A method and device for optimizing nodes in a transportation network

Abstract

This invention provides a method and apparatus for optimizing nodes in a transportation network, comprising: optimizing the utilization problem of nodes in a transportation network into a maximum clique problem; transforming the maximum clique problem into a QUBO model based on the general objective function of the QUBO model; using a graph neural network to characterize the structure and characteristics of the QUBO graph of the QUBO model to construct a deep learning model CONQUER; and training the deep learning model CONQUER to explore the optimal solution to the optimization problem of nodes in the transportation network, thereby obtaining a trained deep learning model CONQUER. By modeling the problem of determining dense regions in transportation network analysis as a maximum clique problem in combinatorial optimization, and analyzing the transportation network structure by finding the maximum clique, this method helps to effectively solve the problem of determining dense regions in transportation network analysis, improving the accuracy and reliability of traffic flow optimization.

Description

Technical Field

[0001] This invention relates to a method for optimizing transportation networks, specifically to a method and apparatus for optimizing nodes in a transportation network. Background Technology

[0002] Traffic network analysis plays a crucial role in urban development, aiming to optimize road use efficiency and reduce traffic congestion. Such analyses typically involve making decisions within complex traffic flows, each potentially impacting traffic volume and road use efficiency. Typical traffic network analysis problems include identifying traffic bottlenecks, determining areas of high traffic density, and predicting traffic flow trends. Identifying areas of high traffic density within the network is a critical task, helping planners understand the interactions between roads and their impact on traffic flow.

[0003] In recent years, at least three main strategies have been proposed in the field of traffic network analysis: exact algorithms, approximate algorithms, and heuristic algorithms. Exact algorithms can obtain the global optimum, but their computational cost is too high for large-scale networks, making them impractical. Approximate algorithms offer theoretical guarantees and polynomial time complexity, but they suffer from difficulties in construction and performance issues. Heuristic algorithms offer fast speed and good practical results, but they lack theoretical guarantees and require customization for specific problems, thus drawing some criticism.

[0004] However, traditional methods face at least two key challenges. First, the equivalent maximum clique problem for this class of problems is inherently NP-hard, making them difficult to solve. Existing strategies often face a trade-off: fast algorithms cannot guarantee solution quality, while high-quality solutions often require longer computation times. Second, most traditional methods are designed with algorithms tailored to the mathematical structure of the problem; changes in the constraints and structure necessitate redesigning the algorithm, which is time-consuming and labor-intensive.

[0005] Therefore, in the field of traffic network analysis, researchers are dedicated to understanding the network of relationships between nodes and edges, as the degree of connectivity between nodes is crucial for traffic flow transmission and optimization. However, traditional traffic flow analysis methods are often time-consuming, labor-intensive, and costly. Therefore, computational methods have become one of the important approaches to analyzing traffic networks.

[0006] In traffic network analysis, a key challenge is determining the connections between nodes and their optimal connectivity within the network. These connections involve factors such as traffic frequency, information transmission, and connection strength. Ideally, researchers hope to find a way to identify the densest subgraphs in a traffic network for traffic optimization and resource allocation. However, due to the complexity of traffic networks, determining the optimal dense subgraphs is not straightforward. Summary of the Invention

[0007] This invention provides a method and apparatus for optimizing nodes in a transportation network, which can solve the technical problem in the prior art of determining the connections between nodes in a transportation network and their optimal connection methods in the network.

[0008] To achieve the above objectives, in a first aspect, embodiments of the present invention provide a node optimization method for a transportation network, comprising:

[0009] The problem of utilizing nodes in a transportation network is optimized into a maximum clique problem, wherein the nodes include: transportation nodes;

[0010] The maximum clique problem is transformed into a QUBO model based on a general objective function of the QUBO model.

[0011] A graph neural network is used to represent the structure and characteristics of the QUBO graph of the QUBO model, and a deep learning model CONQUER is constructed.

[0012] By training the deep learning model CONQUER, the optimal solution to the optimization problem of nodes in a transportation network is explored, and a trained deep learning model CONQUER is obtained. The trained deep learning model CONQUER is used to optimize the utilization problem of nodes in any transportation network, and the node optimization results are obtained. The node optimization results include: the nodes used, the number of nodes, and the road usage frequency between nodes.

[0013] Secondly, embodiments of the present invention provide a node optimization method for a transportation network, further comprising:

[0014] The problem of utilizing the nodes of the traffic network to be solved is input into the aforementioned trained deep learning model CONQUER.

[0015] Output the node optimization results, which include: the nodes used, the number of nodes, and the road usage frequency between nodes.

[0016] Thirdly, embodiments of the present invention provide a node optimization device for a traffic network, comprising:

[0017] The problem transformation unit is used to optimize the utilization problem of nodes in a transportation network into a maximum clique problem, wherein the nodes include transportation nodes;

[0018] The QUBO model building unit is used to transform the maximum clique problem into a model based on the general objective function of the QUBO model.

[0019] The deep learning model building unit is used to represent the structure and characteristics of the QUBO graph of the QUBO model using a graph neural network, and to build the deep learning model CONQUER.

[0020] The training unit is used to train the deep learning model CONQUER to explore the optimal solution of the optimization problem of nodes in a traffic network, and obtain the trained deep learning model CONQUER. The trained deep learning model CONQUER is used to optimize the utilization problem of nodes in any traffic network and obtain the node optimization results, which include: the nodes used, the number of nodes, and the road usage frequency between nodes.

[0021] The above technical solution has the following beneficial effects: By modeling the problem of identifying dense areas in traffic network analysis as a maximum clique problem in combinatorial optimization, and by analyzing the traffic network structure through the search for the maximum clique, it helps to effectively solve the problem of identifying dense areas in traffic network analysis. This helps urban planners and traffic managers better understand the structure and function of traffic networks, and improves the accuracy and reliability of traffic flow optimization. This is of great significance for traffic network operation and maintenance. Attached Figure Description

[0022] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0023] Figure 1 This is a flowchart of a node optimization method for a traffic network according to an embodiment of the present invention;

[0024] Figure 2 This is a structural diagram of a node optimization device for a traffic network according to an embodiment of the present invention;

[0025] Figure 3 This is the solution framework for the QUBO model in this embodiment of the invention;

[0026] Figure 4 These are the ablation experiment results of an embodiment of the present invention. Detailed Implementation

[0027] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0028] like Figure 1As shown, in conjunction with embodiments of the present invention, a node optimization method for a traffic network is provided, comprising:

[0029] S101: Optimize the utilization problem of nodes in the transportation network into a maximum clique problem, wherein the nodes include: transportation nodes;

[0030] S102: A general objective function based on the QUBO model, which transforms the maximum clique problem into a QUBO model;

[0031] S103: Use graph neural networks to represent the structure and characteristics of the QUBO graph of the QUBO model and construct the deep learning model CONQUER;

[0032] S104: By training the deep learning model CONQUER, the optimal solution to the optimization problem of nodes in a traffic network is explored, and the trained deep learning model CONQUER is obtained. The trained deep learning model CONQUER is used to optimize the utilization problem of nodes in any traffic network, and the node optimization results are obtained. The node optimization results include: the nodes used, the number of nodes, and the road usage frequency between nodes.

[0033] Preferably, S101: Optimizing the utilization problem of nodes in the transportation network into a maximum clique problem includes:

[0034] The transportation network is represented as G = (V, E), where V is the set of nodes in the transportation network, containing the interconnected individuals in the network, and E is the set of edges, representing the edges composed of individuals with interactive relationships.

[0035] The symbols and parameters are defined as follows:

[0036] (x_v): A binary variable, where x represents a node in the transportation network and v represents the node's index. The value is 1 when node (v) is selected into the group, and 0 otherwise.

[0037] (N(v)): The set of neighboring nodes of node (v).

[0038] The objective function (f(x)) represents maximizing the size of the clique, which means maximizing the number of selected nodes. The maximum clique problem can be expressed as:

[0039]

[0040] Constraint: Each node in the clique must either be selected or not selected. This constraint can be expressed as:

[0041] x v +x u ≥1, x vx u This represents any two nodes in the transportation network.

