CN113177320B - Simulation optimization method, system, equipment and medium for road dynamic congestion charging - Google Patents
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Abstract
The invention discloses a distributed robust simulation optimization method, a system, equipment and a medium for road dynamic congestion charging, wherein the method comprises the following steps: step 1, for a road network to be subjected to dynamic congestion charging scheme optimization, creating a simulation road network in macroscopic traffic simulation software; step 2, constructing a dynamic congestion charging optimization model of the road by taking the total travel time as a target evaluation index; and 3, initializing the charging scheme set and the traffic demand parameter set, performing simulation evaluation on the created simulation road network by using macroscopic traffic simulation software, and solving the optimization model established in the step 2 by adopting a distributed robust simulation optimization algorithm to obtain a congestion charging scheme with optimal robustness. The method can solve the problems of simulation evaluation and optimization of the road dynamic congestion charging under the condition of traffic demand uncertainty.
Description
Technical Field
The invention relates to the field of road dynamic congestion charging, in particular to a distributed robust simulation optimization method, a system, equipment and a medium for road dynamic congestion charging.
Background
The traffic congestion charging, namely, the management and control measures for applying extra travel fees to the traffic travel in a specific time period, induces the travelers to make travel time and path selection again by increasing the cost of using traffic facilities in a charging area, realizes the transfer of part of the travelers from a congested area to a non-congested area, or selects to travel in a non-charging time period, thereby reducing the traffic demand in the charging area to a certain extent, relieving the contradiction between traffic supply and traffic demand, relieving traffic congestion, enabling road network resources to be more fully utilized, and having positive significance to the healthy development of cities.
The traffic simulation technology is to construct a model to simulate the existing or planning traffic system, so that the user can optimize the researched traffic network system or predict the future traffic state conveniently. However, the traffic simulation technology also has the problems of black box property, long time consumption and the like. Aiming at the problems, a simulation optimization algorithm is generated at the same time, and the calculation speed is greatly improved. The mainstream simulation optimization methods mainly include Gradient-based search methods (Gradient based search methods), Stochastic approximation methods (Stochastic approximation methods), Heuristic algorithms (Heuristic search methods), and Response surface methods (Response surface methods). The response surface method, namely the proxy model method, has the advantages of saving simulation cost and fitting complex and unknown system input and output relations, and the advantages are more prominent under the condition that simulation experiments are time-consuming.
In complex real-world engineering problems, even if the uncertainty effects of the data are ignored, the optimal solution, which is found according to the assumed conditions, is likely to be unstable or even infeasible. Therefore, compared with the global optimal solution, the solution with less sensitivity to disturbance, namely the distributed robust solution, in the practical problem has more realistic significance.
Disclosure of Invention
The invention provides a distributed robust simulation optimization method, a system, equipment and a medium for road dynamic congestion charging, which can solve the problems of road dynamic congestion charging simulation and evaluation under the condition of traffic demand uncertainty.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
a distributed robust simulation optimization method for road dynamic congestion charging comprises the following steps:
step 1, for a road network to be subjected to dynamic congestion charging scheme optimization, creating a simulation road network in macroscopic traffic simulation software;
step 2, taking the total travel time as a target evaluation index, and constructing the following road dynamic congestion charging optimization model:
wherein, S is a congestion charging scheme set, and x is any congestion charging scheme in S; j is the simulation times index, NxTotal number of simulations for x; t is a time segment index, and T is the total number of time segments; o is an initial node set, D is an end node set, OD is an origin and belongs to an OD pair set of which the O end belongs to D, and OD is any OD pair in the OD pair set; a is a road section set in the simulation road network, and a is any road section in the road section set A;
obey normal distribution for the traffic demand of od in the time segment t
And
mean and variance of the traffic demand of od at time segment t, respectively;
a traffic demand matrix for a time segment t, consisting of
Forming;
the random traffic demand matrix obeys normal distribution in the jth simulation; theta is traffic demand
The set of fuzzy normal distributions that is satisfied,
e is a parameter (traffic demand parameter for short) for controlling the traffic demand distribution variance, which represents the uncertainty of the traffic demand, e belongs to [ e [l,eu]Wherein e isl、euUpper and lower limits of e, respectively;
