Node optimization method and device for traffic network

Abstract

The embodiment of the invention provides a node optimization method and device for a traffic network, and the method comprises the steps: optimizing a node utilization problem of the traffic network into a maximum clique problem, and converting the maximum clique problem into a QUBO model based on a universal objective function of the QUBO model; representing the structure and characteristics of a QUBO graph of the QUBO model by using a graph neural network, and constructing to obtain a deep learning model CONQUER; the deep learning model CONQUER is trained to explore the optimal solution of the optimization problem of the nodes of the traffic network, and the trained deep learning model CONQUER is obtained. The dense region determination problem in traffic network analysis is modeled into the maximum group problem in combinatorial optimization, and the traffic network structure is analyzed by searching the maximum group, so that the dense region determination problem in the traffic network analysis can be effectively solved, and the accuracy and reliability of traffic network flow optimization are improved.

Description

Technical Field

[0001] The present invention relates to a traffic network optimization method, and in particular to a traffic network node optimization method and device. Background Art

[0002] Traffic network analysis plays a key role in urban development, with the goal of optimizing road use efficiency and reducing traffic congestion. Such analysis usually involves making decisions in complex traffic flows, each of which may affect traffic flow and the efficiency of road use. Typical traffic network analysis problems include identifying traffic bottlenecks, determining dense traffic areas, and predicting traffic trends. Among them, identifying dense areas in the traffic network is an important task that can help planners understand the interaction 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 global optimal solutions, but the computational cost is too high for large-scale networks and is not realistic. Approximate algorithms have theoretical guarantees and polynomial time complexity, but have some problems in construction difficulty and performance. Heuristic algorithms have fast speed and good results in practice, but lack theoretical guarantees and need to be customized for specific problems, which has led to some criticism.

[0004] However, there are at least two key challenges with traditional methods. First, the equivalent maximum clique problem of this type of problem is inherently NP-hard, which makes them difficult to solve. Existing strategies often face the so-called trade-off dilemma: fast algorithms cannot guarantee the quality of the solution, while high-quality solutions often take longer to solve. Second, the solution algorithms designed by most traditional methods are customized for the mathematical structure of the problem. If the constraints and structure of the problem change, the algorithm needs to be redesigned, which is time-consuming and labor-intensive.

[0005] Therefore, in the field of traffic network analysis, researchers are committed to understanding the relationship network between various nodes and edges, because the degree of connection between nodes is important for the transmission and optimization of traffic flow. However, traditional traffic flow analysis methods are often time-consuming, labor-intensive, and costly. Therefore, computation-based methods have become one of the important ways to analyze traffic networks.

[0006] In traffic network analysis, a key challenge is to determine the connections between nodes and how they are best connected in the network. These connections involve factors such as flow frequency, information transfer, and connection strength. Ideally, researchers would like to find a way to identify the most compact subgraphs in a traffic network so that flow optimization and resource allocation can be targeted at these subgraphs. However, due to the complexity of traffic networks, it is not easy to determine the best compact subgraphs. Summary of the invention

[0007] The embodiment of the present invention provides a method and device for optimizing nodes in a transportation network, which can solve the technical problem in the prior art of difficulty in determining the connection between nodes in a transportation network and their optimal connection mode in the network.

[0008] To achieve the above objectives, in a first aspect, an embodiment of the present invention provides a method for optimizing nodes in a transportation network, comprising:

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

[0010] Based on the universal objective function of the QUBO model, the maximum clique problem is transformed into the QUBO model;

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

[0012] The deep learning model CONQUER is trained to explore the optimal solution to the optimization problem of the nodes of the transportation network, and a trained deep learning model CONQUER is obtained; the trained deep learning model CONQUER is used to optimize the utilization problem of the nodes of any transportation network to obtain node optimization results, and the node optimization results include: the nodes adopted, the number of nodes, and the frequency of road use between nodes.

[0013] In a second aspect, an embodiment of the present invention provides a node optimization method for a transportation network, further comprising:

[0014] Input the node utilization problem of the traffic network to be solved into the aforementioned trained deep learning model CONQUER;

[0015] Output node optimization results, the node optimization results include: adopted nodes, number of nodes, and frequency of road use between nodes.

[0016] In a third aspect, an embodiment of the present invention provides a node optimization device for a transportation network, comprising:

[0017] A problem conversion unit, for optimizing the utilization problem of nodes of a transportation network into a maximum clique problem, wherein the nodes include transportation nodes;

[0018] A QUBO model building unit, used for converting the maximum clique problem into a model based on a general objective function of the QUBO model;

[0019] A deep learning model building unit, used to use a graph neural network to characterize the structure and characteristics of the QUBO graph of the QUBO model, and to build a deep learning model CONQUER;

[0020] The training unit is used to train the deep learning model CONQUER to explore the optimal solution to the optimization problem of the nodes of the transportation network, and obtain the trained deep learning model CONQUER; the trained deep learning model CONQUER is used to optimize the utilization problem of the nodes of any transportation network to obtain the node optimization result, and the node optimization result includes: the nodes adopted, the number of nodes, and the frequency of road use between nodes.

[0021] The above technical solution has the following beneficial effects: by modeling the dense area determination problem in traffic network analysis as the maximum clique problem in combinatorial optimization, and analyzing the traffic network structure by finding the maximum clique, it helps to effectively solve the dense area determination problem in traffic network analysis, thereby helping urban planners and traffic managers to better understand the structure and function of the traffic network, and improving the accuracy and reliability of traffic network flow optimization. This is of great significance to the operation and maintenance of the traffic network. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. 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 creative work.

[0023] Figure 1 is a flow chart of a node optimization method for a transportation network according to an embodiment of the present invention;

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

[0025] Figure 3 It is a solution framework of the QUBO model of the embodiment of the present invention;

[0026] Figure 4 This is the ablation experiment result of the embodiment of the present invention. DETAILED DESCRIPTION

[0027] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work are within the scope of protection of the present invention.

[0028] like Figure 1As shown, in combination with an embodiment of the present invention, a method for optimizing nodes in a transportation network is provided, comprising:

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

[0030] S102: Based on the general objective function of the QUBO model, the maximum clique problem is converted into a QUBO model;

[0031] S103: Using a graph neural network to characterize the structure and characteristics of the QUBO graph of the QUBO model, and constructing a deep learning model CONQUER;

[0032] S104: The deep learning model CONQUER is trained to explore the optimal solution to the optimization problem of the nodes of the transportation network, and a trained deep learning model CONQUER is obtained; the trained deep learning model CONQUER is used to optimize the utilization problem of the nodes of any transportation network to obtain node optimization results, and the node optimization results include: the nodes adopted, the number of nodes, and the frequency of road use between nodes.