[0042] Preferably, S102: A general objective function based on the QUBO model, transforming the maximum clique problem into a QUBO model, includes:

[0043] The general objective function of the QUBO model is expressed as:

[0044]

[0045] Where x = (x1, x2, ..., xn) represents a decision vector consisting of two variables, where the two variables are either 0 or 1. i x j The nodes at both ends of the edge, matrix Q: is a symmetric matrix or an upper triangular matrix, a i =Q ii ,so b ij =Q ij , a i b represents the node weights in the QUBO model. ij This represents the weight of the edge.

[0046] According to H QUBO For the expression corresponding to (x), define a corresponding undirected graph G =<V,E> Node v i ∈V represents H QUBO The decision variables in (x) have weights equal to the coefficients a of the linear terms. i Node v i and v j via edge e ij The connection ∈E has a weight equal to H. QUBO The coefficient b of the quadratic term in the expression corresponding to (x) ij This encodes the objective and constraint information of the maximum clique problem into an undirected graph structure, allowing the neural network to directly learn the objective function of the QUBO model for the maximum clique problem. The objective function of the QUBO model for the maximum clique problem can be expressed as:

[0047]

[0048] Where i∈V represents a node in the traffic network, with node number i, and p represents the penalty coefficient of the QUBO model. This indicates a node that has no connection relationship.

[0049] Preferably, S103: Using a graph neural network to represent the structure and characteristics of the QUBO graph corresponding to the QUBO model, a deep learning model CONQUER is constructed, including:

[0050] The encoder is constructed, specifically comprising: an integration centrality coding layer, a message passing layer, a Transformer layer, and an iterative computation and solution layer; wherein:

[0051] In the integration of centrality coding layer:

[0052] Each node in the QUBO graph is augmented using its corresponding degree to capture the importance of the nodes in the QUBO graph, and then encoded. The vector representation of each node augmented using its corresponding degree and then encoded is as follows:

[0053]

[0054] Here, ReLU refers to the activation function. In this context, 'i' represents the i-th node, 0 represents the initial feature, and x... i It is the initial feature of the node, z deg (v i ) encodes the degree of a node, v i It refers to the node with index i. W1 and W2 are the parameters of the neural network, and they are learnable parameters.

[0055] At the message passing layer:

[0056] The neighborhood aggregation process is used to merge node features to obtain edge feature aggregation, and merge edge features to obtain node feature aggregation. The edge feature aggregation and node feature aggregation are represented as follows:

[0057]

[0058] Among them, h ij =ReLU(W3x ij ) represents the initial edge embedding vector, and x represents the intermediate output of the neural network. ij W4, W5, W6, and W7 are the parameters of the neural network, and all of them are learnable parameters;

[0059] After obtaining the node features in step l Then, the features from the previous step of this node can be combined. To implement residual joins, the residual join is represented as follows:

[0060] Here, W8 represents the parameters of the neural network, and these parameters are learnable. Xi's parameters;

[0061] In the Transformer layer:

[0062] The output of the message passing layer is combined with the output of the global attention layer within the Transformer layer to obtain the updated node features:

[0063]

[0064] Where MHA represents multi-head attention network, LN represents layer normalization, and FFN represents feedforward neural network layer; This represents the node embedding vector obtained in step l-1. This represents the node embedding vector after passing through the multi-head attention network;

[0065] In the iterative computation and solution layer:

[0066] During the solution process, the updated node features output from the Transformer layer are used as input to the ensemble centrality coding layer. The steps of the ensemble centrality coding layer, message passing layer, and Transformer layer are iterated repeatedly. After iteration, the final embedding vector for each node is obtained. The final embedding vector for each node is represented as:

[0067] Summing the final embedding vectors of all nodes yields: z s =∑ i∈V z i The solution to the QUBO model is represented by summation.

[0068] Preferably, S103: Using a graph neural network to represent the structure and characteristics of the QUBO graph of the QUBO model, and constructing a deep learning model CONQUER, further includes:

[0069] Constructing a decoder includes:

[0070] Formally, this forms a Markov decision process described by tuples (S, A, R), where S represents all possible states s. i The set of actions a i ∈A means that for a given state s i Assignment of binary variable x to the QUBO model; state s i Perform action a i The reward r i r i =a i +∑ (i,j)∈E b ij x j ∈R reward r i This indicates the change in the objective function before and after the action is performed;

[0071] The decoder converts a pair of state-action pairs (s) i , a i ) is converted into a scalar Q(s) of a neural network. i ,a i ;Θ), to evaluate in state s i Next action a i The quality of the decoder is expressed by the Q function as follows:

[0072] Q(h,υ;Θ)=W 11 ReLU(W 10 ReLU(W9[z s ,z i ]))

[0073] Where W9, W10, and W11 are the parameters of the neural network, and are learnable parameters, [z s ,z i ] indicates that the vector z s sum vector z i Concatenate the rows.

[0074] Preferably, S104: By training the deep learning model CONQUER to explore the optimal solution to the node utilization problem of the traffic network, the trained deep learning model CONQUER is obtained, including:

[0075] Samples of nodes in the traffic network corresponding to the maximum clique problem are obtained, and the maximum clique problem is transformed into a Hamiltonian minimization problem on a QUBO graph. The problem is solved using a reinforcement learning algorithm, and a trajectory based on a Markov decision process representation is generated based on the QUBO graph.

[0076] A complete training round is the process of finding a solution that minimizes the Hamiltonian on the QUBO graph, requiring all decision variable states to be sequentially flipped from 0 to 1. The trajectory generated in a complete training round is a state-action-reward sequence: s0, a0, r0, s1, a1, r1, ..., s T s0 is the initial state where all decision variables are 0, s T The final state is where all decision variables are 1; training process data is collected during a complete training round: s t ,a t ,r t,t+n ,s t+n s t Let a represent the set of states of all variables at time t. t This represents the action taken at time t. s represents the cumulative reward at time t+n. t+nLet n represent the set of states of all variables at time t+n, where step size n and discount factor γ are hyperparameters.

[0077] Using the collected training process data, the deep learning model CONQUER learns from the collected training process data and updates the network parameters Θ of the deep learning model CONQUER to minimize the following loss function:

[0078]

[0079] Where E represents the maximum expectation, r t,t+n s represents the immediate reward obtained n steps later after performing the action at time t. t+n Let a represent the state at time t+n. t+n This represents the action performed at time t+n, where γ is the discount factor. Indicates that in state s t+n Execution is the target network The action with the largest return value, a t+n The returned reward valuation, For the target network parameters, Q(s) t ,a t ;Θ) indicates that in state s t When performing action a t Based on the reward estimate obtained from the original network Q(Θ), s t Let a represent the state at time t. t This represents the action performed at time t, and Θ represents the parameters of the original network, which are updated using real-time training data.

[0080] The original network Q(Θ) periodically copies the parameter Θ to the target network. parameters To achieve the update of the target network;

[0081] When the loss function value is less than the preset value, a well-trained deep learning model CONQUER can be obtained.

[0082] Preferably, the node optimization method for the transportation network further includes:

[0083] In the sample nodes of the traffic network corresponding to the obtained maximum independent set problem, noise was introduced into the sample when constructing the QUBO graph;

[0084] When the loss function is less than the preset value, the encoder parameters should be frozen and fine-tuned for the corresponding deep learning model CONQUER to obtain the trained deep learning model CONQUER.

[0085] Preferably, the node optimization method for the transportation network further includes:

[0086] When using a trained deep learning model CONQUER to solve the problem of node utilization in a traffic network, if the obtained solution does not meet the feasibility conditions of the traffic network, a greedy search method or a local search method is used to repair the solution.

[0087] In conjunction with embodiments of the present invention, a method for optimizing nodes in a transportation network is also provided, further comprising:

[0088] The problem of utilizing the nodes of the traffic network to be solved is input into any of the aforementioned trained deep learning models, CONQUER.

[0089] Output the node optimization results, which include: the nodes used, the number of nodes, and the road usage frequency between nodes.

[0090] like Figure 2 As shown, in conjunction with embodiments of the present invention, a node optimization device for a traffic network is also provided, comprising:

[0091] Problem transformation unit 21 is used to optimize the utilization problem of nodes in a traffic network into a maximum clique problem, wherein the nodes include traffic nodes;

[0092] QUBO model building unit 22 is used to transform the maximum clique problem into a model based on the general objective function of the QUBO model;

[0093] The deep learning model building unit 23 is used to use a graph neural network to represent the structure and characteristics of the QUBO graph of the QUBO model and build a deep learning model CONQUER.

