Traffic flow prediction and signal timing optimization method based on Gaussian process regression

Abstract

A traffic flow prediction and signal timing optimization method based on Gaussian process regression comprises the following steps: 1, collecting mixed traffic flow data through a traffic detection unit and an Internet of Vehicles terminal, constructing a time sequence data set in combination with historical data, and analyzing and determining a difference interval by using an autocorrelation function to eliminate seasonal influence; 2, establishing a short-time traffic flow prediction model based on Gaussian process regression, and fusing a radial basis function kernel and a periodic kernel to quantify prediction uncertainty; 3, constructing a signal timing optimization model taking average delay, parking times and traffic capacity as multiple targets, wherein constraint conditions comprise green light time and a period duration range; and 4, an improved multi-group genetic algorithm is combined with a simulated annealing solution model, and the global optimization capability is improved through parallel evolution and a probability hopping mechanism. Through data prediction-optimization closed-loop control, the intersection delay is remarkably reduced, the traffic capacity is improved, and the method is suitable for a dynamic traffic scene of mixed driving of intelligent network connection vehicles and manual driving.

Description

Technical Field

[0001] This invention belongs to the field of intelligent traffic control technology, specifically relating to a traffic flow prediction and signal timing optimization method based on Gaussian process regression. Background Technology

[0002] With the surge in urban motor vehicle ownership, traditional fixed-time signal control systems are struggling to cope with dynamic traffic flow changes, resulting in low intersection efficiency and increased congestion. Existing technologies mainly suffer from the following defects: (1) Traditional prediction methods (such as time series analysis and Kalman filtering) are insufficient in capturing the nonlinear characteristics of traffic flow and are difficult to adapt to the complex scenario of mixed traffic of intelligent connected vehicles (CAVs) and manually driven vehicles; (2) In terms of optimization algorithms, static timing models such as Webster's formula cannot respond to changes in traffic conditions in real time, while standard genetic algorithms are prone to getting trapped in local optima, resulting in slow convergence speed and limited optimization effect of signal timing schemes.

[0003] In the field of traffic flow prediction, existing research mostly employs linear models or single machine learning algorithms. For example, some studies have proposed short-term prediction methods based on LSTM, but they do not consider the improvement in prediction accuracy provided by the high-precision trajectory data provided by CAV; other studies use support vector machines for traffic flow prediction, but the deterministic output cannot quantify prediction uncertainty, affecting the reliability of subsequent optimization. In contrast, Gaussian process regression (GPR) combines nonlinear fitting capabilities with probabilistic output advantages, and can combine real-time CAV data to generate prediction results with confidence intervals, but existing technologies have not fully explored its synergistic potential in mixed traffic flow prediction.

[0004] Regarding signal timing optimization, existing studies mostly employ standard genetic algorithms to optimize cycle length, but fail to address the premature convergence problem. Other studies have introduced particle swarm optimization, but suffer from insufficient Pareto front search in multi-objective optimization (delay, queue length, capacity). Furthermore, existing solutions primarily target isolated intersections, lacking a dynamic control mechanism based on prediction-optimization linkage in a CAV (vehicle-road cooperative) environment, resulting in insufficient matching between optimization results and actual traffic demand.

[0005] The development of intelligent connected vehicle technology has provided new opportunities to overcome the aforementioned bottlenecks. CAVs can upload location, speed, and other data in real time via V2X communication, providing high spatiotemporal resolution input for traffic flow prediction. However, existing research mostly uses CAV data only for trajectory planning, without deeply coupling it with signal control. Furthermore, the heterogeneous behaviors of CAVs and manually driven vehicles in mixed traffic flows (such as lane-changing decisions and car-following responses) have not been fully modeled in existing integrated prediction-optimization models.

[0006] In summary, there is an urgent need for a high-precision traffic flow prediction method that integrates the advantages of CAV data and combines it with an improved genetic algorithm to achieve dynamic signal timing optimization, in order to solve the core problems of insufficient prediction reliability, low optimization efficiency and insufficient application of vehicle-road cooperative systems in existing technologies. Summary of the Invention

[0007] The purpose of this invention is to provide an intersection signal control scheme based on the fusion method of Gaussian process regression and intelligent optimization. It systematically realizes a five-step closed-loop control chain from data acquisition, traffic flow prediction, multi-objective modeling, intelligent solution to control feedback, so as to improve the intersection capacity, reduce the average delay and number of stops, and adapt to the dynamic changes in urban traffic flow.