[0033] Preferably, S101: optimizing the utilization problem of nodes in the traffic network into a maximum clique problem, including:

[0034] The transportation network is represented as G = (V, E), where V refers to the node set in the transportation network, including individuals with mutual connections in the transportation network, and E refers to the edge set, which represents the edge composed of individuals with interactive relationships;

[0035] Define the symbols and parameters as follows:

[0036] (x_v): binary variable, where x represents the node of the transportation network, v represents the node number, and is 1 when the node (v) is selected into the group, otherwise it is 0.

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

[0038] Objective function (f(x)): represents maximizing the size of the cluster. Maximizing the size of the cluster means maximizing the number of selected nodes. The maximum cluster problem is expressed as:

[0039]

[0040] Constraints: Each node in the group is either selected or not selected. The constraints are expressed as:

[0041] x v +x u ≥1, x v、x u Represent any two nodes in the transportation network.

[0042] Preferably, S102: based on the general objective function of the QUBO model, converting the maximum clique problem into the 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 binary variables, where the binary variables are 0 or 1, and x i 、x j are 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 represents the node weight in the QUBO model, b ij Represents the weight of the edge.

[0046] According to H QUBO (x) The corresponding formula defines a corresponding undirected graph G =<V,E> , node v i ∈V represents H QUBO The decision variable in (x) has a corresponding weight equal to the coefficient a of the linear term i ; Node v i and v j Through the edge ij ∈E connection, the corresponding weight is equal to H QUBO The coefficient b of the quadratic term in the formula corresponding to (x) ij , thereby encoding the objective and constraint information of the maximum clique problem into an undirected graph structure, so that the neural network can directly learn the objective function of the QUBO model of the maximum clique problem. The objective function of the QUBO model of the maximum clique problem is expressed as:

[0047]

[0048] Among them, i∈V represents a node in the traffic network, the node number is i, and p represents the penalty coefficient of the QUBO model. Indicates nodes that do not have a connection relationship.

[0049] Preferably, S103: using a graph neural network to characterize the structure and characteristics of the QUBO graph corresponding to the QUBO model, and constructing a deep learning model CONQUER, including:

[0050] Constructing an encoder, wherein the encoder construction specifically includes: integrating a centrality encoding layer, a message passing layer, a Transformer layer, and an iterative calculation solution layer; wherein:

[0051] At the integrated centrality encoding layer:

[0052] Each node in the QUBO graph is enhanced by the corresponding degree to capture the importance of the node in the QUBO graph, and then encoded. Each node in the QUBO graph is enhanced by the corresponding degree and encoded to obtain the corresponding vector representation:

[0053]

[0054] Among them, ReLU refers to the activation function, The i in the equation represents the i-th node, 0 represents the initial feature, and x i is the initial feature of the node, z deg (v i ) is used to encode the degree of the node, v i It refers to the node with serial number i, W1 and W2 are the parameters of the neural network, and they are learnable parameters;

[0055] At the messaging layer:

[0056] Using the neighborhood aggregation process, the features of the nodes are merged to obtain the feature aggregation of the edges, and the features of the edges are merged to obtain the feature aggregation of the nodes. The feature aggregation of the edges and the feature aggregation of the nodes are expressed as follows:

[0057]

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

[0059] After obtaining the node features in step l After that, you can concatenate the features of the previous step of the node Implement residual connection and express the residual connection as follows:

[0060] Among them, W8 is the parameter of the neural network and can be learned The parameters of learning;

[0061] In the Transformer layer:

[0062] Aggregate the output of the message passing layer with the output of the global attention layer in the Transformer layer to obtain updated node features:

[0063]

[0064] Among them, MHA represents multi-head attention network, LN represents layer normalization, and FFN represents feed-forward neural network layer; represents the node embedding vector obtained at step l-1, represents the node embedding vector after the multi-head attention network;

[0065] In the iterative calculation solution layer:

[0066] When solving, the updated node features output from the Transformer layer are used as the input of the integrated centrality encoding layer, and the steps of the integrated centrality encoding layer, the message passing layer, and the Transformer layer are repeatedly executed in a loop to iterate. After the iteration is completed, the final embedding vector corresponding to each node is obtained, and the final embedding vector of each node is expressed as:

[0067] Sum the final embedding vectors of all nodes to get: s =∑ i∈V z i , the solution of the QUBO model is characterized by summation.

[0068] Preferably, S103: 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, further comprising:

[0069] Build the decoder, including:

[0070] Formally, a Markov decision process is formed, which is described by the tuple (S, A, R), where S is all possible states s i A collection of actions i ∈A means that for a given state s i The QUBO model assigns a value to a binary variable x; the state s i Execute action a i Rewards received i , r i =a i +∑ (i,j)∈E b ij x j ∈R reward r i Indicates the change of the objective function before and after the action is executed;

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

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

[0073] Among them, W9, W10, W11 are the parameters of the neural network and are learnable parameters. s ,z i ] means to convert the vector z s and vector z i Join by rows.

[0074] Preferably, S104: training the deep learning model CONQUER to explore the optimal solution to the node utilization problem of the transportation network, and obtaining the trained deep learning model CONQUER, includes:

[0075] Obtaining samples of nodes of the traffic network corresponding to the maximum clique problem, converting the maximum clique problem into a Hamiltonian minimization problem on a QUBO graph, solving it using a reinforcement learning algorithm, and generating a trajectory represented by a Markov decision process based on the QUBO graph;

[0076] Among them, a complete training round is the complete process of finding the solution that minimizes the Hamiltonian on the QUBO graph, requiring all decision variable states to flip sequentially 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 is the terminal state 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 represents the state set of all variables at time t, a t represents the action taken at time t, represents the cumulative reward at time t+n, s t+nRepresents the state set of all variables at time t+n, and the step size n and discount factor γ are both hyperparameters;

[0077] Using the collected training process data, the collected training process data is learned by the deep learning model CONQUER, and the network parameters Θ of the deep learning model CONQUER are updated to minimize the following loss function:

[0078]

[0079] Among them, E represents the maximum expectation, r t,t+n represents the immediate reward after n steps after executing the action at time t, s t+n represents the state at time t+n, a t+n represents the action executed at t+n, γ is the discount factor, Indicates that in state s t+n Execution is the target network The action a with the largest return value t+n The reward estimate returned after is the target network parameter, Q(s t ,a t ; Θ) indicates that in state s t Execute action a t According to the reward valuation obtained by the original network Q(Θ), s t represents the state at time t, a t represents the action performed at time t, Θ is the parameter of the original network, which is updated by real-time training process data;

[0080] The original network Q(Θ) periodically copies parameters 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, the trained deep learning model CONQUER can be obtained.