[0094] Training unit 24 is used to train the deep learning model CONQUER to explore the optimal solution of the optimization problem of nodes in a traffic network, and obtain the trained deep learning model CONQUER. The trained deep learning model CONQUER is used to optimize the utilization problem of nodes in any traffic network and obtain the node optimization results, which include: the nodes used, the number of nodes, and the road usage frequency between nodes.

[0095] Preferably, the problem conversion unit 21 is specifically used for:

[0096] The transportation network is represented as G = (V, E), where V is the set of nodes in the transportation network, which contains the individuals that are interconnected in the transportation network, and E is the set of edges, which represents the edges composed of individuals that have interactive relationships.

[0097] The symbols and parameters are defined as follows:

[0098] (x_v): A binary variable, where x represents a node in the transportation network and v represents the node's index. The value is 1 when node (v) is selected into the group, and 0 otherwise.

[0099] (N(v)): The set of neighboring nodes of node (v);

[0100] The objective function (f(x)) represents maximizing the size of the clique, which means maximizing the number of selected nodes. The maximum clique problem can be expressed as:

[0101]

[0102] Constraint: Each node in the clique must either be selected or not selected. This constraint can be expressed as:

[0103] x v +x u ≥1, x v x u This represents any two nodes in the transportation network.

[0104] Preferably, the QUBO model building unit 22 is specifically used for:

[0105] The general objective function of the QUBO model is expressed as:

[0106]

[0107] Where x = (x1, x2, ..., xn) represents a decision vector consisting of two variables, where the two variables are either 0 or 1. i x j The nodes at both ends of the edge, matrix Q: is a symmetric matrix or an upper triangular matrix, a i =Q ij ,so b ij =Q ij , a i b represents the node weight. ij Indicates the weight of the edge;

[0108] According to H QUBO For the expression corresponding to (x), define a corresponding undirected graph G =<V,E> Node v i ∈V represents H QUBO The decision variables in (x) have weights equal to the coefficients a of the linear terms. i Node v i and v j via edge e ij The connection ∈E has a weight equal to H. QUBO The coefficient b of the quadratic term in the expression corresponding to (x)ij This encodes the objective and constraint information of the maximum clique problem into an undirected graph structure, allowing the neural network to directly learn the objective function of the QUBO model for the maximum clique problem. The objective function of the QUBO model for the maximum clique problem can be expressed as:

[0109]

[0110] Where i∈V represents a node in the traffic network, and the node's index is... i p represents the penalty coefficient of the QUBO model. This indicates a node that has no connection relationship.

[0111] Preferably, the deep learning model building unit 23 is specifically used for:

[0112] The encoder is constructed, specifically comprising: an integration centrality coding layer, a message passing layer, a Transformer layer, and an iterative computation and solution layer; wherein:

[0113] In the integration of centrality coding layer:

[0114] Each node in the QUBO graph is augmented using its corresponding degree to capture the importance of the nodes in the QUBO graph, and then encoded. The vector representation of each node augmented using its corresponding degree and then encoded is as follows:

[0115]

[0116] Here, ReLU refers to the activation function. In this context, 'i' represents the i-th node, 0 represents the initial feature, and x... i It is the initial feature of the node, z deg (v i ) encodes the degree of a node, v i It refers to the node with index i. W1 and W2 are the parameters of the neural network, and they are learnable parameters.

[0117] At the message passing layer:

[0118] The neighborhood aggregation process is used to merge node features to obtain edge feature aggregation, and merge edge features to obtain node feature aggregation. The edge feature aggregation and node feature aggregation are represented as follows:

[0119]

[0120] Among them, h ij =ReLU(W3x ij ) represents the initial edge embedding vector, and x represents the intermediate output of the neural network. ijW4, W5, W6, and W7 are the parameters of the neural network, and all of them are learnable parameters;

[0121] After obtaining the node features in step l Then, the features from the previous step of this node can be combined. To implement residual joins, the residual join is represented as follows:

[0122]

[0123] Where W8 are the parameters of the neural network, and these are learnable parameters;

[0124] In the Transformer layer:

[0125] The output of the message passing layer is combined with the output of the global attention layer within the Transformer layer to obtain the updated node features:

[0126]

[0127] Where MHA represents multi-head attention network, LN represents layer normalization, and FFN represents feedforward neural network layer; This represents the node embedding vector obtained in step l-1. This represents the node embedding vector after passing through the multi-head attention network;

[0128] In the iterative computation and solution layer:

[0129] During the solution process, the updated node features output from the Transformer layer are used as input to the ensemble centrality coding layer. The steps of the ensemble centrality coding layer, message passing layer, and Transformer layer are iterated repeatedly. After iteration, the final embedding vector for each node is obtained, represented as: z i =

[0130] Summing the final embedding vectors of all nodes yields: z s =∑ i∈V z i The solution to the QUBO model is represented by summation.

[0131] Preferably, the deep learning model building unit 23 is specifically used for:

[0132] Constructing a decoder includes:

[0133] Formally, this forms a Markov decision process described by tuples (S, A, R), where S represents all possible states s. i The set of actions ai ∈A means that for a given state s i Assignment of binary variable x to the QUBO model; state s i Perform action a i The reward r i r i =a i +∑ (i,j)∈E b ij x j ∈R reward r i This indicates the change in the objective function before and after the action is performed;

[0134] The decoder converts a pair of state-action pairs (s) i , a i ) is converted into a scalar Q(s) of a neural network. i ,a i ;Θ), to evaluate in state s i Next action a i The quality of the decoder is expressed by the Q function as follows:

[0135] Q(h, v; Θ) = W 11 ReLU(W 10 ReLU(W9[z s , z i ]))

[0136] Where W9, W10, and W11 are the parameters of the neural network, and are learnable parameters, [z s ,z i ] indicates that the vector z s sum vector z i Concatenate the rows.

[0137] Preferably, the training unit 24 is specifically used for:

[0138] Samples of nodes in the traffic network corresponding to the maximum clique problem are obtained, and the maximum clique problem is transformed into a Hamiltonian minimization problem on a QUBO graph. The problem is solved using a reinforcement learning algorithm, and a trajectory based on a Markov decision process representation is generated based on the QUBO graph.

[0139] A complete training round is the process of finding a solution that minimizes the Hamiltonian on the QUBO graph, requiring all decision variable states to be sequentially flipped from 0 to 1. The trajectory generated in a complete training round is a state-action-reward sequence: s0, a0, r0, s1, a1, r1, ..., s T s0 is the initial state where all decision variables are 0, s T The final state is where all decision variables are 1; training process data is collected during a complete training round: st ,a t ,r t,t+n ,s t+n s t Let a represent the set of states of all variables at time t. t This represents the action taken at time t. s represents the cumulative reward at time t+n. t+n Let n represent the set of states of all variables at time t+n, where step size n and discount factor γ are hyperparameters.

[0140] Using the collected training process data, the deep learning model CONQUER learns from the collected training process data and updates the network parameters Θ of the deep learning model CONQUER to minimize the following loss function:

[0141]

[0142] Where E represents the maximum expectation, r t,t+n s represents the immediate reward obtained n steps later after performing the action at time t. t+n Let a represent the state at time t+n. t+n This represents the action performed at time t+n, where γ is the discount factor. Indicates that in state s t+n Execution is the target network The action with the largest return value, a t+n The returned reward valuation, For the target network parameters, Q(s) t ,a t ;Θ) indicates that in state s t When performing action a t Based on the reward estimate obtained from the original network Q(Θ), s t Let a represent the state at time t. t This represents the action performed at time t, and Θ represents the parameters of the original network, which are updated using real-time training data.

[0143] The original network Q(Θ) periodically copies the parameter Θ to the target network. parameters To achieve the update of the target network;

[0144] When the loss function value is less than the preset value, a well-trained deep learning model CONQUER can be obtained.

[0145] Preferably, the training unit 24 is specifically used for:

[0146] In the sample nodes of the traffic network corresponding to the obtained maximum independent set problem, noise was introduced into the sample when constructing the QUBO graph;

[0147] When the loss function is less than the preset value, the encoder parameters should be frozen and fine-tuned for the corresponding deep learning model CONQUER to obtain the trained deep learning model CONQUER.

[0148] Preferably, the training unit 24 is specifically used for:

[0149] When using a trained deep learning model CONQUER to solve the problem of node utilization in a traffic network, if the obtained solution does not meet the feasibility conditions of the traffic network, a greedy search method or a local search method is used to repair the solution.

