flow distribution.

3. The method for constructing a transportation network hydrogen pricing model based on variational inequality according to claim 2, characterized in that: The GF-SQP solving algorithm transforms the variational inequality constraint into an equality constraint through the gap function GF, and then solves the general optimization model containing variational inequalities for charging price-controlled traffic flow distribution by designing a sequential quadratic programming SQP iterative algorithm.

4. The method for constructing a transportation network hydrogen pricing model based on variational inequality according to claim 1, characterized in that: The specific method of establishing a general optimization model containing variational inequalities for charging price regulation of traffic flow distribution is as follows: The real traffic network is simplified into a directed graph in is a node set, is a set of directed arcs; directed arcs are the basic elements of a directed graph. A directed edge connecting a pair of nodes is a directed graph. Virtual arcs are introduced to better describe the charging process. 1,v represents the virtual arc introduced, indicating that there is a hydrogen refueling station on the road connecting nodes A and B, and stipulates that the path of the hybrid hydrogen electric vehicle HEV must contain at least one virtual arc. Arc1 represents the real arc, indicating the road connecting nodes A and B in the traffic network. Or O→D is the path of other vehicles that do not need to be charged, is the path of the HEV that needs to be charged, O and D are nodes; Feasible domain of transportation network D T As shown below: in, is the set of real arcs without corresponding virtual arcs, A r is the set of real arcs with corresponding virtual arcs, A v is the set of virtual arcs, S is the set of OD pairs, is the traffic flow at time t corresponding to arc a, is the traffic flow at time t corresponding to path p, δ ap is the incidence matrix of arc a and path p, and are the set of paths with OD ij for HEV and conventional vehicles respectively, and are the demand quantities of conventional vehicles and HEVs with OD ij at time t, respectively; The time travel cost of each arc is described by the BPR function, and the charging cost is the product of the charging unit price and the charging size of hydrogen station a: in, or are the traffic flows of the virtual arc / real arc corresponding to the real arc / virtual arc, is the free travel time of arc a, Ca a is the road capacity corresponding to arc a, α time and α a,charge are the unit driving time cost and the unit charging price of hydrogen filling station a respectively, and E is the charging energy size; The travel cost of each path is obtained from the time travel cost of each arc, as shown in the following formula: Assuming that all HEV and conventional vehicle users in the traffic network are rational, they will minimize the travel cost of their own paths, and through navigation software or other means, they can accurately perceive the time travel cost and charging cost of each road in the corresponding traffic network. Then the corresponding traffic network can achieve mixed user equilibrium, that is, each user cannot reduce his or her own travel cost by changing his or her path choice. The mathematical expression of the user equilibrium state is as follows: in The mathematical programming model of user equilibrium equivalence is shown in the following formula: The global optimal mathematical programming model and its corresponding formula are shown as follows: In fact, regulating the distribution of traffic flow by charging additional fees on roads can be regarded as a two-level optimization problem, as shown in the following formula: The upper-level decision maker is the government, whose goal is to minimize congestion. The decision variable is the additional charge λ for each road. a The decision makers at the lower level are users in the road network, whose goal is to minimize their own travel costs. The decision variables are the vector x composed of the traffic volume of each road. The above two-level optimization problem can be viewed as a unified model for regulating traffic flow allocation using price. a Without any constraints, it means that extra charges can be imposed on each road, and the two-level optimization problem degenerates into the optimal model of the system. a If both are constrained to 0, the two-layer optimization problem degenerates into a user equilibrium model; Therefore, the two-level optimization problem is added with respect to λ a The constraints of are used to simulate charging only on certain roads, and to study how to minimize traffic congestion under limited conditions. At this time, the two-level optimization problem is in an intermediate state between user equilibrium and system optimality. In the hybrid user equilibrium model MUE, there is a factor that affects the cost of transportation, namely, the charging price; therefore, α a,charge E charge cost as lambda a The additional toll costs are used to regulate the distribution of traffic flow within the transportation network, and the additional charges for other sections are all 0.