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

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

[0084] When the loss function is less than a preset value, it is also necessary to freeze the parameters of the encoder and fine-tune the parameters of the encoder for the corresponding deep learning model CONQUER to obtain a trained deep learning model CONQUER.

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

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

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

[0088] Inputting the node utilization problem of the traffic network to be solved into any of the trained deep learning models CONQUER described above;

[0089] Output node optimization results, the node optimization results include: adopted nodes, number of nodes, and frequency of road use between nodes.

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

[0091] A problem conversion unit 21, for optimizing the utilization problem of nodes of a transportation network into a maximum clique problem, wherein the nodes include transportation nodes;

[0092] A QUBO model building unit 22, used for converting the maximum clique problem into a model based on a general objective function of the QUBO model;

[0093] A deep learning model construction unit 23, used to use a graph neural network to characterize the structure and characteristics of the QUBO graph of the QUBO model, and construct a deep learning model CONQUER;

[0094] The training unit 24 is used to train the deep learning model CONQUER to explore the optimal solution to the optimization problem of the nodes of the transportation network, and obtain the trained deep learning model CONQUER; the trained deep learning model CONQUER is used to optimize the utilization problem of the nodes of any transportation network to obtain the node optimization results, and the node optimization results include: the nodes adopted, the number of nodes, and the frequency of road use between nodes.

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

[0096] The transportation network is represented as G = (V, E), where V refers to the node set in the transportation network, including individuals with mutual connections in the transportation network, and E refers to the edge set, which represents the edges composed of individuals with interactive relationships;

[0097] Define the symbols and parameters as follows:

[0098] (x_v): binary variable, x represents the node of the transportation network, v represents the sequence number of the node, when the node (v) is selected into the group, it is 1, otherwise it is 0;

[0099] (N(v)): the set of neighbor nodes of node (v);

[0100] Objective function (f(x)): represents maximizing the size of the cluster. Maximizing the size of the cluster means maximizing the number of selected nodes. The maximum cluster problem is expressed as:

[0101]

[0102] Constraints: Each node in the group is either selected or not selected. The constraints are expressed as:

[0103] x v +x u ≥1, x v 、x u Represent 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 binary variables, where the binary variables are 0 or 1, and x i 、x j are 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 represents the node weight, b ij represents the weight of the edge;

[0108] According to H QUBO (x) The corresponding formula defines a corresponding undirected graph G =<V,E> , node v i ∈V represents H QUBO The decision variable in (x) has a corresponding weight equal to the coefficient a of the linear term i ; Node v i and v j Through the edge ij ∈E connection, the corresponding weight is equal to H QUBO The coefficient b of the quadratic term in the formula corresponding to (x)ij , thereby encoding the objective and constraint information of the maximum clique problem into an undirected graph structure, so that the neural network can directly learn the objective function of the QUBO model of the maximum clique problem. The objective function of the QUBO model of the maximum clique problem is expressed as:

[0109]

[0110] Among them, i∈V represents the node in the traffic network, and the node number is i , p represents the penalty coefficient of the QUBO model, Indicates nodes that do not have a connection relationship.

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

[0112] Constructing an encoder, wherein the encoder construction specifically includes: integrating a centrality encoding layer, a message passing layer, a Transformer layer, and an iterative calculation solution layer; wherein:

[0113] At the integrated centrality encoding layer:

[0114] Each node in the QUBO graph is enhanced by the corresponding degree to capture the importance of the node in the QUBO graph, and then encoded. Each node in the QUBO graph is enhanced by the corresponding degree and encoded to obtain the corresponding vector representation:

[0115]

[0116] Among them, ReLU refers to the activation function, The i in the equation represents the i-th node, 0 represents the initial feature, and x i is the initial feature of the node, z deg (v i ) is used to encode the degree of the node, v i It refers to the node with serial number i, W1 and W2 are the parameters of the neural network, and they are learnable parameters;

[0117] At the messaging layer:

[0118] Using the neighborhood aggregation process, the features of the nodes are merged to obtain the feature aggregation of the edges, and the features of the edges are merged to obtain the feature aggregation of the nodes. The feature aggregation of the edges and the feature aggregation of the nodes are expressed as follows:

[0119]

[0120] Among them, h ij =ReLU(W3x ij ) is the initial edge embedding vector, is the intermediate output of the neural network, and x ijis the edge input feature, W4, W5, W6, and W7 are the parameters of the neural network, and they are all learnable parameters;

[0121] After obtaining the node features in step l After that, you can concatenate the features of the previous step of the node Implement residual connection and express the residual connection as follows:

[0122]

[0123] Among them, W8 is the parameter of the neural network and is a learnable parameter;

[0124] In the Transformer layer:

[0125] Aggregate the output of the message passing layer with the output of the global attention layer in the Transformer layer to obtain updated node features:

[0126]

[0127] Among them, MHA represents multi-head attention network, LN represents layer normalization, and FFN represents feed-forward neural network layer; represents the node embedding vector obtained at step l-1, represents the node embedding vector after the multi-head attention network;

[0128] In the iterative calculation solution layer:

[0129] When solving, the updated node features output from the Transformer layer are used as the input of the integrated centrality encoding layer, and the steps of the integrated centrality encoding layer, the message passing layer, and the Transformer layer are repeatedly executed to iterate. After the iteration is completed, the final embedding vector corresponding to each node is obtained, and the final embedding vector of each node is expressed as: i =

[0130] Sum the final embedding vectors of all nodes to get: s =∑ i∈V z i , the solution of the QUBO model is characterized by summation.

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

[0132] Build the decoder, including:

[0133] Formally, a Markov decision process is formed, which is described by the tuple (S, A, R), where S is all possible states s i A collection of actionsi ∈A means that for a given state s i The QUBO model assigns a value to a binary variable x; the state s i Execute action a i Rewards received i , r i =a i +∑ (i,j)∈E b ij x j ∈R reward r i Indicates the change of the objective function before and after the action is executed;

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

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

[0136] Among them, W9, W10, W11 are the parameters of the neural network and are learnable parameters. s ,z i ] means to convert the vector z s and vector z i Join by rows.