[0150] The technical solutions of the present invention will be described in detail below with reference to specific application examples. For technical details not described in the implementation process, please refer to the relevant descriptions above.

[0151] In this embodiment of the invention, a traffic flow optimization method for discovering dense subgraphs in traffic networks based on QUBO and reinforcement learning is provided. Using CONQUER (solving combinatorial optimization neurally through QUBO transformation and dEepReinforcement learning), the problem of identifying dense traffic areas can be viewed as a maximal clique problem in the field of combinatorial optimization. A maximal clique represents a set of fully connected individuals, indicating a close relationship between them.

[0152] First, the social network analysis problem is transformed into a unified mathematical model. Then, a neural network solver is used to search for high-quality traffic network clusters. These clusters may represent potentially closely related groups, but further validation and adjustments are needed to obtain the final results. Effectively identifying dense subgraphs in the traffic network improves the accuracy and reliability of traffic network flow optimization, which is of great significance for traffic network operation and maintenance.

[0153] CONQUER uses the QUBO model as a "translator" for traffic flow optimization problems. Through specific restatement techniques, once the traffic optimization problem is described in the QUBO language, these problems can be solved using the QUBO solver.

[0154] CONQUER designed a deep learning-based QUBO solver that treats the QUBO solving process as a learning task. The goal is to train a better heuristic algorithm using a large number of problem instances from a specific distribution, enabling efficient handling of new, unseen instances from the same distribution. Once these neural models are well-trained, they can be effectively applied multiple times to solve problems with many similar instances.

[0155] Specifically, CONQUER first transforms various combinatorial optimization problems into a unified QUBO form (quadratic unconstrained binary optimization). Then, it trains a neural solver, QUBO, to search for high-quality policies. These policies are then repaired and checked to obtain a solution to the original combinatorial optimization problem. The QUBO solver is a purely data-driven neural model, independent of task expert knowledge input. To effectively capture the characteristics of the target and the constraints of the combinatorial optimization problem, a graph transformer network is used to represent the QUBO graph, serving as the input to the QUBO solver. DQN is used to train the QUBO solver to find forward-looking solutions with better long-term benefits. Although trained only on a small scale of generated graphs, CONQUER demonstrates good generalization on larger-scale instances and can be easily applied to many real-world datasets. Experiments show that the algorithm achieves state-of-the-art performance on combinatorial optimization problems corresponding to traffic network analysis, helping to optimize traffic flow in dense subgraphs during traffic network analysis and providing important clues and guidance for managers.

[0156] The CONQUER process mainly consists of four key steps:

[0157] 1. Problem Transformation: Obtain a QUBO graph equivalent to the original problem. Traffic nodes are considered as nodes in the graph, and road usage frequencies between nodes are considered as edges. Ultimately, the set of nodes with the densest connections is found to describe potential high-density traffic areas in the traffic network.

[0158] 2. Use a depth map transformer to represent the features of the QUBO map.

[0159] 3. Apply the trained reinforcement learning strategy to search for the solution that defines the minimum Hamiltonian on the QUBO graph.

[0160] 4. Inspect and repair the solution to make it effective for the original problem.

[0161] Compared to previous work, the most significant advantage is that it eliminates the need to tailor the deep learning architecture for specific problems, greatly reducing the cost of problem customization. Extensive experiments on traffic flow optimization tasks, abstracting it as a maximal clique problem in combinatorial optimization, were conducted, and CONQUER was tested on both synthetic and real data. Results show that CONQUER can efficiently solve this problem, outperforming most state-of-the-art methods, including traditional heuristics and learning-based strategies. In some cases, CONQUER even achieves the same accuracy as commercially available CO solvers.

[0162] In traffic network analysis, identifying dense regions within the network is crucial, and finding the densest traffic region can be modeled as a maximal clique problem. Due to the NP-hard nature of this problem, traditional heuristics and integer programming rely on hand-designed heuristics to make decisions that are computationally infeasible (computationally complex or computationally expensive) or lack well-defined mathematical formulas.

[0163] Machine learning (ML) has emerged as an effective solution to this challenge, offering innovative strategies for managing its complexity. In particular, methods such as reinforcement learning (RL), meta-learning, and sampling-based approaches have generated interest in the field of combinatorial optimization (CO). These methods enable models to internalize knowledge from the training dataset or adapt to new problems by drawing on insights from previous similar problems, thereby enhancing their problem-solving capabilities.

[0164] Another approach is to formulate the combinatorial optimization problem modeled after this problem as a QUBO problem, which can be efficiently solved using quantum computing or specialized algorithms. The QUBO formulation allows ML models to leverage the power of quantum computing or heuristic algorithms to find good solutions to combinatorial optimization problems. The integration of QUBO models with graph neural networks (GNNs) opens new avenues for solving combinatorial optimization problems. Furthermore, utilizing deep reinforcement learning to search for optimal flow configurations, and incorporating the QUBO-equivalent maximal clique problem into the reinforcement learning (RL) framework, it is possible to learn policies that lead to optimal solutions.

[0165] In summary, the integration of QUBO with Graph Neural Networks (GNNs) offers a promising approach for solving dense area problems in traffic networks. By leveraging the structural learning capabilities of GNNs and the optimization capabilities of QUBO, researchers can develop more efficient algorithms for traffic flow optimization.

[0166] I. Modeling

[0167] (I) Mathematical Expression

[0168] Modeling the node utilization problem of a traffic network is performed. The distribution of individuals in the traffic network is set as a graph, G = (V, E), where V represents individuals (intersections, road segment start and end points, traffic signal control points, important locations, sensor locations, etc.) that are interconnected in the traffic network, and E represents the set of edges, which represent the interaction relationships. Edges can represent actual roads, road segments, routes, etc. in the traffic network, or they can represent abstract connection relationships between nodes, such as the correlation between traffic lights, traffic flow between two intersections, and other information.

[0169] Define the following symbols and parameters:

[0170] (x_v): A binary variable, where x represents a node in the transportation network and v represents the node's index. The value is 1 when node (v) is selected into the group, and 0 otherwise.

[0171] (N(v)): The set of neighboring nodes of node (v).

[0172] The objective function (f(x)) represents maximizing the clique size, i.e., maximizing the number of selected nodes. It can be expressed as:

[0173]

[0174] Constraint: Each node in the clique must either be selected or not selected.

[0175] x v +x u ≥1,

[0176] Among them, x v x u Represents any two nodes in a transportation network;

[0177] This problem is modeled as a maximum clique (MC, denoted by MC in the experimental results) problem in the field of combinatorial optimization. Solving the maximum clique helps to find possible community groups (which may represent the set of intersections where congestion occurs in a traffic network). That is, the model's borrow is which nodes should be selected and which nodes should not be selected, with 1 for selection and 0 for non-selection; thus, we know the structure and function of the traffic network being analyzed.

[0178] (II) QUBO Model

[0179] The QUBO, as a cost function for a binary combinatorial optimization problem, contains linear and quadratic terms. To convert the mathematical form of the above problem into a QUBO problem, each continuous variable needs to be represented as a binary variable. This can be achieved using techniques such as binary encoding or other encoding schemes. Once the variables are binary, the objective function and constraints are transformed into quadratic forms, which can be represented as a QUBO problem. Specifically, the QUBO problem can be formalized as the objective function of a QUBO model:

[0180]

[0181] Where x = (x1, x2, ..., xn) represents a decision vector consisting of two variables (each variable is 0 or 1), x i x j The nodes at both ends of the edge, matrix Q: usually a symmetric or upper triangular matrix and a i =Q ij ,so b ij =Q ij , a i b represents the weight of the node. ij This represents the weight of the edge. Typically, the objective function value of QUBO (denoted as H) is also used. QUBO This is called the Hamiltonian.

[0182] Recent research advancements have demonstrated that QUBO provides a unified framework for expressing many NP-hard CO problems. Problem constraints can be relatively easily integrated into the objective function using penalties, and then transformed into the standard QUBO form. Furthermore, the profound significance of QUBO problems lies in their equivalence to the Ising model in physics, thus bridging the gap between physics and mathematical optimization. The latter has been proven to express a wide range of complex problems, including Karp's 21 NP-complete problems.

[0183] II. CONQUER, a deep reinforcement learning framework

[0184] Overall framework as follows Figure 3 As shown.