representing macroscopic traffic simulation software xi according to simulation inputs x and
carrying out simulation evaluation on the simulation road network, and outputting the flow of the obtained road section a in the time slice t
And travel time
Step 3, initializing to obtain N charging schemes xiI is 1,2, …, N forms a set S, and M traffic demand parameters e are obtained through initializationjJ ═ 1,2, …, M constitutes set E; each charging plan and traffic demand parameter combination (x)i,ej) Performing simulation evaluation for a plurality of times by using macroscopic traffic simulation software, and solving the optimization model established in the step 2 by using a distributed robust simulation optimization algorithm to obtain a congestion charging scheme with optimal robustness;
the distributed robust simulation optimization algorithm adopted in the step 3 comprises the following specific processes:
step 3.1, for each charging plan in combination with the traffic demand parameter (x)i,ej) Firstly, using macroscopic traffic simulation software to carry out N0Simulation evaluation of/M times, N0The number of times of the preset initial simulation evaluation is obtained; then, the objective function value corresponding to each simulation is calculated according to the obtained flow and travel time, and the mean value and the variance of the objective function values of all simulation evaluations are calculated
Step 3.2, setting the initial value of the iteration number Num to be 0, and setting the maximum iteration number Num to be 0maxIs (B-N.N)0)/N0B is a preset upper limit of simulation evaluation times, and an initial value N of the simulation times of the distribution stagea(0) Setting the initial value of the algorithm convergence index as 0; when the convergence index of the algorithm does not reach the convergence threshold value and the simulation residual resources exist, the following steps are executed:
step 3.2.1, for each charging scenario xiAccording to the mean value and the variance of the objective function values corresponding to the combination of the objective function values and the traffic demand parameters, a random proxy model approximating the response relation between the objective function values and the traffic demand parameters is constructed to be used as a charging scheme xiThe first random agent model of (1);
step 3.2.2, searching the corresponding traffic demand parameter when the objective function value is maximum based on the first random agent model, and recording the traffic demand parameter as word-caseopt,i；
Step 3.2.3, set S and e according to the charging schemeopt,iConstructing a random agent model of a response relation between an approximate charging scheme and a worst-case objective function value as a second random agent model according to the corresponding objective function value;
step 3.2.4, based on the second random agent model, searching for a new charging plan sample point x*Updating congestion charging scheme set S ← S ×*,N←N+1；
Step 3.2.5, applying the same method to x as step 3.1*Combining with traffic demand parameters by Ns(Num +1)/M times of simulation evaluation, Ns(Num+1)＝N0-Na(Num +1) corresponding to x*To communicate withA mean and variance of objective function values of the combination of demand parameters;
step 3.2.6, adopting a simulation resource allocation method to allocate the total simulation times N of the stages in the Num +1 iterationa(Num +1) assigning to all charging schemes and combinations of traffic demand parameters;
step 3.2.7, for each combination (x) according to the additional simulation times assigned in step 3.2.6i,ej) Executing additional simulation evaluation, and counting the mean value and the variance of the corresponding objective function value;
step 3.2.8, if the convergence condition is reached and the simulation residual resources are still available, updating iteration number Num ← Num +1, and returning to execute step 3.2.1; otherwise, outputting a scheme corresponding to the minimum worst-case objective function value in the existing sample set evaluated by the second random agent model as the optimal robust charging scheme. In a more preferred embodiment, an improved expectation-improvement criterion (abbreviated MEI) is employed and x is searched by maximizing the MEI*The expression of the MEI is:
in the formula (I), the compound is shown in the specification,
and
predicted by the second random agent model at xiThe mean and variance of phi is a standard normal distribution function, and psi is a standard normal probability density function;
is the minimum target value evaluated by the second random agent model in the existing charging scheme.
In a more preferred embodiment, step 3.2.7 provides a total number of simulations N to be assigned in the Num +1 iterationa(Num +1) is:
wherein N isminIs the preset minimum simulation times.
In a more preferred technical solution, step 3.2.1 adopts a stochastic kriging model to approximate the response relationship between the traffic demand parameter and the objective function value for each charging scheme, and/or step 3.2.3 adopts the stochastic kriging model to approximate the response relationship between the charging scheme and the worst-case objective function value.
In a more preferred technical scheme, the N charging schemes and the M traffic demand parameters obtained by initialization are obtained by a space uniform sampling method such as Latin hypercube sampling.
In a more preferred technical solution, the macroscopic traffic simulation software employs VISUM.