5. The method for constructing a transportation network hydrogen pricing model based on variational inequality according to claim 4, characterized in that: The two-layer optimization problem can actually be described as a single-layer optimization problem with balance constraints MPEC. The user equilibrium of the lower layer is expressed in the form of variational inequality, which is as follows: is the maximum value vector corresponding to λ, Ω TN for feasible domain, h is the flow variable of each path, GF is a method for solving variational inequalities. By constructing a suitable GF, the variational inequality can be transformed. The D-gap function has good differentiable properties. Using this GF, the original equilibrium constraint is replaced by the following formula: g αβ (h,λ)=0 among them g αβ (h,λ)=ζ α (h,λ)-ζ β (h,λ), ζ α and β Intermediate variables, α and β are parameters, z is the variable of the embedded optimization problem, C(x,λ) is the travel cost vector composed of the travel cost of each path, α and β are two positive constants, and 0<α<β.

6. The method for constructing a transportation network hydrogen pricing model based on variational inequality according to claim 4, characterized in that: When a When there are no constraints, that is, when all roads can be charged, the two-layer optimization is completely equivalent to the system optimal model, that is, the two-layer optimization problem degenerates into the system optimal model, and the additional charge The details are as follows: First, solve the KKT condition for the equilibrium of the lower-level users, as shown in the following formula: The KKT condition for solving the optimal system, that is, the upper model does not consider the constraints of the lower model, is as shown in the following formula: in is the marginal cost MC corresponding to path p p ; Since both user equilibrium and system optimization are convex problems, satisfying the KKT condition and the global optimal solution are both sufficient and necessary conditions for these two problems; therefore, for the solution of the two-layer optimization For , it is necessary to satisfy the KKT conditions of user equilibrium and system optimization at the same time; a Without any constraints, It can satisfy the KKT conditions of both the upper and lower layers at the same time, so the solution to the two-layer optimization problem is 7. The method for constructing a transportation network hydrogen pricing model based on variational inequality according to claim 5, characterized in that: GF-SQP solution algorithm, that is, a solution algorithm combining variational inequality constraints through gap function GF and sequential quadratic programming SQP.

8. The method for constructing a transportation network hydrogen pricing model based on variational inequality according to claim 5, characterized in that: Design a GF-SQP solution algorithm to solve the general optimization model containing variational inequalities for charging price regulation of traffic flow distribution. The specific implementation is as follows: The two-level optimization problem is transformed and written into the following standard form: min x F(x) F(x) is the abstract objective function, h(x) and g(x) are the equality constraint vector and inequality constraint vector respectively, which are then written in the form of Lagrangian function: L(x,λ,μ)=F(x)+γ T h(x)+μ T g(x) γ and μ are the Lagrange multipliers corresponding to the equality constraint and inequality constraint respectively. Then, the following quadratic programming subproblems are solved iteratively, and the iteration points are gradually updated to approach the optimal point. Among them B k is the original Lagrangian function at x k The Hessian matrix at , d is the direction vector, is F(x) at x k The gradient of and are h(x) and g(x)x respectively. k The gradient of The specific iteration process is as follows: Step 1, initialization: given the initial point x0, Lagrange multipliers λ0, μ0, and Hessian matrix B0; Step 2: Solve the quadratic programming sub-problem; Step 3: Update variables: x k+1 =x k +a k d k where α k is the step size, determined by the Goldstein criterion or other methods; Step 4: Update the Hessian matrix: The Hessian matrix is ​​approximated using the BFGS method: in and is the Lagrangian function in (x k+1 ,λ k ,μ k ) and (x k ,λ k ,μ k ), the gradient at x k and x k+1 are the solutions of the kth and k+1th generations respectively, s k and k is an intermediate variable; Step 5: Determine whether the convergence condition is met: ∈1, ∈2 and ∈3 are three convergence thresholds. When the above three termination conditions are met at the same time, it is considered to have converged to the optimal point and the iteration is terminated. Otherwise, jump to step 2.

9. A system for constructing a transportation network hydrogen pricing model based on variational inequality, characterized in that: The method comprises a memory, a processor and computer program instructions stored in the memory and capable of being executed by the processor. When the processor executes the computer program instructions, the method steps as claimed in any one of claims 1 to 8 can be implemented.

10. A computer-readable storage medium having stored thereon computer program instructions that can be executed by a processor, and when the processor executes the computer program instructions, the method steps according to any one of claims 1 to 8 can be implemented.

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