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

[0138] Obtaining samples of nodes of the traffic network corresponding to the maximum clique problem, converting the maximum clique problem into a Hamiltonian minimization problem on a QUBO graph, solving it using a reinforcement learning algorithm, and generating a trajectory represented by a Markov decision process based on the QUBO graph;

[0139] Among them, a complete training round is the complete process of finding the solution that minimizes the Hamiltonian on the QUBO graph, requiring all decision variable states to flip sequentially 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 is the terminal state 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 represents the state set of all variables at time t, a t represents the action taken at time t, represents the cumulative reward at time t+n, s t+n Represents the state set of all variables at time t+n, and the step size n and discount factor γ are both hyperparameters;

[0140] Using the collected training process data, the collected training process data is learned by the deep learning model CONQUER, and the network parameters Θ of the deep learning model CONQUER are updated to minimize the following loss function:

[0141]

[0142] Among them, E represents the maximum expectation, r t,t+n represents the immediate reward after n steps after executing the action at time t, s t+n represents the state at time t+n, a t+n represents the action executed at t+n, γ is the discount factor, Indicates that in state s t+n Execution is the target network The action a with the largest return value t+n The reward estimate returned after is the target network parameter, Q(s t ,a t ; Θ) means in state s t Execute action a t According to the reward valuation obtained by the original network Q(Θ), s t represents the state at time t, a t represents the action performed at time t, Θ is the parameter of the original network, which is updated by real-time training process data;

[0143] The original network Q(Θ) periodically copies parameters 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, the trained deep learning model CONQUER can be obtained.

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

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

[0147] When the loss function is less than a preset value, it is also necessary to freeze the parameters of the encoder and fine-tune the parameters of the encoder for the corresponding deep learning model CONQUER to obtain a trained deep learning model CONQUER.

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

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

[0150] The above technical solution of the embodiment of the present invention is described in detail below in conjunction with specific application examples. For technical details not introduced during the implementation process, please refer to the relevant description in the previous text.

[0151] In an embodiment of the present invention, a traffic optimization method for discovering dense subgraphs of a traffic network 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 regarded as a maximum clique problem in the field of combinatorial optimization. The maximum clique represents a set of individuals with complete connections, indicating that they are closely connected.

[0152] First, the social network analysis problem is transformed into a unified mathematical model, and then a neural network solver is used to search for high-quality traffic network groups. These groups may represent potential close-knit groups, but further verification and adjustment are needed to obtain the final results. Effectively identifying dense subgraphs in traffic networks 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 traffic optimization problems are described in the QUBO language, they can be solved using the QUBO solver.

[0154] CONQUER designs a deep learning based QUBO solver that treats the QUBO solving process as a learning task. The goal is to train better heuristic algorithms through a large number of problem instances from a specific distribution, so that new, unseen instances from the same distribution can be effectively processed. Once these neural models are well trained, they can be effectively applied multiple times and 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 trains a neural solver QUBO to search for high-quality strategies, and then repairs and checks these strategies to obtain solutions to the original combinatorial optimization problems. The QUBO solver is a purely data-driven neural model that does not rely on the input of task expert knowledge. In order 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 as the input of the QUBO solver. The QUBO solver is trained using DQN to find solutions with better long-term benefits and vision. Although only trained on small-scale generated graphs, CONQUER shows good generalization on larger-scale instances and can be easily applied to many real datasets. Experiments show that the algorithm achieves state-of-the-art performance on the combinatorial optimization problem corresponding to traffic network analysis, and can help achieve flow optimization of dense subgraphs in the process of traffic network analysis, providing important clues and guidance for managers.

[0156] CONQUER mainly consists of four key steps:

[0157] 1. Problem transformation: Get the QUBO graph of the original problem equivalent to the original problem. Traffic nodes are regarded as nodes in the graph, and the road usage frequency between nodes is regarded as edges in the graph. Finally, the possible high-density traffic areas in the traffic network are described by finding the set of nodes with the densest connections.

[0158] 2. Use the deep map transformer to represent the features of the QUBO graph.

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

[0160] 4. Check and fix the solution to make it effective for the original problem.

[0161] Compared with previous work, the most significant advantage is that there is no need to adjust the deep learning architecture for a specific problem, which greatly reduces the cost of problem customization. Through extensive experiments on the traffic flow optimization task, it is abstracted as a maximum clique problem in combinatorial optimization, and CONQUER is tested on synthetic and real data. The results show that CONQUER can effectively solve the problem, surpassing most state-of-the-art methods, including traditional heuristic methods and learning-based strategies. In some cases, CONQUER can even achieve the same accuracy as commercial CO solvers.

[0162] In traffic network analysis, it is crucial to identify dense areas in a traffic network, and finding the densest traffic area can be modeled as a maximum clique problem. Due to the NP-hard nature of this problem, traditional heuristic methods and integer programming rely on hand-crafted heuristics to make decisions, which are computationally infeasible (complex or expensive to calculate) or lack well-defined mathematical formulas.

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

[0164] Another approach is to formulate the combinatorial optimization problem after modeling 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 the QUBO model with graph neural networks (GNNs) opens up new avenues for solving combinatorial optimization problems. In addition, using deep reinforcement learning to search for optimal traffic configurations, incorporating the maximum clique problem equivalent to QUBO into the reinforcement learning (RL) framework enables learning strategies that lead to optimal solutions.

[0165] In summary, the integration of QUBO and GNNs provides a promising approach to solving the dense area problem 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] 1. Modeling

[0167] 1. Mathematical Expression

[0168] Modeling the node utilization problem of the traffic network. The distribution of individuals in the traffic network is set as a graph, G = (V, E), where V represents individuals (referring to intersections, starting and ending points of road sections, traffic signal control points, important locations, sensor locations, etc. in the traffic network), individuals that are interconnected in the traffic network, and E represents the edge set, which represents the interaction relationship. The edge can represent the actual existing lines such as roads, sections, and lines in the traffic network, or it can represent the abstract connection relationship between nodes, such as the correlation between traffic lights, the flow of roads between two intersections, and other information.

[0169] Define the following symbols and parameters:

[0170] (x_v): binary variable, x represents the node of the transportation network, v represents the sequence number of the node, and it is 1 when the node (v) is selected into the group, otherwise it is 0.

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

[0172] Objective function (f(x)): represents maximizing the size of the cluster, that is, maximizing the number of selected nodes. It can be expressed as:

[0173]

[0174] Constraints: Each node in the group is either selected or not selected:

[0175] x v +x u ≥1,

[0176] Among them, x v 、x u Represent any two nodes in the transportation network;

[0177] This problem is modeled as the 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 a set of intersections where congestion occurs in a traffic network, etc.), that is, the model determines which nodes are to be selected and which are not to be selected, with selection being 1 and non-selection being 0; thus, the structure and function of the traffic network being analyzed can be understood.

