A Simulation Optimization Method for Bus Lanes Based on Agent-Assisted Evolutionary Algorithm

Abstract

The present invention provides a simulation optimization method for bus lanes based on a proxy-assisted evolutionary algorithm, which comprises the following steps: S1, establishing a road network simulation model and an optimization mathematical model; S2, collecting initial simulation samples of decision variables based on Latin hypercube sampling; S3, establishing a proxy model of the simulation model by using the initial simulation samples; S4, obtaining an optimized solution set of decision variables by using an evolutionary algorithm assisted by the proxy model; S5, selecting the most ideal solution from the optimized solution set based on the proxy model integration method and the sample jackknife method; S6, substituting the most ideal solution into the simulation model for verification and updating the proxy model. Compared with the prior art, the simulation model of the present invention, as an evaluation tool for optimization schemes, can simulate the dynamic evolution process of the traffic system; ② Based on the simulation model and the optimization algorithm, a quantitative optimization scheme for bus lanes in the road network can be obtained; ③ Using the proxy model to replace some expensive calculations that need to be completed by the simulation model reduces the computational amount of simulation optimization.

Description

Technical Field

[0001] The present invention belongs to the field of traffic engineering, and particularly relates to a simulation optimization method for bus lanes based on an agent-assisted evolutionary algorithm for traffic network design. Background Art

[0002] To meet different travel demands, modern urban transportation systems have gradually developed to include diverse transportation models. Multiple transportation modes such as social vehicles, buses, non-motor vehicles, and urban rail transit constitute a multi-modal urban traffic system. The multi-modal system can meet and adapt to diverse resident travel demands, and the transportation modes can complement each other's advantages, effectively enhancing the transportation capacity and efficiency of the urban traffic network. Due to the inclusion of diverse transportation modes and traffic demands in the multi-modal traffic system, and the sharing and competition of limited land and traffic infrastructure resources among various transportation modes, this system is characterized by a large scale, high complexity, and great difficulty in design and control. How to use reasonable methods to design and manage the multi-modal urban traffic system and effectively improve the traffic capacity and efficiency of the traffic network is an important scientific and engineering issue.

[0003] A common multi-modal traffic system is a simple multi-modal system composed of buses and private cars. From the perspective of social fairness, buses with a larger number of passengers should be allocated smoother road resources than private cars with a smaller number of passengers. Therefore, the most convenient way to manage the multi-modal traffic system is to set up bus lanes to give priority to ensuring the travel rights and interests of the majority of public transportation users. Generally, there are two difficulties in setting up bus lanes: one is how to reasonably balance the travel rights and interests of public transportation users and non-public transportation users so that different modes of travelers can fairly use limited road infrastructure resources; the other is how to use scientific and reasonable methods to achieve the optimization design of bus lanes at the large-scale urban road network level.

[0004] Currently, the bus lane design methods proposed at home and abroad can be divided into two categories, which are respectively oriented towards small-scale networks and large-scale networks. The design methods for small-scale channels and networks may cause serious traffic congestion and traffic spillover when applied to actual large-scale networks, and they are not applicable to large-scale networks. And there are also two categories of design methods for large-scale networks: one is optimization-oriented, establishing a mathematical model and solving for the optimal bus lane design scheme through an optimization algorithm. However, the dynamic evolution characteristics of the actual large-scale multi-modal traffic system are difficult to accurately describe through a mathematical model; the other is evaluation-oriented, using a simulation tool to establish a simulation model of the actual traffic network and evaluating the effects of different schemes through the simulation model. Although this type of method uses a simulation model to simulate the traffic system, it does not propose an optimization framework and quantitative analysis method for bus lanes. Summary of the Invention

[0005] The present invention aims to realize the simulation and optimization design of bus lanes in a large-scale multi-mode transportation system based on an agent-assisted evolutionary algorithm. A simulation optimization method for bus lanes based on an agent-assisted evolutionary algorithm includes the following steps:

[0006] S1: Establish a simulation model and an optimization mathematical model of the road network;

[0007] S 1。1 : Obtain the traffic demand and supply data of the road network to be optimized, including the distribution and characteristic information of road network nodes and sections, the OD demand of the road network, the bus lines passing through the road network, and the departure frequencies.