[0008] The technical solution of this invention is: a traffic flow prediction and signal timing optimization method based on Gaussian process regression, comprising the following steps:

[0009] Step 1: Traffic data acquisition and preprocessing;

[0010] Step 2: Establish a traffic flow prediction model based on Gaussian process regression;

[0011] Step 3: Construct a multi-objective nonlinear signal timing optimization model;

[0012] Step 4: Improve the genetic algorithm to solve the timing optimization model.

[0013] Furthermore, in step 1, traffic data preprocessing includes:

[0014] Original traffic flow observation sequence Normalize:

[0015]

[0016] Where x is the original data, For normalized data;

[0017] To simplify data trends and reduce complexity, Differentiation is performed at different time intervals to generate new sequences. ,in As a moment Predictors, difference interval The value is determined by analyzing and calculating using the autocorrelation function (ACF) method in time series analysis;

[0018] The ACF estimate is calculated as follows:

[0019]

[0020] Among them, lag It is the order of the autocorrelation function. and It is a pre-difference sequence middle and Traffic flow observations at any given time It is the average of all observed samples; in calculating various... After estimating the value of the sample autocorrelation function, generate the value of the sample autocorrelation function. The sample ACF plot is for the independent variable.

[0021] Furthermore, in step 2, a traffic flow prediction model based on Gaussian process regression is established, and the specific process is as follows:

[0022] Let the historical dataset be ,in Indicates time characteristics, To correspond to traffic flow, the Gaussian process is defined as follows:

[0023]

[0024] in, It is a mean function. It is the kernel function that defines the covariance structure of the model, and the hyperparameters of the kernel function are determined through training;

[0025] The observation model with additive noise is represented as follows:

[0026]

[0027] in, Indicates independent Gaussian noise;

[0028] Given a training dataset ,in , and It follows a joint Gaussian distribution; therefore, Follows the prior distribution:

[0029]

[0030] in, It is composed of positive definite nuclei The covariance matrix formed It is the noise variance. It is the identity matrix;

[0031] To achieve more accurate predictions, the radial basis function (RBF) and a periodic kernel are combined into the traffic flow prediction model. The RBF kernel is expressed as:

[0032]

[0033] in, and It is an input spatial point. Represents Euclidean distance. It is the Gaussian kernel bandwidth, which controls the radial range and kernel smoothness of the function;

[0034] The difference between periodic kernels and RBF kernels lies in the fact that two hyperparameters need to be optimized, namely the period parameter. and length parameter As shown below:

[0035]

[0036] Let the hyperparameter set be According to Bayes' theorem, the negative log-likelihood function of the conditional probability of the training samples is:

[0037]

[0038] in, set up Taking the partial derivatives of the above equation, we get:

[0039]

[0040] Using the partial derivatives obtained from the above equation, the iterative optimization method minimizes the negative log-likelihood function to obtain the optimal hyperparameters, thereby completing the model training.

[0041] Furthermore, in step 3, a multi-objective nonlinear signal timing optimization model is constructed, and the specific process is as follows:

[0042] The formula for the multi-objective optimization model is as follows:

[0043]

[0044] in, It is the objective function. This represents the weights assigned to different traffic performance metrics. The average delay time, For parking frequency, For traffic capacity;

[0045] Effective green light time of phase i for:

[0046]

[0047] in, This refers to the actual duration of the green light. It refers to the duration of the yellow light. The time lost due to vehicle starting is due to the actual green light time being met. ;

[0048] Signal control cycle It is the interval between consecutive green starts in a given phase, for Phase signal system, Minimum cycle time This ensures that basic transportation needs are met; the calculation formula is as follows. ,in This represents the sum of the flow ratios of key movements. It is the total lost time, and the cycle time is... Within the actual limitations shown; stage Green ratio time for ; saturation It is a key indicator of intersection performance, by Given, among which, This is traffic flow, expressed in vehicles per hour. It is a stage Middle lane saturation flow rate.