A distributed robust simulation optimization platform for road dynamic congestion charging comprises macroscopic traffic simulation software, a control platform and a database management system;
the database management system is to: storing a road network information file, a traffic demand file and a congestion charging scheme set;
the macroscopic traffic simulation software is used for: acquiring a road network information file from a database management system, and creating a corresponding simulation road network; acquiring a traffic demand file and a congestion charging scheme from a database management system, performing simulation evaluation, and outputting the flow and the travel time of each road section;
the control platform is used for: constructing a dynamic congestion charging optimization model of the road by taking the total travel time as a target evaluation index; initializing N charging schemes xiI is 1,2, …, N forms a set S, and M traffic demand parameters e are obtained through initializationjJ ═ 1,2, …, M constitutes set E; controlling the combination of the macroscopic traffic simulation software for each billing plan and traffic demand parameter (x)i,ej) And carrying out simulation evaluation for a plurality of times, and solving the optimization model by adopting a distributed robust simulation optimization algorithm. Updating the congestion charging scheme obtained from each iteration to the database management systemIn the system, the algorithm is ended to finally obtain a robust optimal congestion charging scheme;
the road dynamic congestion charging optimization model comprises the following steps:
wherein, S is a congestion charging scheme set, and x is any congestion charging scheme in S; j is the simulation times index, NxTotal number of simulations for x; t is a time segment index, and T is the total number of time segments; o is an initial node set, D is an end node set, OD is an origin and belongs to an OD pair set of which the O end belongs to D, and OD is any OD pair in the OD pair set; a is a road section set in the simulation road network, and a is any road section in the road section set A;
obey normal distribution for the traffic demand of od in the time segment t
And
mean and variance of the traffic demand of od at time segment t, respectively;
traffic demand matrix for time segment t, consisting of
Forming;
the random traffic demand matrix obeys normal distribution in the jth simulation; theta is traffic demand
The set of fuzzy normal distributions that is satisfied,
e is a parameter (traffic demand parameter for short) for controlling the traffic demand distribution variance, which represents the uncertainty of the traffic demand, e belongs to [ e [l,eu]Wherein e isl、euRespectively the upper and lower limits of e;
representing macroscopic traffic simulation software xi according to simulation inputs x and
carrying out simulation evaluation on the simulation road network, and outputting the flow of the obtained road section a in the time slice t
And travel time
An electronic device comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor is enabled to implement any one of the above-mentioned technical solutions of the distributed robust simulation optimization method.
A computer readable storage medium, on which a computer program is stored, wherein the computer program, when executed by a processor, implements any one of the above-mentioned technical solutions of the distributed robust simulation optimization method.
Advantageous effects
The method can solve the problem of simulation evaluation and optimization of dynamic crowded charging of roads under the condition of uncertain traffic demands, aims to improve the efficiency of a road network, can quickly and accurately optimize and obtain a robust crowded charging scheme by intelligently distributing limited simulation resources, and can evaluate and analyze the charging scheme by various traffic state indexes output by simulation.
Drawings
FIG. 1 is a schematic flow diagram of a distributed robust simulation optimization method according to the present invention;
FIG. 2 is a schematic diagram of a distributed robust simulation optimization system according to the present invention.
Detailed Description
The following describes embodiments of the present invention in detail, which are developed based on the technical solutions of the present invention, and give detailed implementation manners and specific operation procedures to further explain the technical solutions of the present invention.
Example 1
The embodiment provides a distributed robust simulation optimization method for road dynamic congestion charging, as shown in fig. 1, including the following steps:
step 1, for a road network to be subjected to dynamic congestion charging scheme optimization, a simulated road network is created in macroscopic traffic simulation software, and in this embodiment, VISUM is preferred by the macroscopic traffic simulation software.
