A time-dependent path planning method based on discrete space-time network

Abstract

This invention discloses a time-dependent path planning method based on discrete spatiotemporal networks, comprising the following steps: discretizing the road network topology into multiple independent road segments to construct a first discrete spatiotemporal network; employing a spatiotemporal graph convolutional network deep learning model to perform multi-step traffic speed prediction based on the first discrete spatiotemporal network; integrating the predicted speed into the node connection relationship between adjacent time points to construct a second discrete spatiotemporal network; constructing a path planning problem based on the second discrete spatiotemporal network, transforming the time-dependent path planning problem into a time-invariant path planning problem, and solving for the optimal path using a polynomial-time algorithm. This invention can effectively capture the spatiotemporal correlation of traffic flow and has polynomial-time solution characteristics. This invention establishes an integrated analysis framework that combines prediction and optimization, and proposes a data-driven spatiotemporal graph network construction method, effectively solving the real-time path optimization problem in dynamic traffic environments.

Description

Technical Field

[0001] This invention relates to a time-dependent path planning method based on discrete spatiotemporal networks, belonging to the field of traffic path optimization. Background Technology

[0002] With the acceleration of urbanization and the continuous growth of motor vehicle ownership, urban traffic congestion has become increasingly serious. Traditional path planning methods assume that traffic conditions are time-invariant, optimizing paths based solely on static road network information or current traffic conditions, leading to suboptimal decisions in real-world dynamic traffic environments. Existing research shows that time-dependent path planning methods that consider the time-varying characteristics of traffic conditions can significantly improve path efficiency, but they face two major technical bottlenecks: first, the lack of effective methods for accurately predicting traffic conditions in multiple future time periods; and second, the difficulty of simultaneously ensuring computational efficiency and path optimality in existing time-extended network modeling. Summary of the Invention

[0003] Purpose of the invention: To address the limitations of traditional static path planning and the shortcomings of time-dependent path planning, this invention aims to provide a time-dependent path planning method based on discrete spatiotemporal networks. This method transforms the complex time-dependent path planning problem into a polynomial-time solvable time-invariant path planning problem, providing an innovative dynamic optimization solution for modern intelligent transportation systems.

[0004] Technical solution: To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0005] A time-dependent path planning method based on discrete spatiotemporal networks includes the following steps:

[0006] The road network topology is discretized into multiple independent road segments to construct a first discrete spatiotemporal network. In the first discrete spatiotemporal network, each node corresponds to a road segment and a time point. The edges of nodes at the same time point are determined based on the historical speed similarity of the road segments.

[0007] A spatiotemporal graph convolutional network deep learning model is used to perform multi-step traffic speed prediction based on the first discrete spatiotemporal network.

[0008] The predicted velocity is incorporated into the node connection relationship between adjacent time points to construct a second discrete spatiotemporal network. In the second discrete spatiotemporal network, each node corresponds to a road segment and a time point. There are no edges between nodes at the same time point. The unidirectional edges between nodes at adjacent time points are determined based on the predicted velocity, and each edge represents the transition between spatiotemporal states.

[0009] The path planning problem is constructed based on the second discrete spatiotemporal network, transforming the time-dependent path planning problem into a time-invariant path planning problem, and the optimal path is solved using a polynomial-time algorithm.

[0010] Furthermore, in the first discrete spatiotemporal network, the cosine similarity of the historical speed curves of each road segment is calculated based on the K-nearest neighbor algorithm, and a K-nearest neighbor spatial adjacency matrix is ​​constructed, in which each node at the same time is connected to its K most similar neighbors.

[0011] Furthermore, the spatiotemporal graph convolutional network deep learning model adopts the ST-GCN-GRU model, which captures the spatiotemporal dependence of traffic flow through the spatiotemporal graph convolutional network GCN, and combines it with the gated recurrent unit GCN to realize multi-step traffic speed prediction.