[0178] (II) QUBO model

[0179] QUBO is a cost function for binary combinatorial optimization problems, which contains linear and quadratic terms. In order 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 converted into quadratic form and can be represented as a QUBO problem. Specifically, the QUBO problem can be formalized as the objective function of the QUBO model:

[0180]

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

[0182] Research progress in recent years has shown that QUBO provides a unified framework for expressing many NP-hard CO problems. It is relatively easy to use penalties to integrate problem constraints into the objective function, which is then converted into the standard QUBO form. In addition, the profound significance of the QUBO problem is also reflected in its equivalence with the Ising model in physics, thus building a bridge between physics and mathematical optimization. The latter has been shown to be able to express a variety of complex problems, including Karp's 21 NP-complete problems.

[0183] 2. Deep reinforcement learning framework CONQUER

[0184] The overall framework is as follows Figure 3 shown.

[0185] (I) Problem transformation and QUBO graph construction

[0186] According to H QUBO (x) The corresponding formula defines a corresponding undirected graph G =<V,E> , node v i ∈V represents H QUBO The decision variables in (x) have weights equal to the coefficient a of the linear term. i . Node v i and v j Through the edgeij ∈E connection, its weight is equal to E QUBO The coefficient b of the quadratic term in the formula corresponding to (x) ij Compared with previous work in the original problem space, a significant advantage of this graph representation is that the objective and constraint information of the optimization problem can be encoded into the graph structure, so that the objective function of the QUBO model of the maximum clique problem can be directly learned by the neural network: Among them, i∈V represents a node in the traffic network, its serial number is i, p is the penalty coefficient of the model, which is a specific value. In this problem, the value is 1.2. Represents nodes that have no connection relationship, such as two intersections that have no road connection in a transportation network.

[0187] (II) Qubormer-based graph representation

[0188] Intuitively, from the construction of the QUBO graph, we can know that the QUBO graph contains the objective function and constraint information of the problem. Therefore, in an ideal case, we hope to find an embedding vector that not only effectively captures the properties of a single node, but also fully represents the properties of nodes with long-range correlations, thereby accurately mapping the objective function and constraints of the QUBO problem. Considering the unique structure of the QUBO graph, a new graph transformer structure called Qubormer is constructed, which mainly includes two components: encoder and decoder.

[0189] 1. Encoder

[0190] In recent years, many studies have emphasized that traditional message passing networks encounter bottlenecks such as smoothing, which makes them less efficient in processing tasks with long-term dependencies. In order to overcome the shortcomings of traditional neural networks, the transformer mechanism is integrated into the message passing layer. Generally speaking, the encoder includes three key components.

[0191] (1) Centrality coding

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

[0193]

[0194] Among them, ReLU refers to the activation function, The i in the equation represents the i-th node, 0 represents the initial feature, and x i is the initial feature of the node, z deg (v i ) is the degree of the node (degree is a professional term in complex networks, which refers to the node vi The number of adjacent nodes is encoded in the traffic network. For example, if there are 5 intersections directly connected to a certain intersection, its degree is 5, that is, there are 5 roads passing through the intersection. i It refers to the node with serial number i, v is the abbreviation of the English word vertex, W1 and W2 are learnable parameters, and encoding refers to converting the node into a vector.

[0195] (2) Message Passing Layer

[0196] To be precise, converting various problems into QUBO form fundamentally integrates the target information and constraint information into the nodes and edge weights of the QUBO graph, making the 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 ) is the initial edge embedding vector, x ij is the edge input feature. W3, W4…W7 are all learnable parameters. After obtaining the node feature in step l After that, you can concatenate the features of the previous step of the node Implementing residual connections can alleviate the smoothing problem of the excessive model:

[0199]

[0200] Where W8 is a learnable parameter.

[0201] (3) Transformer layer

[0202] In previous studies, such as the GraphTrans model, researchers usually stacked Transformer layers on top of several layers of the message passing network. Although this method enhances the capabilities of the message passing network by introducing positional or structural encoding, it still needs to fundamentally solve core problems such as over-smoothing.

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

[0204]

[0205] Where MHA stands for multi-head attention network, LN stands for layer normalization, and FFN stands for feed-forward neural network layer. represents the node embedding vector obtained at step l-1, Represents the node embedding vector after the multi-head attention network.

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

[0207] 2. Decoder

[0208] Before discussing the details of the decoder, we need to understand the Markov decision process (MDP) for solving the QUBO problem. Formally, consider an MDP described by a tuple (S, A, R), where S is the set of all possible states s i A collection of actions. i ∈A means that in a given state s i The assignment of the binary variable x to the state s i Execute action a i Rewards received i :r i =a i +∑ (i,j)∈E b ij x j ∈R reward r i Indicates the change of the objective function before and after the action is executed.

[0209] The decoder essentially converts a state-action pair (s i , a i ), converted to a scalar Q(s i ,a i ; Θ), namely the neural network, is used to evaluate i Next action a i The quality of (i.e., the value, the greater the value, the greater the possibility of the action being executed), 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] Among them, W9, W10, W11 are learnable parameters, [z s ,z i ] means to convert the vector z s and vector z i Join by rows.

[0212] (III) Using RL to minimize the Hamiltonian on the QUBO graph

[0213] 1. Training

[0214] The widely used DQN is used for model training. The process mainly includes the following steps: First, an instance of the original problem is generated and converted into QUBO form. Then, the training process trajectories are generated based on the QUBO graph and stored in a cache-like memory replay buffer. Then the model agent selects certain trajectories from the memory replay buffer for learning training and updates the neural network parameters accordingly.

[0215] (1) Data preparation

[0216] In fact, 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 necessarily required that the original problem instances must be graphs.

[0217] (2) Trajectory generation

[0218] As mentioned above, the optimization problem of the traffic network is mapped to the maximum clique solving problem on an abstract graph, where the nodes in the graph represent intersections, key points, etc. in the traffic network, while the edges can represent roads, lines, etc. between intersections, and the weights on the edges represent the traffic information of the route. At the same time, the maximum clique solving problem can be converted into the Hamiltonian minimization problem on the QUBO graph, and the reinforcement learning algorithm is used to solve it, that is, the process is regarded as a Markov decision process, in which an episode (complete training round) is the complete process of finding the solution that minimizes the Hamiltonian on the QUBO graph, requiring all decision variable states to flip sequentially 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 is the terminal state where all decision variables are 1. Running a game requires completing a complete episode on the QUBO graph, and the model will collect training process data, i.e., s t ,a t ,r t,t+n ,s t+n , where st represents the state set of all variables at time t, a t represents the action taken at time t, represents the cumulative reward at time t+n, s t+n The state set model representing all variables at time t+n stores them in the memory replay buffer. Here, the delayed reward step n and the discount factor γ are both hyperparameters.