[0185] (I) Problem Transformation and QUBO Graph Construction

[0186] According to H QUBO For the expression corresponding to (x), define a corresponding undirected graph G =<V,E> Node v i ∈V represents H QUBO The decision variables in (x) have weights equal to the coefficients a of the linear terms. i Node v i and v j via edge eij ∈E is connected, and its weight is equal to E. QUBO The coefficient b of the quadratic term in the expression corresponding to (x) ij Compared to previous work in the original problem space, a significant advantage of this graph representation is that it can encode the objective and constraint information of the optimization problem into the graph structure, allowing neural networks to directly learn the objective function of the QUBO model for the maximum clique problem. Where i∈V represents a node in the traffic network with index i, and p is the penalty coefficient of the model, which is a specific numerical value, and in this problem, it takes the value 1.2. This refers to nodes that are not connected, such as two intersections in a transportation network that are not connected by roads.

[0187] (II) Graph Representation Based on Qubormer

[0188] Intuitively, the construction of a QUBO graph reveals that it contains the objective function and constraint information of the problem. Therefore, ideally, we aim to find an embedding vector that not only effectively captures the attributes of individual nodes but also fully represents the attributes of nodes with long-range dependencies, thus accurately mapping the objective function and constraints of the QUBO problem. Considering the unique structure of the QUBO graph, a novel graph transformer structure called Qubormer is constructed, primarily consisting of an encoder and a decoder.

[0189] 1. Encoder

[0190] In recent years, many studies have emphasized that traditional message-passing networks encounter bottlenecks such as smoothing, making them inefficient when handling tasks with long-term dependencies. To overcome the shortcomings of traditional neural networks, the transformer mechanism is integrated into the message-passing layer. Generally, the encoder consists of three key components.

[0191] (1) Centrality coding

[0192] By integrating centrality encoding, the importance of nodes in the graph can be captured. Each node is augmented with degree, thus providing a measure of its relative importance in the network topology.

[0193]

[0194] Here, ReLU refers to the activation function. In this context, 'i' represents the i-th node, 0 represents the initial feature, and x... i It is the initial feature of the node, z deg (v i ) refers to the degree of a node (degree is a technical term in complex networks, referring to the degree of a node v).i The number of adjacent nodes, specifically in a transportation network (for example, if an intersection has 5 directly connected roads, then its degree is 5, meaning 5 roads pass through that intersection), is used for encoding. i This refers to the node with index i, v is an abbreviation for the English word "vertex", W1 and W2 are learnable parameters, and encoding refers to turning the node into a vector.

[0195] (2) Message Passing Layer

[0196] To be precise, transforming various problems into QUBO form fundamentally integrates the target and constraint information into the nodes and edge weights of the QUBO graph, thus making edge information the primary information of the QUBO graph. Therefore, a two-step neighborhood aggregation process is adopted, including edge feature aggregation and node feature aggregation, to merge the features of nodes and edges to obtain edge feature aggregation and node feature aggregation:

[0197]

[0198] Among them, h ij =ReLU(W3x ij x is the initial edge embedding vector. ij The edge input features are used. W3, W4…W7 are all learnable parameters. The node features obtained in step l are then processed. Then, the features from the previous step of this node can be combined. Implementing residual connections can alleviate the smoothing problem of overmodeling.

[0199]

[0200] W8 is a learnable parameter.

[0201] (3) Transformer layer

[0202] In previous studies, such as the GraphTrans model, researchers typically stacked Transformer layers on top of several layers in a message-passing network. While this approach enhances the capabilities of message-passing networks by introducing positional or structural encoding, it still needs to address core issues such as oversmoothing at their root.

[0203] Therefore, this embodiment of the invention proposes a new perspective: in each layer, the output of the message passing network is aggregated with the output of the global attention layer to collaboratively update node features.

[0204]

[0205] Where MHA stands for Multi-Head Attention Network, LN stands for Layer Normalization, and FFN stands for Feedforward Neural Network Layer. This represents the node embedding vector obtained in step l-1. This represents the node embedding vector after passing through a multi-head attention network.

[0206] Finally, the above calculations are iterated over layer T to obtain the final embedding vector for each node. This final embedding vector can be represented as the learned node feature representation and can be used in the downstream maximum clique task. After layer T, the final embedding vector for each node vi is represented as... At the same time, the embedding information z of all nodes is aggregated by summation. s =∑ i∈V z i This is used to encapsulate information related to the entire QUBO problem instance.

[0207] 2. Decoder

[0208] Before discussing the details of the decoder, it is necessary to understand the Markov Decision Process (MDP) for solving the QUBO problem. Formally, consider an MDP described by tuples (S, A, R), where S represents all possible states s. i A set of actions. i ∈A means that in a given state s i Assigning values ​​to the binary variable x. State s. i Perform action a i The reward r i :r i =a i +∑ (i,j)∈E b ij x j ∈R reward r i This indicates the change in the objective function before and after the action is performed.

[0209] The decoder essentially converts a pair of state-action pairs (s... i , a i ), convert to a scalar Q(s) i ,a i ;Θ), that is, a neural network, is used to evaluate the state s i Next action a i The quality (i.e., value; the greater the value, the greater the likelihood of the action being performed), Θ is a learnable parameter, and the Q function is expressed as follows:

[0210] Q(h, v; Θ) = W 11 ReLU(W 10 ReLU(W9[z s , z i ]))

[0211] Where W9, W10, and W11 are learnable parameters, [z s ,z i ] indicates that the vector z s sum vector z i Concatenate the rows.

[0212] (III) Minimizing the Hamiltonian on the QUBO graph using RL

[0213] 1. Training

[0214] Model training is performed using the widely adopted DQN. The process mainly includes the following steps: First, instances of the original problem are generated and transformed into QUBO form. Then, training trajectory projects are generated based on the QUBO graph and stored in a replay buffer, similar to a cache. The model agent then selects certain trajectories from the replay buffer for training and updates the neural network parameters accordingly.

[0215] (1) Data preparation

[0216] In practice, it is necessary to generate instances of the original problem. These instances are determined by the characteristics of the original problem itself, and it is not necessary for the instances of the original problem to be graphs.

[0217] (2) Trajectory generation

[0218] As mentioned earlier, the optimization problem of a traffic network is mapped to an abstract maximum clique problem on a graph. Nodes in the graph represent intersections, key points, etc., while edges represent roads and routes between intersections, and the weights of the edges represent traffic flow information for that route. The maximum clique problem can be transformed into a Hamiltonian minimization problem on a QUBO graph, solved using reinforcement learning algorithms. This process is viewed as a Markov decision process, where an episode (a complete training epoch) is the complete process of finding the solution that minimizes the Hamiltonian on the QUBO graph, requiring all decision variables to be sequentially flipped from 0 to 1. The trajectory (training trajectory data or training process data) generated in an episode is a state-action-reward sequence s0, a0, r0, s1, a1, r1, ..., s T Where s0 is the initial state where all decision variables are 0, s T The final state is when all decision variables are 1. Running a game requires completing a full episode on the QUBO graph, and the model collects training process data, i.e., s. t ,a t ,r t,t+n ,s t+n , where st Let a represent the set of states of all variables at time t. t This represents the action taken at time t. s represents the cumulative reward at time t+n. t+n The model represents the set of states of all variables at time t+n, which is stored in the replay buffer. Here, the delayed reward step size n and the discount factor γ are both hyperparameters.

[0219] (3) Update Qubormer parameters

[0220] Using empirical transformations selected from the replay buffer, CONQUER is able to learn and update the network parameters Θ to minimize the following loss function.

[0221]

[0222] Where E represents the maximum expectation, r t,t+n s represents the immediate reward obtained n steps later after performing the action at time t. t+n Let a represent the state at time t+n. t+n This represents the action executed at time t+n, where r is the discount factor (hyperparameter, typically 0.99). Indicates that in state s t+n Execution is the target network The action with the largest return value, a t+n The returned reward valuation, of which For the target network parameters, Q(s) t ,a t ;Θ) indicates that in state s t When performing action a t Based on the reward estimate obtained from the original network Q(Θ), where s t Let a represent the state at time t. t This represents the action performed at time t, and Θ represents the parameters of the original network, which are updated using real-time data. Furthermore, the original network Q(Θ) periodically copies its parameters Θ to the target network. parameters To enable network updates. 2. Online application and fine-tuning of off-distribution data.

