A signal intersection lane assignment method and device based on bayesian optimization

Abstract

The application discloses a signal intersection lane assignment method and device based on Bayesian optimization, which comprises the following steps: obtaining traffic demand to be assigned; constructing a two-stage stochastic programming model for signal intersection lane assignment; solving the two-stage stochastic programming model by using an improved Bayesian optimization method to obtain a benchmark lane assignment scheme result; the optimization target of the first-stage stochastic programming model is to minimize the expected value of delay of k scenes, and the benchmark control scheme is provided for the second stage; the optimization target of the second-stage stochastic programming model is to minimize the average delay of vehicles in each scene, and the delay evaluation result is provided for the first stage; the improved Bayesian optimization method can not only guarantee that the lane assignment problem converges to a global optimal solution, but also accelerate the convergence speed by fusing traffic physical information. The application has high accuracy and high efficiency, is helpful to improve the vehicle passing efficiency of the signal intersection, and can be widely applied to the technical field of intelligent transportation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent transportation, and in particular to a signal intersection lane assignment method and device based on Bayesian optimization. BACKGROUND

[0002] The rapid development of social economy stimulates the continuous growth of residents' travel demand, causing the increasingly prominent traffic congestion problem. Improving the road supply capacity can alleviate the imbalance between traffic supply and demand, and thus improve the traffic congestion status. The signal intersection is a key node in the traffic network, and reasonable lane function assignment is conducive to improving the intersection capacity and reducing the waiting time of vehicles passing through the intersection. In view of the random characteristics of traffic demand, the existing intersection lane assignment method constructs a two-stage stochastic programming model, and proposes a solving algorithm to obtain a reasonable and feasible benchmark lane assignment scheme. However, due to the complexity of the two-stage stochastic programming problem, the existing solving algorithm is easy to fall into a local optimal solution, and the calculation accuracy needs to be further improved.

[0003] The existing technology has the following disadvantages: first, in the random traffic demand scenario, the lane assignment problem of the signal intersection can be modeled as a two-stage stochastic programming problem, and the traditional solving algorithm of this kind of problem is easy to fall into a local optimal solution. The Bayesian optimization method is a global optimization method, and it has not been applied to solve this kind of problem. Second, the two-stage stochastic programming problem has high computational complexity, and the conventional Bayesian optimization method cannot effectively utilize the traffic physical information contained in the lane assignment problem, and needs to consume high computational resources to converge to the global optimal solution. SUMMARY

[0004] The main purpose of the embodiments of the present application is to provide an accurate and efficient signal intersection lane assignment method and device based on Bayesian optimization, which can improve the vehicle passing efficiency of the signal intersection.

[0005] To achieve the above-mentioned purpose, one aspect of the embodiments of the present application provides a signal intersection lane assignment method based on Bayesian optimization, comprising the following steps:

[0006] Obtaining a traffic demand to be assigned;

[0007] According to the traffic demand to be assigned, a two-stage stochastic programming model for the signal intersection lane assignment problem is constructed;

[0008] An improved Bayesian optimization method is used to solve the two-stage stochastic programming model to obtain a benchmark lane assignment scheme result;

[0009] The optimization objective of the first-stage stochastic programming model is to minimize the expected delay value of the k scenarios, and the first-stage stochastic programming model provides a benchmark control scheme for the second stage; the optimization objective of the second-stage stochastic programming model is to minimize the average delay of vehicles in each scenario, and the second-stage stochastic programming model provides a delay evaluation result for the first stage, wherein the traffic flow randomness of the kth scenario is responded to by adjusting the benchmark signal timing scheme;

[0010] The improved Bayesian optimization method comprises two core parts, i.e., a probability surrogate model and an acquisition function, and the Gaussian process model and the expected improvement criterion are respectively used according to the characteristics of the lane assignment problem; the approximate delay value corresponding to the to-be-observed control scheme is taken as prior traffic physical information, the kernel function design in the Gaussian process model is improved, and the algorithm is accelerated to converge to a global optimal solution.

[0011] Optionally, the expression of the two-stage stochastic programming model is as follows:

[0012]

[0013] wherein,

[0014] D represents the delay expectation value of all traffic demand scenarios; E represents the operation of taking expectation; κ represents the scenario number of traffic demand; Dr κ (·) represents the average delay of scenario κ; P κ represents the possibility of the occurrence of scenario κ, and is uniformly set as 1 / K; N * is a benchmark lane assignment scheme; G b is a benchmark signal timing scheme; G κ is an executed signal timing scheme of scenario κ; Θ κ is a traffic demand scheme of scenario κ; φ represents a cycle number; i represents an import number of an intersection; k represents a lane number of the intersection; represents the traffic flow of import i lane k in scenario κ cycle φ; c κ,φ represents the cycle length of scenario κ cycle φ; represents the vehicle delay of import i lane k in scenario κ cycle φ;

[0015] The vehicle delay is calculated by using the shadow area method, and the calculation formula is as follows:

[0016]

[0017] wherein, represents the saturation flow rate of import i lane k in scenario κ cycle φ; represents the remaining queuing vehicle number of import i lane k in scenario κ cycle φ.

[0018] Optionally, the two-stage stochastic programming model satisfies three lane assignment constraints and two signal timing constraints.

[0019] wherein the first lane assignment constraint is that the sum of the number of lanes for various turning functions within the import i is equal to the total number of import lanes;

[0020] the second lane assignment constraint is that the number of lanes for various turning functions within the import i should not exceed the corresponding total number of export lanes;

[0021] the third lane assignment constraint is that the constraint lane flow ratio is equal to the total lane flow rate divided by the saturation flow rate, and the corresponding turning flow ratio should be equal when the shared lane is set;

[0022] the first signal timing constraint is that the green time for left turn, straight and right turn of the same import in the two-phase scheme should be equal; the green time for left turn of an import should be equal to the green time for left turn of the opposite import; and the sum of the green time and the phase interval time is equal to the signal cycle length;

[0023] the second signal timing constraint is the maximum and minimum constraints of the green time and the cycle length.