[0219] (3) Update Qubormer parameters

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

[0221]

[0222] Among them, E represents the maximum expectation, r t,t+n represents the immediate reward after n steps after executing the action at time t, s t+n represents the state at time t+n, a t+n represents the action to be performed at time t+n, r is the discount factor (hyperparameter, usually 0.99), Indicates that in state s t+n Execution is the target network The action a with the largest return value t+n The reward estimate returned after is the target network parameter, Q(s t ,a t ; Θ) indicates that in state s t Execute action a t The reward valuation obtained according to the original network Q(Θ), where s t represents the state at time t, a t represents the action executed at time t, Θ is the parameter of the original network, which updates its parameters through real-time data. In addition, the original network Q(Θ) periodically copies its parameters Θ to the target network Parameters 2. Online application and fine-tuning of out-of-distribution data

[0223] In the application, the state of each decision variable in the QUBO graph is iteratively flipped from 0 to 1 through a greedy strategy. 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, in the field of machine learning, out-of-distribution generalization is a prominent challenge. To address this challenge, an embodiment of the present invention proposes a concise and efficient fine-tuning method.

[0225] First, data augmentation is performed on the tuning dataset, such as introducing noise in the QUBO graph, dividing the dataset into training / validation / test subsets, and sampling the QUBO graph. Then, the pre-trained model is loaded and its encoder part is frozen. Only the task head of the downstream task is fine-tuned based on the downstream task data, and only certain parameters are updated to save fine-tuning time. Finally, the adjusted 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, which represents the value of the decision variables that minimizes the Hamiltonian. In order to obtain the solution to the original problem, a decision reduction process is required. Specifically, this can be roughly divided into two main types. The first type involves "yes / no" decision outputs, which are used to determine whether the decision variables are included in the solution set, examples of which include MaxCut and MIS. The second type involves sequential decision outputs, as observed in TSP, which explicitly defines the order in which each city is visited. At this time, 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 in the solution set.

[0229] 2. Check and repair the solution

[0230] If the agent is not fully trained due to data sparsity or insufficient training time, or the penalty term is set too low, the solution found by the neural network may not meet the feasibility conditions of the original problem. To alleviate these problems, the legality of the solution must first be ensured. If the solution meets the feasibility conditions of the original problem, it is directly output; if not, it needs to be repaired to meet these conditions. In general, the repair method is simple and cheap, usually using common greedy or local search methods to repair solutions that do not meet the constraints. Solution repair is only needed when dealing with real data sets and very large-scale graphs, and the simplest greedy method is used.

[0231] 3. Experiment

[0232] 1. Experimental setup

[0233] 1. Baseline method

[0234] A baseline of semidefinite programming, called SDP, is used to obtain relaxed solutions. In addition, two heuristic methods, greedy and mean field annealing (MFA), are combined. The comparison of learning-based methods includes the classic S2V-DQN implemented by ourselves and two probabilistic view-based methods, ERDOS and ANNEAL. In addition, the current 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, and their enhanced versions Meta-EGN. In addition, a state-of-the-art method, VAG-CO, which improves the mean field annealing algorithm, is compared. Although VAG-CO formulates the combinatorial optimization problem as Ising formulation, its main contribution lies in the improvement of the annealing process.

[0235] 2. Evaluation Metrics

[0236] In keeping with previous work, a comprehensive evaluation metric is employed that considers the best ratio (R*) and the average ratio (R) of the results obtained from the proposed method to those obtained by the Gurobi optimizer within one hour, as well as the corresponding standard errors.

[0237] (II) Experimental results

[0238] The MC problem is similar to the MIS problem because the MC problem can be abstracted as solving the MIS problem on its complementary graph. Therefore, the experiment focuses on the ENZYMES and IMDB-BINARY datasets, and adopts the same dataset partitioning method as the MIS problem. Training is performed on an RB graph of size 100, and then the dataset is fine-tuned. The experimental results of the MC problem are shown in Table 1. Similar to the MIS problem, the method of the embodiment of the present invention is always better than other methods in all experiments.

[0239] Table 1 Experimental results

[0240] Comparison of the best performance indicators of the algorithm (the larger the better, mean ± variance)

[0241] Methods / Dataset 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 performance indicators of algorithms (the larger the better, mean ± variance)

[0243] Methods / Dataset 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 experiment

[0245] In order to verify the effectiveness of Qubormer, ablation experiments were conducted to remove the centrality encoding, remove the transformer layer, and replace the message passing layer in Qubormer with GCN. The results are shown in the figure. Figure 4As shown in Figure 2, Quormer (GCN) performs the worst, indicating that the aggregation methods from node to edge and edge to node are more suitable for QUBO graphs because the edges contain rich feature information. Qubormer-no-trans performs slightly better, which highlights 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] By modeling the dense area determination problem in traffic network analysis as the maximum clique problem in combinatorial optimization, the traffic network structure is analyzed by finding the maximum clique. Subsequently, the maximum clique problem is transformed into the QUBO form, and an innovative development of an end-to-end deep learning reinforcement learning architecture customized for this problem is demonstrated. Considering the particularity of the QUBO graph structure, the transformer mechanism is introduced into the message passing network to effectively capture the long-term dependencies between nodes. Then, the corresponding decision reduction strategy is designed, and a simple and effective fine-tuning method is designed for real data sets that are different from the training set distribution. Unlike previous studies, it stands out by avoiding adjustments across different problem instances or fine-tuning scenarios for specific tasks. Experimental results show that the method of the embodiment of the present invention is significantly better than the existing state-of-the-art learning-based and manually designed methods. It helps to effectively solve the dense area determination problem in traffic network analysis, thereby helping urban planners and traffic managers to better understand the structure and function of traffic networks. Effectively identifying dense subgraphs in traffic networks improves the accuracy and reliability of traffic network 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 can be rearranged without departing from the scope of protection of the present disclosure. The attached method claims present the elements of the various steps in an exemplary order and are not intended to be limited to the specific order or hierarchy described.