[0223] In the application, a greedy strategy is used to iteratively flip the state of each decision variable in the QUBO graph from 0 to 1. Subsequently, the state of the decision variable associated with the flipping process is determined as the optimal solution to the QUBO problem, which produces the lowest Hamiltonian.

[0224] However, out-of-distribution generalization is a significant challenge in the field of machine learning. To address this challenge, this invention proposes a concise and efficient fine-tuning method.

[0225] First, data augmentation is performed on the tuning dataset, such as introducing noise into the QUBO graph, splitting the dataset into training / validation / test subsets, and sampling the QUBO graph. Then, the pre-trained model is loaded and its encoder portion is frozen. The task headers for downstream tasks are fine-tuned only based on the downstream task data, with only certain parameters updated to save fine-tuning time. Finally, the tuned model is tested to reflect the process of the online application.

[0226] (iv) Solution Output

[0227] 1. Result Expression

[0228] In fact, the solution obtained directly from the model is the solution to the QUBO problem, representing the values ​​of the decision variables that minimize the Hamiltonian. To obtain the solution to the original problem, a decision reduction process is needed. Specifically, this can be broadly categorized into two main types. The first type involves "yes / no" decision outputs to determine whether the decision variables are included in the solution set; examples include MaxCut and MIS. The second type involves ordering decision outputs, as observed in TSP, which explicitly defines the order in which each city is visited. In this case, it is necessary not only to determine whether the decision variables are included in the solution set, but also to determine the order of these variables within the solution set.

[0229] 2. Inspection and repair

[0230] If the agent fails to train sufficiently due to data sparsity or insufficient training time, or if the penalty term is set too low, the solution found by the neural network may not satisfy the feasibility conditions of the original problem. To mitigate these issues, the legitimacy of the solution must first be ensured. If the solution meets the feasibility conditions of the original problem, it is output directly; otherwise, it needs to be repaired to satisfy these conditions. Generally, repair methods are simple and inexpensive, typically employing common greedy or local search methods to repair solutions that do not meet the constraints. Solution repair is only necessary when dealing with real-world datasets and extremely large-scale graphs, and in these cases, the simplest greedy method is used.

[0231] III. Experiment

[0232] (I) Experimental Setup

[0233] 1. Baseline method

[0234] A semidefinite programming baseline (called SDP) is used to obtain relaxed solutions. Furthermore, two heuristics, greedy and mean-field annealing (MFA), are combined. Comparisons of learning-based methods include a self-implemented classic S2V-DQN and two probabilistic view-based methods, ERDOS and ANNEAL. Additionally, the state-of-the-art method GFlowNet, which samples from the solution space, is evaluated. The baseline includes two unsupervised learning methods, RUN-CSP and EGN, as well as their enhanced version, Meta-EGN. Furthermore, the state-of-the-art method VAG-CO, which improves upon the mean-field annealing algorithm, is compared. Although VAG-CO formulates the combinatorial optimization problem using the Ising formula, its main contribution lies in improving the annealing process.

[0235] 2. Evaluation Indicators

[0236] Consistent with previous work, a comprehensive evaluation metric was adopted, which considers the best ratio (R*) and average ratio (R) of the results obtained from the proposed method to the results obtained by the Gurobi optimizer within one hour, as well as the corresponding standard error.

[0237] (II) Experimental Results

[0238] The Monte Carlo (MC) problem is similar to the Mind-Installation (MIS) problem because the MC problem can be abstracted as solving the MIS problem on its complementary graph. Therefore, the experiments focus on the ENZYMES and IMDB-BINARY datasets, employing the same dataset partitioning method as for the MIS problem. Training is performed on an RB graph of size 100, followed by fine-tuning on the dataset. Experimental results for the MC problem are shown in Table 1. Similar to the MIS problem, the method of this embodiment consistently outperforms other methods in all experiments.

[0239] Table 1 Experimental Results

[0240] Comparison of optimal algorithm performance metrics (higher is better: mean ± variance)

[0241] Methods / Datasets ENZYMES IMDB-BINARY EGN 0.883±0.156 0.936±0.175 NSFE 0.933±0.148 0.961±0.143 REINFORCE 0.751±0.301 0.881±0.240 Straight-through 0.725±0.268 0.917±0.253 Greedy 0.9485±0.0034 0.9875±0.0008 MFA 0.9766±0.001 0.999±0.009 MFA-Anneal 0.9921±0.0017 0.999±0.0001 CONQUER 1 1

[0242] Comparison of average algorithm performance metrics (higher is better: mean ± variance)

[0243] Methods / Datasets ENZYMES IMDB-BINARY MFA 0.764±0.013 0.983±0.009 MFA-Anneal 0.806±0.004 0.974±0.004 MFA-Anneal 0.943±0.012 0.993±0.0013 CONQUER 0.9445±0.0081 0.9814±0.0046 CONQUER-ft 0.9478±0.0078 0.9948±0.0039

[0244] (III) Ablation Test

[0245] To verify the effectiveness of Qubormer, ablation experiments were conducted by removing centrality encoding, removing the transformer layer, and replacing the message passing layer in Qubormer with GCN. The results are as follows: Figure 4As shown, Quormer (GCN) performs the worst, indicating that aggregation methods from nodes to edges and from edges to nodes are more suitable for QUBO graphs because edges contain rich feature information. Quormer-no-trans performs slightly better, highlighting the important role of the transformer layer in capturing node and edge dependencies.

[0246] The beneficial technical effects achieved by the embodiments of the present invention are as follows:

[0247] This paper models the problem of identifying dense regions in traffic network analysis as a maximal clique problem in combinatorial optimization, and analyzes the traffic network structure by finding the maximal clique. Subsequently, the maximal clique problem is transformed into a QUBO form, and an innovative end-to-end deep learning reinforcement learning architecture customized for this problem is demonstrated. Considering the special characteristics of the QUBO graph structure, a transformer mechanism is introduced into the message passing network to effectively capture long-term dependencies between nodes. Next, a corresponding decision reduction strategy is designed, and a simple yet effective fine-tuning method is devised for real datasets with distributions different from the training set. Unlike previous studies, this approach stands out by avoiding adjustments across different problem instances or fine-tuning scenarios for specific tasks. Experimental results show that the method of this invention significantly outperforms existing state-of-the-art learning-based and manually designed methods. It helps to effectively solve the problem of identifying dense regions in traffic network analysis, thereby helping urban planners and traffic managers better understand the structure and function of traffic networks. It effectively identifies dense subgraphs in traffic networks, improving the accuracy and reliability of traffic flow optimization. This is of great significance for traffic network operation and maintenance.

[0248] It should be understood that the specific order or hierarchy of steps in the disclosed process is an example of an exemplary method. Based on design preferences, it should be understood that the specific order or hierarchy of steps in the process may be rearranged without departing from the scope of this disclosure. The appended method claims provide elements of various steps in an exemplary order and are not intended to limit the scope to the specific order or hierarchy described.

[0249] In the above detailed description, various features are combined together in a single embodiment to simplify this disclosure. This approach to disclosure should not be construed as reflecting an intention that embodiments of the claimed subject matter require more features than are explicitly stated in each claim. Rather, as reflected in the appended claims, the invention is presented with fewer features than all of the features of the single disclosed embodiment. Therefore, the appended claims are hereby explicitly incorporated into the detailed description, wherein each claim stands alone as a preferred embodiment of the invention.

[0250] The disclosed embodiments have been described above to enable any person skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be applied to other embodiments without departing from the spirit and scope of this disclosure. Therefore, this disclosure is not limited to the embodiments given herein, but is consistent with the broadest scope of the principles and novel features disclosed in this application.

[0251] The foregoing description includes examples of one or more embodiments. It is certainly impossible to describe all possible combinations of components or methods in order to describe the above embodiments, but those skilled in the art will recognize that further combinations and arrangements of the various embodiments are possible. Therefore, the embodiments described herein are intended to cover all such changes, modifications, and variations that fall within the scope of the appended claims. Furthermore, the term "comprising" as used in the specification or claims is interpreted in a manner similar to the term "including," as interpreted when used as a conjunction in the claims. Additionally, the use of any term "or" in the specification of the claims is intended to mean "non-exclusive or."