[0024] Optionally, the expression of the first lane assignment constraint is:

[0025] n i,l +n i,ls +n i,s +n i,sr +n i,r +n i,lsr =k i,max

[0026] n i,ls ≤1,n i,sr ≤1,n i,lsr ≤1

[0027] (n i,ls +n i,s +n i,sr )·n i,lsr =0

[0028]

[0029] wherein n i,l , n i,ls , n i,s , n i,sr , n i,r , n i,lsr represent the number of exclusive left turn lanes, straight-left shared lanes, exclusive straight lanes, straight-right shared lanes, exclusive right turn lanes and straight-left-right shared lanes of import i respectively; Q i,1 , Qi,2 ,Q i,3 respectively represent the left-turn, straight and right-turn traffic volume of the import i, and M is a sufficiently large positive number;

[0030] The expression of the second lane assignment constraint is:

[0031]

[0032] wherein E i,1 ,E i,2 ,E i,3 respectively represent the total number of exit lanes corresponding to the left-turn, straight and right-turn traffic volume of the import i;

[0033] The expression of the third lane assignment constraint is:

[0034]

[0035]

[0036] wherein j represents the turning direction, j = 3 / 2 / 1 respectively represent left-turn, straight and right-turn; represents the turning j traffic volume of the import i lane k in the scene κ period φ; represents the lane traffic ratio of the import i lane k in the scene κ period φ; represents the turning traffic ratio of the import i turning j in the scene κ period φ;

[0037] The expression of the first signal timing constraint is:

[0038]

[0039] wherein A κ,φ represents the phase interval time in the scene κ period φ;

[0040] The expression of the second signal timing constraint is:

[0041]

[0042] wherein, represents the turning green time of the import i turning j in the scene κ period φ, and respectively correspond to the minimum / maximum value of the turning green time; respectively correspond to the minimum / maximum value of the period length.

[0043] Optionally, the improved Bayesian optimization method is used to solve the two-stage stochastic programming model, comprising the following steps:

[0044] A two-stage stochastic programming model of the lane assignment problem at signalized intersections is constructed; parameters such as the target iteration number T, the initial point number T0, and the input point number N of each iteration are set; T0 sets of control schemes satisfying the constraints are extracted as initial observation points by the Latin hypercube sampling method, and the delay expectation values calculated are taken as observation values; the current iteration number t is set to T0; max , the initial point number T0, and the input point number N of each iteration are set; T0 sets of control schemes satisfying the constraints are extracted as initial observation points by the Latin hypercube sampling method, and the delay expectation values calculated are taken as observation values; the current iteration number t is set to T0;

[0045] When the iteration number of the algorithm meets the target iteration number, the next step is executed until the iteration of the target iteration number is completed.

[0046] If t>T0 is true, the delay expectation value of the new observation point is calculated as its observation value, and the next step is executed; if not, the next step is directly entered.

[0047] The traffic physical information of all observation points is calculated, and the current Gaussian process model is updated.

[0048] N input points satisfying the constraint conditions are randomly extracted by interpolation method, the traffic physical information of each input point is calculated, the prediction mean and variance of the objective function corresponding to each input point are calculated, and the expected improvement value of each input point is calculated to determine the observation point of the next iteration.

[0049] Optionally, the improved Bayesian optimization method is used to solve the two-stage stochastic programming model, and the method further comprises at least one of the following steps:

[0050] According to the characteristics of the lane assignment problem, a Gaussian process model is used as a probability surrogate model, wherein the prior probability distribution of the Gaussian process is represented by a multivariate normal distribution, and for a new input point, the Gaussian process predicts the mean and variance of the objective function by estimating the multivariate normal distribution.

[0051] The surface smoothness of the objective function based on the delay expectation value is unknown, and a Matern kernel function is used to calculate the covariance between two observation points.

[0052] According to the characteristics of the lane assignment problem, an expected improvement criterion is used as a sampling strategy.

[0053] Optionally, the expression of the Matern kernel function is as follows:

[0054]

[0055] Wherein, k(τ m ,τ n ) represents the covariance between observation point τ m and observation point τ n ; r represents the observation point τ m and the observation point τ nThe Euclidean distance between them; l is a hyperparameter;

[0056] The expression for the sampling strategy is:

[0057]

[0058] Where EI(x) represents the expected improvement value of input point x; f(x) represents the objective function of input point x calculated according to the probabilistic surrogate model; f* represents the currently known global optimal objective function value; p(f(x)|τ 1:t ) represents the observation point τ. 1:t Given the condition, the posterior probability distribution of the objective function.

[0059] In some embodiments, calculating the traffic physical information of all observation points and updating the current Gaussian process model includes the following steps:

[0060] The traffic physical information at the observation point refers to the Webster approximate delay value calculated based on the baseline control scheme, and its expression is:

[0061]

[0062]

[0063] in, Represents a given baseline lane assignment scheme N n Timing scheme with reference signal The Webster delay value is calculated using this as input; c represents the baseline lane flow rate of lane i at the entrance; b Indicates the duration of the reference period; This indicates the baseline lane delay for import lane i (k); y i,k x represents the baseline lane flow ratio for lane i at entrance k, i.e., the ratio between the flow rate and the saturation flow rate; i,k This represents the baseline lane saturation of lane i at the entrance, i.e., the ratio between the flow rate ratio and the green light ratio.

[0064] The update process of the Gaussian process model includes the calculation of the Matern kernel function, and the Matern kernel function is improved by incorporating traffic physics information from the observation points. Its expression is:

[0065]

[0066] Where r' represents the correlation between the two observation points; r represents the Euclidean distance between the two observation points; Dr b (τ n ) indicates that when the observation point is τ nAt that time, the approximate delay value is obtained by calculating the corresponding baseline control scheme using the Webster delay formula; l and h are both hyperparameters.

[0067] Another aspect of this invention provides a Bayesian-optimized lane allocation device for signalized intersections, comprising:

[0068] The first module is used to obtain traffic demand to be allocated;

[0069] The second module is used to construct a two-stage stochastic programming model for the lane allocation problem at signalized intersections based on the traffic demand to be allocated.

[0070] The third module is used to solve the two-stage stochastic programming model using an improved Bayesian optimization method to obtain the baseline lane allocation scheme result.

[0071] The optimization objective of the first-stage stochastic programming model is to minimize the expected delay value of k scenarios. The first-stage stochastic programming model provides a baseline control scheme for the second stage. The optimization objective of the second-stage stochastic programming model is to minimize the average vehicle delay in each scenario and provide delay evaluation results for the first stage. The randomness of traffic flow in the kth scenario is addressed by adjusting the baseline signal timing scheme.

[0072] The improved Bayesian optimization method comprises two core components: a probabilistic surrogate model and a data acquisition function. Based on the characteristics of the lane allocation problem, a Gaussian process model and an expected improvement criterion are used for specific implementation. The approximate delay value corresponding to the control scheme to be observed is used as prior traffic physical information, and the kernel function design in the Gaussian process model is improved to accelerate the algorithm's convergence to the global optimum.

[0073] Another aspect of the present invention provides an electronic device, including a processor and a memory;

[0074] The memory is used to store programs;

[0075] The processor executes the program to implement the method described above.

[0076] Another aspect of this invention provides a computer-readable storage medium storing a program that is executed by a processor to implement the methods described above.

[0077] This invention also discloses a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions, causing the computer device to perform the aforementioned method.