[0249] In the above detailed description, various features are grouped together in a single embodiment to simplify the disclosure. This method of disclosure should not be interpreted as reflecting an intention that the embodiments of the claimed subject matter require more features than are clearly stated in each claim. On the contrary, as reflected in the appended claims, the invention is in a state of having less than all the features of the disclosed individual embodiments. Therefore, the appended claims are hereby expressly incorporated into the detailed description, with each claim standing on its own as a separate preferred embodiment of the invention.

[0250] The disclosed embodiments are described above to enable any person skilled in the art to implement or use the present invention. Various modifications of these embodiments are obvious to those skilled in the art, and the general principles defined herein may also be applied to other embodiments without departing from the spirit and scope of the present disclosure. Therefore, the present 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 above description includes examples of one or more embodiments. Of course, it is impossible to describe all possible combinations of components or methods for the purpose of describing the above embodiments, but it should be recognized by those skilled in the art that the various embodiments may be further combined and arranged. Therefore, the embodiments described herein are intended to cover all such changes, modifications and variations that fall within the scope of protection of the appended claims. In addition, with respect to the term "comprising" used in the specification or claims, the word is covered in a manner similar to the term "including", just as "including," is explained as a transitional word in the claims. In addition, any term "or" used in the specification of the claims is intended to mean "non-exclusive or".

[0252] Those skilled in the art may also understand that the various illustrative logical blocks, units, and steps listed in the embodiments of the present invention may be implemented by electronic hardware, computer software, or a combination of the two. In order to clearly demonstrate the interchangeability of hardware and software, the various illustrative components, units, and steps described above have generally described their functions. Whether such functions are implemented by hardware or software depends on the specific application and the design requirements of the entire system. Those skilled in the art may use various methods to implement the described functions for each specific application, but such implementation should not be understood 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 the present invention can be implemented or operated by a general-purpose processor, a digital signal processor, an application-specific integrated circuit (ASIC), a field programmable gate array or other programmable logic device, a discrete gate or transistor logic, a discrete hardware component, or any combination of the above. The general-purpose processor can be a microprocessor, and optionally, the general-purpose processor can also be any conventional processor, controller, microcontroller or state machine. The processor can also be implemented by a combination of computing devices, such as a digital signal processor and a microprocessor, a plurality of microprocessors, one or more microprocessors combined with a digital signal processor core, or any other similar configuration.

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

[0255] In one or more exemplary designs, the above functions described in the embodiments of the present invention can be implemented in hardware, software, firmware or any combination of the three. If implemented in software, these functions can be stored on a computer-readable medium, or transmitted in the form of one or more instructions or codes on a computer-readable medium. Computer-readable media include computer storage media and communication media that facilitate the transfer of computer programs from one place to another. The storage medium can be any available medium that can be accessed by any general or special computer. For example, such computer-readable media can include but are not limited to RAM, ROM, EEPROM, CD-ROM or other optical disk storage, disk storage or other magnetic storage devices, or any other medium that can be used to carry or store program codes in the form of instructions or data structures and other forms that can be read by general or special computers, or general or special processors. In addition, any connection can be appropriately defined as a computer-readable medium, for example, if the software is transmitted from a website site, server or other remote resource through 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 disk and disc include compact disk, laser disk, optical disk, DVD, floppy disk and blue-ray disk. Disks usually copy data magnetically, while discs usually copy data optically with lasers. The above combination can also be included 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: Optimizing the utilization problem of nodes of a transportation network as a maximum clique problem, the nodes including transportation nodes; Based on the universal objective function of the QUBO model, the maximum clique problem is transformed into the QUBO model; A graph neural network is used to characterize the structure and characteristics of the QUBO graph of the QUBO model, and a deep learning model CONQUER is constructed; The deep learning model CONQUER is trained to explore the optimal solution to the optimization problem of the nodes of the transportation network, and a trained deep learning model CONQUER is obtained; the trained deep learning model CONQUER is used to optimize the utilization problem of the nodes of any transportation network to obtain node optimization results, and the node optimization results include: the nodes adopted, the number of nodes, and the frequency of road use between nodes.

2. The node optimization method of the traffic network according to claim 1, characterized in that: The node utilization problem of the transportation network is optimized as a maximum clique problem, including: The transportation network is represented as G = (V, E), where V refers to the node set in the transportation network, including individuals with mutual connections in the transportation network, and E refers to the edge set, which represents the edges composed of individuals with interactive relationships; Define the symbols and parameters as follows: (x_v): binary variable, x represents the node of the transportation network, v represents the sequence number of the node, when the node (v) is selected into the group, it is 1, otherwise it is 0; (N(v)): the set of neighbor nodes of node (v); Objective function (f(x)): represents maximizing the size of the cluster. Maximizing the size of the cluster means maximizing the number of selected nodes. The maximum cluster problem is expressed as: Constraints: Each node in the group is either selected or not selected. The constraints are expressed as: x v 、x u Represent any two nodes in the transportation network.

3. The node optimization method of the traffic network according to claim 2, characterized in that: Based on the universal objective function of the QUBO model, the maximum clique problem is transformed into the 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 binary variables, where the binary variables are 0 or 1, and x i 、x j are the nodes at both ends of the edge, the matrix Q is a symmetric matrix or an upper triangular matrix, a i =Q ij ,so b ij =Q ij , a i represents the node weight, b ij represents the weight of the edge; According to H QUBO (x) corresponds to the formula, define a corresponding undirected graph G =<V,E> , node v i ∈V represents H QUBO The decision variable in (x) has a corresponding weight equal to the coefficient a of the linear term i ; Node v i and v j Through the edge ij ∈E connection, the corresponding weight is equal to H QUBO The coefficient b of the quadratic term in the formula corresponding to (x) ij , thereby encoding the objective and constraint information of the maximum clique problem into an undirected graph structure, so that the neural network can directly learn the objective function of the QUBO model of the maximum clique problem. The objective function of the QUBO model of the maximum clique problem is expressed as: Among them, i∈V represents a node in the traffic network, the node number is i, and p represents the penalty coefficient of the QUBO model. Indicates nodes that do not have a connection relationship.