[0012] Furthermore, the ST-GCN-GRU model employs two stacked GCN layers to extract higher-order spatial features, with the propagation rule being: ;in: For the first Layer nodes represent matrices. This represents the adjacency matrix after adding self-joins. for The degree matrix, Indicates the first The layer's weight matrix, with ReLU as the activation function; spatial features are temporally aggregated using the GRU module, and the GRU output is mapped to multi-step prediction values ​​for the speed of all road segments in the future time period through a fully connected prediction layer.

[0013] Furthermore, in the second discrete spatiotemporal network, the connection edge between the node at time t and the node at time t+1 is determined as follows: the reachability of each road segment node at time t to the adjacent road segment node at time t+1 is calculated based on the predicted speed. If the vehicle can travel from road segment i at time t to road segment j at time t+1 within a unit time interval under the predicted speed condition, then a directed edge is established between the corresponding nodes.

[0014] Furthermore, the path planning problem constructed based on the second discrete-time network is a binary variable integer programming model, employing binary variables. Indicate the usage state of the edge: if at time Vehicles from node Driving towards the node ,but ;otherwise The path planning objective is... ;in Represents a set of nodes. Indicates time Connect to time nodes The set of nodes, Represents a set of times; constraints include:

[0015]

[0016]

[0017]

[0018] in Indicates the starting node index. Indicates the index of the endpoint node. Indicates the feasible time to reach the destination. Indicates at time Connect to time nodes The set of nodes, This represents the set of all intermediate nodes except for the starting and ending nodes.

[0019] Furthermore, the problem of multiple endpoints is addressed by connecting the endpoints of adjacent time-layer nodes with virtual edges.

[0020] Furthermore, the optimal path can be obtained by solving the path planning problem using Dijkstra's algorithm or A* algorithm.

[0021] A computer system includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the steps of the time-dependent path planning method based on discrete spatiotemporal networks.

[0022] A computer program product includes a computer program that, when executed by a processor, implements the steps of the time-dependent path planning method based on discrete spatiotemporal networks.

[0023] Beneficial Effects: This invention innovatively proposes a discrete spatiotemporal network modeling method based on speed rather than travel time, ensuring the network satisfies the FIFO (First-In, First-Out) characteristic and transforming the complex time-dependent path planning problem into a time-invariant path planning problem solvable in polynomial time. Compared to existing technologies, this invention achieves more accurate modeling of the spatiotemporal dynamic characteristics of urban traffic flow, and the proposed discrete spatiotemporal network effectively solves the problem of coordinating traffic state prediction and path optimization. By constructing a data-driven discrete spatiotemporal network, this invention can automatically capture the spatiotemporal evolution of traffic flow, providing a scientific basis for dynamic path planning. The ST-GCN-GRU deep learning model constructed in this invention can achieve high-precision multi-step traffic speed prediction, without relying on precise physical road network information, and can operate stably under different data conditions, making it particularly suitable for urban areas with incomplete or outdated road network information; this invention can improve the operational efficiency of urban transportation systems. By optimizing vehicle route selection in real time, the system can effectively alleviate traffic congestion, reduce travel time costs, and improve the overall capacity of the road network. Attached Figure Description

[0024] Figure 1 This is a flowchart of a method according to an embodiment of the present invention.

[0025] Figure 2 This is a schematic diagram of the ST-GCN-GRU model architecture.

[0026] Figure 3 This is a schematic diagram illustrating the connection relationships between different time layers.

[0027] Figure 4 This is a schematic diagram of the second discrete-time network.

[0028] Figure 5 This is a schematic diagram of the test road network.

[0029] Figure 6 This diagram illustrates the path selection and vehicle speeds along the route for both time-dependent and time-invariant models.

[0030] Figure 7 A comparison chart of travel times for time-dependent and time-invariant models.