[0049] Furthermore, in step 4, the genetic algorithm is improved to solve the timing optimization model. The specific process is as follows:

[0050] The duration of the green light for the four signal phases is encoded into binary chromosomes, and the population is iteratively evolved using a genetic algorithm to minimize the objective function. And meet traffic constraints;

[0051] Continuous variable: Actual green light duration Encoded as binary values ​​within the range The corresponding decoded value The calculation is as follows:

[0052]

[0053] The fitness evaluation function is:

[0054]

[0055] in, For fitness value, The objective function value, The upper limit threshold of the objective function is used; a new population is generated using roulette wheel selection, crossover, and mutation operations, and its individuals... The probability of being selected is Crossover generates offspring through gene recombination, and mutations randomly flip bits with a low probability; a multi-population genetic algorithm is used to maintain parallel evolving subpopulations, exchanging optimal individuals through circular topology; a simulated annealing mechanism is introduced, at a specific temperature... Below, energy increases The new solution, its acceptance probability for:

[0056]

[0057] Temperature according to renew, The high-temperature phase promotes global exploration, and the solution converges to a high-quality solution after the temperature decreases.

[0058] Compared with the prior art, the present invention has the following advantages:

[0059] 1. Improved Prediction Accuracy and Adaptability. This invention employs a Gaussian process regression model to model and predict short-term traffic flow at intersections, fully considering the nonlinearity and temporal characteristics of traffic flow. The model output includes the prediction mean and variance, quantifying prediction uncertainty. Compared to traditional time series methods, this method offers higher prediction accuracy and stronger robustness, providing a more precise traffic flow input basis for signal timing.

[0060] 2. Optimizing Multiple Objectives to Improve Overall Traffic Efficiency. The timing optimization model comprehensively considers multiple key indicators such as average delay, number of stops, and intersection capacity, constructing a multi-objective nonlinear optimization model. The designed objective function and constraints effectively reflect real-world traffic control needs. In actual simulations, the optimized scheme significantly reduces average delay and stopping frequency, improves overall traffic efficiency, and enhances the service level of the intersection.

[0061] 3. Intelligent algorithm integration enhances global optimization capability and stability. A multi-population genetic algorithm with simulated annealing mechanism is introduced as the solver. Through parallel evolution, population communication, and probabilistic jump mechanisms, it effectively overcomes the shortcomings of traditional genetic algorithms, such as slow convergence and susceptibility to local optima. This improves the stability of the timing scheme and the search efficiency for the global optimum, adapting to different traffic flow patterns and traffic density scenarios, and possesses strong engineering practical value and promising prospects for widespread application. Attached Figure Description

[0062] Figure 1 This is a schematic diagram of an eight-signal phase crossroads according to the present invention.

[0063] Figure 2 This is the original dataset for an embodiment of the present invention.

[0064] Figure 3 This is the ACF analysis result of the original dataset in the embodiments of the present invention.

[0065] Figure 4 The prediction results are for the RBF kernel used in the embodiments of the present invention.

[0066] Figure 5 The prediction results and 95% confidence intervals using the RBF kernel are shown in this embodiment of the invention.

[0067] Figure 6 The prediction results are for the use of periodic kernels in embodiments of the present invention.

[0068] Figure 7 The prediction results and 95% confidence intervals using the periodic kernel are presented in this embodiment of the invention.

[0069] Figure 8 The comparison results of three genetic algorithms in the embodiments of the present invention are shown.

[0070] Figure 9 This is the SUMO co-simulation platform in this embodiment of the invention.

[0071] Figure 10 This invention illustrates the traffic flow changes at different sampling points over five time periods in an embodiment of the invention. Detailed Implementation

[0072] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0073] A traffic flow prediction and signal timing optimization method based on Gaussian process regression includes the following steps.

[0074] Step 1: Traffic data acquisition and preprocessing.

[0075] like Figure 1 As shown, in a crossroads scenario with eight traffic signal phases, traffic detection units, such as radar, video recognition systems, geomagnetic sensors, or V2I-based vehicle networking terminals, are deployed at the target intersection to collect dynamic traffic parameters, such as traffic flow at different times for each approach lane, and to construct a traffic time-series dataset by combining historical traffic flow data.