4. The node optimization method of the traffic network according to claim 3, characterized in that: The graph neural network is used to characterize the structure and characteristics of the QUBO graph corresponding to the QUBO model, and a deep learning model CONQUER is constructed, including: Constructing an encoder, wherein the encoder construction specifically includes: integrating a centrality encoding layer, a message passing layer, a Transformer layer, and an iterative calculation solution layer; wherein: At the integrated centrality encoding layer: Each node in the QUBO graph is enhanced by the corresponding degree to capture the importance of the node in the QUBO graph, and then encoded. Each node in the QUBO graph is enhanced by the corresponding degree and encoded to obtain the corresponding vector representation: Among them, ReLU refers to the activation function, The i in the equation represents the i-th node, 0 represents the initial feature, and x i is the initial feature of the node, z deg (v i ) is used to encode the degree of the node, v i It refers to the node with serial number i, W1 and W2 are the parameters of the neural network, and they are learnable parameters; At the messaging layer: Using the neighborhood aggregation process, the features of the nodes are merged to obtain the feature aggregation of the edges, and the features of the edges are merged to obtain the feature aggregation of the nodes. The feature aggregation of the edges and the feature aggregation of the nodes are expressed as follows: Among them, h ij =ReLU(W3x ij ) is the initial edge embedding vector, is the intermediate output of the neural network, and x ij is the edge input feature, W4, W5, W6, and W7 are the parameters of the neural network, and they are all learnable parameters; After obtaining the node features in step l After that, you can concatenate the features of the previous step of the node Implement residual connection and express the residual connection as follows: Among them, W8 is the parameter of the neural network and is a learnable parameter; In the Transformer layer: Aggregate the output of the message passing layer with the output of the global attention layer in the Transformer layer to obtain updated node features: Among them, MHA represents multi-head attention network, LN represents layer normalization, and FFN represents feed-forward neural network layer; represents the node embedding vector obtained at step l-1, represents the node embedding vector after the multi-head attention network; In the iterative calculation solution layer: When solving, the updated node features output from the Transformer layer are used as the input of the integrated centrality encoding layer, and the steps of the integrated centrality encoding layer, the message passing layer, and the Transformer layer are repeatedly executed in a loop to iterate. After the iteration is completed, the final embedding vector corresponding to each node is obtained, and the final embedding vector of each node is expressed as: Sum the final embedding vectors of all nodes to get: s =∑ i∈V z i , the solution of the QUBO model is characterized by summation.

5. The node optimization method of the traffic network according to claim 4, characterized in that: The graph neural network is used to characterize the structure and characteristics of the QUBO graph corresponding to the QUBO model, and a deep learning model CONQUER is constructed, which also includes: Build the decoder, including: Formally, a Markov decision process is formed, which is described by the tuple (S, A, R), where S is all possible states s i A collection of actions i ∈A means that for a given state s i The QUBO model assigns a value to a binary variable x; the state s i Execute action a i Rewards received i , r i =a i +∑ (i,j)∈E b ij x j ∈R reward r i Indicates the change of the objective function before and after the action is executed; Through the decoder, a pair of state-action pairs (s i , a i ) is converted to a scalar Q(s) of the neural network i ,a i ; Θ), to evaluate i Next action a i The quality of the decoder is expressed as follows: Q(h,v;Θ)=W 11 ReLU(W 10 ReLU(W9[z s ,With i ])) Among them, W9, W10, W11 are the parameters of the neural network and are learnable parameters. s ,z i ] means to convert the vector z s and vector z i Join by rows.

6. The node optimization method of the traffic network according to claim 5, characterized in that: By training the deep learning model CONQUER to explore the optimal solution to the node utilization problem of the transportation network, the trained deep learning model CONQUER is obtained, including: Obtaining samples of nodes of the traffic network corresponding to the maximum clique problem, converting the maximum clique problem into a Hamiltonian minimization problem on a QUBO graph, solving it using a reinforcement learning algorithm, and generating a trajectory represented by a Markov decision process based on the QUBO graph; Among them, a complete training round is the complete process of finding the solution that minimizes the Hamiltonian on the QUBO graph, requiring all decision variable states to flip sequentially 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 is the terminal state 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 represents the state set of all variables at time t, a t represents the action taken at time t, represents the cumulative reward at time t+n, s t+n Represents the state set of all variables at time t+n, and the step size n and discount factor γ are both hyperparameters; Using the collected training process data, the collected training process data is learned by the deep learning model CONQUER, and the network parameters Θ of the deep learning model CONQUER are updated to minimize the following loss function: Among them, E represents the maximum expectation, r t,t+n represents the immediate reward after n steps after executing the action at time t, s t+n represents the state at time t+n, a t+n represents the action executed at t+n, γ is the discount factor, Indicates that in state s t+n The target network for execution is The action a with the largest return value t+n The reward estimate returned after is the target network parameter, Q(s t ,a t ; Θ) indicates that in state s t Execute action a t According to the reward valuation obtained by the original network Q(Θ), s t represents the state at time t, a t represents the action performed at time t, Θ is the parameter of the original network, which is updated by real-time training process data; The original network Q(Θ) periodically copies parameters 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, the trained deep learning model CONQUER can be obtained.

7. The node optimization method of the traffic network according to claim 6, characterized in that: Also includes: In the samples of nodes of the traffic network corresponding to the maximum independent set problem obtained, noise is introduced into the samples when constructing the QUBO graph; When the loss function is less than a preset value, it is also necessary to freeze the parameters of the encoder and fine-tune the parameters of the encoder for the corresponding deep learning model CONQUER to obtain a trained deep learning model CONQUER.

8. The node optimization method of the traffic network according to claim 7, characterized in that: Also includes: When the trained deep learning model CONQUER is used to solve the node utilization problem of the traffic network to be solved, when the obtained solution does not meet the feasibility conditions of the traffic network to be solved, a greedy search method or a local search method is used to repair the solution.

9. A method for optimizing nodes in a transportation network, characterized in that: Also includes: Inputting the node utilization problem of the traffic network to be solved into the trained deep learning model CONQUER described in any one of claims 1 to 8; Output node optimization results, the node optimization results include: adopted nodes, number of nodes, and frequency of road use between nodes.

10. A node optimization device for a traffic network, characterized in that: include: A problem conversion unit, for optimizing the utilization problem of nodes of a transportation network into a maximum clique problem, wherein the nodes include transportation nodes; A QUBO model building unit, used for converting the maximum clique problem into a model based on a general objective function of the QUBO model; A deep learning model building unit, used to use a graph neural network to characterize the structure and characteristics of the QUBO graph of the QUBO model, and to build a deep learning model CONQUER; The training unit is used to train the deep learning model CONQUER to explore the optimal solution to the optimization problem of the nodes of the transportation network, and obtain the trained deep learning model CONQUER; the trained deep learning model CONQUER is used to optimize the utilization problem of the nodes of any transportation network to obtain the node optimization result, and the node optimization result includes: the nodes adopted, the number of nodes, and the frequency of road use between nodes.

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