[0078] The embodiments of this invention include at least the following beneficial effects: This invention provides a method and apparatus for lane allocation at signalized intersections based on Bayesian optimization. First, the invention obtains the traffic demand to be allocated; then, based on the traffic demand, it constructs a two-stage stochastic programming model for lane allocation at signalized intersections; finally, it uses an improved Bayesian optimization method to solve the two-stage stochastic programming model to obtain a baseline lane allocation scheme result. The optimization objective of the first-stage stochastic programming model is to minimize the expected delay values ​​of k scenarios, and the first-stage stochastic programming model provides a baseline control scheme for the second stage. The optimization objective of the second-stage stochastic programming model is to minimize the average vehicle delay in each scenario and provide a delay evaluation result for the first stage. The randomness of traffic flow in the kth scenario is addressed by adjusting the baseline signal timing scheme. The improved Bayesian optimization method includes two core parts: a probabilistic surrogate model and a data acquisition function. Based on the characteristics of the lane allocation problem, a Gaussian process model and an expected improvement criterion are used for specific implementation. The approximate delay value corresponding to the observed control scheme is used as prior traffic physical information, and the kernel function design in the Gaussian process model is improved, accelerating the algorithm's convergence to the global optimum. This invention is highly accurate and efficient, which helps to improve the traffic flow efficiency of signalized intersections. Attached Figure Description

[0079] Figure 1 This is a schematic diagram of an implementation environment provided by an embodiment of the present invention;

[0080] Figure 2 This is a flowchart of the overall steps provided in the embodiments of the present invention;

[0081] Figure 3 This is an overall framework diagram provided in the embodiments of the present invention;

[0082] Figure 4 This is a schematic diagram of the shadow area calculation method for lane delay provided in an embodiment of the present invention;

[0083] Figure 5 This is a schematic diagram of lane types provided in an embodiment of the present invention;

[0084] Figure 6 This is a schematic diagram of a two-phase scheme provided in an embodiment of the present invention;

[0085] Figure 7 This is a schematic diagram of the Bayesian optimization method provided in an embodiment of the present invention;

[0086] Figure 8 This is a schematic diagram of an intersection provided in an embodiment of the present invention;

[0087] Figure 9This is a schematic diagram of the experimental results of a simplified traffic demand scenario provided in an embodiment of the present invention. Detailed Implementation

[0088] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the embodiments of this invention; they are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this invention as detailed in the appended claims.

[0089] It is understood that the terms “first,” “second,” etc., used in this invention may be used herein to describe various concepts, but unless specifically stated otherwise, these concepts are not limited by these terms. These terms are used only to distinguish one concept from another. For example, first information may also be referred to as second information without departing from the scope of embodiments of the invention, and similarly, second information may also be referred to as first information. Depending on the context, the words “if,” “when,” or “in response to determination” as used herein may be interpreted as “when…” or “when…” or “in response to determination.”

[0090] The terms “at least one,” “multiple,” “each,” “any,” etc., used in this invention, “at least one” includes one, two, or more than two; “multiple” includes two or more than two; “each” refers to each of the corresponding multiple; and “any” refers to any one of the multiple.

[0091] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein is for the purpose of describing embodiments of the invention only and is not intended to limit the invention.

[0092] The Bayesian-optimized lane allocation method and apparatus for signalized intersections provided in this invention relates to the field of intelligent transportation technology. The Bayesian-optimized lane allocation method for signalized intersections provided in this invention can be applied to a terminal, a server, or software running on either a terminal or a server. In some embodiments, the terminal can be a smartphone, tablet, laptop, desktop computer, smart speaker, smartwatch, or vehicle-mounted terminal, but is not limited to these. The server can be configured as an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms. The server can also be a node server in a blockchain network. The software can be an application implementing the Bayesian-optimized lane allocation method for signalized intersections, but is not limited to the above forms.

[0093] This invention can be used in a wide variety of general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices. This invention can be described in the general context of computer-executable instructions, such as program modules, that are executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform specific tasks or implement specific abstract data types. This invention can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0094] like Figure 1 The diagram shown is a schematic representation of an implementation environment provided by an embodiment of the present invention. (Refer to...) Figure 1 The implementation environment includes at least one terminal 102 and a server 101. The terminal 102 and the server 101 can be connected via a network, either wirelessly or via a wired connection, to complete data transmission and exchange.

[0095] Server 101 can be a standalone physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN (Content Delivery Network), and big data and artificial intelligence platforms.

[0096] Additionally, server 101 can also be a node server in a blockchain network. Blockchain is a novel application model of computer technologies such as distributed data storage, peer-to-peer transmission, consensus mechanisms, and encryption algorithms.

[0097] Terminal 102 can be a smartphone, tablet, laptop, desktop computer, smart speaker, smartwatch, etc. It can also be a vehicle-mounted terminal of the various device types described above, but is not limited to these. Terminal 102 and server 101 can be directly or indirectly connected via wired or wireless communication, and this embodiment of the invention does not impose any limitations.

[0098] Exemplary based on Figure 1 The implementation environment shown in this embodiment of the invention provides a Bayesian optimization-based lane allocation method for signalized intersections. The following description uses the application of this Bayesian optimization-based lane allocation method in server 101 as an example. It can be understood that this method can also be applied in terminal 102.

[0099] To address the problems existing in current technologies, this invention provides a lane allocation method for signalized intersections based on improved Bayesian optimization. The method includes the following steps: First, mathematically modeling the lane allocation problem at signalized intersections under stochastic traffic demand scenarios, resulting in a two-stage stochastic programming model with the objective function of minimizing the expected delay value; Second, based on the characteristics of the lane allocation problem, the two core components of the conventional Bayesian optimization method—the probabilistic surrogate model and the acquisition function—are respectively modified using a Gaussian process model and an expectation improvement criterion to initially solve the lane allocation problem; Third, using the approximate delay value corresponding to the observed control scheme as prior traffic physical information, the kernel function design in the Gaussian process model is improved, accelerating the algorithm's convergence to the global optimum; Specific implementation steps of the improved Bayesian optimization method are provided. This invention can improve the solution accuracy of the lane allocation problem and reduce computational costs, and can be widely applied in road traffic management, intelligent transportation, and other technical fields.

[0100] Reference Figure 2 , Figure 2The flowchart illustrates a Bayesian-optimized lane allocation method for signalized intersections applied to a server, as provided in this embodiment of the invention. The execution entity of this method can be any of the aforementioned computer devices (including a server or a terminal). (Refer to...) Figure 2 The method may include the following steps:

[0101] Obtain the traffic demand to be allocated;

[0102] Based on the traffic demand to be allocated, a two-stage stochastic programming model is constructed for the lane allocation problem at signalized intersections.

[0103] An improved Bayesian optimization method was used to solve the two-stage stochastic programming model to obtain the baseline lane allocation scheme.