[0076] Preprocess the dataset, including normalization:

[0077]

[0078] in, It is the raw data. It is normalized data.

[0079] To simplify the data's changing trends and reduce complexity, the original traffic flow observation sequence Difference was performed at different time intervals. The resulting new sequence is ,in As a moment Predictors It is the difference interval. The value is determined by analysis and calculation using the autocorrelation function (ACF) method in time series analysis.

[0080] The ACF estimate is calculated as follows:

[0081]

[0082] Among them, lag It is the order of the autocorrelation function. and It is a pre-difference sequence middle and Traffic flow observations at any given time It is the average of all observed samples. This was calculated after considering various... After estimating the value of the sample autocorrelation function, a dataset was generated with... The sample ACF plot is for the independent variable. If it corresponds to two adjacent positive correlation peaks... The difference between the values ​​is This indicates the existence of a period. The seasonal pattern. Therefore, the difference interval was set to .

[0083] Step 2: Establish a traffic flow prediction model based on Gaussian process regression.

[0084] Gaussian Process Regression (GPR) is used to predict short-term traffic flow. GPR is a non-parametric Bayesian modeling method that uses a covariance function (kernel function) to measure the similarity between input data and learn the input-output mapping relationship.

[0085] Let the historical dataset be ,in Indicates time characteristics (such as timestamps, time period identifiers, etc.). To correspond to traffic flow, the function It is assumed to be a Gaussian process, in the following form:

[0086]

[0087] in, It is a mean function. This defines the kernel function for the model's covariance structure. The hyperparameters of the kernel function are determined through training, and the choice of kernel function has a significant impact on model performance.

[0088] The observation model with additive noise is represented as follows:

[0089]

[0090] in, This represents independent Gaussian noise.

[0091] Given a training dataset ,in , and It follows a joint Gaussian distribution. Therefore, Follows the prior distribution:

[0092]

[0093] in, It is composed of positive definite nuclei The covariance matrix formed It is the noise variance. It is an identity matrix.

[0094] Let the prediction dataset be... . and prediction The joint distribution is:

[0095]

[0096] Given a new input , The posterior distribution is:

[0097]

[0098] Average estimate of the predicted values and variance estimates for:

[0099]

[0100] In the process of solving the problem, the optimization of kernel function hyperparameters is related to the fit of the dataset and is part of Gaussian regression training. Hyperparameters are embedded in the covariance function. In this study, nonlinear optimization methods, such as Bayesian maximum likelihood estimation, are used to solve for the hyperparameters. The posterior distribution of these parameters is defined as follows:

[0101]

[0102] Follow these steps and enter a new one. This will yield the final prediction, i.e., the posterior mean. To assess the uncertainty of the prediction, it is necessary to determine the posterior variance. To use GPR for traffic forecasting, the relevant forecasting factors must first be identified. Based on empirical analysis, historical traffic flow and corresponding timestamps are used as inputs. The forecasting problem can be formulated as follows:

[0103]

[0104] in, It is time Predicted flow at the location, It is the average prediction function. It contains historical traffic data and timestamps. This represents the predicted noise.

[0105] To achieve more accurate predictions, radial basis functions (RBF) and periodic kernels are combined into the traffic flow prediction model. The RBF kernel is represented as:

[0106]

[0107] in, and It is an input spatial point. Represents Euclidean distance. The bandwidth of the Gaussian kernel controls the radial range and smoothness of the function. The RBF kernel has significant non-zero values ​​only within a finite spatial region. Before applying the RBF kernel, seasonal effects in the original traffic data must be eliminated. This is achieved by differencing the input data using the following formula:

[0108]

[0109] in, It is time Predicted flow at that time It is in time Flow observation value at that time and There are two times. and The difference, It is the average prediction function. It is prediction noise. After differencing the input data, we obtain... The posterior distribution enables the model to predict short-term traffic flow in the traffic signal timing optimization model.