[0008] S 1。2 : Use the traffic demand and supply information to establish a simulation model of the road network to be optimized. The type of the simulation model is not limited, such as numerical simulation based on traffic flow theory, or microscopic and mesoscopic simulation models based on simulation software. Establish a two-layer optimization mathematical model as follows:

[0009] 1. Top-level model:

[0010]

[0011] Δ = {δ1,..., δ n} T δ i ∈ {0, 1} Equation (2)

[0012]

[0013] δ1 = δ2 (if δ1 = 1) Equation (4)

[0014] δ n-1 = δ n (if δ n = 1) Equation (5)

[0015]

[0016] 2. Bottom-level model:

[0017]

[0018]

[0019]

[0020]

[0021]

[0022] Where: δ i—— The value of the \(i\)-th bus lane candidate section, where 0 indicates that no bus lane is set on this section, and 1 indicates that a bus lane is set;

[0023] T —— The travel time of all users in the road network;

[0024] T b —— The travel time of all bus users in the road network;

[0025] T c —— The travel time of all non-bus users in the road network;

[0026] q a，c —— The non-bus traffic flow on section \(a\);

[0027] q a，b —— The bus traffic flow on section \(a\);

[0028] λ —— The flow conversion coefficient between buses and non-buses;

[0029] d rs —— The traffic demand from origin \(r\) to destination \(s\);

[0030] —— The path flow of the \(k\)-th path from origin \(r\) to destination \(s\).

[0031] Equation (1) is the objective function of the top-level model, with the minimum travel time of all users as the optimization goal; Equation (2) is the decision variable to be optimized; Equations (3)-(6) are the constraints for continuous bus lane layout; Equation (7) is the objective function of the bottom-level model, i.e., user equilibrium; Equations (8)-(11) are the flow conservation constraints.

[0032] S2: Obtain the simulation sample data set \(S\) of decision variables based on Latin Hypercube Sampling (LHS):

[0033] S 2。1 : Use Latin Hypercube Sampling to uniformly sample within the solution space of the variables to be optimized, and select \(p\) solutions that meet the constraints of the top-level model from the sampling results:

[0034] X ini = {Δ1, Δ2,..., Δ p} Equation (12)

[0035] S 2。２ : Sequentially substitute the solutions Δ ini in X i into the simulation model to calculate the objective function value and establish the simulation sample data set \(S\):

[0036]

[0037] S3: Establish a surrogate model of the simulation model using the sample data set;

[0038] S 3。1 : Select a suitable machine learning model as the surrogate model of the simulation model. The present invention provides four machine learning models S 3。2 : Calibrate the hyperparameters of the selected surrogate model based on N-fold cross-validation and grid search to make the fitting ability and generalization ability of the surrogate model for the sample data set S the best. The parameters to be calibrated and their value ranges for the four models are shown in Table 1:

[0039] Table 1 Hyperparameters to be calibrated for the surrogate model

[0040]

[0041] S 3。3 : Substitute the optimal hyperparameters into the machine learning model and train a surrogate model of the simulation optimization objective function using the simulation sample data set S;

[0042] S4: Use the surrogate model-assisted evolutionary algorithm (SAEA) to obtain the optimal solution set of the decision variables. The present invention uses a multi-population genetic algorithm with strong global optimization ability, and the surrogate model is the fitness evaluation function of the population. After a finite number of iterations of the evolutionary algorithm, the optimal solution set E of the decision variables is obtained T = {Δ1, Δ2,..., Δ n};

[0043] S5: Select the most ideal solution from the optimal solution set based on the idea of surrogate model integration and sample jackknife method;

[0044] S 5。1 : Divide the simulation sample data set S into m non-overlapping subsets S1, S2,..., S m .

[0045] S 5。2 : Use the m non-overlapping subsets S1, S2,..., S m to establish m new data sets:

[0046]

[0047] The travel time of all users includes the travel time of bus users and non-bus users, and the calculation formula is shown in Formulas (I)-(III):

[0048] t c = ρ1∑ a∈A x a p(x a + λx a，bus ) Formula (I)

[0049]

[0050] t = t c + t b Equation (III)

[0051] where: t is the travel time of all users, t c is the travel time of non-bus users, t b is the travel time of bus users, λ is the equivalent conversion coefficient of buses, ρ1 is the number of passengers carried by non-buses, ρ2 is the number of passengers carried by buses, x a is the non-bus flow on section a, x a，bus is the bus flow on section a;