[0104] The optimization objective of the first-stage stochastic programming model is to minimize the expected delay value of k scenarios. The first-stage stochastic programming model provides a baseline control scheme for the second stage. The optimization objective of the second-stage stochastic programming model is to minimize the average vehicle delay in each scenario and provide delay evaluation results for the first stage. The randomness of traffic flow in the kth scenario is addressed by adjusting the baseline signal timing scheme.

[0105] The improved Bayesian optimization method comprises two core components: a probabilistic surrogate model and a data acquisition function. Based on the characteristics of the lane allocation problem, a Gaussian process model and an expected improvement criterion are used for specific implementation. The approximate delay value corresponding to the control scheme to be observed is used as prior traffic physical information, and the kernel function design in the Gaussian process model is improved to accelerate the algorithm's convergence to the global optimum.

[0106] like Figure 3 As shown, the overall solution of the present invention can be described in the following three steps:

[0107] Part 1: Modeling the Lane Assignment Problem

[0108] Considering the stochastic nature of traffic demand, the lane allocation problem at signalized intersections can be modeled as a two-stage stochastic programming model. Assuming there are K stochastic traffic demand scenarios, the optimization objective of the first stage is to minimize the expected delay value for each of the K scenarios. The baseline lane allocation scheme and baseline signal timing scheme obtained from the solution are used as the optimization input for the second stage. The optimization objective of the second stage is to minimize the average vehicle delay for each scenario. The κ-th scenario can be adjusted by modifying the baseline signal timing scheme to more flexibly address the randomness of traffic flow. The minimized delay values ​​for each scenario are then passed back to the first stage to calculate the expected delay value. The two-stage stochastic programming model is expressed as follows:

[0109]

[0110] in:

[0111]

[0112] Equation (1) is used to minimize the expected delay values ​​for K scenarios, i.e., to minimize D = E[Dr(·)]. Where D represents the expected delay value for all traffic demand scenarios; E represents the operation of taking the expected value; κ represents the scenario number of the traffic demand; Dr κ (·) represents the average delay of scenario κ; P κ The probability of scenario κ occurring is uniformly set to 1 / K; N * For the baseline lane allocation scheme; G b For reference signal timing scheme; G κ The execution signal timing scheme for scenario κ; Θ κ Let κ be the traffic demand scheme. Equation (2) is used to minimize the average delay of scenario κ, that is, to minimize Dr. κ (·). Where φ represents the cycle number; i represents the intersection entrance number; and k represents the intersection lane number; c represents the traffic flow in lane k of entrance i during period φ of scenario κ; κ,φ The duration of the period φ represents the period of the scene κ; This represents the vehicle delay in lane k of import i during the cycle φ of scenario κ.

[0113] To characterize the randomness of vehicle arrivals at signalized intersections, we adopted... Figure 4 The shaded area method shown is used to calculate lane delay. The formula is as follows:

[0114]

[0115] Among them, the first equation in equation (3) applies to the case where there are no remaining queued vehicles in scenario κ period φ, that is, it needs to meet the condition. The second equation in equation (3) applies to the scenario where there are remaining queued vehicles in period φ of scenario κ, that is, the condition needs to be met. This represents the saturation flow rate of lane k at inlet i in scenario κ period φ; The remaining number of vehicles queuing in lane k of entrance i during period φ of scenario κ is represented by the following formula:

[0116]

[0117] In addition, the two-stage stochastic programming model also needs to satisfy a series of lane allocation constraints (see constraints 1-3) and signal timing constraints (see constraints 4-5).

[0118] Constraint 1: The total number of lanes with various steering functions within the entrance i should be equal to the total number of entrance lanes, and the lane settings need to meet certain rules.

[0119] n i,l +n i,ls +n i,s +n i,sr +n i,r +n i,lsr =k i,max (5)

[0120] n i,ls ≤1, n i,sr ≤1, n i,lsr ≤1 (6)

[0121] (n i,ls +n i,s +n i,sr )·n i,lsr =0 (7)

[0122]

[0123] Where, n i,l ,n i,ls ,n i,s ,n i,sr ,n i,r ,n i,lsr These represent the number of dedicated left-turn lanes, shared straight-left lanes, dedicated straight lanes, shared straight-right lanes, dedicated right-turn lanes, and shared straight-left-right lanes for entrance i, respectively. Figure 5 As shown; Q i,1 Q i,2 Q i,3 Let M represent the traffic flow for left turns, straight ahead, and right turns at entrance i, respectively, where M is a sufficiently large positive number. Equation (5) constrains the total number of lanes; Equation (6) constrains the maximum number of shared lanes of the three types to be 1; Equation (7) constrains that when a shared lane for straight and left turns is set up, a shared lane for straight and left turns, a dedicated straight lane, and a shared lane for straight and right turns are not allowed to be set up, and vice versa; Equation (8) constrains that when the traffic flow for a certain turn at entrance i is greater than 0, a lane with the corresponding turning function should be set up.

[0124] Constraint 2: The number of lanes with various steering functions within the inlet i should not exceed the total number of corresponding exit lanes.

[0125]

[0126] Among them, E i,1 E i,2 E i,3 These represent the total number of exit lanes corresponding to the left-turning, straight-going, and right-turning traffic flows of inlet i, respectively.

[0127] Constraint 3: Calculation of the flow ratio of each lane within inlet i, and equal flow ratio constraint.

[0128]

[0129] Where j represents the direction of traffic flow, and j = 3 / 2 / 1 represent left turn / straight ahead / right turn respectively; This represents the traffic flow at the turning point j of lane i at the entrance in scenario κ during period φ. This represents the lane flow ratio of inlet lane i to lane k in the cycle φ of scenario κ; This represents the turning flow ratio of inlet i to turning j in the cycle φ of scenario κ; these two can be based on the lane assignment scheme N = (n i,l ,n i,ls ,n i,s ,n i,sr ,n i,r ,n i,lsr ) Mutual conversion. Equation (10) constrains the lane flow ratio to be equal to the sum of lane flows divided by the saturation flow rate; Equation (11) constrains that the corresponding turning flow ratios should be equal when a shared lane is set up. Taking the first formula of Equation (11) as an example, when a shared straight and left lane is set up, the left turn flow ratio and the straight flow ratio should be equal.

[0130] Constraint 4: Use a two-phase scheme to calculate the correspondence between green light time and cycle duration.

[0131]

[0132] Among them, A κ,φ This represents the phase interval time within the period φ of scene κ. For example... Figure 6 As shown, Equation (12) constrains the green light times for left turns, straight ahead and right turns at the same entrance in the two-phase scheme to be equal; Equation (13) constrains the green light time for left turns at a certain entrance to be equal to the green light time for left turns at the opposite entrance; Equation (14) constrains the sum of the green light time and the phase interval time to be equal to the signal cycle duration.

[0133] Constraint 5: Maximum and minimum values ​​for green light time and cycle duration.