[0110] The difference between periodic kernels and RBF kernels lies in the fact that two hyperparameters need to be optimized, namely the period parameter. and length parameter As shown below:

[0111]

[0112] Since periodic kernels can model periodic data without difference, the periodic values ​​estimated by ACF can narrow the search range to... Let the hyperparameter set be... According to Bayes' theorem, the negative log-likelihood function of the conditional probability of the training samples is:

[0113]

[0114] in, set up Taking the partial derivatives of the above equation, we get:

[0115]

[0116] Using the partial derivatives obtained from the above equation, the iterative optimization method minimizes the negative log-likelihood function to obtain the optimal hyperparameters, thereby completing the model training.

[0117] Step 3: Construct a multi-objective nonlinear signal timing optimization model.

[0118] Signal phase is a key component of this model. A phase is defined as the time interval within which a traffic signal allows a specific movement at an intersection. Each phase can include one or more traffic flows from different directions. Effective green light time for:

[0119]

[0120] in, This refers to the actual duration of the green light. It refers to the duration of the yellow light, and This refers to the time lost due to vehicle starting. The actual green light time must meet the following requirements. .

[0121] Signal control cycle It is the interval between consecutive green starts in a given phase. For Phase signal system, Minimum cycle time This ensures that basic transportation needs are met; the calculation formula is as follows. ,in This represents the sum of the flow ratios of key movements. This is the total lost time. The cycle time must be... Within the actual limitations shown. Phase Green ratio time for Saturation It is a key indicator of intersection performance, by Given, among which, It is traffic flow (vehicles / hour). It is a stage Middle lane saturation flow rate.

[0122] The optimization model considers three key performance indicators.

[0123] Average vehicle delay at an intersection, expressed as The calculation is as follows:

[0124]

[0125] in, It is a stage Middle lane The average delay is determined by the following formula:

[0126]

[0127] Average vehicle stopping frequency at intersections It is given by the following formula:

[0128]

[0129] in, It is a stage middle The formula for calculating the number of stops in a lane is as follows: .

[0130] Maximum capacity of the intersection Defined as:

[0131]

[0132] in, It is a stage Middle lane The traffic capacity is calculated using the following formula: .

[0133] The formula for the multi-objective optimization problem is as follows:

[0134]

[0135] in, It is the objective function. This indicates the weights assigned to different traffic performance metrics.

[0136] This model is based on the following assumptions:

[0137] 1. Vehicles turning right may proceed without traffic signals.

[0138] 2. All access roads are below capacity.

[0139] 3. Pedestrian interference is negligible.

[0140] These assumptions ensure that the model remains tractable while capturing the basic dynamics of traffic flow.

[0141] Step 4: Improve the genetic algorithm to solve the timing optimization model.

[0142] A genetic algorithm (GA) is used to solve the traffic signal timing optimization problem. Each individual in the GA population encodes the green duration of the four signal phases as a binary chromosome. The GA iteratively evolves the population to minimize a predefined objective function while adhering to traffic constraints. The main parameters of the GA are shown in the table below.

[0143]

[0144] Continuous variable: Actual green light duration Encoded as binary values ​​within the range The corresponding decoded value The calculation is as follows:

[0145]

[0146] The fitness evaluation function is:

[0147]

[0148] in, It is the fitness value. It is the objective function value. The upper threshold of the objective function is used to transform "finding the minimum of the objective function" into "maximizing the fitness value".

[0149] Assuming the population size is Individual fitness value from Indicates. Uses a roulette wheel selection method, where a single... probability Calculated as Hybridization produces offspring by recombining the genes of selected parents, while mutation introduces genetic diversity by randomly flipping bits with a low probability.

[0150] The algorithm iteratively selects, crosses over, and mutates until a termination condition is met, such as reaching the maximum generation count or achieving convergence. To handle constraints, a fitness penalty method is employed: individuals that violate preset constraints are assigned a very low fitness value, thereby achieving natural selection during evolution.

[0151] To improve the performance of genetic algorithms, a multi-population genetic algorithm (MPGA) is proposed. This method involves maintaining several subpopulations that evolve in parallel, each with different characteristics. Interactions between subpopulations introduce high-quality individuals into the main population, thereby increasing genetic diversity and avoiding premature convergence. Each subpopulation evolves independently, and the best individuals are exchanged in a circular topology. Performance comparisons show that this method improves convergence speed and stability.