[0031] Figure 8 A comparison chart of the solution time for time-dependent and time-invariant models. Detailed Implementation

[0032] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0033] like Figure 1 As shown in the figure, the time-dependent path planning method based on discrete spatiotemporal networks disclosed in this invention mainly includes the following steps:

[0034] (1) Construction of the first discrete spatiotemporal network: The road network topology is discretized into multiple independent road segments to construct the first discrete spatiotemporal network; each node corresponds to a road segment and a time, and the edges of nodes at the same time are determined according to the historical speed similarity of the road segments.

[0035] (2) Traffic speed prediction: A spatiotemporal graph convolutional network deep learning model is adopted to perform multi-step traffic speed prediction based on the first discrete spatiotemporal network.

[0036] (3) Construction of the second discrete spatiotemporal network: The predicted velocity is incorporated into the node connection relationship between adjacent time points to construct the second discrete spatiotemporal network; where each node corresponds to a road segment and a time point, there are no edges between nodes at the same time point, and the unidirectional edges between nodes at adjacent time points are determined based on the predicted velocity, and each edge represents the transition between spatiotemporal states;

[0037] (4) Solving time-dependent path optimization: Based on the second discrete spatiotemporal network, the path planning problem is constructed, and the time-dependent path planning problem is transformed into a time-invariant path planning problem. The optimal path is solved by a polynomial time algorithm.

[0038] In step (1), two processes were implemented: process 1 - road network topology discretization and process 2 - spatiotemporal network construction.

[0039] For Process 1, the speed dataset containing hourly average speeds is integrated into a unified spatiotemporal modeling matrix. To ensure sampling regularity, a global hourly time index covering the earliest to latest observation times is first generated, and then the time series of each road segment are aligned with this index. Missing values ​​are filled in through cascaded processing of linear interpolation and forward and backward padding, ultimately obtaining a complete and continuous record of road segment speeds.

[0040] The urban road network topology is discretized into N independent road segments. The cosine similarity of the historical speed curves of each road segment is calculated based on the KNN algorithm. A k-nearest neighbor spatial adjacency matrix is ​​constructed to ensure that each node is connected to its k most similar neighbors.

[0041] For process 2, a first discrete spatiotemporal graph is constructed based on the k-nearest neighbor spatial adjacency matrix and temporal continuity. Specifically, each node in the graph is defined as a unique combination of a specific road segment and a time step. If the spatial dimension contains N road segments and the temporal dimension contains T discrete time steps, the constructed graph contains N×T nodes. To ensure the effective capture of spatiotemporal dependencies and the full integration of spatial correlation and temporal continuity, in this discrete spatiotemporal graph, the node connections in the spatial dimension are entirely based on the road segment similarity calculated by the k-nearest neighbor algorithm, and the node connections in the temporal dimension follow the principle of temporal continuity. Directed edges are established between nodes of the same road segment at adjacent time steps, thereby constructing a unified spatiotemporal graph structure that combines spatial correlation and temporal dependence.

[0042] In step (2), this embodiment proposes an ST-GCN-GRU architecture for predicting road network traffic speeds, specifically designed for jointly modeling the spatiotemporal dependencies of urban traffic systems. In this structure, each node represents a specific road segment at a specific time step, and edges connect spatially or temporally adjacent nodes. In a network context, information is conceptualized as graph data containing nodes and edges: nodes represent entity features, and edges represent relationships between nodes. The ST-GCN-GRU architecture comprises three main components: a stacked GCN layer, a GRU processing unit, and a fully connected prediction layer, the structure of which is as follows: Figure 2 As shown.

[0043] Two stacked GCN layers extract high-order spatial features from the spatiotemporal graph. The first discrete spatiotemporal network is denoted as... ,in N represents the number of road segments, and T represents the number of discrete time steps. This represents a sparse adjacency matrix of a network, detailing the connections between nodes. Matrix elements take values ​​of 0 or 1. This indicates that nodes i and j are connected, otherwise they are not. At time t, the characteristic representation of all nodes in the road network is denoted as... The input for traffic speed prediction is the road network. and characteristic matrix ,in Indicates the length of the input time window. The number of feature dimensions for each node is expressed as:

[0044] (1)

[0045] The data is processed through a mapping function. Generate traffic speed predictions for subsequent time steps Through iterative updates The aim is to minimize the difference between predicted and actual values, thereby reducing time series forecasting errors.