[0134]

[0135]

[0136] in, This represents the green light time for the turn signal at inlet i turning j within the cycle φ of scenario κ, and... These correspond to the minimum and maximum values ​​of the turn signal green light time, respectively. These correspond to the minimum / maximum values ​​of the cycle duration; turn signal green light time. Lane green light time Alternatively, it can be based on lane allocation scheme N = (n i,l ,n i,ls ,n i,s ,n i,sr ,n i,r ,n i,lsr They can be transformed into each other.

[0137] Part Two: Conventional Bayesian Optimization Methods.

[0138] Bayesian optimization methods comprise two core components: a probabilistic surrogate model and a data acquisition function. For solving the two-stage stochastic programming model of the lane allocation problem, the computational complexity primarily lies in solving the second stage model. This is because the second stage requires simulating and optimizing numerous traffic demand scenarios to evaluate the expected delay of a given baseline control scheme. In Bayesian optimization, the probabilistic surrogate model can fit the true objective function; that is, given a set of baseline control schemes as input points, it can quickly calculate the predicted mean and confidence level of the objective function value, corresponding to the expected delay and uncertainty of the baseline control scheme. The data acquisition function, based on the fitting results of the input points, calculates the potential for a decrease in the expected delay, guiding the selection of the next evaluation point.

[0139] Taking the t-th evaluation process as an example, the observation points τ1, τ2, K, τ are known. t The nth observation point τ n Based on the baseline lane allocation scheme N n Timing scheme with reference signal Composition, that is Substituting each observation point into the two-stage stochastic programming model, the expected delay values ​​are calculated, namely the observed values ​​f(τ1), f(τ2), K, and f(τ). t The role of the probabilistic surrogate model is based on the set of observed point-value pairs {(τ1,f(τ1)),(τ2,f(τ2)),...,(τ...}. t ,f(τ t Predict a given input point τ t+1 The objective function value is calculated, and a confidence interval for the predicted function value is provided. The acquisition function then calculates the optimization "potential" of each input point based on the information provided by the surrogate model, and determines the input point with the highest "potential". As the observation point for the (t+1)th evaluation. Figure 7 As shown, throughout the entire iteration process, since the input point with the greatest optimization potential is selected for the next evaluation each time, the Bayesian optimization method can converge to the global optimum after a few iterations.

[0140] A probabilistic surrogate model consists of a prior model and an observation model. The prior model typically makes initial assumptions about the objective function based on the characteristics of the problem, while the observation model describes how the observed data is generated from the objective function. As new observations are continuously added, the prior model and the observation model update the posterior model, i.e., the probabilistic surrogate model, using Bayes' theorem, as shown in the following expression:

[0141]

[0142] Where, τ 1:t Represents the observation points τ1,τ2,K,τ t ; p(f) represents the prior probability distribution of the objective function f; p(τ) 1:t |f) represents the likelihood distribution of the observed values, i.e., the probability that the observed data conforms to the prior distribution of the objective function; p(τ) 1:t ) represents the marginal likelihood distribution of the marginalized f, i.e., the understanding of the observed data itself; p(f|τ) 1:t ) represents the posterior probability distribution of f, describing how the probabilistic surrogate model utilizes the observed data τ. 1:t This is used to correct the prior distribution, thereby predicting the distribution of f and quantifying the confidence level of f.

[0143] Based on the characteristics of the lane assignment problem, this invention employs a Gaussian process model as the probabilistic surrogate model. The prior probability distribution of the Gaussian process is represented by a multivariate normal distribution. For a new input point τ... t+1 Gaussian processes predict the objective function f by estimating the multivariate normal distribution. t+1 mean μ t+1 and variance Since the Gaussian process assumes the objective function f t It follows a joint Gaussian distribution, therefore the input point τ t+1 Also conforming to the joint Gaussian distribution, it is written as:

[0144]

[0145] K(τ 1:t ,τ t+1 )=[k(τ1,τ t+1 ),k(τ2,τ t+1 ),...,k(τ t ,τ t+1 (19)

[0146]

[0147] According to equation (18), we can obtain the following about the input point τ. t+1 Predicted distribution:

[0148]

[0149] μ t+1 =m(τ) t+1 )+K(τ 1:t ,τ t+1 ) T [K(τ 1:t ,τ 1:t )+τ 2 I] -1 (f 1:t -m(τ t+1 )) (twenty two)

[0150]

[0151] Where, μ 1:t Represents the observation point τ 1:t The vector consisting of the corresponding observations; m(τ) t+1 ) represents based on input point τ t+1 The obtained prior mean. k(τ) m ,τ n ) represents the observation point τ m and observation point τ n In Gaussian process models, the covariance between two observations is also known as the kernel function. Considering the unknown smoothness of the objective function surface for the expected delay value, this invention uses the Matern kernel function to calculate the covariance between two observation points. The smoothness can be adjusted using a smoothing parameter v; the larger the value of v, the smoother the result. When v = 3 / 2, the expression for the Matern kernel function is as follows:

[0152]

[0153] In conventional Bayesian optimization methods, r typically represents the observation point τ. m and observation point τ n The Euclidean distance between them; l is a hyperparameter.

[0154] The role of the sampling function is to calculate the optimization "potential" of the objective function value corresponding to each input point after the probabilistic surrogate model has calculated the predicted mean and confidence level for each input point, and to determine the input point with the highest "potential" as the new observation point. Based on the characteristics of the lane allocation problem, this invention adopts the expected improvement criterion as the sampling strategy. The expected improvement criterion can balance the global search and local search of the optimal control scheme, improving sampling efficiency. Its expression is as follows:

[0155]

[0156] Where EI(x) represents the expected improvement value of input point x, i.e., the optimization "potential"; f(x) represents the objective function of input point x calculated according to the probabilistic surrogate model; f* represents the currently known global optimal objective function value; p(f(x)|τ 1:t ) represents the observation point τ. 1:t Given the condition, the posterior probability distribution of the objective function is given. Equation (25) evaluates the potential expectation that the result will exceed the current optimum when the input point x is observed.

[0157] In the t-th evaluation process, the expected improvement value of each input point is calculated according to equation (25), and the input point with the largest expected improvement value is determined. As an observation point for the next evaluation process, its expression is as follows:

[0158]

[0159] Part 3: Improved Bayesian optimization methods.

[0160] The Gaussian process model used in this invention assumes uniform continuity or Lipschitz continuity smoothness: when the observation point x i and x j When the distance between them is very small, their corresponding observation values ​​y i and y j The differences between them are also very small. In other words, when predicting a new input point, the closer the observed samples are to it, the more information they can provide. In the Gaussian process model, the kernel function is used to calculate the similarity between two observation points, characterizing the smoothness and amplitude of the true objective function. Different kernel functions have different effects on measuring distance. Therefore, the choice of kernel function directly affects the ability of the Gaussian process model to predict new input points based on observed data.