[0252] Those skilled in the art will also understand that the various illustrative logical blocks, units, and steps listed in the embodiments of the present invention can be implemented by electronic hardware, computer software, or a combination of both. To clearly demonstrate the interchangeability of hardware and software, the functions of the various illustrative components, units, and steps described above have been generally described. Whether such functionality is implemented through hardware or software depends on the specific application and the overall system design requirements. Those skilled in the art can implement the described functions using various methods for each specific application, but such implementation should not be construed as exceeding the scope of protection of the embodiments of the present invention.

[0253] The various illustrative logic blocks or units described in the embodiments of this invention can be implemented or operate the described functions using a general-purpose processor, digital signal processor, application-specific integrated circuit (ASIC), field-programmable gate array or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof. The general-purpose processor can be a microprocessor; alternatively, it can be any conventional processor, controller, microcontroller, or state machine. The processor can also be implemented using a combination of computing devices, such as a digital signal processor and a microprocessor, multiple microprocessors, one or more microprocessors combined with a digital signal processor core, or any other similar configuration.

[0254] The steps of the methods or algorithms described in the embodiments of this invention can be directly embedded in hardware, a software module executed by a processor, or a combination of both. The software module can be stored in RAM, flash memory, ROM, EPROM, EEPROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium in the art. Exemplarily, the storage medium can be connected to the processor so that the processor can read information from and write information to the storage medium. Optionally, the storage medium can also be integrated into the processor. The processor and storage medium can be housed in an ASIC, which can be housed in a user terminal. Optionally, the processor and storage medium can also be housed in different components of the user terminal.

[0255] In one or more exemplary designs, the functions described in the embodiments of the present invention can be implemented in hardware, software, firmware, or any combination of these three. If implemented in software, these functions can be stored on a computer-readable medium or transmitted on a computer-readable medium in the form of one or more instructions or code. Computer-readable media include computer storage media and communication media that facilitate the transfer of computer programs from one place to another. Storage media can be any available media that can be accessed by a general-purpose or special-purpose computer. For example, such computer-readable media can include, but is not limited to, RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store program code in the form of instructions or data structures and other forms that can be read by a general-purpose or special-purpose computer, or a general-purpose or special-purpose processor. Furthermore, any connection can be suitably defined as a computer-readable medium, for example, if the software is transmitted from a website, server or other remote resource via a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL) or wirelessly, such as infrared, wireless and microwave, it is also included in the defined computer-readable medium. The disks and discs mentioned include compressed disks, laser discs, optical discs, DVDs, floppy disks, and Blu-ray discs. Disks typically copy data magnetically, while disks typically copy data optically using lasers. Combinations of the above can also be contained in computer-readable media.

[0256] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A node optimization method for a transportation network, characterized in that, include: The problem of utilizing nodes in a transportation network is optimized into a maximum clique problem, where the nodes include transportation nodes; The maximum clique problem is transformed into a QUBO model based on a general objective function of the QUBO model. A graph neural network is used to represent the structure and characteristics of the QUBO graph of the QUBO model, and a deep learning model CONQUER is constructed. By training the deep learning model CONQUER, the optimal solution to the optimization problem of nodes in a traffic network is explored, and a trained deep learning model CONQUER is obtained. The trained deep learning model CONQUER is used to optimize the utilization problem of nodes in any traffic network, and the node optimization results are obtained. The node optimization results include: the nodes used, the number of nodes, and the road usage frequency between nodes. The problem of utilizing nodes in a transportation network is optimized into a maximum clique problem, including: The traffic network is represented as G = (V, E), where V is the set of nodes in the traffic network, which includes interconnected individuals in the traffic network. These individuals include: intersections, road segment start and end points, traffic signal control points, important locations, and sensor locations. E is the set of edges, which represents the edges composed of individuals with interactive relationships. Edges represent roads, road segments, and routes in the traffic network, and / or edges represent abstract connection relationships between nodes: the correlation between traffic lights, the traffic flow on the road between two intersections; The symbols and parameters are defined as follows: (x_v): A binary variable, where x represents a node in the transportation network and v represents the node's index. The value is 1 when node (v) is selected into the group, and 0 otherwise. (N(v)): The set of neighboring nodes of node (v); The objective function (f(x)) represents maximizing the size of the clique, which means maximizing the number of selected nodes. The maximum clique problem can be expressed as: Constraint: Each node in the clique must either be selected or not selected. This constraint can be expressed as: x v x u Represents any two nodes in a transportation network; Based on the general objective function of the QUBO model, the maximum clique problem is transformed into a QUBO model, including: The general objective function of the QUBO model is expressed as: Where x = (x1, x2, ..., xn) represents a decision vector consisting of two variables, where the two variables are either 0 or 1. i x j These are the nodes at both ends of the edge, matrix Q is a symmetric matrix or an upper triangular matrix, and a i =Q ij ,so b ij =Q ij , a i b represents the node weight. ij Indicates the weight of the edge; According to H QUBO For the expression corresponding to (x), define a corresponding undirected graph G =<V,E> Node v i ∈V represents H QUBO The decision variables in (x) have weights equal to the coefficients a of the linear terms. i Node v i and v j via edge e ij The connection ∈E has a weight equal to H. QUBO The coefficient b of the quadratic term in the expression corresponding to (x) ij This encodes the objective and constraint information of the maximum clique problem into an undirected graph structure, allowing the neural network to directly learn the objective function of the QUBO model for the maximum clique problem. The objective function of the QUBO model for the maximum clique problem can be expressed as: Where i∈V represents a node in the traffic network, with node number i, and p represents the penalty coefficient of the QUBO model. This indicates a node that has no connection relationship. A graph neural network is used to represent the structure and characteristics of the QUBO graph corresponding to the QUBO model, and a deep learning model CONQUER is constructed, including: The encoder is constructed, specifically comprising: an integration centrality coding layer, a message passing layer, a Transformer layer, and an iterative computation and solution layer; wherein: In the integration of centrality coding layer: Each node in the QUBO graph is augmented using its corresponding degree to capture the importance of the nodes in the QUBO graph, and then encoded. The vector representation of each node augmented using its corresponding degree and then encoded is as follows: Here, ReLU refers to the activation function. In this context, 'i' represents the i-th node, 0 represents the initial feature, and x... i It is the initial feature of the node, z deg (v i ) encodes the degree of a node, v i It refers to the node with index i. W1 and W2 are the parameters of the neural network, and they are learnable parameters. At the message passing layer: The neighborhood aggregation process is used to merge node features to obtain edge feature aggregation, and merge edge features to obtain node feature aggregation. The edge feature aggregation and node feature aggregation are represented as follows: Among them, h ij =ReLU(W3x ij ) represents the initial edge embedding vector, and x represents the intermediate output of the neural network. ij W4, W5, W6, and W7 are the parameters of the neural network, and all of them are learnable parameters; After obtaining the node features in step l Then, the features from the previous step of this node can be combined. To implement residual joins, the residual join is represented as follows: Where W8 are the parameters of the neural network, and these are learnable parameters; In the Transformer layer: The output of the message passing layer is combined with the output of the global attention layer within the Transformer layer to obtain the updated node features: Where MHA represents multi-head attention network, LN represents layer normalization, and FFN represents feedforward neural network layer; This represents the node embedding vector obtained in step l-1. This represents the node embedding vector after passing through the multi-head attention network; In the iterative computation and solution layer: During the solution process, the updated node features output from the Transformer layer are used as input to the ensemble centrality coding layer. The steps of the ensemble centrality coding layer, message passing layer, and Transformer layer are iterated repeatedly. After iteration, the final embedding vector for each node is obtained. The final embedding vector for each node is represented as: Summing the final embedding vectors of all nodes yields: z s =∑ i∈V z i The solution to the QUBO model is represented by summation.

2. The node optimization method for a transportation network according to claim 1, characterized in that, The deep learning model CONQUER is constructed by using a graph neural network to represent the structure and characteristics of the QUBO graph corresponding to the QUBO model, and also includes: Constructing a decoder includes: Formally, this forms a Markov decision process described by tuples (S, A, R), where S represents all possible states s. i The set of actions a i ∈A means that for a given state s i Assignment of binary variable x to the QUBO model; state s i Perform action a i The reward r i r i =a i +∑ (i,j)∈E b ij x j ∈R reward r i This indicates the change in the objective function before and after the action is performed; The decoder converts a pair of state-action pairs (s) i , a i ) is converted into a scalar Q(s) of a neural network. i ,a i ;Θ), to evaluate in state s i Next action a i The quality of the decoder is expressed by the Q function as follows: Q(h,v;Θ)=W 11 ReLU(W 10 ReLU(W9[z s ,With i ])) Where W9, W10, and W11 are the parameters of the neural network, and are learnable parameters, [z s ,z i ] indicates that the vector z s sum vector z i Concatenate the rows.