Step 2, taking the total travel time as a target evaluation index, and constructing the following road dynamic congestion charging optimization model:
wherein, S is a congestion charging scheme set, and x is any congestion charging scheme in S; j is the simulation times index, NxTotal number of simulations for x; t is a time segment index, and T is the total number of time segments; o is an initial node set, D is an end node set, OD is an origin and belongs to an OD pair set of which the O end belongs to D, and OD is any OD pair in the OD pair set; a is a road section set in the simulation road network, and a is any road section in the road section set A;
obey normal distribution for the traffic demand of od in the time segment t
And
mean and variance of the traffic demand of od at time segment t, respectively;
traffic demand matrix for time segment t, consisting of
Forming;
the random traffic demand matrix obeys normal distribution in the jth simulation; theta is traffic demand
The set of fuzzy normal distributions that is satisfied,
e is a parameter (traffic demand parameter for short) for controlling the traffic demand distribution variance, which represents the uncertainty of the traffic demand, e belongs to [ e [l,eu]Wherein e isl、euRespectively the upper and lower limits of e;
representing macroscopic traffic simulation software xi according to simulation inputs x and
carrying out simulation evaluation on the simulation road network, and outputting the flow of the obtained road section a in the time slice t
And travel time
In this embodiment, a distributed robust congestion charging optimization model aiming at improving the road network efficiency is constructed, and the optimization of the charging level and the charging position is specifically as follows: the distributed robust congestion charging optimization model aiming at improving the road network efficiency is established by taking a charging level and a charging position as decision variables, traffic demand uncertain parameters as environment variables and a total travel time as an objective function, and relates to traffic demand uncertainty. Assuming that traffic demand follows a normal distribution
And defining a fuzzy set based thereon
Wherein
The value of (b) is determined by historical traffic demand data, so that a specific normal distribution can be determined by determining e.
The charging scheme comprises a charging level and a charging position, the current stage comprises a road section-based charging scheme and a region-based charging scheme, and other charging scheme forms appearing later are also within the protection scope of the patent.
Step 3, obtaining N charging schemes x by Latin hypercube sampling initializationiI is 1,2, …, N forms a set S, and M traffic demand parameters e are obtained through initializationjJ ═ 1,2, …, M constitutes set E; each charging plan and traffic demand parameter combination (x)i,ej) Performing simulation evaluation for a plurality of times by using macroscopic traffic simulation software, and solving the optimization model established in the step 2 by using a distributed robust simulation optimization algorithmAnd obtaining a robust optimal congestion charging scheme.
The specific process of solving and obtaining the optimal congestion scheme by adopting the distributed robust simulation optimization algorithm in the step 3 is as follows:
step 3.1, for each charging plan in combination with the traffic demand parameter (x)i,ej) Firstly, using macroscopic traffic simulation software to carry out N0Simulation evaluation of/M times, N0The number of times of the preset initial simulation evaluation is obtained. Then, the objective function value corresponding to each simulation is calculated according to the obtained flow and travel time, and the mean value and the variance of the objective function values of all the simulation evaluations are calculated
Step 3.2, setting the initial value of the iteration number Num to be 0, and setting the maximum iteration number Num to be 0maxIs (B-N.N)0)/N0Wherein B is the upper limit of simulation evaluation times and the initial value N of the simulation times of the distribution stagea(Num) is 0, the convergence index of the algorithm is set to be the MEI value, and the initial value is 0.5; when MEI is not less than the set algorithm convergence value (in the embodiment, the convergence threshold is set to be 0.01), and simulation residual resources (B-N.N) are also available0-Na(Num +1) > 0), the following steps are performed:
step 3.2.1, for each charging scenario xjAccording to the mean value and the variance of the objective function values corresponding to the combination of the objective function values and the traffic demand parameters, a random kriging model is adopted to construct a random proxy model approximating the response relation between the objective function values and the traffic demand parameters, and leave-one-out cross validation is performed to serve as xiThe first random proxy model of (1), denoted SSM-I.
Step 3.2.2, based on SSM-I, searching the corresponding traffic demand parameter when the objective function value is maximum, and recording the traffic demand parameter as word-caseopt,i。
Step 3.2.3, set S and e according to the charging schemeopt,iCorresponding objective function value, adopting random Kriging model to construct random proxy model of response relation between approximate charging scheme and worst-case objective function value, and executing leave-one cross validationIs a second random proxy model, denoted SSM-II.
Step 3.2.4, based on SSM-II, search for new charging plan sample points x with improved expected improvement criterion (MEI) and by maximizing MEI*Updating congestion charging scheme set S ← S ×*N ← N + 1. Other methods suitable for searching for new sample points by the random proxy model are also within the scope of the present patent.
Step 3.2.5, applying the same method to x as step 3.1*Combining with traffic demand parameters by Ns(Num +1)/M times of simulation evaluation processing are carried out, and a charging scheme x is correspondingly obtained*Mean and variance of objective function values combined with traffic demand parameters. Wherein N iss(Num+1)＝N0-Na(Num+1)。
Step 3.2.6, adopting a simulation resource allocation method to allocate the total simulation times N of the stages in the Num +1 iterationa(Num +1) is assigned to all charging schemes in combination with the traffic demand parameter, so that simulation resources can be assigned to more promising charging schemes, i.e. charging schemes with small mean or large variance. The simulation resource allocation method includes, but not limited to, toa (theoretical optimal allocation), ea (equivalent allocation), ptv (procedural to variance), ocba (optimal computing budget), and ROCBA (Ramdomized optimal computing budget).