[0161] To address the unique characteristics of lane assignment problems, this invention introduces prior traffic physics information into the conventional Matern kernel function, thereby improving the solution efficiency of Bayesian optimization methods in high-dimensional problems. Specifically, the concept of correlation is defined, and when calculating the similarity between two observation points, not only is their Euclidean distance considered, but also the difference in approximate delay values ​​of their corresponding control schemes. The improved Matern kernel function is expressed as follows:

[0162]

[0163] Where r' represents the correlation between the two observation points; r represents the Euclidean distance between the two observation points; Dr b (τ n ) indicates that when the observation point is τ nWhen the corresponding baseline control scheme is calculated using the Webster delay formula, the approximate delay value is obtained; l and h are both hyperparameters. In equation (28), the calculation of the correlation r' introduces the adjustment term r / h. This design is to balance the influence of Euclidean distance and traffic physical information on the update of the Gaussian process model: when the distance between two points is relatively short, the calculation of r' relies more on the accurate Euclidean distance information; when the distance between two points is relatively long, the calculation of r' utilizes more the traffic physical information corresponding to the approximate delay value. By introducing the concept of correlation to improve the design of the Matern kernel function, the similarity between observation points can be more accurately characterized, the update strategy of the Gaussian process model can be optimized, and the Bayesian optimization method can converge to the global optimum more quickly.

[0164] In addition, the known observation point τ n The corresponding baseline lane allocation scheme N n Timing scheme with reference signal The Webster delay formula is expressed as follows:

[0165]

[0166] Among them, in equation (29) c represents the baseline lane flow rate of lane i at the entrance; b Indicates the duration of the reference period; This represents the baseline lane delay for lane i at entry point k. The y in equation (30) i,k x represents the baseline lane flow ratio for lane i at entrance k, i.e., the ratio between the flow rate and the saturation flow rate; i,k This represents the baseline lane saturation of lane k in lane i, which is the ratio between the flow rate ratio and the green light ratio. The baseline green light ratio is the ratio between the lane's green light time and the cycle duration. All of the above parameters can be obtained from the baseline control scheme.

[0167] This invention employs an improved Bayesian optimization method to solve a two-stage stochastic programming model for the lane assignment problem. The implementation steps are summarized below:

[0168] Step 1. Model and Parameter Initialization: Construct a two-stage stochastic programming model for the lane assignment problem at a signalized intersection; set the target number of iterations T. max The parameters include the number of initial points T0 and the number of input points N in each iteration; T0 sets of control schemes that meet the constraints are selected as initial observation points by Latin hypercube sampling method, and the expected delay value is calculated according to formulas (1) and (2) as its observation value; let the current iteration number t = T0, and proceed to step 2;

[0169] Step 2. Determine the algorithm termination condition: Determine t <T maxCheck if the condition is met. If it is met, proceed to step 3; otherwise, terminate the algorithm process.

[0170] Step 3. Calculate the true objective function value of the new observation point: Determine whether t>T0 holds true. If it does, calculate the expected delay value of the new observation point according to formulas (1) and (2) and use it as its observation value, then proceed to step 4; otherwise, proceed directly to step 4.

[0171] Step 4. Update the Gaussian process model: Calculate the traffic physics information of all observation points, i.e., the approximate delay value, according to formulas (29) and (30); update the current Gaussian process model according to formulas (17) and (20); proceed to step 5;

[0172] Step 5. Determine new observation points according to the expected improvement criteria: randomly select N input points that meet the constraints by interpolation; calculate the traffic physical information of each input point according to formulas (29) and (30); calculate the predicted mean and variance of the objective function corresponding to each input point according to formulas (19), (22) and (23); calculate the expected improvement value of each input point according to formula (25), and determine the observation point for the next iteration according to formula (26); let t = t + 1, and proceed to step 2.

[0173] The specific implementation process of the present invention will be described in detail below with reference to the accompanying drawings and specific application scenarios:

[0174] like Figure 8 As shown in the example, the selected embodiment is a four-lane east-west intersection and a three-lane north-south intersection. The signal control at this intersection uses a two-phase scheme, with the east-west direction being released first, followed by the north-south direction. The minimum green light time is 20 seconds, the maximum green light time is 60 seconds, the minimum cycle time is 45 seconds, and the maximum cycle time is 120 seconds. The two phases are connected by a total of 5 seconds of all-red time, and the saturation flow rate is 1965 pcu / h / lane. To simulate the randomness of traffic demand, it is assumed that the traffic demand at this intersection follows a normal distribution. in, The value of the basic traffic flow for import i turning j is shown in Table 1.

[0175] Table 1 Basic Traffic Flow

[0176]

[0177] In Table 1, α represents the degree of fluctuation in traffic demand; a larger value indicates greater randomness in the arrival of traffic at intersections. Furthermore, in this embodiment, 50 random scenarios are calculated to simulate the randomness of traffic demand. Ten control schemes satisfying the constraints are selected as initial observation points using the Latin hypercube sampling method, and the corresponding observation values ​​are calculated. The maximum number of iterations is limited to 50 (including the initial observation points).

[0178] The example first simplifies the traffic demand scenario, considering only the east and south entrances, while setting the traffic demand for the other two entrances to zero, and setting α to 0.6 to simulate a scenario with greater randomness. The example compares the iterative performance of genetic algorithms, traditional Bayesian optimization methods, and Bayesian optimization methods incorporating physical models in solving the lane allocation problem. The genetic algorithm is a conventional heuristic solution method. Experimental results are as follows: Figure 9 As shown, although the traditional Bayesian optimization method does not converge to the global optimum within 50 iterations, its solution accuracy is still higher than that of the genetic algorithm. The improved Bayesian optimization method proposed in this invention can reach the global optimum in less than 20 iterations, verifying the superiority of the improved Bayesian method in terms of solution accuracy and computational efficiency when solving the lane assignment problem.

[0179] Furthermore, the embodiment also considers the complete traffic demand scenario of the intersection, i.e., setting the traffic flow of the four entrances according to the basic traffic demand in Table 1. α is set to 0.2, 0.5, and 0.6 respectively to simulate different stochastic scenarios. The embodiment compares the improved Bayesian optimization method with the baseline method, where the baseline method is a decoupled solution method based on service level reliability, belonging to a classic method for solving a two-stage stochastic programming model for lane allocation problems. Experimental results are shown in Table 2.

[0180] Table 2 Experimental results for complete intersection demand scenarios

[0181] Degree of fluctuation a Reference method (s) Improved Bayesian optimization method (s) Delay reduction ratio (%) 0.2 7.36 7.13 3.13 0.5 11.13 9.97 10.42 0.6 12.00 10.76 10.33

[0182] In Table 2, for different fluctuation levels α, the average vehicle delay of the improved Bayesian optimization method is less than that of the baseline method, with a delay reduction ratio of 3.13%-10.42%, which further verifies that the present invention can improve the solution accuracy of the lane allocation problem and improve the operation efficiency of the intersection.