[0052] S 5。3 : Use datasets SN1, SN2,..., SN m to train m different surrogate models respectively;

[0053] S 5。4 : Predict the objective function values of the optimal solution set E T based on m different surrogate models to obtain the objective function value matrix of the optimal solution set

[0054]

[0055] where: —— The predicted value of the objective function value of the solution Δ j established by the surrogate model based on the dataset SN i of the objective function value

[0056] S 5。5 : Calculate the mean and variance of the objective function values corresponding to each solution in the optimal solution set E T :

[0057]

[0058]

[0059] i = 1, 2,..., n

[0060]

[0061]

[0062] S 5。6 : Calculate the expected improvement EI that the solutions in the optimal solution set E T are better than the current optimal solution in turn:

[0063]

[0064] EI(X) = [EI(Δ1), EI(Δ2),..., EI(Δ n )] Equation (24)

[0065] Where: Φ — Distribution function of the standard normal distribution; φ — Probability density function of the standard normal distribution;

[0066] S 5。7 : Select the most ideal solution Δ from the optimization solution set E according to the expected value EI T opt :

[0067]

[0068] S6: Substitute the most ideal solution Δ opt into the simulation model to calculate its true objective function value and add the new simulation sample to the real sample data set:

[0069]

[0070] Furthermore, the algorithm process iterates. When the number of iterations t meets the following conditions, the algorithm terminates and outputs the optimal solution Δ best :

[0071]

[0072] The pseudo - code for the optimization design of bus - only lanes in the road network proposed by the present invention is shown in Table II, and the algorithm process is as follows Figure 1 :

[0073] Table II Pseudo - code for optimization design

[0074]

[0075]

[0076] Compared with the prior art, the present invention makes full use of the simulation and characterization ability of the traffic simulation model for the dynamic evolution characteristics of large - scale traffic systems. Combining with the evolutionary optimization algorithm, it uses the combined advantages of the simulation model and the optimization algorithm to realize the optimization design of bus - only lanes in large - scale networks. The present invention fully utilizes the idea of simulation optimization, trains the surrogate model using part of the known simulation model sample information, and uses the surrogate - assisted evolutionary algorithm to reduce the number of times of calling the expensive simulation model during the optimization process. Different from common simulation optimization methods, the present invention uses a machine - learning model with strong non - linear mapping ability as the surrogate model, and proposes a model management strategy based on the surrogate model integration method and the sample jackknife method, further improving the computational efficiency of the surrogate - assisted evolutionary algorithm in the simulation optimization problem of bus - only lanes in large - scale road networks. ​

[0077] The present invention has the following beneficial effects:

[0078] 1. The present invention uses a simulation model as an evaluation tool for optimizing the optimization scheme, can simulate the dynamic evolution process of the traffic system, and the optimization method does not depend on a specific simulation model, having high portability.

[0079] 2. Based on the simulation model and the optimization algorithm, the present invention can obtain a quantitative optimization scheme for the bus lanes on the road network.

[0080] 3. Using a surrogate model to replace some of the expensive calculations that need to be completed by the simulation model greatly reduces the computational amount of simulation optimization.

[0081] 4. A process of establishing a surrogate model by using a machine learning method and predicting the simulation results is proposed, which has higher optimization efficiency than the traditional simulation optimization method. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 Schematic diagram of the traffic network algorithm process adopted in the embodiment of the present invention;

[0083] Figure 2 Simulation road network of Sioux Falls used in the embodiment of the present invention;

[0084] Figure 3 Flow chart of the numerical simulation method adopted in the embodiment of the present invention;

[0085] Figure 4 Simulation sample data set obtained based on Latin hypercube sampling in the embodiment of the present invention;

[0086] Figure 5 Accuracy comparison of different surrogate models established in the embodiment of the present invention;

[0087] Figure 6 Computing time comparison of different surrogate models established in the embodiment of the present invention;

[0088] Figure 7 Iterative efficiency of different surrogate-assisted evolutionary algorithms adopted in the embodiment of the present invention;

[0089] Figure 8 Optimization result in the embodiment of the present invention;

[0090] Figure 9 Comparison of the road network travel times under different bus lane layout schemes in the embodiment of the present invention;

[0091] Figure 10 Method flow block diagram of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0092] The following will describe in detail the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention: This embodiment is implemented on the premise of the technical solution of the present invention, and gives a detailed implementation manner and specific operation process. However, the protection scope of the present invention is not limited to the following examples. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the protection scope of the present invention.