Wherein the total simulation total times N distributed in the Num +1 th iterationa(Num +1) is:
wherein N isminA preset minimum number of simulations of the congestion charging scheme.
Step 3.2.7, for each combination (x) according to the additional simulation times assigned in step 3.2.6i,ej) Additional simulation evaluations were performed and the mean and variance of the corresponding objective function values were counted.
3.2.8, if the convergence condition is not reached, and furtherWhen simulation residual resources exist, updating iteration times Num ← Num +1, and returning to the step 3.2.1; otherwise, use each combination (x)i,ej) And outputting a scheme corresponding to the minimum worst-case objective function value in the existing charging scheme set evaluated by the second random agent model as the optimal robust charging scheme.
In this embodiment, a new charging plan is searched for using the improved desired improvement criterion, and therefore, the convergence condition may be set as whether the MEI value is smaller than a set value, for example, 0.01, and when the improved charging plan cannot be found, the algorithm is terminated.
Example 2
The embodiment provides a distributed robust simulation optimization platform for road dynamic congestion charging, which, as shown in fig. 2, includes a macroscopic traffic simulation software, a control platform and a database management system;
the database management system is to: storing a road network information file, a traffic demand file and a congestion charging scheme set;
the macroscopic traffic simulation software is used for: acquiring a road network information file from a database management system, and creating a corresponding simulation road network; acquiring a traffic demand file and a congestion charging scheme from a database management system, performing simulation evaluation, and outputting the flow and the travel time of each road section;
the control platform is used for: constructing a dynamic congestion charging optimization model of the road by taking the total travel time as a target evaluation index; initializing N charging schemes xiI is 1,2, …, N forms a set S, and M traffic demand parameters e are obtained through initializationjJ ═ 1,2, …, M constitutes set E; controlling the combination of the macroscopic traffic simulation software for each billing plan and traffic demand parameter (x)i,ej) And carrying out simulation evaluation for a plurality of times, and solving the optimization model by adopting a distributed robust simulation optimization algorithm. Updating the congestion charging scheme obtained by each iteration into a database management system, and finally obtaining the congestion charging scheme with optimal robustness after the algorithm is ended;
the road dynamic congestion charging optimization model comprises the following steps:
wherein, S is a congestion charging scheme set, and x is any congestion charging scheme in S; j is the simulation times index, NxTotal number of simulations for x; t is a time segment index, and T is the total number of time segments; o is an initial node set, D is an end node set, OD is an origin and belongs to an OD pair set of which the O end belongs to D, and OD is any OD pair in the OD pair set; a is a road section set in the simulation road network, and a is any road section in the road section set A;
obey normal distribution for the traffic demand of od in the time segment t
And
mean and variance of the traffic demand of od at time segment t, respectively;
a traffic demand matrix for a time segment t, consisting of
Forming;
the random traffic demand matrix obeys normal distribution in the jth simulation; theta is traffic demand
The set of fuzzy normal distributions that is satisfied,
e is a parameter (traffic demand parameter for short) for controlling the traffic demand distribution variance, which represents the uncertainty of the traffic demand, e belongs to [ e [l,eu]Wherein e isl、euUpper and lower limits of e, respectively;
representing macroscopic traffic simulation software xi according to simulation inputs x and
carrying out simulation evaluation on the simulation road network, and outputting the flow of the obtained road section a in the time slice t
And travel time
The control platform described in this embodiment obtains the optimal congestion charging scheme by solving the dynamic congestion charging optimization model of the road by using a distributed robust simulation optimization algorithm, and the specific solving method is the same as that described in embodiment 1, and is not described again in this embodiment.
In a more preferred embodiment, the macro traffic simulation software may adopt VISUM, the control platform may adopt MATLAB, Python, or the like, and the database management system may adopt ACCESS, and the present invention does not limit the specific types.
Example 3
The present embodiment provides an electronic device, which includes a memory and a processor, where the memory stores a computer program, and when the computer program is executed by the processor, the processor implements the distributed robust simulation optimization method described in embodiment 1.