3. The node optimization method for a transportation network according to claim 2, characterized in that, By training the deep learning model CONQUER to explore the optimal solution to the node utilization problem in a transportation network, the trained deep learning model CONQUER is obtained, including: Samples of nodes in the traffic network corresponding to the maximum clique problem are obtained, and the maximum clique problem is transformed into a Hamiltonian minimization problem on a QUBO graph. The problem is solved using a reinforcement learning algorithm, and a trajectory based on a Markov decision process representation is generated based on the QUBO graph. A complete training round is the process of finding a solution that minimizes the Hamiltonian on the QUBO graph, requiring all decision variable states to be sequentially flipped from 0 to 1. The trajectory generated in a complete training round is a state-action-reward sequence: s0, a0, r0, s1, a1, r1, ..., s T s0 is the initial state where all decision variables are 0, s T The final state is where all decision variables are 1; training process data is collected during a complete training round: s t ,a t ,r t , t+n ,s t+n s t Let a represent the set of states of all variables at time t. t This represents the action taken at time t. s represents the cumulative reward at time t+n. t+n Let n represent the set of states of all variables at time t+n, where step size n and discount factor γ are both hyperparameters; Using the collected training process data, the deep learning model CONQUER learns from the collected training process data and updates the network parameters Θ of the deep learning model CONQUER to minimize the following loss function: Where E represents the maximum expectation, r t,t+n s represents the immediate reward obtained n steps later after performing the action at time t. t+n Let a represent the state at time t+n. t+n This represents the action performed at time t+n, where γ is the discount factor. Indicates that in state s t+n Execution is the target network The action with the largest return value, a t+n The returned reward valuation, For the target network parameters, Q(s) t ,a t ;Θ) indicates that in state s t When performing action a t Based on the reward estimate obtained from the original network Q(Θ), s t Let a represent the state at time t. t This represents the action performed at time t, and Θ represents the parameters of the original network, which are updated using real-time training data. The original network Q(Θ) periodically copies the parameter Θ to the target network. parameters To achieve the update of the target network; When the loss function value is less than the preset value, a well-trained deep learning model CONQUER can be obtained.

4. The node optimization method for a transportation network according to claim 3, characterized in that, Also includes: In the sample nodes of the traffic network corresponding to the obtained maximum independent set problem, noise was introduced into the sample when constructing the QUBO graph; When the loss function is less than the preset value, the encoder parameters should be frozen and fine-tuned for the corresponding deep learning model CONQUER to obtain the trained deep learning model CONQUER.

5. The node optimization method for a transportation network according to claim 4, characterized in that, Also includes: When using a trained deep learning model CONQUER to solve the problem of node utilization in a traffic network, if the obtained solution does not meet the feasibility conditions of the traffic network, a greedy search method or a local search method is used to repair the solution.

6. A node optimization method for a transportation network, characterized in that, Also includes: The problem of utilizing the nodes of the traffic network to be solved is input into the trained deep learning model CONQUER as described in any one of claims 1-5; Output the node optimization results, which include: the nodes used, the number of nodes, and the road usage frequency between nodes.

7. A node optimization device for a transportation network, characterized in that, include: The problem transformation unit is used to optimize the utilization problem of nodes in a transportation network into a maximum clique problem, wherein the nodes include transportation nodes; The QUBO model building unit is used to transform the maximum clique problem into a model based on the general objective function of the QUBO model. The deep learning model building unit is used to represent the structure and characteristics of the QUBO graph of the QUBO model using a graph neural network, and to build the deep learning model CONQUER. The training unit is used to train the deep learning model CONQUER to explore the optimal solution of the optimization problem of nodes in the traffic network, and obtain the trained deep learning model CONQUER. The trained deep learning model CONQUER is used to optimize the utilization problem of nodes in any traffic network and obtain the node optimization results, which include: the nodes used, the number of nodes, and the road usage frequency between nodes. The problem transformation unit is specifically used for: The traffic network is represented as G = (V, E), where V is the set of nodes in the traffic network, which includes interconnected individuals in the traffic network. These individuals include: intersections, road segment start and end points, traffic signal control points, important locations, and sensor locations. E is the set of edges, which represents the edges composed of individuals with interactive relationships. Edges represent roads, road segments, and routes in the traffic network, and / or edges represent abstract connection relationships between nodes: the correlation between traffic lights, the traffic flow on the road between two intersections; The symbols and parameters are defined as follows: (x_v): A binary variable, where x represents a node in the transportation network and v represents the node's index. The value is 1 when node (v) is selected into the group, and 0 otherwise. (N(v)): The set of neighboring nodes of node (v); The objective function (f(x)) represents maximizing the size of the clique, which means maximizing the number of selected nodes. The maximum clique problem can be expressed as: Constraint: Each node in the clique must either be selected or not selected. This constraint can be expressed as: x v x u Represents any two nodes in a transportation network. QUBO model building units are specifically used for: The general objective function of the QUBO model is expressed as: Where x = (x1, x2, ..., xn) represents a decision vector consisting of two variables, where the two variables are either 0 or 1. i x j These are the nodes at both ends of the edge, matrix Q is a symmetric matrix or an upper triangular matrix, and a i =Q ij ,so b ij =Q ij , a i b represents the node weight. ij Indicates the weight of the edge; According to H QUBO For the expression corresponding to (x), define a corresponding undirected graph G =<V,E> Node v i ∈V represents H QUBO The decision variables in (x) have weights equal to the coefficients a of the linear terms. i Node v i and v j via edge e ij The connection ∈E has a weight equal to H. QUBO The coefficient b of the quadratic term in the expression corresponding to (x) ij This encodes the objective and constraint information of the maximum clique problem into an undirected graph structure, allowing the neural network to directly learn the objective function of the QUBO model for the maximum clique problem. The objective function of the QUBO model for the maximum clique problem can be expressed as: Where i∈V represents a node in the traffic network, with node number i, and p represents the penalty coefficient of the QUBO model. This indicates a node with no connection relationship. Deep learning model building unit, specifically used for: The encoder is constructed, specifically comprising: an integration centrality coding layer, a message passing layer, a Transformer layer, and an iterative computation and solution layer; wherein: In the integration of centrality coding layer: Each node in the QUBO graph is augmented using its corresponding degree to capture the importance of the nodes in the QUBO graph, and then encoded. The vector representation of each node augmented using its corresponding degree and then encoded is as follows: Here, ReLU refers to the activation function. In this context, 'i' represents the i-th node, 0 represents the initial feature, and x... i It is the initial feature of the node, z deg (v i ) encodes the degree of a node, v i It refers to the node with index i. W1 and W2 are the parameters of the neural network, and they are learnable parameters. At the message passing layer: The neighborhood aggregation process is used to merge node features to obtain edge feature aggregation, and merge edge features to obtain node feature aggregation. The edge feature aggregation and node feature aggregation are represented as follows: Among them, h ij =ReLU(W3x ij ) represents the initial edge embedding vector, and x represents the intermediate output of the neural network. ij W4, W5, W6, and W7 are the parameters of the neural network, and all of them are learnable parameters; After obtaining the node features in step l Then, the features from the previous step of this node can be combined. To implement residual joins, the residual join is represented as follows: Where W8 are the parameters of the neural network, and these are learnable parameters; In the Transformer layer: The output of the message passing layer is combined with the output of the global attention layer within the Transformer layer to obtain the updated node features: Where MHA represents multi-head attention network, LN represents layer normalization, and FFN represents feedforward neural network layer; This represents the node embedding vector obtained in step l-1. This represents the node embedding vector after passing through the multi-head attention network; In the iterative computation and solution layer: During the solution process, the updated node features output from the Transformer layer are used as input to the ensemble centrality coding layer. The steps of the ensemble centrality coding layer, message passing layer, and Transformer layer are iterated repeatedly. After iteration, the final embedding vector for each node is obtained. The final embedding vector for each node is represented as: Summing the final embedding vectors of all nodes yields: z s =∑ i∈V z i The solution to the QUBO model is represented by summation.

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