[0046] GCN module uses road network and characteristic matrix As input, its core is the graph convolutional layer—which calculates the output based on node and neighbor information. Indicates the first Layer nodes:

[0047] (2)

[0048] in For the first Layer node represents a matrix (when When =0, The specific variations of the model lie in the choice and parameterization of the mapping function:

[0049] (3)

[0050] in Indicates the first Layer weight matrix, Represents a non-linear activation function. This represents a normalized adjacency matrix containing self-connection information, used to aggregate the feature information of nodes and their neighbors.

[0051] Adjacency matrix The multiplication operation means summing the feature vectors of all neighboring nodes (excluding the node itself) for each node. Therefore, this problem can be solved by introducing a self-loop in the graph:

[0052] (4)

[0053] in This represents the adjacency matrix after adding the self-connection correction matrix. It is an identity matrix.

[0054] Original adjacency matrix Usually unnormalized, therefore Multiplication operations can significantly alter the scale of eigenvectors. This can be addressed through normalization. Ensuring that the sum of all rows is 1 can alleviate this problem, denoted as . ,in This is the degree matrix of the diagonal nodes. The multiplication operation is equivalent to averaging the features of neighboring nodes. This embodiment uses symmetric normalization. To address this issue, considering the above factors, the propagation rule adopted is as follows:

[0055] (5)

[0056] in express The degree matrix (i.e.) ), σ is selected Activation function:

[0057] (6)

[0058] Secondly, GRU is used to perform temporal aggregation on the extracted spatial features. GRU processes the spatial feature sequence of past time steps, learns the temporal dependencies including periodic trends and short-term fluctuations, and its final hidden state serves as a comprehensive representation of the spatiotemporal context.

[0059] Finally, the fully connected prediction layer maps the GRU output to multi-step predictions of speed forecasts for all road segments over future time periods. This model can output prediction results in tensor form, enabling simultaneous prediction across multiple steps and nodes.

[0060] In this embodiment, the time-varying characteristics of traffic flow are a key consideration in route planning. The ST-GCN-GRU model can predict the average vehicle speed of each road segment in future time periods. Integrating these future traffic states into the route planning model allows for the establishment of a time-dependent route planning model that considers dynamic traffic characteristics. For clarity, Table 1 lists the notation system used in the model.

[0061] In step (3), the second discrete-time network , composed of node set Edge set and time set composition.

[0062] Table 1. List of Symbols

[0063]

[0064] The second discrete-time network structure in this embodiment extends the time dimension based on the first discrete-time network used in GCN. To accurately describe vehicle positions, the original edges are discretized, resulting in a significant increase in the number of nodes and edges. To handle the time-varying characteristics of vehicle speed, this network incorporates speed into node connections, unlike time-invariant networks that use travel time as edge cost. Connections between continuous-time layers are established based on the average speed of road segments, connecting nodes at time t to nodes at time t+1. Edges exist only between adjacent time segments, and their connectivity is determined by the speed at the previous time segment: there are no edges between nodes at the same time segment (because instantaneous movement is impossible), and all edges are unidirectional (consistent with time irreversibility). The optimization objective of path planning is to minimize the total travel time. Each edge represents a transition in spatiotemporal state, hence it is assigned a unit time cost of 1. Specifically, the reachability of each road segment node at time t to adjacent road segment nodes at time t+1 is calculated based on the predicted speed. If a vehicle can travel from road segment i at time t to road segment j at time t+1 within a unit time interval under the predicted speed conditions, then a directed edge is established between the corresponding nodes. Figure 3 As shown, the rules for establishing connecting edges are based on the relationship between velocity and spatiotemporal reachability: when the predicted velocity v = Δx / Δt ( Figure 3 (a)) In a unit time interval Δt, a vehicle can only move one road segment unit distance Δx, therefore the node at time t can only be connected to the adjacent node at time t+1; when the predicted speed is increased to v=2Δx / Δt ( Figure 3 (b)) The vehicle can move two road segments within the same time interval, expanding the connection range and forming an inclined connection pattern; when the speed further increases to v=3Δx / Δt ( Figure 3 (c) The reachable range continues to expand, and the slope of the connecting line increases. Through this dynamic connection mechanism based on predicted speed, the second discrete-time network can accurately reflect the changes in traffic conditions and vehicle mobility at different times, achieving accurate modeling of time-dependent path planning problems.