Example 4
The present embodiment provides a computer-readable storage medium, on which a computer program is stored, which, when executed by a processor, implements the distributed robust simulation optimization method of embodiment 1.
The above embodiments are preferred embodiments of the present application, and those skilled in the art can make various changes or modifications without departing from the general concept of the present application, and such changes or modifications should fall within the scope of the claims of the present application.
Claims (9)
1. A distributed robust simulation optimization method for road dynamic congestion charging is characterized by comprising the following steps:
step 1, for a road network to be subjected to dynamic congestion charging scheme optimization, creating a simulation road network in macroscopic traffic simulation software;
step 2, taking the total travel time as a target evaluation index, and constructing the following road dynamic congestion charging optimization model:
wherein, S is a congestion charging scheme set, and x is any congestion charging scheme in S; j is simulation frequency index, NxTotal number of simulations for x; t is a time segment index, and T is the total number of time segments; o is an initial node set, D is an end node set, OD is an origin and belongs to an OD pair set of which the O end belongs to D, and OD is any OD pair in the OD pair set; a is a road section set in the simulation road network, and a is any road section in the road section set A;
obey normal distribution for the traffic demand of od in the time segment t
And
mean and variance of the traffic demand of od at time segment t, respectively;
a traffic demand matrix for a time segment t, consisting of
Forming;
the random traffic demand matrix obeys normal distribution in the jth simulation; theta is traffic demand
The set of fuzzy normal distributions that is satisfied,
e is a traffic demand parameter which represents the uncertainty of the traffic demand, and e belongs to [ e ∈ ]l,eu]Wherein e isl、euUpper and lower limits of e, respectively;
representing the simulation input x and x of macroscopic traffic simulation software xi in a simulation road network
Carrying out simulation evaluation, and outputting the flow of the obtained road section a in the time segment t
And travel time
Step 3, initializing to obtain N charging schemes xiI is 1,2, …, N forms a set S, and M traffic demand parameters e are obtained through initializationjJ ═ 1,2, …, M constitutes set E; each charging plan and traffic demand parameter combination (x)i,ej) Performing simulation evaluation for a plurality of times by using macroscopic traffic simulation software, and solving the optimization model established in the step 2 by using a distributed robust simulation optimization algorithm to obtain a congestion charging scheme with optimal robustness;
the distributed robust simulation optimization algorithm adopted in the step 3 comprises the following specific processes:
step 3.1, for each charging plan in combination with the traffic demand parameter (x)i,ej) Firstly, using macroscopic traffic simulation software to carry out N0Simulation evaluation of/M times, N0The number of times of the preset initial simulation evaluation is obtained; calculating objective function values corresponding to each simulation according to the flow and travel time obtained by simulation evaluation, and then calculating the mean value and variance of all objective function values
Step 3.2, setting the initial value of the iteration number Num to be 0, and setting the maximum iteration number Num to be 0maxIs (B-N.N)0)/N0B is a preset simulation evaluation frequency upper limit, and simulation frequency N of the distribution stagea(Num), setting an initial value of an algorithm convergence index; when the convergence index of the algorithm does not reach the convergence threshold value and the simulation residual resources exist, the following steps are executed:
step 3.2.1, for each charging scenario xiAccording to the mean value and the variance of the objective function values corresponding to the combination of the objective function values and the traffic demand parameters, a random proxy model approximating the response relation between the objective function values and the traffic demand parameters is constructed to be used as a charging scheme xiThe first random agent model of (1);
step 3.2.2, searching the corresponding traffic demand parameter when the objective function value is maximum based on the first random agent model, and recording the traffic demand parameter as worst-case trafficRequirement parameter eopt,i；
Step 3.2.3, set S and e according to the charging schemeopt,iConstructing a random agent model of a response relation between an approximate charging scheme and a worst-case objective function value as a second random agent model according to the corresponding objective function value;
step 3.2.4, search for a new charging scenario x based on the second stochastic proxy model*Updating congestion charging scheme set S ← S ×*,N←N+1；
Step 3.2.5, applying the same method to x as step 3.1*Combining with traffic demand parameters by Ns(Num +1)/M times of simulation evaluation, Ns(Num+1)＝N0-Na(Num +1) corresponding to x*A mean and variance of objective function values combined with the traffic demand parameters;
step 3.2.6, adopting a simulation resource allocation method to allocate the total simulation times N of the stages in the Num +1 iterationa(Num +1) assigning to all charging schemes and combinations of traffic demand parameters;
step 3.2.7, for each combination (x) according to the additional simulation times assigned in step 3.2.6i,ej) Executing additional simulation evaluation, and counting the mean value and the variance of the corresponding objective function value;
step 3.2.8, if the convergence condition is not reached and there are simulation remaining resources, updating iteration number Num ← Num +1, and returning to execute step 3.2.1; otherwise, outputting a scheme corresponding to the minimum worst-case objective function value in the existing sample set evaluated by the second random agent model as the optimal robust charging scheme.