[0093] Embodiment 1: Figure 2 It is the simulated road network of Sioux Falls used in the embodiment of the present invention. This simulated road network is developed based on the traffic road network of Sioux Falls, South Dakota, USA. The entire road network includes 24 traffic analysis zones, 24 nodes, 76 road segments, and 576 traffic OD demands. In this embodiment, 2 bus lines are assumed to be introduced in the Sioux Falls network, and 20 candidate road segments for bus lanes are determined on the road segments passed by the bus lines. Therefore, the dimension of the decision space in this embodiment is 20. The traffic supply and demand data of this embodiment are shown in Tables 3 to 5.

[0094] Table 3 Embodiment Road Network Supply Data

[0095]

[0096]

[0097]

[0098] Table 4 Embodiment Road Network Non-Public Transport Demand Data

[0099]

[0100]

[0101]

[0102] Table 5 Embodiment Road Network Public Transport Demand Data

[0103] Bus line Demand 3，2，7，37，38，35，5，1 1500 6，9，13，25，28，45，37，43，26，23，11，8 1500

[0104] Establish a traffic simulation model and an optimization mathematical model of the multi-modal traffic system to be optimized according to the demand and supply data of the embodiment road network. The bus lane optimization design method proposed by the present invention does not depend on a specific simulation model, and various simulation methods such as numerical simulation, microscopic simulation, and mesoscopic simulation can be used to simulate the multi-modal traffic system. The simulation model used in this embodiment is a numerical simulation model for solving the deterministic user equilibrium based on the improved Frank-Wolfe algorithm. The flow chart of the numerical simulation model is as Figure 3As shown below. The optimized mathematical model and the parameter values in the model are as follows:

[0105] 1. Top - level model:

[0106]

[0107]

[0108]

[0109] Δ = {δ1,..., δ n} T , δ i ∈ {0, 1}

[0110] s.t.

[0111]

[0112] δ1 = δ2 (if δ1 = 1)

[0113] δ n-1 = δ n (if δ n = 1)

[0114]

[0115] 2. Bottom - level model:

[0116]

[0117]

[0118]

[0119]

[0120]

[0121] Where: δ i —— The value of the i - th bus - only lane candidate section, 0 means no bus - only lane is set on this section, 1 means a bus - only lane is set; λ is the flow conversion coefficient between buses and ordinary vehicles, which is 2.5 in this embodiment; ρ1 is the passenger capacity of ordinary vehicles, which is 2 in this embodiment; ρ2 is the passenger capacity of buses, which is 15 in this embodiment. At the same time, in this embodiment, it is stipulated that the capacity of the bus - only lane is 5000 PCEs / time unit, and the free - flow time of the bus - only lane is 1.2 times that of the ordinary section.

[0122] In this embodiment, the convergence threshold of the bottom - level model is set to 10 -3 :

[0123]

[0124] Secondly, based on Latin hypercube sampling, sample information of the simulation model is obtained, and a sample data set of the objective function is established. The sample data set S of this embodiment is as Figure 4 shown.

[0125] Based on the sample data set, a machine learning model can be selected to establish a surrogate model. The following surrogate model evaluation indicators are established in this embodiment:

[0126]

[0127]

[0128]

[0129]

[0130]

[0131] For any solution Δ i , is the objective function value predicted by the surrogate model, and is the objective function value evaluated by the simulation model. The calculation accuracy and efficiency results of each surrogate model are shown in Table VI. It can be seen from Table VI that the calculation efficiency and calculation accuracy of the machine learning-based surrogate model used in this method are significantly better than those of the traditional Gaussian process-based surrogate model.

[0132] Table VI Road network supply data of the embodiment

[0133]

[0134] Figure 5 and Figure 6 are the model accuracy and calculation efficiency of different surrogate models established in this embodiment. Compared with the surrogate model KPLS commonly used in the traditional simulation optimization method, the calculation time of the machine learning-based surrogate model is shorter, and the prediction accuracy of some surrogate models (such as SVR and XGB) is relatively ideal.