[0065] To address the inefficiency issue, virtual edges with a cost of 0.01 are established between the endpoints of adjacent time-level nodes. This ensures that the solution always contains the optimal path when the selected endpoint is located at any feasible time, thus efficiently handling multi-endpoint problems without redundant computation. In this embodiment, the schematic diagram of the final constructed second discrete-time network structure is shown below. Figure 4 As shown.

[0066] In step (4), a binary variable is used. Indicate the usage state of the edge: if at time Vehicles from node Driving towards the node ,but ;otherwise After establishing the second discrete-time network, the path planning model considering time-varying characteristics is expressed as follows:

[0067] (7)

[0068] The constraints include:

[0069] (8)

[0070] (9)

[0071] (10)

[0072] in Let represent the set of all intermediate nodes except the starting node and the ending node. The objective function (7) represents minimizing the total travel time from the starting node o to the ending node d. Constraints (8)-(10) ensure the flow balance within the model. Specifically, constraint (8) is the starting node outflow constraint, ensuring that the vehicle starts from the starting node o at the initial time and the outflow is 1 unit, guaranteeing the starting condition of the path planning. Constraint (9) is the ending node inflow constraint, ensuring that the vehicle arrives at the ending node d within the specified time and the inflow is 1 unit, guaranteeing the termination condition of the path planning. Constraint (10) is the intermediate node flow balance constraint, ensuring that the inflow of all intermediate nodes except the starting node and the ending node at any time t must be equal to the outflow, guaranteeing the continuity and conservation of vehicles in the network, and preventing vehicles from accumulating or disappearing at intermediate nodes.

[0073] Unlike traditional time-extended networks that establish inter-time topological connections using travel time, the second discrete-time network in this embodiment establishes connections based on velocity. This method ensures that each node at any given time is connected to the corresponding node in the next time layer, guaranteeing the FIFO characteristic and transforming the problem into a time-invariant path planning problem, which can then be solved using existing polynomial-time algorithms such as Dijkstra's algorithm and A*.

[0074] The effectiveness of the present invention will be verified through experiments below.

[0075] This invention provides an embodiment of a path optimization model built based on the Sioux Falls test network. For example... Figure 5As shown, the network contains 24 nodes and 76 arcs. First, each link in the network is discretized into a minimum segment, the length of which represents the distance traveled per unit time at a speed of 1. The entire network contains 7,906 segments. Then, speed information is randomly generated for each segment at different times to simulate variability. To more realistically reflect actual traffic conditions, the speed of each segment is designed to exhibit peak-peak characteristics—lower average speed during peak hours and higher speed during off-peak hours. To highlight the model's characteristics, the peak times for each segment are intentionally not completely overlapping. Peak hours are randomly assigned within the range of 0-70 time units, with a speed of 3 during this period; speeds in other time periods are negatively correlated with the distance from the peak hour, with a maximum speed of 10, indicating that 3 to 10 segments can be traversed per unit time.

[0076] First, we analyze the differences between the two models through a small-scale case study. When planning the path from node 2 to node 13 at t=0, the time-dependent model considers future traffic speeds, while the time-invariant model only plans based on the speed at t=0. Figure 6 The path selection and speed along the route are shown for the two models: the time-dependent model selects a path consisting entirely of unobstructed road sections, and although some road sections are congested at certain times, the path successfully avoids these road sections; while the time-invariant model's path is fastest at t=0, but encounters congestion on some road sections, resulting in an increase in total travel time (64 units for the time-dependent model vs. 94 units for the time-invariant model). Considering future information reduces the travel time by 31.9%.