2. The method of claim 1, wherein an improved expected improvement criterion, abbreviated MEI, is employed and a new charging scheme is searched by maximizing the MEI, wherein an algorithm convergence index is a MEI value, and wherein the MEI is expressed as:
in the formula (I), the compound is shown in the specification,
and
predicted by the second random agent model at xiThe mean and variance of phi is a standard normal distribution function, and psi is a standard normal probability density function;
is the minimum target value evaluated by the second random agent model in the existing charging scheme.
3. The method of claim 1, wherein step 3.2.7 provides a total number of simulations N to be assigned in the Num +1 th iterationa(Num +1) is:
wherein N isa(0)＝0，NminA preset minimum number of simulations of the congestion charging scheme.
4. A method according to claim 1, characterised in that step 3.2.1 approximates the response between the traffic demand parameter and the objective function value for each charging scheme using a stochastic kriging model, and/or step 3.2.3 approximates the response between the charging scheme and the worst-case objective function value using a stochastic kriging model.
5. Method according to claim 1, characterized in that the obtained N charging schemes x are initializediAnd M traffic demand parameters ejAll obtained by a spatially uniform sampling method.
6. The method of claim 1, wherein the macro traffic simulation software employs VISUM.
7. A distributed robust simulation optimization platform for road dynamic congestion charging is characterized by comprising macroscopic traffic simulation software, a control platform and a database management system;
the database management system is to: storing a road network information file, a traffic demand file and a congestion charging scheme set;
the macroscopic traffic simulation software is used for: acquiring a road network information file from a database management system, and creating a corresponding simulation road network; acquiring a traffic demand file and a congestion charging scheme from a database management system, performing simulation evaluation, and outputting the flow and the travel time of each road section;
the control platform is used for: constructing a dynamic congestion charging optimization model of the road by taking the total travel time as a target evaluation index; initializing N charging schemes xiI is 1,2, …, N forms a set S, and M traffic demand parameters e are obtained through initializationjJ ═ 1,2, …, M constitutes set E; controlling the combination of the macroscopic traffic simulation software for each billing plan and traffic demand parameter (x)i,ej) Carrying out simulation evaluation for a plurality of times, and solving an optimization model by adopting a distributed robust simulation optimization algorithm; updating the congestion charging scheme obtained by each iteration into a database management system, and finally obtaining the congestion charging scheme with optimal robustness after the algorithm is ended;
the road dynamic congestion charging optimization model comprises the following steps:
wherein, S is a congestion charging scheme set, and x is any congestion charging scheme in S; j is the number of times of simulationNumber index, NxTotal number of simulations for x; t is a time segment index, and T is the total number of time segments; o is an initial node set, D is an end node set, OD is an origin and belongs to an OD pair set of which the O end belongs to D, and OD is any OD pair in the OD pair set; a is a road section set in the simulation road network, and a is any road section in the road section set A;
obey normal distribution for the traffic demand of od in the time segment t
And
mean and variance of the traffic demand of od at time segment t, respectively;
a traffic demand matrix for a time segment t, consisting of
Forming;
the random traffic demand matrix obeys normal distribution in the jth simulation; theta is the traffic demand
The set of fuzzy normal distributions that is satisfied,
e is a parameter for controlling traffic demand distribution variance, referred to as traffic demand parameter for short, and represents the uncertainty of traffic demand, e belongs to [ e [ ]l,eu]Wherein e isl、euUpper and lower limits of e, respectively;
representing macroscopic traffic simulation software xi according to simulation inputs x and
carrying out simulation evaluation on the simulation road network, and outputting the flow of the obtained road section a in the time slice t
And travel time
8. An electronic device comprising a memory and a processor, the memory having stored therein a computer program, wherein the computer program, when executed by the processor, causes the processor to implement the method of any of claims 1-6.
9. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the method according to any one of claims 1 to 6.
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