[0135] The bus-only lane of the Sioux Falls network can be optimized by using the surrogate model-assisted evolutionary algorithm. Figure 7 is the optimization efficiency of different surrogate-assisted evolutionary algorithms in this embodiment. It can be seen that XGB-GA can converge to the optimal value after 10-20 iterations, and has a higher iteration efficiency than the commonly used KPLS-GA.

[0136] Figure 8 is the optimized design scheme of the bus-only lane of the Sioux Falls network obtained.Figure 9 The travel times of users under different scenarios are recorded. If bus lanes are set on all candidate road segments, the travel time of all users is 2.4165×10 7 s. If no bus lanes are set, the travel time of all users is 2.4400×10 7 s. Under the optimal bus lane setting scenario, the travel time of all users is 2.2974×10 7 s. Compared with the scenario of setting bus lanes on all road segments, the travel time of all users is reduced by 4.93% under the optimal scenario. Compared with the scenario of not setting bus lanes, the travel time of all users is reduced by 5.84%. It can be seen that the bus lane design method proposed in the present invention can significantly reduce the travel time of all users in a multi-modal transportation network and effectively improve the traffic efficiency of the multi-modal transportation system.

Claims

1. A simulation optimization method for bus lanes based on an agent-assisted evolutionary algorithm, characterized in that: The specific implementation steps are as follows: S1: Establish a road network simulation model and an optimization mathematical model; establish a two-layer model to optimize the bus lanes of large-scale road networks. The top-level model aims to minimize the travel time of all users, and the decision variables are n 0-1 variables. The bottom-level model is a deterministic user equilibrium model; S2: Collect initial simulation samples of decision variables based on Latin hypercube sampling; uniformly sample within the solution space of the variables to be optimized based on Latin hypercube sampling, screen the solutions that meet the constraints from the sampling results, substitute them into the simulation model to calculate the objective function value, and finally establish a simulation sample data set; Among them, the travel time of all users includes the travel time of bus users and non-bus users, and the calculation formulas are shown in Formulas (I)-(III): t c = ρ1Σ a∈A x a p(x a + λx a,bus ) Equation (I) t = t c + t b Formula (III) Where: t is the travel time of all users, t c is the travel time of non-bus users, t b is the travel time of bus users, λ is the equivalent conversion coefficient of buses, ρ1 is the passenger capacity of non-buses, ρ2 is the passenger capacity of buses, x a is the non-bus flow on section a, x a，bus is the bus flow on section a; S3: Use the initial simulation samples to establish a surrogate model of the simulation model; S4: Use the surrogate model-assisted evolutionary algorithm to obtain the optimized solution set of decision variables; S5: Select the most ideal solution from the optimized solution set based on the surrogate model integration method and the sample jackknife method; the specific implementation steps are as follows: calculate the uncertainty of the predicted value of the objective function calculated by the surrogate model based on the ideas of surrogate model integration and sample jackknife method. The specific steps are as follows: Divide the simulation sample data set S into m non - overlapping subsets S1, S2, ..., Sm m , and use the m non - overlapping subsets S1, S2, ..., Sm m to establish m new data sets: Use datasets SN1, SN2, ..., SN respectively m Train to obtain m different surrogate models, and predict the objective function values of the solutions based on the m different surrogate models Calculate the mean of the predicted values and variance S6: Substitute the most ideal solution into the simulation model for verification and update the surrogate model.

2. The bus lane simulation optimization method based on the proxy-assisted evolutionary algorithm according to claim 1, characterized in that: Use common machine learning methods such as KNN, RF, SVR, or XGB as surrogate models.

3. A bus lane simulation optimization method based on an agent-assisted evolutionary algorithm according to claim 1, characterized in that: Use the surrogate-assisted evolutionary algorithm to search for the optimal bus lane layout plan.

4. A bus lane simulation optimization method based on an agent-assisted evolutionary algorithm according to claim 1, characterized in that Based on the actual characteristics of the continuous appearance of bus lanes in the road network, constraints related to the continuity of bus lanes are set in the top-level model.

5. A bus lane simulation optimization method based on an agent-assisted evolutionary algorithm according to claim 1, characterized in that Calibrate the hyperparameters of the selected surrogate model based on N-fold cross-validation and grid search method to make the fitting ability and generalization ability of the surrogate model for the sample data set S the best.

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