[0183] Compared with the prior art, the present invention has the following characteristics:

[0184] First, the Bayesian optimization method is used to solve the lane assignment problem.

[0185] This invention employs a Bayesian optimization method to solve a two-stage stochastic programming model for the lane assignment problem. The probabilistic surrogate model part uses a Gaussian process model to predict the mean and variance of the objective function for new input points based on observed information. The acquisition function part uses the expectation improvement criterion to evaluate the optimization potential of the objective function for input points and determine the input point with the greatest potential as the new observation point for the next iteration. The Bayesian optimization method can converge to the global optimum after a few iterations.

[0186] Second, improve the kernel function design in the Gaussian process model.

[0187] This invention integrates traffic physics information of the lane assignment problem into the kernel function calculation of the conventional Gaussian process model. Specifically, it defines the concept of correlation and additionally considers the approximate delay value information corresponding to the observation points when calculating the similarity between two observation points. More accurate similarity characterization can improve the update strategy of the Gaussian process model, thereby improving the convergence speed of the algorithm.

[0188] Compared with the prior art, the present invention has the following advantages:

[0189] For the two-stage stochastic programming model of the lane allocation problem, existing solutions are prone to getting trapped in local optima. In contrast, the Bayesian optimization method employed in this invention can converge to the global optimum after a few iterations, and the optimal lane allocation scheme can effectively improve the road supply capacity of signalized intersections. Furthermore, this invention improves the kernel function design in conventional Bayesian optimization methods, fully integrating traffic physical information from the lane allocation problem, further reducing the number of iterations required to converge to the global optimum and significantly improving solution efficiency. Therefore, the improved Bayesian optimization method provided by this invention can balance the solution accuracy and computational efficiency of the lane allocation problem, helping to alleviate traffic congestion at signalized intersections.

[0190] Another aspect of this invention provides a Bayesian-optimized lane allocation device for signalized intersections, comprising:

[0191] The first module is used to obtain traffic demand to be allocated;

[0192] The second module is used to construct a two-stage stochastic programming model for the lane allocation problem at signalized intersections based on the traffic demand to be allocated.

[0193] The third module is used to solve the two-stage stochastic programming model using an improved Bayesian optimization method to obtain the baseline lane allocation scheme result.

[0194] The optimization objective of the first-stage stochastic programming model is to minimize the expected delay value of k scenarios. The first-stage stochastic programming model provides a baseline control scheme for the second stage. The optimization objective of the second-stage stochastic programming model is to minimize the average vehicle delay in each scenario and provide delay evaluation results for the first stage. The randomness of traffic flow in the kth scenario is addressed by adjusting the baseline signal timing scheme.

[0195] The improved Bayesian optimization method comprises two core components: a probabilistic surrogate model and a data acquisition function. Based on the characteristics of the lane allocation problem, a Gaussian process model and an expected improvement criterion are used for specific implementation. The approximate delay value corresponding to the control scheme to be observed is used as prior traffic physical information, and the kernel function design in the Gaussian process model is improved to accelerate the algorithm's convergence to the global optimum.

[0196] It is understood that the content of the above method embodiments is applicable to the present device embodiments. The specific functions implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0197] This invention also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the aforementioned Bayesian-optimized lane allocation method for signalized intersections. This electronic device can be any smart terminal, including a tablet computer or an in-vehicle computer.

[0198] It is understood that the content of the above method embodiments is applicable to this device embodiment. The specific functions implemented by this device embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0199] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described Bayesian-optimized lane allocation method for signalized intersections.

[0200] It is understood that the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0201] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0202] The embodiments described in this invention are for the purpose of more clearly illustrating the technical solutions of the embodiments of this invention, and do not constitute a limitation on the technical solutions provided by the embodiments of this invention. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by the embodiments of this invention are also applicable to similar technical problems.

[0203] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of the present invention, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0204] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0205] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0206] The terms "first," "second," "third," "fourth," etc. (if present) in the specification and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0207] It should be understood that in this invention, "at least one (item)" refers to one or more, and "more than one" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0208] In the several embodiments provided by this invention, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of the units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0209] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0210] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0211] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes multiple instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0212] The preferred embodiments of the present invention have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present invention. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and spirit of the present invention should be within the scope of the claims of the present invention.

Claims

1. A lane allocation method for signalized intersections based on Bayesian optimization, characterized in that, Includes the following steps: Obtain the traffic demand to be allocated; Based on the traffic demand to be allocated, a two-stage stochastic programming model is constructed for the lane allocation problem at signalized intersections. An improved Bayesian optimization method was used to solve the two-stage stochastic programming model to obtain the baseline lane allocation scheme. The first-stage stochastic programming model aims to minimize the expected delay values ​​for k scenarios and provides a baseline control scheme for the second stage. The second-stage stochastic programming model aims to minimize the average vehicle delay for each scenario and provides delay evaluation results for the first stage. The randomness of traffic flow in the kth scenario is addressed by adjusting the baseline signal timing scheme. The improved Bayesian optimization method comprises two core components: a probabilistic surrogate model and a data acquisition function. Based on the characteristics of the lane allocation problem, a Gaussian process model and an expected improvement criterion are used for specific implementation. The approximate delay value corresponding to the control scheme to be observed is used as prior traffic physical information, and the kernel function design in the Gaussian process model is improved to accelerate the algorithm's convergence to the global optimum. The expression for the two-stage stochastic programming model is: in, , This represents the expected delay value for all traffic demand scenarios; This represents the operation of obtaining the desired result; The scenario number representing traffic demand; Representing a scene Average delay; Representing a scene The probability of occurrence is uniformly set as ; The baseline lane allocation scheme; The timing scheme for the reference signal; For the scene The execution signal timing scheme; For the scene Traffic demand solutions; Indicates the period number; Indicates the entrance number of the intersection; Indicates the lane number at the intersection; Representing a scene cycle China imports Lane Traffic flow; Representing a scene cycle The duration of the cycle; Representing a scene cycle China imports Lane Vehicle delays; The vehicle delay is calculated using the shaded area method, and the calculation formula is as follows: ， in, Representing a scene cycle China imports Lane saturation flow rate; Representing a scene cycle China imports Lane The number of vehicles remaining in the queue; Representative scenarios cycle China imports Lane The green light time.

2. The method for lane allocation at a signalized intersection based on Bayesian optimization according to claim 1, characterized in that, The two-stage stochastic programming model satisfies three lane allocation constraints and two signal timing constraints. The first lane allocation constraint is: [Inlet] The total number of lanes with various steering functions inside equals the total number of entrance lanes; The second lane allocation constraint is: entrance The number of lanes with various steering functions should not exceed the total number of corresponding exit lanes; The third lane allocation constraint is: the lane flow ratio is equal to the sum of lane flows divided by the saturation flow rate, and the corresponding turning flow ratios should be equal when shared lanes are set. The first signal timing constraint is as follows: the green light time for left turns, straight ahead, and right turns at the same entrance in the two-phase scheme should be equal; the green light time for left turns at a certain entrance should be equal to the green light time for left turns at the opposite entrance; and the sum of the green light time and the phase interval time should be equal to the signal cycle length. The second signal timing constraint is: the maximum and minimum values ​​of the green light time and cycle duration.