[0152] To further improve search performance, simulated annealing (SA) is integrated into MPGA. SA helps escape local optima by accepting worse solutions with decreasing probability over time, an inspiration drawn from the metallurgical annealing process. At temperature Below, energy increases The acceptance probability of the new solution Given by the following formula

[0153]

[0154] The hybrid approach integrates SA into the evolutionary cycle of each subpopulation:

[0155] (1) Initialize temperature And generate an initial solution.

[0156] (2) in each At that point, generate an adjacent solution and compute... .

[0157] (3) The probability of accepting the new solution is .

[0158] (4) Update temperature , .

[0159] In the early stages, high temperatures help with exploration and prevent premature convergence. As the temperature decreases, the algorithm stabilizes near high-quality solutions.

[0160] Example

[0161] This embodiment collected traffic data at a monitoring intersection in Zhenjiang City, Jiangsu Province, from May 6th to May 12th, 2024, totaling 480 samples with a sampling interval of 15 minutes. The original dataset is as follows: Figure 2 As shown. To assess periodicity, the ACF analysis results are as follows. Figure 3 As shown, this illustrates a non-stationary time series with a seasonal pattern.

[0162] To simulate traffic flow, GPR is applied using RBF and a periodic kernel. When the RBF kernel is selected, a time interval of 96 is used based on the characteristics of the GPR differentially processed data. The prediction results are as follows: Figure 4 As shown. The trend of the next 96 predicted data points used 480 samples collected from May 6th to May 12th. Figure 5 The document shows the prediction results and 95% confidence intervals for the last 96 samples on May 12th. The optimized hyperparameters of the GPR model were trained as follows: .

[0163] When using a periodic kernel, the prediction results are as follows: Figure 6 As shown, based on 480 samples collected from May 6 to May 12, the last 96 samples were used as the test set. Figure 7 The prediction results and 95% confidence intervals for the test sequence are shown. The optimized hyperparameters of the GPR model are as follows: and .

[0164] To evaluate the predictions of the regression model, three metrics were calculated: root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). The error coefficients for the RBF and periodic kernel models are listed in the table below.

[0165]

[0166] Although the two kernels perform similarly, the periodic kernel excels at capturing seasonal trends, making it more reliable for traffic flow prediction.

[0167] To optimize signal timing at intersections, three algorithms were compared: the standard genetic algorithm, MPGA, and the hybrid genetic algorithm with simulated annealing (SAGA). The fitness convergence curves of the three methods are compared as follows: Figure 8 As shown in the figure, SAGA exhibits the best convergence speed and solution accuracy.

[0168] To validate the proposed model and optimization algorithm, a Python SUMO co-simulation platform was established, such as... Figure 9 As shown. The SUMO simulation simulated an intersection scenario. Figure 10 The data shows the changes in traffic flow at different sampling points over five time periods.

[0169] Simulations compared three control strategies: (1) the traditional Webster method, (2) offline optimization, and (3) GPR-based online optimization. The evaluation focused on key performance indicators, including average vehicle delay, number of stops, and throughput under real traffic flow input over multiple time periods. The results are shown in the table below.

[0170]

[0171] in, This represents the green light time for the four signal phases of the control lane group. The GPR-based online optimization method achieved a minimum average delay of 373 seconds and a maximum capacity of 69 vehicles per cycle. This demonstrates its excellent adaptability and robustness in dynamic traffic environments.

Claims

1. A traffic flow prediction and signal timing optimization method based on Gaussian process regression, characterized in that, Includes the following steps: Step 1: Traffic data acquisition and preprocessing; Step 2: Establish a traffic flow prediction model based on Gaussian process regression; Step 3: Construct a multi-objective nonlinear signal timing optimization model; Step 4: Improve the genetic algorithm to solve the timing optimization model.