[0077] A comprehensive analysis was performed on all possible origin-destination (OD) pair combinations in the network (552 pairs in total), and the travel time was calculated using two different models (e.g., Figure 7 (As shown). Analysis shows that the time-dependent model consistently outperforms the time-invariant model in decision-making, and the difference between the two models gradually widens as travel time increases. Therefore, OD pairs are categorized into short, medium, and long distances based on travel time.

[0078] Table 2 shows the average travel time and model differences for the three types of OD pairs. For short distances, the difference between the two models is minimal (only 1.8%); for medium distances, the time-dependent model improves performance by 9.3% compared to the time-invariant model; and for long distances, the difference widens to 14.4%. This indicates that the advantage of considering future speed information becomes more significant as distance increases.

[0079] Table 2. Comparison of average travel time for all OD (Outbound Direction)

[0080]

[0081] Computational efficiency is a key indicator of the model. Figure 8 The solution time for all OD pairs in the scene is shown for both models: the average solution time for the time-dependent model increases rapidly with distance.

[0082] The average solution time and differences for the three types of OD pairs were statistically analyzed according to the same classification criteria (as shown in Table 3). The solution time of the two models differed significantly, and the time-dependent model was more sensitive to distance, while the time-invariant model maintained a lower solution time for all three types of distances.

[0083] Table 3. Comparison of average calculation time for all OD pairs (seconds)

[0084]

[0085] Comparative experiments were conducted to evaluate the time-dependent model based on discrete-time-space networks (DISCNs) compared with other models that consider future velocity information. The future-means model was chosen for comparison—predicting future velocities and averaging them over a specified time window, then using these average velocities for time-invariant path planning. This model can consider future velocities to some extent. The selected time windows were 1, 15, 30, 45, 60, 75, 90, 105, and 120 units. Notably, when the time window is 1 unit, this model is equivalent to a time-invariant model that only considers current velocity information. The comparison results are shown in Table 4: the time-dependent model based on DISCNs outperforms the future-means model for any time window because DISCNs can fully integrate velocity information at any given time, while the future-means model loses detailed velocity information and cannot guarantee optimal path selection. Among the future-means models with different time windows, the 15-unit window showed the highest accuracy, indicating that for this network, the velocity average over the next 15 time units best reflects its time-varying characteristics and provides a good approximation method for rapid computation.

[0086] Table 4. Comparison of average travel time for different models with full OD

[0087]

[0088] This embodiment further uses Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and Coefficient of Determination (R²) to evaluate the performance of the ST-GCN-GRU model. Each indicator reflects prediction quality from different dimensions: MAE measures the overall prediction error and is insensitive to outliers; RMSE is sensitive to outliers and is used to analyze prediction stability; MAPE reflects the degree of bias but is affected by the magnitude of the true values; R² evaluates the proportion of variance in the observed data explained by the model and serves as a goodness-of-fit indicator. The calculation formula is as follows:

[0089] (11)

[0090] (12)

[0091] (13)

[0092] (14)

[0093] in This represents the test set. For indexing, For the size of the test set, The mean of the observed data, For the true value, For the first One data prediction value.

[0094] Z-score standardization was applied to the input velocity data based on the statistical characteristics of the training set to stabilize the training process. The model was trained by minimizing the mean squared error (MSE) between the predicted and actual velocities. An early stopping mechanism based on the mean absolute error (MAE) of the validation set was employed, with a patience value of 10 epochs set to prevent overfitting. Experiments were conducted with a 12-time-step input time window, a batch size of 32, the Adam algorithm as the optimizer, and a learning rate of 0.001. The adjacency matrix was sparsely stored in coordinate (COO) format to reduce memory usage and accelerate matrix operations. The model's predictive performance was evaluated using multiple prediction time domains at 1 to 6 time steps.