3. The method for lane allocation at a signalized intersection based on Bayesian optimization according to claim 2, characterized in that, The expression for the first lane assignment constraint is: in, They represent imports respectively. The number of dedicated left-turn lanes, the number of lanes that can be used for both straight and left turns, the number of dedicated straight lanes, the number of lanes that can be used for both straight and right turns, the number of dedicated right-turn lanes, and the number of lanes that can be used for both straight and left turns; Indicates import The total number of lanes; They represent imports respectively. The traffic flow for left turns, straight ahead, and right turns. It is a sufficiently large positive number; The expression for the second lane assignment constraint is: in, They represent imports respectively. The total number of exit lanes corresponding to left-turning, straight-going, and right-turning traffic flows; The expression for the third lane assignment constraint is: in, Indicates a change in traffic flow. These represent left turn / straight ahead / right turn respectively; Representing a scene cycle China imports Lane Turning Traffic flow; Representing a scene cycle China imports Lane The lane flow ratio; Representing a scene cycle China imports Turning The turning flow ratio; The expression for the first signal timing constraint is: in, Representing a scene cycle Phase interval time in the middle; The expression for the second signal timing constraint is: in, Representing a scene cycle China imports Turning The green light time for turning, and These correspond to the minimum and maximum values ​​of the turn signal green light time, respectively. These correspond to the minimum and maximum values ​​of the period duration, respectively.

4. The method for lane allocation at a signalized intersection based on Bayesian optimization according to claim 1, characterized in that, The method of solving the two-stage stochastic programming model using an improved Bayesian optimization method includes the following steps: Construct a two-stage stochastic programming model for the lane assignment problem at signalized intersections; set the target number of iterations. Number of initial points Number of input points in each iteration Parameters; Samples satisfying the constraints are drawn using the Latin hypercube sampling method. The group control scheme is used as the initial observation point, and the calculated expected delay value is used as the observation value; let the current iteration number be... ; If the number of algorithm iterations does not reach the target number of iterations, proceed to the next step until the target number of iterations is completed; judge If the condition is true, calculate the expected delay value of the new observation point as its observed value and proceed to the next step; otherwise, proceed directly to the next step. Calculate traffic physics information for all observation points and update the current Gaussian process model; Randomly selected using interpolation. Given input points that meet the constraints, calculate the traffic physical information for each input point; calculate the predicted mean and variance of the objective function for each input point; calculate the expected improvement value for each input point, and determine the observation point for the next iteration.

5. The signalized intersection lane allocation method based on Bayesian optimization according to claim 4, characterized in that, Solving the two-stage stochastic programming model using the improved Bayesian optimization method further includes at least one of the following steps: Based on the characteristics of the lane assignment problem, a Gaussian process model is adopted as a probabilistic surrogate model, where... The prior probability distribution of a Gaussian process is represented by a multivariate normal distribution. For a new input point, the Gaussian process predicts the mean and variance of the objective function by estimating the multivariate normal distribution. Since the surface smoothness of the objective function for the expected delay value is unknown, the Matern kernel function is used to calculate the covariance between two observation points. Based on the characteristics of the lane assignment problem, the expected improvement criterion is adopted as the sampling strategy.

6. The method for lane allocation at a signalized intersection based on Bayesian optimization according to claim 5, characterized in that, The expression for the Matern kernel function is: in, Indicates the observation point and observation points Covariance between them; Indicates the observation point and observation points The Euclidean distance between them; It is a hyperparameter; The expression for the sampling strategy is: in, Indicates input point Expected improvement value; This represents the input point calculated based on the probabilistic surrogate model. The objective function; This represents the currently known globally optimal objective function value; Indicates at a known observation point Given the condition, the posterior probability distribution of the objective function.

7. A lane allocation method for signalized intersections based on Bayesian optimization according to claim 4, characterized in that, The calculation of traffic physical information for all observation points and the updating of the current Gaussian process model include the following steps: The traffic physical information at the observation point refers to the Webster approximate delay value calculated based on the baseline control scheme, and its expression is: ， ， in, Indicates a given baseline lane assignment scheme Timing scheme with reference signal The Webster delay value is calculated using this as input; Indicates import Lane The baseline lane flow rate; Indicates the duration of the reference period; Indicates import Lane Delay in the baseline lane; Indicates import Lane The baseline lane flow ratio, which is the ratio between flow rate and saturation flow rate; Indicates import Lane The baseline lane saturation is the ratio between the flow rate ratio and the green light ratio. The update process of the Gaussian process model includes the calculation of the Matern kernel function, and the Matern kernel function is improved by incorporating traffic physics information from the observation points. Its expression is: ， in, This indicates the correlation between two observation points; This represents the Euclidean distance between two observation points; Indicates when the observation point is At that time, the approximate delay value is obtained by calculating the corresponding baseline control scheme using the Webster delay formula; Indicates when the observation point is At that time, the approximate delay value is obtained by calculating the corresponding baseline control scheme using the Webster delay formula; and All of these are hyperparameters.

8. An apparatus for implementing the Bayesian optimization-based lane allocation method for signalized intersections as described in any one of claims 1-7, characterized in that, include: The first module is used to obtain traffic demand to be allocated; The second module is used to construct a two-stage stochastic programming model for the lane allocation problem at signalized intersections based on the traffic demand to be allocated. The third module is used to solve the two-stage stochastic programming model using an improved Bayesian optimization method to obtain the baseline lane allocation scheme result. The optimization objective of the first-stage stochastic programming model is to minimize the expected delay value of k scenarios. The first-stage stochastic programming model provides a baseline control scheme for the second stage. The optimization objective of the second-stage stochastic programming model is to minimize the average vehicle delay in each scenario and provide delay evaluation results for the first stage. The randomness of traffic flow in the kth scenario is addressed by adjusting the baseline signal timing scheme. The improved Bayesian optimization method comprises two core components: a probabilistic surrogate model and a data acquisition function. Based on the characteristics of the lane allocation problem, a Gaussian process model and an expected improvement criterion are used for specific implementation. The approximate delay value corresponding to the control scheme to be observed is used as prior traffic physical information, and the kernel function design in the Gaussian process model is improved to accelerate the algorithm's convergence to the global optimum.

9. An electronic device, characterized in that, Including the processor and memory; The memory is used to store programs; The processor executes the program to implement the method as described in any one of claims 1 to 7.

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