2. The traffic flow prediction and signal timing optimization method based on Gaussian process regression according to claim 1, characterized in that, In step 1, traffic data preprocessing includes: Original traffic flow observation sequence Normalize: ， Where x is the original data, For normalized data; To simplify data trends and reduce complexity, Differentiation is performed at different time intervals to generate new sequences. ,in As a moment Predictors, difference interval The value is determined by analyzing and calculating using the autocorrelation function (ACF) method in time series analysis; The ACF estimate is calculated as follows: ， Among them, lag It is the order of the autocorrelation function. and It is a pre-difference sequence middle and Traffic flow observations at any given time It is the average of all observed samples; in calculating various... After estimating the value of the sample autocorrelation function, generate the value of the sample autocorrelation function. The sample ACF plot is for the independent variable.

3. The traffic flow prediction and signal timing optimization method based on Gaussian process regression according to claim 2, characterized in that, In step 2, a traffic flow prediction model based on Gaussian process regression is established. The specific process is as follows: Let the historical dataset be ,in Indicates time characteristics, To correspond to traffic flow, the Gaussian process is defined as follows: ， in, It is a mean function. It is the kernel function that defines the covariance structure of the model, and the hyperparameters of the kernel function are determined through training; The observation model with additive noise is represented as follows: ， in, Indicates independent Gaussian noise; Given a training dataset ,in , and It follows a joint Gaussian distribution; therefore, Follows the prior distribution: ， in, It is composed of positive definite nuclei The covariance matrix formed It is the noise variance. It is the identity matrix; To achieve more accurate predictions, the radial basis function (RBF) and a periodic kernel are combined into the traffic flow prediction model. The RBF kernel is expressed as: ， in, and It is an input spatial point. Represents Euclidean distance. It is the Gaussian kernel bandwidth, which controls the radial range and kernel smoothness of the function; The difference between periodic kernels and RBF kernels lies in the fact that two hyperparameters need to be optimized, namely the period parameter. and length parameter As shown below: ， Let the hyperparameter set be According to Bayes' theorem, the negative log-likelihood function of the conditional probability of the training samples is: ， in, set up Taking the partial derivatives of the above equation, we get: ， Using the partial derivatives obtained from the above equation, the iterative optimization method minimizes the negative log-likelihood function to obtain the optimal hyperparameters, thereby completing the model training.

4. The traffic flow prediction and signal timing optimization method based on Gaussian process regression according to claim 3, characterized in that, In step 3, a multi-objective nonlinear signal timing optimization model is constructed. The specific process is as follows: The formula for the multi-objective optimization model is as follows: ， in, It is the objective function. This represents the weights assigned to different traffic performance metrics. The average delay time, For parking frequency, For traffic capacity; Effective green light time of phase i for: ， in, This refers to the actual duration of the green light. It is the duration of the yellow light. The time lost due to vehicle starting is due to the actual green light time being met. ; Signal control cycle It is the interval between consecutive green starts in a given phase, for Phase signal system, Minimum cycle time This ensures that basic transportation needs are met; the calculation formula is as follows. ,in This represents the sum of the flow ratios of key movements. It is the total lost time, and the cycle time is... Within the actual limitations shown; stage Green ratio time for ; saturation It is a key indicator of intersection performance, by Given, among which, This is traffic flow, expressed in vehicles per hour. It is a stage Middle lane saturation flow rate.

5. The traffic flow prediction and signal timing optimization method based on Gaussian process regression according to claim 4, characterized in that, In step 4, the improved genetic algorithm is used to solve the timing optimization model. The specific process is as follows: The duration of the green light for the four signal phases is encoded into binary chromosomes, and the population is iteratively evolved using a genetic algorithm to minimize the objective function. And meet traffic constraints; Continuous variable: Actual green light duration Encoded as binary values ​​within the range The corresponding decoded value The calculation is as follows: ， The fitness evaluation function is: ， in, For fitness value, The objective function value, The upper limit threshold of the objective function is used; a new population is generated using roulette wheel selection, crossover, and mutation operations, and its individuals... The probability of being selected is Crossover generates offspring through gene recombination, and mutations randomly flip bits with a low probability; a multi-population genetic algorithm is used to maintain parallel evolving subpopulations, exchanging optimal individuals through circular topology; a simulated annealing mechanism is introduced, at a specific temperature... Below, energy increases The new solution, its acceptance probability for: ， Temperature according to renew, The high-temperature phase promotes global exploration, and the solution converges to a high-quality solution after the temperature decreases.

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