[0095] Table 5 summarizes key evaluation metrics including mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and coefficient of determination (R²). The results show that the model achieves the highest prediction accuracy in the first-step prediction time domain, with an MAE of 0.9212 and an R² of 0.7999, indicating good consistency between predicted and actual traffic speeds. As expected, performance gradually declines with increasing prediction time domain, reflected in a slight increase in MAE and RMSE and a corresponding decrease in R². Notably, MAPE remains relatively stable at approximately 10% across all time domains, indicating that the model maintains consistent relative accuracy even with extended prediction windows. This demonstrates the model's robustness in controlling proportional error in long-term predictions. Overall, the consistently high R² values ​​(all above 0.77) across all time domains validate the model's effectiveness in capturing the spatiotemporal dynamics of traffic flow. The slight performance degradation with extended prediction windows provides direction for further optimization, including incorporating external factors (such as weather and events), improving temporal feature extraction, or exploring hybrid architectures.

[0096] Table 5. Performance of the ST-GCN-GRU model

[0097]

[0098] To verify the effectiveness of the proposed ST-GCN-GRU model in traffic speed prediction, the following models were selected as baselines for comparative evaluation: (1) Historical Average (HA), a naive but widely used baseline method for estimating future traffic speeds based on the average speed of historical datasets; (2) LightGBM, a gradient boosting framework based on decision trees; and (3) Long Short-Term Memory (LSTM), a recurrent neural network capable of capturing sequence dependencies in time-series data. All experiments were conducted on a personal computer equipped with an Apple M2 Pro chip, which includes a 12-core CPU and a 19-core integrated GPU, and 16GB of LPDDR5 unified memory. The model implementation was developed using Python 3.10, and the deep learning components were executed using PyTorch 2.7.1.

[0099] Table 6 presents a comprehensive comparison of the baseline models across all prediction time domains. Experimental results demonstrate that the ST-GCN-GRU model outperforms the historical averaging method, LightGBM, and LSTM across all prediction time domains from 1 to 6 time steps. Specifically, ST-GCN-GRU achieves the lowest MAE and RMSE values ​​and the highest R² score in each setting, exhibiting best performance in the 1-step prediction time domain. In contrast, the historical averaging method and LightGBM perform weaker, particularly in capturing temporal trends. While LSTM outperforms the historical averaging method and LightGBM, it still lags behind ST-GCN-GRU, especially as the prediction time domain increases. Notably, ST-GCN-GRU maintains a stable MAPE value (approximately 10%) and an R² value consistently above 0.77 across all time domains, indicating strong temporal generalization ability. These results highlight the advantages of combining spatial dependency integration via graph convolutional networks with temporal modeling through gated recurrent units, supported by discrete spatiotemporal graph structures. This architecture enables the model to extract high-order spatiotemporal patterns while remaining robust to sparse or missing topological information, making it a practical and scalable solution for real-world traffic speed prediction and time-dependent route planning applications.

[0100] Table 6. Comparison of Model Performance

[0101]

[0102] This invention also discloses a computer system, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is executed by the processor, it implements the steps of the time-dependent path planning method based on discrete spatiotemporal networks.

[0103] This invention also discloses a computer program product, including a computer program that, when executed by a processor, implements the steps of the time-dependent path planning method based on discrete spatiotemporal networks.

[0104] The program code used to implement the method of the present invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the steps of the method of the present invention to be performed. The program code can be executed entirely on the machine, partially on the machine, partially on the machine and partially on a remote machine as a standalone software package, or entirely on a remote machine or server. All aspects not detailed in this invention are well-known to those skilled in the art.

Claims

1. A time-dependent path planning method based on discrete spatiotemporal networks, characterized in that, Includes the following steps: The road network topology is discretized into multiple independent road segments to construct a first discrete spatiotemporal network. In the first discrete spatiotemporal network, each node corresponds to a road segment and a time point. The edges of nodes at the same time point are determined based on the historical speed similarity of the road segments. A spatiotemporal graph convolutional network deep learning model is used to perform multi-step traffic speed prediction based on the first discrete spatiotemporal network. The predicted velocity is incorporated into the node connection relationship between adjacent time points to construct a second discrete spatiotemporal network. In the second discrete spatiotemporal network, each node corresponds to a road segment and a time point. There are no edges between nodes at the same time point. The unidirectional edges between nodes at adjacent time points are determined based on the predicted velocity, and each edge represents the transition of spatiotemporal state. The path planning problem is constructed based on the second discrete spatiotemporal network, and the time-dependent path planning problem is transformed into a time-invariant path planning problem. The optimal path is then solved using a polynomial-time algorithm. In the first discrete spatiotemporal network, the cosine similarity of the historical speed curves of each road segment is calculated based on the K nearest neighbor algorithm, and a K nearest neighbor spatial adjacency matrix is ​​constructed. Each node at the same time is connected to its K most similar neighbors. The spatiotemporal graph convolutional network deep learning model adopts the ST-GCN-GRU model. It captures the spatiotemporal dependence of traffic flow through the spatiotemporal graph convolutional network GCN and combines it with the gated recurrent unit GCN to realize multi-step traffic speed prediction. In the second discrete-time network, the connection edge between the node at time t and the node at time t+1 is determined as follows: the reachability of each road segment node at time t to the adjacent road segment node at time t+1 is calculated based on the predicted speed. If the vehicle can travel from road segment i at time t to road segment j at time t+1 within a unit time interval under the predicted speed condition, then a directed edge is established between the corresponding nodes. The path planning problem constructed based on the second discrete-time network is a binary variable integer programming model, employing binary variables. Indicate the usage state of the edge: if at time Vehicles from node Driving towards the node ,but ;otherwise The path planning objective is... ;in Represents a set of nodes. Indicates time Connect to time nodes The set of nodes, Represents a set of times; constraints include: ， ， ， in Indicates the starting node index. Indicates the index of the endpoint node. Indicates the feasible time to reach the destination. Indicates at time Connect to time nodes The set of nodes, This represents the set of all intermediate nodes except the starting and ending nodes. The first constraint is the starting point outflow constraint, ensuring that the vehicle starts from the starting node o at the initial time and the outflow is 1 unit, guaranteeing the starting condition of the path planning. The second constraint is the ending point inflow constraint, ensuring that the vehicle reaches the ending node d within the specified time and the inflow is 1 unit, guaranteeing the termination condition of the path planning. The third constraint is the intermediate node flow balance constraint, which requires that the inflow of all intermediate nodes except the starting and ending nodes at any time t must be equal to the outflow.

2. The time-dependent path planning method based on discrete spatiotemporal networks according to claim 1, characterized in that, The ST-GCN-GRU model uses two stacked GCN layers to extract high-order spatial features, and the propagation rule is as follows: ;in: For the first Layer nodes represent matrices. This represents the adjacency matrix after adding self-joins. for The degree matrix, Indicates the first The layer's weight matrix, with ReLU as the activation function; spatial features are temporally aggregated using the GRU module, and the GRU output is mapped to multi-step prediction values ​​for the speed of all road segments in the future time period through a fully connected prediction layer.

3. The time-dependent path planning method based on discrete spatiotemporal networks according to claim 1, characterized in that, The problem of multiple endpoints is addressed by connecting the endpoints of adjacent time-layer nodes with virtual edges.

4. The time-dependent path planning method based on discrete spatiotemporal networks according to claim 1, characterized in that, The optimal path can be obtained by using Dijkstra's algorithm or A* algorithm to solve the path planning problem.

5. A computer system comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is executed by the processor, it implements the steps of the time-dependent path planning method based on discrete spatiotemporal networks according to any one of claims 1-4.

6. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the time-dependent path planning method based on discrete spatiotemporal networks according to any one of claims 1-4.

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